liangzid/robench2024b_all_setphysicsSCP-s · Datasets at Hugging Face

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A: This nascent appreciation that environments and their (possibly non-Markovian) dynamics could be active and potentially programmable components of future quantum devices raises exciting possibilities that could be accessible with current nanofabrication techniques and experimental probes [26, 27, 28, 29, 30]. In this work we address a relatively unexplored aspect of ‘environment-assisted’ phenomena that is of relevance for all of the examples and topics given aboveB: Most theoretical descriptions of interacting arrays of open quantum systems utilize models in which each component (qubits, chromophores, quantum dots, etc.) interact with ‘local’, independent environments, i.e. while the components may interact with each other, their dissipative environments do notC: Energy and/or information dissipated into these local environments is forever lost to the global multicomponent system. However, as the density of components increases – as required for more sophisticated quantum devices – the independence of these local environments becomes harder to justify [31]: propagating perturbations (excitations) of their common medium at one location become able to affect the dynamics of spatially remote systems, and maybe even do so on timescales that could be comparable to the intrinsic inter-system dynamics (see Fig. 1(a)).	ABC	ACB	ACB	CBA	Selection 1
A: The abstract version here is the (weighted) enumeration of all matchings of a graphB: However, when there is a single monomer on the boundary of a plane graph, the partition function can indeed be written as a Pfaffian [Wu06].C: The weights are interpreted as energies and are positive real numbers. This is known to be a computationally difficult problem [Jer87] and the partition function here does not have such a clean formula	CBA	ABC	ACB	CAB	Selection 3
A: This and other issues such as different input states, nonsymmetric two-qubit gates, and nonideal local operations remain open questionsB: A possible drawback is that one cannot know with certainty the final maximally entangled state produced by the protocolC: However, this work aims to introduce a concept of globally optimized recurrence protocols that is flexible enough to incorporate the aforementioned points in further investigations.	ABC	CBA	BAC	CAB	Selection 3
A: Concerning the changes in the activation function shown at the top of the table, we observe that our choice, the Sigmoid, has the highest convergence rate of r=66.9%𝑟percent66.9r=66.9\%italic_r = 66.9 % for this architectureB: Not only this, but Sigmoids also yield the lowest (and hence best) energy value. In contrast, ReLU and Softplus come at considerably higher energies. C: This is contrast to r<15%𝑟percent15r<15\%italic_r < 15 % for both the ReLU and Softplus functions, indicating that models have a harder time converging for these functions	CBA	CBA	BAC	ACB	Selection 4
A: The section numbers for the proof of the classification under OBCs and the BBC are shown for each topological number.B: Table S3: Point-gap topological phases in 6 classes without SLSC: These classes do not show the skin effects, and thus the classification under the OBCs coincides with that under the PBC	ACB	ABC	CAB	ABC	Selection 3
A: johri2021nearest , and where necessary, the larger IonQ Aria machine with a capacity of 32 physical and 20 algorithmic qubits (ionq2022aria, )B: A crucial point to bear in mind with quantum computing is that the memory capacityC: Experiments below used the 11-qubit trapped ion quantum computer described by Johri et al	ABC	ACB	BCA	CBA	Selection 3
A: When the fixed-point operator evaluations are the dominant computational cost of AAR, one may choose to approximate the evaluations of the fixed-point operator to reduce the computational cost of the evaluationsB: When instead solving the least-squares problem for the Anderson mixing is the most expensive step of AAR, one may solve the least-squares problem approximately to reduce the computational cost of the least-squares solver. Our theoretical results open a new path to efficiently apply AAR to solve problems in addition to sparse linear systems, including non-linear fixed-point iterations arising from quantum mechanics, plasma astrophysics, and computational fluid dynamics where fixed-point operator evaluations are often expensive 18. In this context, the use of AAR allows to leverage less expensive operator evaluations without affecting the final attainable accuracy of the non-linear physics solver.C: Our theoretical results allow for accuracy reduction in different calculations performed by AAR on linear fixed-point problems	ABC	BCA	CBA	BAC	Selection 2
A: Below we explicitly analyse Statement 2 for the dynamical map generated by quantum SWITCH. For that particular dynamical map, it is straightforward to show (from Eq. (IV)) thatB: (IV)C: statement 1 and Statement 2 are quite general to the family of dynamics given by Eq	CAB	BAC	CBA	BCA	Selection 3
A: Practical quantum circuits have a regular structureB: For example, the ripple-carry adder has a V-shape of Toffoli gates, and quantum multiplication circuits are built on top of quantum additionC: We use the example of a multiplication circuit, and construct manually the multiplier circuit from [33] (see Appendix for its circuit diagram) by tiling the tiles from Fig. 1.	BAC	ABC	CBA	CBA	Selection 2
A: (2015) showed that such an agglomeration of neutrons is generic and the exotic nuclei can be expected to grow quite large. This means that dark matter self-interaction is suppressed and the bounds from the Bullet Cluster Randall et al. (2008) can be evaded.B: The dark matter will be dominated by the neutrons in the exotic sector with the lightest Higgs mass. Furthermore, the pions in these sectors are much lighter than the SM pions, so these neutrons can form large nuclei Krnjaic and Sigurdson (2015); Hardy et alC: (2015). In fact, Hardy et al	CBA	CAB	ACB	BAC	Selection 2
A: In this section, we demonstrated the applicability of TERP for probing black-box models designed to analyze time-series data coming from MD simulationsB: In addition to assigning confidence to these models, TERP can be used to extract valuable insights (relevant degrees of freedom) learned by the modelC: In the future, we expect an increased adoption of TERP-like methods in the domain of AI-enhanced MD simulations for investigating conformational dynamics, nucleation, target-drug interactions, and other relevant molecular phenomena.	BCA	ACB	ACB	ABC	Selection 4
A: S2, the Fig. S31 is similar to Fig. S3) are obtained. Analogously, the similar precision results (the FigB: S33 is similar to Fig. S14, the Fig. S34 is similar to Fig. S17) are obtained. These show that our quantitative framework is not affected by the random removal percentage.C: In the main text, we show the analysis for 20% random removal links. For robustness check, we here repeat the analysis for 10% random removal. The similar AUC results (the Fig. S32 is similar to Fig	ACB	ABC	BCA	CBA	Selection 3
A: B: where D⁢(O)⋅ρ=1/2⁢(O⁢ρ⁢O†−O†⁢O⁢ρ−ρ⁢O†⁢O)bold-⋅𝐷𝑂𝜌12𝑂𝜌superscript𝑂†superscript𝑂†𝑂𝜌𝜌superscript𝑂†𝑂{D(O)\bm{\cdot}\rho=1/2(O\rho O^{\dagger}-O^{\dagger}O\rho-\rho O^{\dagger}O)}italic_D ( italic_O ) bold_⋅ italic_ρ = 1 / 2 ( italic_O italic_ρ italic_O start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT - italic_O start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT italic_O italic_ρ - italic_ρ italic_O start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT italic_O ), and {\|j⟩}j=0,1,2..\{\|j\rangle\}_{j=0,1,2..}{ \| italic_j ⟩ } start_POSTSUBSCRIPT italic_j = 0 , 1 , 2 C: end_POSTSUBSCRIPT are eigenvectors of the Hamiltonian H𝐻Hitalic_H with eigenenergy ϵjsubscriptitalic-ϵ𝑗\epsilon_{j}italic_ϵ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT. The decay rates read	BAC	CAB	CAB	CAB	Selection 1
A: The methods proposed in [19, 20, 21, 22] rely on the magnitude of thermoelectric coefficients like the Seebeck coefficient to probe the presence and nature of MBS. On the other hand, we rely on the symmetry of the thermoelectric coefficients to the Aharonov-Bohm flux and the Fermi energy to probe the absence or presence of MBS as well as their nature (coupled/individual). Additionally, RefB: [19] relies on the violation of Wiedemann-Franz law (WF law) [23]. In this paper, we, too, employ the violation of WF law to probe the presence of MBS. An upshot of this work is that none of the previous works that aim to probe MBS via thermal coefficients use Aharonov-Bohm flux as a parameter.C: In this work, we aim to probe MBS in topological insulators that contain a superconducting and ferromagnetic interface (STIM interface) [5] by studying the symmetry of various thermoelectric coefficients. We see that thermoelectric coefficients like Seebeck, Peltier coefficients, and the thermal conductance [14, 15, 16, 17, 18] are symmetric or asymmetric to the Aharonov-Bohm flux, Fermi energy and can indicate existence and nature of MBS. Several methods of probing MBS via thermoelectric transport have been put forward before [19, 20, 21, 22]	ACB	CBA	BCA	BAC	Selection 3
A: For b≪1much-less-than𝑏1b\ll 1italic_b ≪ 1, corresponding to an annihilation with a much lighter particle, the correction can be large.B: However, when the exponential suppression is weaker (b<1𝑏1{b<1}italic_b < 1), instantaneous freezeout may no longer be a good approximation for estimating the relic abundance, as shown in Ref. Kim:2019udq ; Kramer:2020sbb C: Instantaneous freezeout is a good approximation in many scenarios, because the annihilation rate is dropping exponentially with time (or temperature)	BCA	CBA	CAB	BCA	Selection 2
A: or equivalently connected coversB: HurwitzC: The double Hurwitz numbers Hg∙⁢(α,β)superscriptsubscript𝐻𝑔∙𝛼𝛽H_{g}^{\bullet}(\alpha,\beta)italic_H start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ∙ end_POSTSUPERSCRIPT ( italic_α , italic_β ) and Hg⁢(α,β)subscript𝐻𝑔𝛼𝛽H_{g}(\alpha,\beta)italic_H start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT ( italic_α , italic_β ) were first studied by Okounkov [MRL]	BCA	ACB	BCA	CBA	Selection 2
A: probabilitiesB: (15) is the special case where C=𝒵→𝐶→𝒵C={\overrightarrow{\mathcal{Z}}}italic_C = over→ start_ARG caligraphic_Z end_ARG, ρ=π0𝜌subscript𝜋0{\rho}={\pi}_{0}italic_ρ = italic_π start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, andC: Jarzynski’s Equality Eq	ACB	CBA	ABC	BAC	Selection 1
A: By varying the film thickness up to 800 nm, we have verified the dominant role of strain in this peculiar system. We find that the unit cell differs from the bulk even at dimensions of several hundreds of nanometersB: In this work we present the properties of a𝑎aitalic_a-axis oriented YBCO thin films, at various doping levels from the optimally doped down to the insulating state, obtained by a careful oxygen annealing procedure. X-ray diffraction (XRD) analysis shows that the films are fully detwinned, implying the presence of CuO chains, aligned throughout the sample along the in-plane b𝑏bitalic_b directionC: The resistance vs temperature measurements are characterized by sharp superconducting transitions, showing that the superconducting properties of the films are rather homogeneous. We observe a strong in-plane anisotropy of the resistance, comparable, also for rather thick films, to the best results achieved on detwinned single crystals. This opens up the possibility of studying potential modifications of the ground state induced by confinement in films with only a few unit cells in thickness.	CBA	BCA	ACB	BAC	Selection 4
A: In our experimental demonstrations of section 4 we study both applications by simultaneously performing the mcm-rb suite across 12 control and 5 ancilla qubits on our device. While simultaneous Clifford gates on control qubits can introduce cross-talk error, since mcm-rb and delay-rb operate under the same control conditions with simultaneous gates they equivalently experience cross-talk. Thus, we can still use delay-rb as the reference sequence to quantify the error induced by measurement in mcm-rb.B: While Fig. 1 shows as an example only a single control and ancilla qubit, the mcm-rb suite can be applied simultaneously to multiple control and ancilla qubitsC: This can be used, for example, to test the impact of measurement of a central ancilla on multiple control qubits, or to test the impact of the measurement of multiple ancilla qubits on a single control	BAC	ABC	CAB	ABC	Selection 3
A: Although the final state may have correlations between the system and the ancilla, the second condition implies that the ancillary system A𝐴Aitalic_A is returned exactly in the same state as before and thus acts as a catalyst in the processB: [26] considered noise as a resource, and interestingly, here the noise is not consumed in the process and can be reused again. Furthermore, note that Eq. (102) emphasises that every possible state transition utilising randomness can be accomplished if a dephasing map can be constructed and Boes et al. [26] provided an explicit protocol for that.C: As mentioned previously, Boes et al	ABC	ACB	ABC	BCA	Selection 2
A: After this introduction, the analytical expressions and properties of the potential flow field around an axially-symmetric paraboloid are derived and discussed in Section 2B: The paper is structured as followsC: Thereafter, Section 3 presents the analytical derivation and discussion of a magnetic field B→→𝐵\vec{B}over→ start_ARG italic_B end_ARG being passively advected in this flow by solving the stationary induction equation of ideal MHD	CAB	BAC	CBA	ABC	Selection 2
A: The quantum-optical decoherence in driven systems can have a significant impact on the design of quantum memories and quantum operationsB: To achieve long quantum information storage times, sophisticated control protocols have been developed, that typically involve time-periodic electromagnetic fieldsC: Using dynamical decoupling, quantum information could be conserved for more than six hours in rare-earth atoms embedded in a crystal structure [112], and more than 50⁢s50s50\,\text{s}50 s in trapped ions [111]. In both cases, the quantum information is stored in the hyper-fine levels of the ground-state manifold, which are energetically separated in the radio-frequency regime.	BAC	CAB	ABC	CBA	Selection 3
A: Ashtekar’s formalism thus opened a new approach to quantizing gravity non-perturbatively; other approaches include loop quantum gravity, causal dynamical triangulations, spin foam and causal sets, which are non-perturbative approaches that attempt to yield a self-consistent quantization of gravityB: Many of these approaches have had difficulties in making contact to a semi-classical limitC: Moreover, while the Kodama state is a candidate for describing a ground state of quantum gravity with a positive cosmological constant non-perturbatively, it suffers from a number of issues, including non-normalizability, its CPT-violating properties (and consequent impossibility of having a positive energy), and lack of gauge invariance under large gauge transformations [3].	ABC	BCA	CBA	CAB	Selection 1
A: Among others, Goddard and Miller[36] derived constitutive equations for the rheological behavior of a suspension of slightly deformed viscoelastic spheres in the dilute limit. Misbah [37] derived equations which describe the vesicle orientation in the flow and its shape evolution, and outlined a rheological law for a dilute vesicle suspensionB: Matsunaga and Imai [48] systematically investigated the effect of viscosity ratio on the viscoelastic character of capsule suspension for a wide range of oscillatory shear rate frequencies. By employing continuum modeling, in particular the Oldroyd 8-constant framework, Saengow et al. [50] assessed the non-Newtonian character of human blood under uni-directional large-amplitude oscillatory shear (LAOS) flow, which is generated by superposing LAOS onto a steady shear flow. Clarifying the cellular-scale dynamics under oscillatory flow allows us to build precise continuum models of suspensions [51, 52, 53], and may lead us to novel biomedical applications [54], such as phenotype cell screening, and circulating tumor cell isolation in a chip [55]. However, this can be achieved only after fully grasping the effect of the particle deformations induced by the oscillations of the bulk suspension.C: Along with these analytical and numerical studies, recent computer simulation approaches have successfully been used to investigate rheological properties of a dilute and semi-dilute suspension of deformable particles in steady shear flow, e.g., elastic initially spherical particles [39, 40, 41] and capsule [42]. Numerical analyses of semi-dilute and jammed particle suspensions under oscillatory shear flow have been reported recently, e.g., rigid spherical particles at finite inertia [43], soft particle glasses [44], viscoelastic particles [45], bubbles [46], vesicles [47], and spherical capsule in dilute condition [48]. The recent theoretical work by Armstrong et al. [49] compared viscoelastic moduli obtained with several viscoelastic(-thixotropic) models and laboratory measurements under oscillatory shear flow	CBA	ACB	BAC	BCA	Selection 2
A: PB: has been partially supported by the Brazilian science foundations Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG), and by the University of Tor Vergata.C: A	CBA	BCA	ABC	ACB	Selection 2
A: (2017), HRG model with HS Noronha-Hostler et al. (2009) and SMASH transport model Rose et al. (2020).B: Schee (2022), LQCD (Lattice1 Meyer (2008), Lattice3 Astrakhantsev et al. (2018) and Lattice5 Karsch et alC: (2008), with 68.3% C.L.), hybrid model (McGill) Ryu et al. (2015), holographic model (Holo) Rougemont et al	ACB	CAB	CBA	BCA	Selection 2
A: On the other hand, the multi-shell model in Ref.[25] (and Appendix A) considers both the time evolution of continuously many null shells and the backreaction of the evaporation in a common time coordinate and examines whether an apparent horizon is formed, without assuming anything about the magnitude of the energy-momentum tensor a prioriB: Solving (1.1) self-consistently, each shell will never cross its shrinking Schwarzschild radius, and a surface pressure will occur on each shell [25], which becomes the large tangential pressure (2.15) in a continuum limit, leading to the dense configuration without forming horizonsC: Thus, the 4D dynamics of (1.1) including the tangential direction makes the difference.	BAC	ACB	ABC	CAB	Selection 3
A: For the two atomistic systems, alanine dipeptide and chignolin, we describe the systems using two different types of high-dimensional representations (distances and dihedral angles, respectively) to show that the framework can work regardless of the chosen configuration variables.B: To demonstrate the validity of our framework, we apply diffusion map to standard testing systems such as a particle moving on an analytical potential and alanine dipeptideC: For the stochastic embedding methods, we choose a mini-protein chignolin	ACB	ABC	CAB	CBA	Selection 3
A: Let x𝑥xitalic_x and y𝑦yitalic_y denote the positions of the big and small balls, respectively. The small ball satisfies the Schrödinger equationB: As shown in FigC: 2, the classical big ball and the wall constitute a one-dimensional infinite potential well, as the quantum small ball is situated between them. The motions of the two balls are governed by their interaction	CAB	ABC	ACB	CBA	Selection 1
A: The red squares in Fig. 6, represent the oscillation amplitudes due to the isotropic component of the gravitational force for both Yukawa and power-law corrections. Because the corrections to Newtonian gravity are small, the isotropic component of the torque oscillations are largely independent of the details of the correction term. B: A plot of the isotropic and anisotropic oscillation amplitudes as a function of N𝑁Nitalic_N are shown in Fig. 6C: For both the Yukawa and power-law cases, increasing N𝑁Nitalic_N from 10101010 to 30303030 suppresses the fundamental isotropic peak by eight orders of magnitude	BAC	BAC	CAB	BCA	Selection 3
A: Moreover, even in challenging scenarios, the proposal exhibits resilience, indicating that a robotic spacecraft can handle those difficult conditions. Other algorithms could be developed to identify such challenging scenarios and guide the spacecraft toward more favorable operating conditions. B: These scenarios serve to demonstrate that, from a GN&C perspective, an autonomous robotic spacecraft does not necessarily require extensive navigation campaigns to reduce uncertainties to very low levelsC: Once again, the selection of scenarios is intended to underscore the proposal’s robustness under unfavorable conditions, while also incorporating conservative assumptions	CAB	CBA	BAC	ABC	Selection 2
A: This work has made use of the ESA Gaia mission, processed by the Gaia DPAC. J. Farihi acknowledges support from STFC grant ST/R000476/1. T. G. Wilson acknowledges support from STFC consolidated grants ST/R000824/1, ST/V000861/1, and UKSA grant ST/R003203/1. B: The authors thank an anonymous reviewer for a careful reading of the manuscript. J. Farihi thanks D. Koester and G. Fontaine for key discussions over the years that helped to form the foundation of this work, E. Dennihy for confirming the fact that no DQ star has a suspected infrared excess from circumstellar dust, A. Rebassa-Mansergas for sharing his full white dwarf-main sequence binary catalog, and valuable exchanges with E. B. Bauer, R. R. Rafikov, and J. J. EldridgeC: Several colleagues provided feedback on an earlier version of the manuscript, including those mentioned above, as well as T. von Hippel, A. J. Mustill, A. Swan, and B. Zuckerman. The authors acknowledge the European Southern Observatory for the award of telescope time via programs 095.D-0706, 096.D-0076, and 097.D-0063	BCA	ABC	ABC	CAB	Selection 4
A: Active elongated particles and rods present a different situation where the pressure becomes dependent on particle-wall interactions [40]. Active pressure has been investigated on boundaries with different geometries such as flat walls [37, 36], curved surfaces [35, 34, 41, 36], corners [35], and sinusoidal and flexible interfaces [44, 43]. In addition to the geometry of boundaries, active pressure can vary depending on intrinsic features of active particles such as chirality [41], interparticle interactions, and local concentration [34, 38, 18].B: A particularly interesting facet of active suspensions is the so-called active or swim pressure produced by the constituent self-propelled particles [35, 39, 40, 37, 38, 18, 36, 42, 34, 41]. In equilibrium systems, pressure can be calculated using thermodynamic, mechanical, and hydrodynamical approaches, leading to the same result. This result follows a state equation and thus varies only with bulk properties such as temperature and densityC: In active systems, a state equation may not generally exist [40]. Therefore, the pressure is mainly defined via mechanical and hydrodynamical approaches [39, 40, 38]. More specifically, in the case of self-propelled spheres next to flat walls, the pressure can be described as a state function using activity-dependent effective temperature and bulk number density of spheres [38, 37]	CBA	CBA	CAB	CBA	Selection 3
A: Section 5 presents numerical methods to compute χ⁢(X),𝜒𝑋\chi(X),italic_χ ( italic_X ) , and to find relations among the integrals we study. Appendix A proves a vanishing result on cohomology groupsB: It is also made available, together with our other computational examples, on the MathRepo [23] page https://mathrepo.mis.mpg.de/EulerIntegrals hosted by MPI MiS.C: In Appendix B, we provide the code used for computations in Section 5	ABC	ACB	BAC	CBA	Selection 2
A: When the temperature is low, the rate constants will be faster at low pressures, according to the graphB: To explain this, it should be noted that at low pressure values, the deficiency of collisions means that the Boltzmann distribution does not hold since there is not much energy exchange. The result of this is that the collision frequency will be the dominant term in determining the rate constant. Its value is then lower at high temperatures due to the fact that collision frequency is inversely proportional to temperature at constant pressure.C: However, the reverse trend is seen at high pressure	CBA	BAC	ACB	CAB	Selection 3
A: Supplementary Fig. 1: Evidence the source crystal is Bernal trilayer grapheneB: Blue and green spots indicate where Raman spectra were obtained. (b) STM topograph of the fabricated TDTG stack showing a trilayer step at the edge of the twisted region. C: (a) Raman spectra of the 2D-mode acquired on two different spots of the source crystal with 514 nm laser wavelength. Inset: optical micrographs of the source crystal before (top) and after (bottom) AFM cutting	CBA	ABC	ABC	ACB	Selection 4
A: This is highlighted in Fig. 7 where we additionally consider an L𝐿Litalic_L-layered HEE and see that increasing expressivity can accelerate the exponential decay.B: While Proposition 1 is derived with a tensor product embedding, similar results are expected when dealing with more general unstructured embeddings such as hardware efficient embeddingsC: This is because the additional complexity from using an unstructured embedding can only increase the kernel concentration (due to increased expressivity and entanglement)	ABC	ABC	CBA	CAB	Selection 4
A: Notice that this conclusion contradicts the conjecture in [36], which proposes that non-maximal giant gravitons are also integrableB: As a result, the shift two symmetry of the boundary state results in a vanishing overlap between the boundary state and these Bethe roots. Hence, the calculations in this section imply that only two giant gravitons correspond to the integrable boundary state. C: However, in [36], it was shown that the Bethe roots that do not satisfy the root pairing also fail to satisfy the zero momentum condition	BCA	CBA	ACB	CBA	Selection 3
A: This calculation is further coupled with an Equation of State (EoS) incorporating a CEP in the universality class of the Ising model Parotto et alB: (2019), from which a prominent enhancement around CEP is found for q^^𝑞\hat{q}over^ start_ARG italic_q end_ARG. Such an enhancement, named as “partonic critical opalescence" (PCO)C: (2020); Martinez et al	CAB	CBA	BAC	ACB	Selection 4
A: (2012) or of a red-detuned optical potential attracting the atoms away from the low magnetic field region Lin et al. (2009). Here, we have followed the latter strategy.B: In order to prevent Majorana losses caused by the vanishing magnetic field in the center of the quadrupole trap, several strategies can be implemented. They include the addition of a rotating homogeneous field in the case of a TOP trap Petrich et alC: (1995), of a repulsive optical potential focused in the quadrupole center as for plugged traps Davis et al. (1995); Naik and Raman (2005); Dubessy et al	ABC	ABC	BAC	CAB	Selection 4
A: As we showed here, the mean square displacement differs for fermions and bosons. Also, we have verified the fluctuation-dissipation theorem for zero and non-zero chemical potentials for both statistics. As these results are presented in terms of the metric components, this is a quite general result. B: For a general diagonal metric, we obtained expressions for linear response function, mean square displacement, correlations functions and diffusion coefficient, in terms of the metric elementsC: In this work we presented some results regarding the dynamics of a particle in a thermal bath at finite density, in the linear regime, using holographic methods	CAB	ACB	CBA	BAC	Selection 3
A: Recently, there is growing interest in including a physics-based prior into neural networksB: RefsC: 16, 17, 18 introduce concepts from Lagrangian or Hamiltonian mechanics into neural networks, allowing them to learn and respect conservation laws for deterministic dynamical systems. These dynamical priors have subsequently been incorporated into VAEs19, 20, 21, 22. Incorporating domain knowledge from physics also encompasses alternative approaches, such as the use of physical laws as regularization terms to augment the loss function23, 24, 25.	CAB	CAB	ACB	ABC	Selection 4
A: Conversely, lissencephalic patterns are generally found in species with smaller brains or a lower risk of head impacts. Intermediate patterns exist between these two extremes.B: Furthermore, this analysis offers insights into various patterns of gyrificationC: Complex gyrification is more likely observed in species with larger brains, or those facing a high risk of head impacts due to lifestyle factors or intense echolocation signals	ABC	ABC	CBA	CAB	Selection 4
A: [17, 18, 19, 20, 34]. There are a variety of approaches to describe pedestrian motion, the most prominent of which are fluid dynamics models, particle models, agent-based models, e.gB: The mathematical modeling of pedestrian flows, which is an interesting academic problem, has high practical importance [17, 18, 20]. Indeed, it is directly related to the effective planning of public places, transportation systems, evacuation strategies in emergencies, and the organization of pedestrian fluxes in an epidemic, e.gC: [17, 18, 19, 20, 34], and models based on cellular automata [35, 36, 37]. Conceptually, the agent-based approach is similar to the molecular dynamics approach, in which the motion of all molecules is simulated by solving Newtons’ laws. Obviously, this is the most microscopic approach that provides the maximum possible information about the system.	ACB	BAC	ABC	CBA	Selection 2
A: These results are then extended to the general von Neumann algebraic setting in Section 4. Finally, examples and applications to quantum circuit complexity and quantum learning theory are provided in Sections 5 and 6. B: Section 3 is devoted to the statement and proof of our main results, namely a quantum L1superscript𝐿1L^{1}italic_L start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT-Poincaré inequality (Theorem 3.1), quantum Talagrand inequality (Theorem 3.2), and quantum KKL theorem (Theorem 3.9) and a quantum Friedgut’s Junta theorem (Theorem 3.11 and Corollary 3.12)C: The rest of the paper is organized as follows: in Section 2, we recall useful definitions and results from the Fourier analysis on the quantum Boolean hypercubes including Poincaré inequality, hypercontractivity, intertwining and gradient estimates	CAB	ACB	CBA	ABC	Selection 3
A: Specifically: B: Constraints on cosmological parameters were obtained using the cosmological Markov chain Monte Carlo (MCMC) software Cobaya [47, 48]C: This was done using a combination of Planck CMB measurements, Pantheon Type Ia supernovae, constraints on the absolute magnitude of Type Ia supernovae, baryonic acoustic oscillations and redshift space distortion measurements	ACB	BAC	CAB	ABC	Selection 3
A: Acknowledgements: The author thanks Niky Kamran for discussions, guidance and careful proofreading of the manuscript, as well as Felix Finster for helpful comments and discussionsB: This work was supported by the Natural Sciences and Engineering Research Council (NSERC) Undergraduate Student Research Award (USRA) program and by NSERC grant RGPIN 105490-2018. C: The author also thanks the referee for valuable comments and suggestions	ACB	ABC	CBA	BAC	Selection 1
A: This uncertainty is called as the first kind of residual scale dependence due to unknown higher-order terms [105]B: For the present case, the residual scale dependence (29) is much smaller than conventional scale uncertainty (25).C: Such residual scale dependence is distinct from the conventional scale ambiguities and is suppressed due to the perturbative nature of the PMC scale	ABC	ABC	BCA	ACB	Selection 4
A: This type of spontaneous symmetry breaking is associated with non-Hermitian phase transitions [13, 14, 15, 16, 17, 18, 19, 20]. PT-symmetrical systems are one of the most famous examples of systems with this type of spontaneous symmetry breaking [15, 16]B: In recent decades, it has been shown that in non-Hermitian systems, it is possible that the symmetry of the eigenstates is lower than the symmetry of the system Hamiltonian [6, 7, 8]. As a result, one can observe another type of spontaneous symmetry breaking [8, 9, 10, 11, 12], which manifests as the decrease of the symmetry of eigenstates with simultaneous conservation of the Hamiltonian symmetryC: In these systems, the change in the system parameters leads to passing through an exceptional point (EP) [15, 16], at which the eigenstates cease to be PT-symmetrical, whereas the Hamiltonian is still PT-symmetrical. In addition to PT-symmetrical systems, non-Hermitian phase transitions can also occur in strongly coupled cavity-atom systems [15, 21], polariton [22, 23], optomechanical [24, 25, 26, 27, 28, 29], and laser [30, 31, 32, 33, 34] systems. The systems with the phase transitions at the EP find a number of the applications [35, 36, 37, 38, 39, 40].	ACB	BAC	ABC	BCA	Selection 2
A: (2020). The resulting primordial GW signal contains key signatures of ultraviolet physics that would otherwise remain far beyond the reach of regular ground detection. This is why such signal is a main focus of current and future investigations of the stochastic GW background (SGWB) (Maggiore, 2000; Romano and Cornish, 2017; Caprini and Figueroa, 2018; Christensen, 2019). In addition, observation of such a signal (Lentati et al., 2015; Arzoumanian et al., 2018, 2020) can be a complementary probe to the range of SHDM mass if one assumes that such DM particles are produced by emission of the PBHs.B: Cosmic strings restore that broken Abelian symmetry at the core of these topological defects with vortex types of behavior (Nielsen and Olesen, 1973)C: Their network loses energy through the shrinking of its closed loops following their emission of GWs Vachaspati and Vilenkin (1985); Auclair et al	CBA	ACB	CBA	CAB	Selection 4
A: Hints at a deeper perspective come from recent works on chiral twisted graphene tarnopolskyOriginMagicAngles2019a; ledwithFractionalChernInsulator2020a; popovHiddenWaveFunction2021; shefferChiralMagicAngleTwisted2021a; renWKBEstimateBilayer2021a; wangChiralApproximationTwisted2021a; naumisReductionTwistedBilayer2021a; navarro-labastidaWhyFirstMagicangle2022; beckerSpectralCharacterizationMagic2021a; beckerFineStructureFlat2022; beckerIntegrabilityChiralModel2022, which focused on the “trace condition” ledwithFractionalChernInsulator2020a; ledwithFamilyIdealChern2022; wangExactLandauLevel2021a; ledwithStrongCouplingTheory2021B: The exactly flat Chern bands of chiral twisted graphene not only satisfy the trace condition but also have a transparent real-space structureC: This structure enables the construction of “short range ground states (SRI-GS)”:	CAB	CBA	BAC	ABC	Selection 4
A: This properness assumption, in fact, implies that the spacetime must be globally hyperbolic with compact Cauchy level sets (see Section 3.2). Both approaches yield local encodement of causality on any stably causal spacetime (see Theorem 3.4 and [SaSo]Thm. 1.1). Upon studying the proofs of [SaSo] we noticed that by combining part of their local arguments [SaSo]Thm. 1.1 with our global proof of Theorem 3.3 we can obtain Theorem 1.9 which is optimal both in view of regularity as well as causality. It is precisely this optimality, together with the observation that τ𝜏\tauitalic_τ having future (or past) Cauchy level sets is actually sufficient, that allows us to conclude with the following application. B: The ⟹⟹\Longrightarrow⟹ direction in Theorem 1.9 is trivial. Sormani and Vega [SoVe]Thm. 3.25 showed that the converse holds for warped product spacetimes with complete Riemannian fiber and suitable temporal functions. It remained an open problem to determine under which general circumstances causality is encodedC: Our Theorem 1.9 provides a sharp answer both in terms of regularity as well as the causality class (see counterexamples in Section 3.3). Initially we proved this result for Cauchy temporal functions in Theorem 3.3. Independently and simultaneously, Sakovich and Sormani [SaSo]Thm. 4.1 have obtained a different global causality encoding result where they allow for general anti-Lipschitz time functions, but require them to be proper	ACB	CAB	CBA	ACB	Selection 2
A: The simplest network scenario is provided by entanglement swapping [22]B: The generalization of the bilocality scenario to network, is the so-called n𝑛nitalic_n-locality scenario, where the number of independent sources of states is increased to arbitrary n𝑛nitalic_n [14, 15, 16, 23, 24, 25]. Some new interesting effects, such as the possibility to certify quantum nonlocality “without inputs”, are offered by the network structure [10, 11, 26, 27]. C: To contrast classical and quantum correlation in this scenario, the so-called bilocality assumption where the classical models consist of two independent local hidden variables (LHV), has been considered [9, 10]	ACB	BCA	BAC	CAB	Selection 1
A: In each case we compare the properties of the 4DEGB solution for multiple values of the coupling constant to the analogous GR result, and discuss how the rotational corrections affect these properties. B: We discuss the location and angular velocity of the black hole horizons, the equatorial geodesics – including the innermost stable circular orbit, photon rings (and associated Lyapunov exponents) – as well as the black hole shadowC: In this section we study physical properties of the solutions derived above	CBA	ABC	CAB	ABC	Selection 1
A: Ref. ZhangBHRV:16 for the risk when the number of parameters exceeds the number of data points). Since Lüscher’s formula is the only model-independent approach, this lead to our central conclusion that we get a neural network reprint of the numerical Lüscher’s formula.B: e.gC: (see	BAC	CBA	BCA	ABC	Selection 2
A: We will introduce the term genuine quantum superposition by associating the remaining matrix elements with both quantum superposition and basis state indistinguishability. Subsequently, we will generalize existing superposition measures for genuine quantum superposition. The measures introduced herein hold promise for quantifying non-classicality in chemical bonding phenomena within the realm of quantum chemistry, as evidenced by recent research where we successfully calculated electron delocalization in aromatic molecules [35].B: To set the ground for this discussion, we propose utilizing a pseudo-Hermitian matrix representation of a quantum state to investigate its properties concerning a nonorthogonal basis. This approach entails expressing the state within the biorthogonal extension of the given basis, a well-established mathematical technique in the literature (see, for example, Refs. [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29])C: Although independently rediscovered to represent free operations in the resource theory of superposition [13, 14, 15], this method has not been extended to encompass quantum states. Here, we will demonstrate that the diagonal elements of the pseudo-Hermitian representation of quantum states are biorthogonal Kirkwood-Dirac quasi-probabilities [30, 31, 32, 33, 34]	CBA	CAB	ABC	ABC	Selection 2
A: The author thanks Stephan De Bièvre and Kailiang Lin for insightful discussions. The author thanks Tao Li for reading the manuscriptB: The author also thanks the anonymous referees for constructive comments. After completing this work, I became aware of the recent work [60] which discussed the structure of Kirkwood-Dirac classical mixed states.C: This work was supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2022JM-012)	BCA	CBA	CAB	BAC	Selection 1
A: Then, one can identify the best possible operations for the sender and receiver to perform in order to maximize their transmission rateB: This section includes a short introduction into entanglement-assisted communication in Section III-A, which will serve as a basis for the coding scheme in our main result, followed by a description of the setup for fault-tolerant entanglement-assisted communication and our strategy for its analysis in Section III-B. C: When a sender and a receiver are connected by many copies of a quantum channel T𝑇Titalic_T and have access to entanglement, they can use this setup to transmit a classical message via entanglement-assisted communication	BCA	CAB	CAB	BAC	Selection 1
A: The GW bright sirens from SMBHBs that can be detected by PTA in the nanohertz band can serve as a late-universe cosmological probe with great potential to independently measure the absolute distances of the sourcesB: In this work, we investigate the capabilities of future bright siren observations from SKA-era PTAs on constraining the cosmological parameters in the IDE modelsC: We select some existing SMBHB candidates, and use the Fisher information matrix to forecast their accuracies of luminosity distances based on the simulation of timing residuals of pulsar signals. Then, we use the MCMC method to show how the future GW bright sirens from SKA-era PTAs can determine the cosmological parameters and play a key role in breaking the parameter degeneracies inherent in the CMB data.	ACB	ABC	CAB	BAC	Selection 2
A: Recently, Braun et al. [2, 3] developed a unified mathematical framework that exploits the low-rank defect structure to characterize the elastic far-fieldsB: This novel formulation exposes avenues for improved convergence rates in cell problems concerning cell size, as demonstrated theoretically. However, a notable challenge arises in the practical implementation of multipole expansions for simulating crystalline defects, given that the terms associated with multipole moments are defined on an infinite lattice, rendering their direct evaluation unfeasible within finite computational domains.C: In this framework, the defect equilibrium is decomposed into a sum of continuum correctors and discrete multipole terms	BCA	BCA	BAC	ACB	Selection 4
A: As we discussed in our previous work (de Lima et al., 2020), these systematics roughly translate into uncertainties of up to 5%percent55\%5 % for the NS mass and 7%percent77\%7 % for the NS radius. However, these uncertainties are still smaller than the reliable ones we estimated for the mass and radius of 3XMM J1852+0033. B: We also stress that the choice of model to compute the unabsorbed fluxes for the normalization leads to systematic uncertainties in our parameter estimationsC: As mentioned, these values generally agree within 10%−15%percent10percent1510\%-15\%10 % - 15 % for different models in the whole band (0.3–10 keV)	BAC	ABC	CBA	CAB	Selection 4
A: The observed order k 8 of the percolating clique cluster is anomalous for the characteristic connectome density, and we observed how such clique structure appear in the model under the limitation on the connection length during the formation of the model networkB: Indeed, connections of limited length are typical for the human structural connectome, which is especially characteristic for connections with high edge confidence. The emergence of a percolation clique cluster under a constraint on the allowed connection length is similar to a second-order structural phase transition. C: We then proposed a model for emerging high-order clique community structures characteristic of human connectomes	CBA	ACB	BCA	ABC	Selection 3
A: This work is funded by the French National Research Agency (ANR) within the project ANR-13-BS05-0007 and the “Investments for the future” programme ENIGMASS LabEx (ANR-11-LABX-0012)B: Authors are grateful for the technical and administrative support of the ILL for the installation and operation of the Stereo detectorC: We further acknowledge the support of the CEA, the CNRS/IN2P3 and the Max Planck Society.	CBA	CBA	ABC	ACB	Selection 3
A: (2002); Schnedermann et alB: (1993); Broniowski and Florkowski (2001). C: One should recall that collective radial expansion (specified by the radial velocity v𝑣vitalic_v) and resonance decays also affect the momentum distribution of hadrons Florkowski et al	ABC	ABC	BAC	BCA	Selection 4
A: To put a number on this observation we fitted function of the form:B: In Figure 1 we can see that value of A is not only smaller but also that it converges to 00 with growing ϵitalic-ϵ\epsilonitalic_ϵ faster than B and CC: similarly to the random matrix ensembles (Fact 7)	BAC	BCA	ACB	CBA	Selection 4
A: Gargaté et alB: (2019, 2019) used hybrid simulations (with kinetic ions and fluid electrons) to follow the instability on longer time-scales, well into the non-linear regime when saturation occurs. Their results supported a saturation mechanism similar to that described by Riquelme & Spitkovsky (2009), who used full PIC simulations: saturation occurs due to the deceleration of CRs and simultaneous acceleration of the background plasma, which reduces the CR current, an effect also seen in the earlier work of Lucek & Bell (2000).C: (2010); Weidl et al	BAC	ACB	ABC	ABC	Selection 2
A: Regarding the accidental background, radioactivity is the primary source of the prompt signal below 3.5 MeV, where stringent background control measures are essential, as outlined in Abusleme et alB: (2021b)C: Conversely, solar neutrino ES events become the leading prompt signal above 3.5 MeV. For the prompt energy range from 3.5 to 5 MeV, the cosmogenic correlated background is significantly higher than that in the region above 5 MeV, as depicted in Fig. 1, while the signal efficiency is considerably lower between 3.5 and 5 MeV due to the multiplicity cut. Additional technical details in this regard will be reported elsewhere in the future.	CAB	BAC	CAB	ABC	Selection 4
A: The absorption of the pump pulse energy results in an increase of the electron temperature (see Fig. 2(a) below) and thus an increase in the real part of the permittivity (see Fig. 4(a) below)B: This causes the ENZ resonance to slip away from the incoming frequencies so that the local field and the absorptivity decrease (see Fig. 5); consequently, the total absorbed energy, the maximum electron and phonon temperature increases sublinearly (rather than linearly) with the illumination intensityC: As shown below, this effect explains the high damage threshold of ITO. The changes of the imaginary part of the ITO permittivity are also large, and similar in nature to those occurring in noble metals (see, e.g., [21, 22]), but are secondary compared to the large ENZ resonance shift.	BCA	ACB	CBA	ABC	Selection 4
A: Recently, industry research labs have been shifting towards the hexagonal architecture for their quantum computersB: This architecture has the advantage of reducing the number of distinct frequencies, and thus crosstalkC: The surface code [14] structure has been modified to a topological code with a heavy hexagonal structure [15] in order to become more suitable for these architectures. The heavy hexagonal code [15] uses a combination of degree-two and degree-three vertices in the topology, and can be considered as a hybrid of a surface code and a Bacon-Shor code [16]. This QECC reduces the distinct number of frequencies required in their realization by introducing more ancilla qubits (termed as flag qubits) for entanglement in the syndrome measurement	BCA	BCA	ABC	ACB	Selection 3
A: While illustrated qualitatively in Figure 1g, this oscillatory behavior has been verified for both the NEID and HPF spectrographs, and qualitatively analogous behavior has been found for the etalon system of the ESPRESSO Schmidt et al. (2022) spectrograph. Surprisingly, it implies that the optical length of the etalon is effectively increasing and decreasing in length at different wavelength regions. This poses a clear problem for high-precision RV spectrograph calibration, as such etalon mode drifts are undetectable and thus unaccounted for unless the entire etalon spectrum is continuously compared to a high-precision and broadband absolute frequency reference (i.e., an LFC, but requiring a secondary calibrator defeats the purpose of developing the etalon as a calibrator in the first place)B: (2018); de Hond et al. (2017); Bohlouli-Zanjani et al. (2006); Dawel et al. (2024); Riedle et al. (1994), particularly when those modes have large spectral separation. C: This drift behavior also raises important considerations for experiments that utilize multiple FP cavity modes for frequency referencing in precision spectroscopy Hill et al. (2021); Wang et al. (2020); Milani et al. (2017); Arias et al	ACB	BAC	BAC	ABC	Selection 1
A: Initially applied to precipitation nowcasting based on 2D radar images (Suman et al., 2021; Shi et al., 2017), DL-based models have recently surpassed traditional methods for longer forecast periods (Lam et al., 2022). These methods usually work with highly structured dataB: Radar precipitation data, for example, can be organized as images and analyzed using convolutional neural networks. For 3D regular spherical grid data, graph neural networks or spherical CNNs are employed (Lam et al., 2022; Esteves et al., 2023)C: However, in our study, the data set is distributed sparsely in space, which hinders the use of these traditional architectures. The use of DL for modeling dynamical systems, in general, has also seen recent advancements (Li et al., 2021; Gupta & Brandstetter, 2022; Pfaff et al., 2020) but most approaches in this field typically operate on regularly-spaced data or irregular but fixed mesh.	CBA	BAC	ABC	ACB	Selection 3
A: The first is needed to define the solution of the Wick-ordered heat equation for large times, the second is needed for the convergence to the KPZ equation. B: We need this in two different settingsC: The first is for fixed drift as the size of the exceptional set tends to zero, and the second is a uniform bound as the drift increases	ACB	CAB	CBA	ACB	Selection 2
A: (c-e) Snapshots of the dislocation network at strain 0.8 extracted from (c) MD, (d) old DDD and (e) new DDD.B: Figure 6: Evolution of stress (a) and dislocation density (b) predicted in three simulations performed under identical conditions: MD simulation (green), DDD simulation with the old kinematic rules for 3-node motion (blue) and DDD simulation with the new kinematic rules permitting additional modes of 3-node motion (red)C: In all three simulations uniaxial compression along the [001] axis of a BCC single crystal of tantalum was performed under a constant straining rate of 2×1082superscript1082\times 10^{8}2 × 10 start_POSTSUPERSCRIPT 8 end_POSTSUPERSCRIPT s-1	BCA	CAB	ACB	ACB	Selection 2
A: Zumbühl, G. A. D. Briggs, M. A. Osborne, D. Sejdinovic and N. Ares, ”Deep reinforcement learning for efficient measurement of quantum devices,” npj Quantum Inf 7, 100 (2021).B: V. Nguyen, S. B. Orbell, D. T. Lennon, HC: Moon, F. Vigneau, L. C. Camenzind, L. Yu, D. M	ABC	ACB	BCA	CAB	Selection 4
A: OTOCs in different systems Swingle et al. (2016); Zhu et al. (2016); Gärttner et alB: (2020); Braumüller et al. (2022); Zhao et al. (2022). OTOCs have been found to be useful for measuring entanglement entropy and theC: (2017); Li et al. (2017); Lewis-Swan et al. (2019); Nie et al	ACB	ABC	CAB	CAB	Selection 1
A: Therefore, the atomic interference signal in Fig. 6 not only includes the fundamental frequency, but also the second harmonic signal. When the output of the fiber-optic gyroscope is compared with that of the AI gyroscopes, the open-loop dynamic range of the AI is estimated to be ∼similar-to\sim∼0.0157 rad/s, which is slightly different from the theoretical value (0.0118 rad/s). This may be due to the difference between the theoretical and measured values of the AI scale factor, such as the measurement error in atomic velocity. In addition, the sensing axes of the two gyroscopes may be not completely consistent, and the measurement may not be synchronized completely. B: A rotational test was performed to verify the inertial sensitivity of the AI gyroscope. The entire sensor was placed on a platform, which was floating on four pneumatic vibration isolators (I-2000, Newport, USA) and adjusted to be perpendicular to the direction of local gravitational acceleration using a tilt sensor. A fiber-optic gyroscope was fixed on the same platform to measure the rotation rate simultaneously using the same sensing axis as the AI gyroscope. The AI gyroscope was operated in open-loop mode. Figure 5 shows the signals measured with the AI gyroscope and the fiber-optic gyroscope when an external force was applied to turn the entire platform around the central axisC: The two AIs pick up the change in the rotation rate induced by the applied force and output two oscillating signals with frequencies of 1.25 Hz and 1.33 Hz deduced from their Fourier transform spectra, as shown in Fig. 6. The output signal from the fiber-optic gyroscope also responds to the applied force with an oscillation frequency of 1.33 Hz, which agrees well with the AI results. In addition, some umbilications appear in the peaks and troughs of the dual-AI signals that are caused by the measurement ambiguity of the interferometric sensor, as shown in Fig. 5 (green dashed circles)	CBA	CAB	ABC	ABC	Selection 2
A: (2020), which showed that a detection with an effective signal-to-noise ratio of 3 would be seen in five years of LIGO and Virgo operation at their design (O4) sensitivities. The results of Boersma et alB: This approach was performed in Boersma et alC: (2020) are consistent with those of Hübner et al. (2020) in terms of the number of events which were needed.	CBA	ACB	BCA	BAC	Selection 4
A: The surface resistance of cold beam pipes is as well an important subject, as the anomalous skin effect can cause a large contribution to the beam driven wall losses [12], and direct cooling is not possible in many cases. In space-flight, many RF devices are exposed to varying temperatures in the range as discussed here. For these applications, it is sufficient to only know the resistive part R𝑅Ritalic_R of the surface impedance Z𝑍Zitalic_Z. B: Other topics to apply the geometric model are for example copper components in superconducting cavities – like power couplersC: It is of great importance to know exactly the thermal losses at these surfaces, which can’t be cooled efficiently in an easy way[18], and which are drifting to intermediate temperature levels depending on the operating conditions	BCA	ABC	ACB	CAB	Selection 4
A: We found that the skewness of the distribution of genotypes coded in each chromosome is essential to determining the probability of evolving new traits. Because skewness peaked with a finite number of chromosomes (FigB: 2B).C: 2F), there is an optimal number of chromosomes for evolving novel traits (Fig	BCA	ACB	CAB	CBA	Selection 2
A: Similar to SBM, ScBM also can not model overlapping networks. The Directed Mixed Membership Stochastic Blockmodels (DiMMSB) (Qing & Wang, 2021) was proposed to address this limitation by allowing nodes to belong to multiple communities. DiMMSB can be seen as a direct extension of MMSB from un-directed un-weighted networks to bipartite un-weighted networks. To estimate memberships under DiMMSB, Qing & Wang (2021) designed a spectral algorithm with a theoretical guarantee of estimation consistency.B: Spectral algorithms with theoretical guarantees on consistent estimation have been designed to estimate groups of nodes under ScBM and DCScBM, see algorithms proposed in Rohe et al. (2016); Zhou & A.Amini (2019); Wang et al. (2020)C: For community detection of bipartite un-weighted networks, Rohe et al. (2016) proposed Stochastic co-Blockmodel (ScBM) and Degree-Corrected Stochastic co-Blockmodel (DCScBM). ScBM and DCScBM can be seen as direct extensions of SBM and DCSBM from un-directed un-weighted networks to bipartite un-weighted networks, respectively	ACB	CBA	ACB	BAC	Selection 2
A: We have used these observations in [2] to understand the orbit structure of such systemsB: To obtain analogous results for general two-sided automata, we first perform some shifts and reduce to a counting problem for more general coincidence sets rather than periodic points (that are coincidence sets for iterates of a map and the identity map), to which the methods from [2] can also be applied. C: The results can be directly translated to the setting of one-sided cellular automata; to the best of our knowledge, in this generality the results are new	BCA	BAC	BCA	ACB	Selection 4
A: Within the infinite lattice [17, 18], configurations with more sites in the trap would be particularly interesting, through which one can seed diverse initial fluctuations, and investigate the correlations between the particle emission and the leadsB: There have been various theoretical works exploring several aspects of the highly nonequilibrium phenomena [11, 12, 13, 14, 15, 16, 17, 18], from the dynamics of the stimulating process of the observed pair emission [14, 15, 16] and a unique single-particle emission [17], to the characterizations of rapid density oscillations, typical threshold behavior [18] and high-harmonic generations [12]C: Accordingly, if one wanted to explore the competitions among different modes in the collective emission, extended models should be employed. From the theoretical point of view, one can configure synthetic traps, condensates and couplings based upon demands, to study the properties of the resulting particle jets.	CBA	BCA	BAC	ABC	Selection 3
A: Data are available from the authors upon reasonable request and with the permission of [third party]. B: Restrictions apply to the availability of these data, which were used under license for this studyC: The data that support the findings of this study are available from [third party]	ABC	CBA	ABC	ABC	Selection 2
A: Acknowledgment: We thank C. H. Keitel, K. Z. Hatsagortsyan, P. Zhang, and I. PB: Ivanov for helpful discussions. We are grateful to Q. Zhao for his help during the revision of our manuscript. This work is supported by the National Natural Science Foundation of China (Grants No. 11874295, No. 12022506, No. U2267204, NoC: 11905169, No. 12275209, No. 12147176, No. 12135001, No. 11825502, No. 11921006, and No. U2241281), the Foundation of Science and Technology on Plasma Physics Laboratory (No. JCKYS2021212008), and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSY014).	BCA	ABC	CBA	BCA	Selection 2
A: It implements the hypothetical Wilsonian perspective that the coarse-grained perturbative description should determine the complete non-perturbative description at any scale. Therefore, assuming that S~~𝑆\tilde{S}over~ start_ARG italic_S end_ARG and the inter-system couplings can be derived from S𝑆Sitalic_S, we can state that the coarse-grained descriptions of the two subsystems are related,222In Banerjee:2017ozx , a derivation of the semi-holographic procedure was proposed by noting that the perturbative series has renormalons which forbid Borel resummation, and this can be cured by considering non-perturbative contributionsB: The mutual effective metric coupling thus leads to a full energy-momentum tensor (6) which can be obtained ultra-locally from the subsystem energy-momentum tensors alone, and does not require any further microscopic input. This ensures that a coarse-grained hydrodynamic description of the full energy-momentum tensor in terms of those of the subsystemsC: A physical observable, such as the full energy-momentum tensor, which receives contributions from both sectors, should be a function of the perturbative coupling with a finite radius of convergence, provided that the intersystem couplings are appropriate functions of the perturbative couplings. This was illustrated in a toy bi-holographic set-up. and the full hydrodynamic description can be constructed in terms of the subsystem hydrodynamic variables. A detailed description will follow soon.	ACB	CBA	BCA	BAC	Selection 4
A: When the shock front reaches the tropopause, then the escaping neutral H-atom flux is no longer limited by diffusion but is directly coupled to the winds and circulation within the troposphere of the planetary body, and greatly enhancedB: Then, the depth that this shock front eats into the planet body depends on the incoming photon flux levelC: This transition may be paralleled with a phase transition from an entropy-limited regime to an energy-limited regime.	BAC	BCA	BCA	ACB	Selection 1
A: The physical effects discussed below also occur in other lattices with NNN hopping, including the 1D chain and 3D simple cubic latticeB: The square U⁢V𝑈𝑉UVitalic_U italic_V model serves as a convenient proxy for all hyper-cubic U⁢V𝑈𝑉UVitalic_U italic_V modelsC: The non-interacting (one particle) dispersion of Eq. (4) is	BCA	ACB	ABC	ACB	Selection 3
A: Following similar projection methods as described in §3.3, we take our velocity magnitude v𝑣vitalic_v, and randomly sample two angular components for latitudinal and longitudinal velocity components999We assume a Maxwellian distribution for PBH velocities as a computational shortcut, but use mean speeds following the Eddington inversion results from Lacroix et alB: However, we do not expect this simplifying assumption to be a dominant source of uncertainty in our analysis.. The longitudinal component is sampled uniformly between [0, 2⁢π2𝜋2\pi2 italic_π], while the latitudinal component is sampled uniformly on the unit sphere (i.e., uniform in cos⁡(latitude)latitude\cos({\rm latitude})roman_cos ( roman_latitude ) between [−11-1- 1, 1111]).C: (2018) (which assumes velocities deviate from the truncated Maxwellian of the SHM)	ACB	CBA	BCA	BCA	Selection 1
A: Red: analysis of PSR J0030+0451 from Riley et al. (2019). Green: latest analysis of HESS J1731-347 from Doroshenko et al. (2022). Orange error bars: analysis of 3XMM J185246.6+003317 from de Lima et al. (2022).B: Blue: analysis of PSR J0740+6620 from NICER and XMM-Newton data from Miller et al. (2021). Magenta: analysis of 4U 1702-429 from Nättilä et al. (2017)C: Figure 1: Mass-radius relation of QSs from Bombaci et al. (2021) (solid red), Ferrer et al. (2015) (solid blue) and Traversi et al. (2022) (solid black) with observational constraints at 68% of confidence level (dotted) and at 90% (dashed)	CBA	CAB	CAB	CAB	Selection 1
A: Therefore, there is no additional data to the boundary observables and the boundary data is trivialB: the factor of 1/2⁢m12𝑚1/2m1 / 2 italic_m in (43)) are not sufficient to capture the interactions in the bulk and reconstruct the EFT. C: In other words, the prefactors of the delta functions (e.g	CBA	ABC	ACB	CBA	Selection 3
A: In computing language, the Margolus-Levitin’s theorem on the maximum rate at which a quantum system can evolve through distinct states, translates into a theoretical upper limit on the number of operations that can be performed in a unit time. Lloyd applied Margolus–Levitin’s results to derive an upper bound for the computation speed of any system and argued that the maximum rate is actually attained by black holes compution B: The saturation of the Lloyd’s bound by black holes has been then rigorously demonstrated using quantum complexity and its relation to fidelity qc1 ; qc2 . If black holes can contain hairs, e.gC: quantum fields in equilibrium with the black hole, neither infalling nor escaping to infinity, such configurations would conceptually represent the fastest achievable quantum computers. In the presence of modifications of quantum mechanics (e.g. induced by quantum gravitational effects), the corresponding bounds would be even lower due to the increased quantum speed limit.	CBA	ACB	CAB	ABC	Selection 4
A: The action of the algebraic torus ℂsuperscriptℂ\mathbb{C}^{}blackboard_C start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT is quotient out by the equivalence relationB: As one can note the CY condition is automatically implemented by the fact that the vectors are coplanarC: and a possible solution is Q=(1,−1,1,−1)𝑄1111Q=(1,-1,1,-1)italic_Q = ( 1 , - 1 , 1 , - 1 )	CBA	CAB	CAB	ABC	Selection 1
A: The non-linear memory signal from eccentric binary orbits was calculated at 3-PN order in [33] and the 3-PN calculation for eccentric orbits including the tail contributions is done in [35]. B: The non-linear memory signal, for binaries in a quasi-circular orbit, already occurs at the 0-PN order [18, 29]C: In [30, 32] the non-linear memory for the quasi-circular orbit was computed at the 3-PN (Post-Newtonian) order	BAC	ACB	CBA	CAB	Selection 4
A: The variation of this action gives equation of motion and a boundary term which depends on the normal derivative of the boundary metric. To solve the variational principle one usually adds Gibbons Hawking term and various counter terms such that in the end total variation of the action is only proportional to the boundary component and not its derivativeB: We expect the variational problem that gives rise to chiral symmetry algebra in NU gauge to hold for these gauges as well. We leave a comparison of these boundary terms with that of standard Gibbon-Hawking term and other counterterms for future work. The derivation of finding boundary terms for locally AdS4 follows identically to Gupta:2021cwo and therefore we use only the final answer here. The boundary action that we add to Einstein-Hilbert action is,C: This is the usual procedure when one works in FG gauge. As we are working in NU gauge, we use the boundary terms that we found in Gupta:2021cwo for the case of asymptotically locally flat spacetimes in NU gauge.666Normally the boundary action for AdSd+1 gravity in Fefferman-Graham gauge Balasubramanian:1999re ; Brown:1992br or the gauge used to describe ‘boosted black brane’ Bhattacharyya:2007vjd is invariant under d𝑑ditalic_d-dimensional boundary preserving diffeomorphisms unlike the boundary terms used here in context of NU gauge	CAB	BAC	BAC	ACB	Selection 4
A: The immediate model-building challenge is that we are asking for effects derived from thermal equilibrium to result in a far-out-of-equilibrium configuration. Further, this asymmetry in abundances must remain as the symmetry-breaking scalar later rolls back to the origin and the sectors become exactly degenerate at low temperatures.B: The idea is to use the high-temperature ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT-breaking phase to set up an initial asymmetry in the energy densities of the SM and mirror sectorsC: Here we present a minimal module to effect the asymmetric reheating of a degenerate mirror sector via inverse symmetry breaking	BCA	ACB	ABC	CBA	Selection 4
A: The polynomial decay of the fractional charge correlation also characterises the delocalisation, and the polynomial lower and upper bounds were established in [25, 26]. In the localised phase, the Debye screening (cfB: [11, 52] for the lattice sine-Gordon model and [8] for the DG model) induces exponential decay of the truncated charge correlationC: The same type of result was studied for the dimer model in [45, 19].	ABC	CAB	ACB	ACB	Selection 1
A: The observation of bi-stability and the single superconducting qubit coupling to the Kittel mode are interesting developments in this field [23, 24]B: Li et alC: illustrated how to create tripartite entanglement in a system of microwave cavity photons entangled to the magnon and phonon modes of a YIG sphere in a magnomechanical cavity [25]. This study was followed by an investigation of magnon-magnon entanglement between two YIG spheres in cavity magnomechanics [26].	CBA	CAB	ABC	BCA	Selection 3
A: The transport current I𝐼Iitalic_I has been applied in this direction, after cutting the sample into rectangular shape; this resulted in approximate orientation of the I𝐼Iitalic_I (to within 10-20 deg) with one of the main in-plane axes. B: For magnetization and transport measurements the crystals were cleaved, with cleavage plane always perpendicular to the c𝑐citalic_c-axisC: The in-plane shape was slightly elongated in the direction of one of the in-plane main crystallographic axes, as confirmed by X-ray examination	CAB	ACB	BAC	CBA	Selection 1
A: To date, our knowledge about this matter is restricted, and it is recommended from a practical standpoint that the terms of drift and diffusion should be maintained when applying the equationB: Although this approximation is widely practised and has shown some level of precision, more rigorous mathematical examination and extensive numerical testing are crucial to confirm and improve this approximation. Furthermore, it might be beneficial to investigate under what conditions an infinite-order jet can be effectively represented by a finite-order jet, considering that the kinetic equation is an outcoming of an infinite-order jet. C: Utilizing the infinite-order kinetic equation in real-world scenarios presents a formidable challenge	BAC	ACB	CBA	BCA	Selection 4
A: The routine use of DKI in the clinic has nonetheless lagged due the inability to robustly estimate the kurtosis metric (Veraart et al., 2011a; Tabesh et al., 2010; Kuder et al., 2011; Henriques et al., 2021). A known requirement for estimating kurtosis in DKI is to restrict the maximum b-value to 2000 s/mm2 ssuperscriptmm2\text{ s}/\text{mm}^{2}s / mm start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-3000 s/mm2 ssuperscriptmm2\text{ s}/\text{mm}^{2}s / mm start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT for brain studies (Jensen et al., 2005; Jensen and Helpern, 2010; Poot et al., 2010), with the optimal maximum b-value found to be dependent on tissue type (Poot et al., 2010)B: This suggests that the traditional kurtosis model is less accurate at representing the diffusion signal at large b-values. Moreover, multiple b-shell, multiple direction high quality DW-MRI data can take many minutes to acquire, which poses challenges for clinical imaging protocols involving a multitude of MRI contrasts already taking tens of minutes to executeC: Reduction of DKI data acquisition times through parallel imaging, optimisation of b-shells and directions have been investigated (Zong et al., 2021; Heidemann et al., 2010; Zelinski et al., 2008), and DW-MRI data necessary for DKI analysis has been shown to supersede the data required for DTI (Veraart et al., 2011b). Therefore, an optimised DKI protocol can potentially replace clinical DTI data acquisitions without adversely affecting the estimation of DTI metrics.	ABC	BCA	BCA	BAC	Selection 1

**A**: This nascent appreciation that environments and their (possibly non-Markovian) dynamics could be active and potentially programmable components of future quantum devices raises exciting possibilities that could be accessible with current nanofabrication techniques and experimental probes [26, 27, 28, 29, 30]. In this work we address a relatively unexplored aspect of ‘environment-assisted’ phenomena that is of relevance for all of the examples and topics given above**B**: Most theoretical descriptions of interacting arrays of open quantum systems utilize models in which each component (qubits, chromophores, quantum dots, etc.) interact with ‘local’, independent environments, i.e. while the components may interact with each other, their dissipative environments do not**C**: Energy and/or information dissipated into these local environments is forever lost to the global multicomponent system. However, as the density of components increases – as required for more sophisticated quantum devices – the independence of these local environments becomes harder to justify [31]: propagating perturbations (excitations) of their common medium at one location become able to affect the dynamics of spatially remote systems, and maybe even do so on timescales that could be comparable to the intrinsic inter-system dynamics (see Fig. 1(a)).

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**A**: The abstract version here is the (weighted) enumeration of all matchings of a graph**B**: However, when there is a single monomer on the boundary of a plane graph, the partition function can indeed be written as a Pfaffian [Wu06].**C**: The weights are interpreted as energies and are positive real numbers. This is known to be a computationally difficult problem [Jer87] and the partition function here does not have such a clean formula

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**A**: This and other issues such as different input states, nonsymmetric two-qubit gates, and nonideal local operations remain open questions**B**: A possible drawback is that one cannot know with certainty the final maximally entangled state produced by the protocol**C**: However, this work aims to introduce a concept of globally optimized recurrence protocols that is flexible enough to incorporate the aforementioned points in further investigations.

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**A**: Concerning the changes in the activation function shown at the top of the table, we observe that our choice, the Sigmoid, has the highest convergence rate of r=66.9%𝑟percent66.9r=66.9\%italic_r = 66.9 % for this architecture**B**: Not only this, but Sigmoids also yield the lowest (and hence best) energy value. In contrast, ReLU and Softplus come at considerably higher energies. **C**: This is contrast to r<15%𝑟percent15r<15\%italic_r < 15 % for both the ReLU and Softplus functions, indicating that models have a harder time converging for these functions

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**A**: The section numbers for the proof of the classification under OBCs and the BBC are shown for each topological number.**B**: Table S3: Point-gap topological phases in 6 classes without SLS**C**: These classes do not show the skin effects, and thus the classification under the OBCs coincides with that under the PBC

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**A**: johri2021nearest , and where necessary, the larger IonQ Aria machine with a capacity of 32 physical and 20 algorithmic qubits (ionq2022aria, )**B**: A crucial point to bear in mind with quantum computing is that the memory capacity**C**: Experiments below used the 11-qubit trapped ion quantum computer described by Johri et al

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**A**: When the fixed-point operator evaluations are the dominant computational cost of AAR, one may choose to approximate the evaluations of the fixed-point operator to reduce the computational cost of the evaluations**B**: When instead solving the least-squares problem for the Anderson mixing is the most expensive step of AAR, one may solve the least-squares problem approximately to reduce the computational cost of the least-squares solver. Our theoretical results open a new path to efficiently apply AAR to solve problems in addition to sparse linear systems, including non-linear fixed-point iterations arising from quantum mechanics, plasma astrophysics, and computational fluid dynamics where fixed-point operator evaluations are often expensive 18. In this context, the use of AAR allows to leverage less expensive operator evaluations without affecting the final attainable accuracy of the non-linear physics solver.**C**: Our theoretical results allow for accuracy reduction in different calculations performed by AAR on linear fixed-point problems

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**A**: Below we explicitly analyse Statement 2 for the dynamical map generated by quantum SWITCH. For that particular dynamical map, it is straightforward to show (from Eq. (IV)) that**B**: (IV)**C**: statement 1 and Statement 2 are quite general to the family of dynamics given by Eq

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**A**: Practical quantum circuits have a regular structure**B**: For example, the ripple-carry adder has a V-shape of Toffoli gates, and quantum multiplication circuits are built on top of quantum addition**C**: We use the example of a multiplication circuit, and construct manually the multiplier circuit from [33] (see Appendix for its circuit diagram) by tiling the tiles from Fig. 1.

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**A**: (2015) showed that such an agglomeration of neutrons is generic and the exotic nuclei can be expected to grow quite large. This means that dark matter self-interaction is suppressed and the bounds from the Bullet Cluster Randall et al. (2008) can be evaded.**B**: The dark matter will be dominated by the neutrons in the exotic sector with the lightest Higgs mass. Furthermore, the pions in these sectors are much lighter than the SM pions, so these neutrons can form large nuclei Krnjaic and Sigurdson (2015); Hardy et al**C**: (2015). In fact, Hardy et al

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**A**: In this section, we demonstrated the applicability of TERP for probing black-box models designed to analyze time-series data coming from MD simulations**B**: In addition to assigning confidence to these models, TERP can be used to extract valuable insights (relevant degrees of freedom) learned by the model**C**: In the future, we expect an increased adoption of TERP-like methods in the domain of AI-enhanced MD simulations for investigating conformational dynamics, nucleation, target-drug interactions, and other relevant molecular phenomena.

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**A**: S2, the Fig. S31 is similar to Fig. S3) are obtained. Analogously, the similar precision results (the Fig**B**: S33 is similar to Fig. S14, the Fig. S34 is similar to Fig. S17) are obtained. These show that our quantitative framework is not affected by the random removal percentage.**C**: In the main text, we show the analysis for 20% random removal links. For robustness check, we here repeat the analysis for 10% random removal. The similar AUC results (the Fig. S32 is similar to Fig

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**A**: **B**: where D⁢(O)⋅ρ=1/2⁢(O⁢ρ⁢O†−O†⁢O⁢ρ−ρ⁢O†⁢O)bold-⋅𝐷𝑂𝜌12𝑂𝜌superscript𝑂†superscript𝑂†𝑂𝜌𝜌superscript𝑂†𝑂{D(O)\bm{\cdot}\rho=1/2(O\rho O^{\dagger}-O^{\dagger}O\rho-\rho O^{\dagger}O)}italic_D ( italic_O ) bold_⋅ italic_ρ = 1 / 2 ( italic_O italic_ρ italic_O start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT - italic_O start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT italic_O italic_ρ - italic_ρ italic_O start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT italic_O ), and {|j⟩}j=0,1,2..\{|j\rangle\}_{j=0,1,2..}{ | italic_j ⟩ } start_POSTSUBSCRIPT italic_j = 0 , 1 , 2 **C**: end_POSTSUBSCRIPT are eigenvectors of the Hamiltonian H𝐻Hitalic_H with eigenenergy ϵjsubscriptitalic-ϵ𝑗\epsilon_{j}italic_ϵ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT. The decay rates read

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**A**: The methods proposed in [19, 20, 21, 22] rely on the magnitude of thermoelectric coefficients like the Seebeck coefficient to probe the presence and nature of MBS. On the other hand, we rely on the symmetry of the thermoelectric coefficients to the Aharonov-Bohm flux and the Fermi energy to probe the absence or presence of MBS as well as their nature (coupled/individual). Additionally, Ref**B**: [19] relies on the violation of Wiedemann-Franz law (WF law) [23]. In this paper, we, too, employ the violation of WF law to probe the presence of MBS. An upshot of this work is that none of the previous works that aim to probe MBS via thermal coefficients use Aharonov-Bohm flux as a parameter.**C**: In this work, we aim to probe MBS in topological insulators that contain a superconducting and ferromagnetic interface (STIM interface) [5] by studying the symmetry of various thermoelectric coefficients. We see that thermoelectric coefficients like Seebeck, Peltier coefficients, and the thermal conductance [14, 15, 16, 17, 18] are symmetric or asymmetric to the Aharonov-Bohm flux, Fermi energy and can indicate existence and nature of MBS. Several methods of probing MBS via thermoelectric transport have been put forward before [19, 20, 21, 22]

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**A**: For b≪1much-less-than𝑏1b\ll 1italic_b ≪ 1, corresponding to an annihilation with a much lighter particle, the correction can be large.**B**: However, when the exponential suppression is weaker (b<1𝑏1{b<1}italic_b < 1), instantaneous freezeout may no longer be a good approximation for estimating the relic abundance, as shown in Ref. Kim:2019udq ; Kramer:2020sbb **C**: Instantaneous freezeout is a good approximation in many scenarios, because the annihilation rate is dropping exponentially with time (or temperature)

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Selection 2

**A**: or equivalently connected covers**B**: Hurwitz**C**: The double Hurwitz numbers Hg∙⁢(α,β)superscriptsubscript𝐻𝑔∙𝛼𝛽H_{g}^{\bullet}(\alpha,\beta)italic_H start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ∙ end_POSTSUPERSCRIPT ( italic_α , italic_β ) and Hg⁢(α,β)subscript𝐻𝑔𝛼𝛽H_{g}(\alpha,\beta)italic_H start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT ( italic_α , italic_β ) were first studied by Okounkov [MRL]

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**A**: probabilities**B**: (15) is the special case where C=𝒵→𝐶→𝒵C={\overrightarrow{\mathcal{Z}}}italic_C = over→ start_ARG caligraphic_Z end_ARG, ρ=π0𝜌subscript𝜋0{\rho}={\pi}_{0}italic_ρ = italic_π start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, and**C**: Jarzynski’s Equality Eq

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**A**: By varying the film thickness up to 800 nm, we have verified the dominant role of strain in this peculiar system. We find that the unit cell differs from the bulk even at dimensions of several hundreds of nanometers**B**: In this work we present the properties of a𝑎aitalic_a-axis oriented YBCO thin films, at various doping levels from the optimally doped down to the insulating state, obtained by a careful oxygen annealing procedure. X-ray diffraction (XRD) analysis shows that the films are fully detwinned, implying the presence of CuO chains, aligned throughout the sample along the in-plane b𝑏bitalic_b direction**C**: The resistance vs temperature measurements are characterized by sharp superconducting transitions, showing that the superconducting properties of the films are rather homogeneous. We observe a strong in-plane anisotropy of the resistance, comparable, also for rather thick films, to the best results achieved on detwinned single crystals. This opens up the possibility of studying potential modifications of the ground state induced by confinement in films with only a few unit cells in thickness.

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Selection 4

**A**: In our experimental demonstrations of section 4 we study both applications by simultaneously performing the mcm-rb suite across 12 control and 5 ancilla qubits on our device. While simultaneous Clifford gates on control qubits can introduce cross-talk error, since mcm-rb and delay-rb operate under the same control conditions with simultaneous gates they equivalently experience cross-talk. Thus, we can still use delay-rb as the reference sequence to quantify the error induced by measurement in mcm-rb.**B**: While Fig. 1 shows as an example only a single control and ancilla qubit, the mcm-rb suite can be applied simultaneously to multiple control and ancilla qubits**C**: This can be used, for example, to test the impact of measurement of a central ancilla on multiple control qubits, or to test the impact of the measurement of multiple ancilla qubits on a single control

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Selection 3

**A**: Although the final state may have correlations between the system and the ancilla, the second condition implies that the ancillary system A𝐴Aitalic_A is returned exactly in the same state as before and thus acts as a catalyst in the process**B**: [26] considered noise as a resource, and interestingly, here the noise is not consumed in the process and can be reused again. Furthermore, note that Eq. (102) emphasises that every possible state transition utilising randomness can be accomplished if a dephasing map can be constructed and Boes et al. [26] provided an explicit protocol for that.**C**: As mentioned previously, Boes et al

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**A**: After this introduction, the analytical expressions and properties of the potential flow field around an axially-symmetric paraboloid are derived and discussed in Section 2**B**: The paper is structured as follows**C**: Thereafter, Section 3 presents the analytical derivation and discussion of a magnetic field B→→𝐵\vec{B}over→ start_ARG italic_B end_ARG being passively advected in this flow by solving the stationary induction equation of ideal MHD

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Selection 2

**A**: The quantum-optical decoherence in driven systems can have a significant impact on the design of quantum memories and quantum operations**B**: To achieve long quantum information storage times, sophisticated control protocols have been developed, that typically involve time-periodic electromagnetic fields**C**: Using dynamical decoupling, quantum information could be conserved for more than six hours in rare-earth atoms embedded in a crystal structure [112], and more than 50⁢s50s50\,\text{s}50 s in trapped ions [111]. In both cases, the quantum information is stored in the hyper-fine levels of the ground-state manifold, which are energetically separated in the radio-frequency regime.

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**A**: Ashtekar’s formalism thus opened a new approach to quantizing gravity non-perturbatively; other approaches include loop quantum gravity, causal dynamical triangulations, spin foam and causal sets, which are non-perturbative approaches that attempt to yield a self-consistent quantization of gravity**B**: Many of these approaches have had difficulties in making contact to a semi-classical limit**C**: Moreover, while the Kodama state is a candidate for describing a ground state of quantum gravity with a positive cosmological constant non-perturbatively, it suffers from a number of issues, including non-normalizability, its CPT-violating properties (and consequent impossibility of having a positive energy), and lack of gauge invariance under large gauge transformations [3].

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Selection 1

**A**: Among others, Goddard and Miller[36] derived constitutive equations for the rheological behavior of a suspension of slightly deformed viscoelastic spheres in the dilute limit. Misbah [37] derived equations which describe the vesicle orientation in the flow and its shape evolution, and outlined a rheological law for a dilute vesicle suspension**B**: Matsunaga and Imai [48] systematically investigated the effect of viscosity ratio on the viscoelastic character of capsule suspension for a wide range of oscillatory shear rate frequencies. By employing continuum modeling, in particular the Oldroyd 8-constant framework, Saengow et al. [50] assessed the non-Newtonian character of human blood under uni-directional large-amplitude oscillatory shear (LAOS) flow, which is generated by superposing LAOS onto a steady shear flow. Clarifying the cellular-scale dynamics under oscillatory flow allows us to build precise continuum models of suspensions [51, 52, 53], and may lead us to novel biomedical applications [54], such as phenotype cell screening, and circulating tumor cell isolation in a chip [55]. However, this can be achieved only after fully grasping the effect of the particle deformations induced by the oscillations of the bulk suspension.**C**: Along with these analytical and numerical studies, recent computer simulation approaches have successfully been used to investigate rheological properties of a dilute and semi-dilute suspension of deformable particles in steady shear flow, e.g., elastic initially spherical particles [39, 40, 41] and capsule [42]. Numerical analyses of semi-dilute and jammed particle suspensions under oscillatory shear flow have been reported recently, e.g., rigid spherical particles at finite inertia [43], soft particle glasses [44], viscoelastic particles [45], bubbles [46], vesicles [47], and spherical capsule in dilute condition [48]. The recent theoretical work by Armstrong et al. [49] compared viscoelastic moduli obtained with several viscoelastic(-thixotropic) models and laboratory measurements under oscillatory shear flow

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**A**: P**B**: has been partially supported by the Brazilian science foundations Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG), and by the University of Tor Vergata.**C**: A

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**A**: (2017), HRG model with HS Noronha-Hostler et al. (2009) and SMASH transport model Rose et al. (2020).**B**: Schee (2022), LQCD (Lattice1 Meyer (2008), Lattice3 Astrakhantsev et al. (2018) and Lattice5 Karsch et al**C**: (2008), with 68.3% C.L.), hybrid model (McGill) Ryu et al. (2015), holographic model (Holo) Rougemont et al

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**A**: On the other hand, the multi-shell model in Ref.[25] (and Appendix A) considers both the time evolution of continuously many null shells and the backreaction of the evaporation in a common time coordinate and examines whether an apparent horizon is formed, without assuming anything about the magnitude of the energy-momentum tensor a priori**B**: Solving (1.1) self-consistently, each shell will never cross its shrinking Schwarzschild radius, and a surface pressure will occur on each shell [25], which becomes the large tangential pressure (2.15) in a continuum limit, leading to the dense configuration without forming horizons**C**: Thus, the 4D dynamics of (1.1) including the tangential direction makes the difference.

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**A**: For the two atomistic systems, alanine dipeptide and chignolin, we describe the systems using two different types of high-dimensional representations (distances and dihedral angles, respectively) to show that the framework can work regardless of the chosen configuration variables.**B**: To demonstrate the validity of our framework, we apply diffusion map to standard testing systems such as a particle moving on an analytical potential and alanine dipeptide**C**: For the stochastic embedding methods, we choose a mini-protein chignolin

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**A**: Let x𝑥xitalic_x and y𝑦yitalic_y denote the positions of the big and small balls, respectively. The small ball satisfies the Schrödinger equation**B**: As shown in Fig**C**: 2, the classical big ball and the wall constitute a one-dimensional infinite potential well, as the quantum small ball is situated between them. The motions of the two balls are governed by their interaction

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Selection 1

**A**: The red squares in Fig. 6, represent the oscillation amplitudes due to the isotropic component of the gravitational force for both Yukawa and power-law corrections. Because the corrections to Newtonian gravity are small, the isotropic component of the torque oscillations are largely independent of the details of the correction term. **B**: A plot of the isotropic and anisotropic oscillation amplitudes as a function of N𝑁Nitalic_N are shown in Fig. 6**C**: For both the Yukawa and power-law cases, increasing N𝑁Nitalic_N from 10101010 to 30303030 suppresses the fundamental isotropic peak by eight orders of magnitude

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**A**: Moreover, even in challenging scenarios, the proposal exhibits resilience, indicating that a robotic spacecraft can handle those difficult conditions. Other algorithms could be developed to identify such challenging scenarios and guide the spacecraft toward more favorable operating conditions. **B**: These scenarios serve to demonstrate that, from a GN&C perspective, an autonomous robotic spacecraft does not necessarily require extensive navigation campaigns to reduce uncertainties to very low levels**C**: Once again, the selection of scenarios is intended to underscore the proposal’s robustness under unfavorable conditions, while also incorporating conservative assumptions

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**A**: This work has made use of the ESA Gaia mission, processed by the Gaia DPAC. J. Farihi acknowledges support from STFC grant ST/R000476/1. T. G. Wilson acknowledges support from STFC consolidated grants ST/R000824/1, ST/V000861/1, and UKSA grant ST/R003203/1. **B**: The authors thank an anonymous reviewer for a careful reading of the manuscript. J. Farihi thanks D. Koester and G. Fontaine for key discussions over the years that helped to form the foundation of this work, E. Dennihy for confirming the fact that no DQ star has a suspected infrared excess from circumstellar dust, A. Rebassa-Mansergas for sharing his full white dwarf-main sequence binary catalog, and valuable exchanges with E. B. Bauer, R. R. Rafikov, and J. J. Eldridge**C**: Several colleagues provided feedback on an earlier version of the manuscript, including those mentioned above, as well as T. von Hippel, A. J. Mustill, A. Swan, and B. Zuckerman. The authors acknowledge the European Southern Observatory for the award of telescope time via programs 095.D-0706, 096.D-0076, and 097.D-0063

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**A**: Active elongated particles and rods present a different situation where the pressure becomes dependent on particle-wall interactions [40]. Active pressure has been investigated on boundaries with different geometries such as flat walls [37, 36], curved surfaces [35, 34, 41, 36], corners [35], and sinusoidal and flexible interfaces [44, 43]. In addition to the geometry of boundaries, active pressure can vary depending on intrinsic features of active particles such as chirality [41], interparticle interactions, and local concentration [34, 38, 18].**B**: A particularly interesting facet of active suspensions is the so-called active or swim pressure produced by the constituent self-propelled particles [35, 39, 40, 37, 38, 18, 36, 42, 34, 41]. In equilibrium systems, pressure can be calculated using thermodynamic, mechanical, and hydrodynamical approaches, leading to the same result. This result follows a state equation and thus varies only with bulk properties such as temperature and density**C**: In active systems, a state equation may not generally exist [40]. Therefore, the pressure is mainly defined via mechanical and hydrodynamical approaches [39, 40, 38]. More specifically, in the case of self-propelled spheres next to flat walls, the pressure can be described as a state function using activity-dependent effective temperature and bulk number density of spheres [38, 37]

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**A**: Section 5 presents numerical methods to compute χ⁢(X),𝜒𝑋\chi(X),italic_χ ( italic_X ) , and to find relations among the integrals we study. Appendix A proves a vanishing result on cohomology groups**B**: It is also made available, together with our other computational examples, on the MathRepo [23] page https://mathrepo.mis.mpg.de/EulerIntegrals hosted by MPI MiS.**C**: In Appendix B, we provide the code used for computations in Section 5

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**A**: When the temperature is low, the rate constants will be faster at low pressures, according to the graph**B**: To explain this, it should be noted that at low pressure values, the deficiency of collisions means that the Boltzmann distribution does not hold since there is not much energy exchange. The result of this is that the collision frequency will be the dominant term in determining the rate constant. Its value is then lower at high temperatures due to the fact that collision frequency is inversely proportional to temperature at constant pressure.**C**: However, the reverse trend is seen at high pressure

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**A**: Supplementary Fig. 1: Evidence the source crystal is Bernal trilayer graphene**B**: Blue and green spots indicate where Raman spectra were obtained. (b) STM topograph of the fabricated TDTG stack showing a trilayer step at the edge of the twisted region. **C**: (a) Raman spectra of the 2D-mode acquired on two different spots of the source crystal with 514 nm laser wavelength. Inset: optical micrographs of the source crystal before (top) and after (bottom) AFM cutting

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**A**: This is highlighted in Fig. 7 where we additionally consider an L𝐿Litalic_L-layered HEE and see that increasing expressivity can accelerate the exponential decay.**B**: While Proposition 1 is derived with a tensor product embedding, similar results are expected when dealing with more general unstructured embeddings such as hardware efficient embeddings**C**: This is because the additional complexity from using an unstructured embedding can only increase the kernel concentration (due to increased expressivity and entanglement)

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**A**: Notice that this conclusion contradicts the conjecture in [36], which proposes that non-maximal giant gravitons are also integrable**B**: As a result, the shift two symmetry of the boundary state results in a vanishing overlap between the boundary state and these Bethe roots. Hence, the calculations in this section imply that only two giant gravitons correspond to the integrable boundary state. **C**: However, in [36], it was shown that the Bethe roots that do not satisfy the root pairing also fail to satisfy the zero momentum condition

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**A**: This calculation is further coupled with an Equation of State (EoS) incorporating a CEP in the universality class of the Ising model Parotto et al**B**: (2019), from which a prominent enhancement around CEP is found for q^^𝑞\hat{q}over^ start_ARG italic_q end_ARG. Such an enhancement, named as “partonic critical opalescence" (PCO)**C**: (2020); Martinez et al

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**A**: (2012) or of a red-detuned optical potential attracting the atoms away from the low magnetic field region Lin et al. (2009). Here, we have followed the latter strategy.**B**: In order to prevent Majorana losses caused by the vanishing magnetic field in the center of the quadrupole trap, several strategies can be implemented. They include the addition of a rotating homogeneous field in the case of a TOP trap Petrich et al**C**: (1995), of a repulsive optical potential focused in the quadrupole center as for plugged traps Davis et al. (1995); Naik and Raman (2005); Dubessy et al

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**A**: As we showed here, the mean square displacement differs for fermions and bosons. Also, we have verified the fluctuation-dissipation theorem for zero and non-zero chemical potentials for both statistics. As these results are presented in terms of the metric components, this is a quite general result. **B**: For a general diagonal metric, we obtained expressions for linear response function, mean square displacement, correlations functions and diffusion coefficient, in terms of the metric elements**C**: In this work we presented some results regarding the dynamics of a particle in a thermal bath at finite density, in the linear regime, using holographic methods

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**A**: Recently, there is growing interest in including a physics-based prior into neural networks**B**: Refs**C**: 16, 17, 18 introduce concepts from Lagrangian or Hamiltonian mechanics into neural networks, allowing them to learn and respect conservation laws for deterministic dynamical systems. These dynamical priors have subsequently been incorporated into VAEs19, 20, 21, 22. Incorporating domain knowledge from physics also encompasses alternative approaches, such as the use of physical laws as regularization terms to augment the loss function23, 24, 25.

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**A**: Conversely, lissencephalic patterns are generally found in species with smaller brains or a lower risk of head impacts. Intermediate patterns exist between these two extremes.**B**: Furthermore, this analysis offers insights into various patterns of gyrification**C**: Complex gyrification is more likely observed in species with larger brains, or those facing a high risk of head impacts due to lifestyle factors or intense echolocation signals

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**A**: [17, 18, 19, 20, 34]. There are a variety of approaches to describe pedestrian motion, the most prominent of which are fluid dynamics models, particle models, agent-based models, e.g**B**: The mathematical modeling of pedestrian flows, which is an interesting academic problem, has high practical importance [17, 18, 20]. Indeed, it is directly related to the effective planning of public places, transportation systems, evacuation strategies in emergencies, and the organization of pedestrian fluxes in an epidemic, e.g**C**: [17, 18, 19, 20, 34], and models based on cellular automata [35, 36, 37]. Conceptually, the agent-based approach is similar to the molecular dynamics approach, in which the motion of all molecules is simulated by solving Newtons’ laws. Obviously, this is the most microscopic approach that provides the maximum possible information about the system.

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**A**: These results are then extended to the general von Neumann algebraic setting in Section 4. Finally, examples and applications to quantum circuit complexity and quantum learning theory are provided in Sections 5 and 6. **B**: Section 3 is devoted to the statement and proof of our main results, namely a quantum L1superscript𝐿1L^{1}italic_L start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT-Poincaré inequality (Theorem 3.1), quantum Talagrand inequality (Theorem 3.2), and quantum KKL theorem (Theorem 3.9) and a quantum Friedgut’s Junta theorem (Theorem 3.11 and Corollary 3.12)**C**: The rest of the paper is organized as follows: in Section 2, we recall useful definitions and results from the Fourier analysis on the quantum Boolean hypercubes including Poincaré inequality, hypercontractivity, intertwining and gradient estimates

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**A**: Specifically: **B**: Constraints on cosmological parameters were obtained using the cosmological Markov chain Monte Carlo (MCMC) software Cobaya [47, 48]**C**: This was done using a combination of Planck CMB measurements, Pantheon Type Ia supernovae, constraints on the absolute magnitude of Type Ia supernovae, baryonic acoustic oscillations and redshift space distortion measurements

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**A**: Acknowledgements: The author thanks Niky Kamran for discussions, guidance and careful proofreading of the manuscript, as well as Felix Finster for helpful comments and discussions**B**: This work was supported by the Natural Sciences and Engineering Research Council (NSERC) Undergraduate Student Research Award (USRA) program and by NSERC grant RGPIN 105490-2018. **C**: The author also thanks the referee for valuable comments and suggestions

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**A**: This uncertainty is called as the first kind of residual scale dependence due to unknown higher-order terms [105]**B**: For the present case, the residual scale dependence (29) is much smaller than conventional scale uncertainty (25).**C**: Such residual scale dependence is distinct from the conventional scale ambiguities and is suppressed due to the perturbative nature of the PMC scale

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**A**: This type of spontaneous symmetry breaking is associated with non-Hermitian phase transitions [13, 14, 15, 16, 17, 18, 19, 20]. PT-symmetrical systems are one of the most famous examples of systems with this type of spontaneous symmetry breaking [15, 16]**B**: In recent decades, it has been shown that in non-Hermitian systems, it is possible that the symmetry of the eigenstates is lower than the symmetry of the system Hamiltonian [6, 7, 8]. As a result, one can observe another type of spontaneous symmetry breaking [8, 9, 10, 11, 12], which manifests as the decrease of the symmetry of eigenstates with simultaneous conservation of the Hamiltonian symmetry**C**: In these systems, the change in the system parameters leads to passing through an exceptional point (EP) [15, 16], at which the eigenstates cease to be PT-symmetrical, whereas the Hamiltonian is still PT-symmetrical. In addition to PT-symmetrical systems, non-Hermitian phase transitions can also occur in strongly coupled cavity-atom systems [15, 21], polariton [22, 23], optomechanical [24, 25, 26, 27, 28, 29], and laser [30, 31, 32, 33, 34] systems. The systems with the phase transitions at the EP find a number of the applications [35, 36, 37, 38, 39, 40].

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**A**: (2020). The resulting primordial GW signal contains key signatures of ultraviolet physics that would otherwise remain far beyond the reach of regular ground detection. This is why such signal is a main focus of current and future investigations of the stochastic GW background (SGWB) (Maggiore, 2000; Romano and Cornish, 2017; Caprini and Figueroa, 2018; Christensen, 2019). In addition, observation of such a signal (Lentati et al., 2015; Arzoumanian et al., 2018, 2020) can be a complementary probe to the range of SHDM mass if one assumes that such DM particles are produced by emission of the PBHs.**B**: Cosmic strings restore that broken Abelian symmetry at the core of these topological defects with vortex types of behavior (Nielsen and Olesen, 1973)**C**: Their network loses energy through the shrinking of its closed loops following their emission of GWs Vachaspati and Vilenkin (1985); Auclair et al

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**A**: Hints at a deeper perspective come from recent works on chiral twisted graphene tarnopolskyOriginMagicAngles2019a; ledwithFractionalChernInsulator2020a; popovHiddenWaveFunction2021; shefferChiralMagicAngleTwisted2021a; renWKBEstimateBilayer2021a; wangChiralApproximationTwisted2021a; naumisReductionTwistedBilayer2021a; navarro-labastidaWhyFirstMagicangle2022; beckerSpectralCharacterizationMagic2021a; beckerFineStructureFlat2022; beckerIntegrabilityChiralModel2022, which focused on the “trace condition” ledwithFractionalChernInsulator2020a; ledwithFamilyIdealChern2022; wangExactLandauLevel2021a; ledwithStrongCouplingTheory2021**B**: The exactly flat Chern bands of chiral twisted graphene not only satisfy the trace condition but also have a transparent real-space structure**C**: This structure enables the construction of “short range ground states (SRI-GS)”:

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Selection 4

**A**: This properness assumption, in fact, implies that the spacetime must be globally hyperbolic with compact Cauchy level sets (see Section 3.2). Both approaches yield local encodement of causality on any stably causal spacetime (see Theorem 3.4 and [SaSo]*Thm. 1.1). Upon studying the proofs of [SaSo] we noticed that by combining part of their local arguments [SaSo]*Thm. 1.1 with our global proof of Theorem 3.3 we can obtain Theorem 1.9 which is optimal both in view of regularity as well as causality. It is precisely this optimality, together with the observation that τ𝜏\tauitalic_τ having future (or past) Cauchy level sets is actually sufficient, that allows us to conclude with the following application. **B**: The ⟹⟹\Longrightarrow⟹ direction in Theorem 1.9 is trivial. Sormani and Vega [SoVe]*Thm. 3.25 showed that the converse holds for warped product spacetimes with complete Riemannian fiber and suitable temporal functions. It remained an open problem to determine under which general circumstances causality is encoded**C**: Our Theorem 1.9 provides a sharp answer both in terms of regularity as well as the causality class (see counterexamples in Section 3.3). Initially we proved this result for Cauchy temporal functions in Theorem 3.3. Independently and simultaneously, Sakovich and Sormani [SaSo]*Thm. 4.1 have obtained a different global causality encoding result where they allow for general anti-Lipschitz time functions, but require them to be proper

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**A**: The simplest network scenario is provided by entanglement swapping [22]**B**: The generalization of the bilocality scenario to network, is the so-called n𝑛nitalic_n-locality scenario, where the number of independent sources of states is increased to arbitrary n𝑛nitalic_n [14, 15, 16, 23, 24, 25]. Some new interesting effects, such as the possibility to certify quantum nonlocality “without inputs”, are offered by the network structure [10, 11, 26, 27]. **C**: To contrast classical and quantum correlation in this scenario, the so-called bilocality assumption where the classical models consist of two independent local hidden variables (LHV), has been considered [9, 10]

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**A**: In each case we compare the properties of the 4DEGB solution for multiple values of the coupling constant to the analogous GR result, and discuss how the rotational corrections affect these properties. **B**: We discuss the location and angular velocity of the black hole horizons, the equatorial geodesics – including the innermost stable circular orbit, photon rings (and associated Lyapunov exponents) – as well as the black hole shadow**C**: In this section we study physical properties of the solutions derived above

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Selection 1

**A**: Ref. ZhangBHRV:16 for the risk when the number of parameters exceeds the number of data points). Since Lüscher’s formula is the only model-independent approach, this lead to our central conclusion that we get a neural network reprint of the numerical Lüscher’s formula.**B**: e.g**C**: (see

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Selection 2

**A**: We will introduce the term genuine quantum superposition by associating the remaining matrix elements with both quantum superposition and basis state indistinguishability. Subsequently, we will generalize existing superposition measures for genuine quantum superposition. The measures introduced herein hold promise for quantifying non-classicality in chemical bonding phenomena within the realm of quantum chemistry, as evidenced by recent research where we successfully calculated electron delocalization in aromatic molecules [35].**B**: To set the ground for this discussion, we propose utilizing a pseudo-Hermitian matrix representation of a quantum state to investigate its properties concerning a nonorthogonal basis. This approach entails expressing the state within the biorthogonal extension of the given basis, a well-established mathematical technique in the literature (see, for example, Refs. [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29])**C**: Although independently rediscovered to represent free operations in the resource theory of superposition [13, 14, 15], this method has not been extended to encompass quantum states. Here, we will demonstrate that the diagonal elements of the pseudo-Hermitian representation of quantum states are biorthogonal Kirkwood-Dirac quasi-probabilities [30, 31, 32, 33, 34]

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**A**: The author thanks Stephan De Bièvre and Kailiang Lin for insightful discussions. The author thanks Tao Li for reading the manuscript**B**: The author also thanks the anonymous referees for constructive comments. After completing this work, I became aware of the recent work [60] which discussed the structure of Kirkwood-Dirac classical mixed states.**C**: This work was supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2022JM-012)

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**A**: Then, one can identify the best possible operations for the sender and receiver to perform in order to maximize their transmission rate**B**: This section includes a short introduction into entanglement-assisted communication in Section III-A, which will serve as a basis for the coding scheme in our main result, followed by a description of the setup for fault-tolerant entanglement-assisted communication and our strategy for its analysis in Section III-B. **C**: When a sender and a receiver are connected by many copies of a quantum channel T𝑇Titalic_T and have access to entanglement, they can use this setup to transmit a classical message via entanglement-assisted communication

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**A**: The GW bright sirens from SMBHBs that can be detected by PTA in the nanohertz band can serve as a late-universe cosmological probe with great potential to independently measure the absolute distances of the sources**B**: In this work, we investigate the capabilities of future bright siren observations from SKA-era PTAs on constraining the cosmological parameters in the IDE models**C**: We select some existing SMBHB candidates, and use the Fisher information matrix to forecast their accuracies of luminosity distances based on the simulation of timing residuals of pulsar signals. Then, we use the MCMC method to show how the future GW bright sirens from SKA-era PTAs can determine the cosmological parameters and play a key role in breaking the parameter degeneracies inherent in the CMB data.

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Selection 2

**A**: Recently, Braun et al. [2, 3] developed a unified mathematical framework that exploits the low-rank defect structure to characterize the elastic far-fields**B**: This novel formulation exposes avenues for improved convergence rates in cell problems concerning cell size, as demonstrated theoretically. However, a notable challenge arises in the practical implementation of multipole expansions for simulating crystalline defects, given that the terms associated with multipole moments are defined on an infinite lattice, rendering their direct evaluation unfeasible within finite computational domains.**C**: In this framework, the defect equilibrium is decomposed into a sum of continuum correctors and discrete multipole terms

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Selection 4

**A**: As we discussed in our previous work (de Lima et al., 2020), these systematics roughly translate into uncertainties of up to 5%percent55\%5 % for the NS mass and 7%percent77\%7 % for the NS radius. However, these uncertainties are still smaller than the reliable ones we estimated for the mass and radius of 3XMM J1852+0033. **B**: We also stress that the choice of model to compute the unabsorbed fluxes for the normalization leads to systematic uncertainties in our parameter estimations**C**: As mentioned, these values generally agree within 10%−15%percent10percent1510\%-15\%10 % - 15 % for different models in the whole band (0.3–10 keV)

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Selection 4

**A**: The observed order k 8 of the percolating clique cluster is anomalous for the characteristic connectome density, and we observed how such clique structure appear in the model under the limitation on the connection length during the formation of the model network**B**: Indeed, connections of limited length are typical for the human structural connectome, which is especially characteristic for connections with high edge confidence. The emergence of a percolation clique cluster under a constraint on the allowed connection length is similar to a second-order structural phase transition. **C**: We then proposed a model for emerging high-order clique community structures characteristic of human connectomes

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Selection 3

**A**: This work is funded by the French National Research Agency (ANR) within the project ANR-13-BS05-0007 and the “Investments for the future” programme ENIGMASS LabEx (ANR-11-LABX-0012)**B**: Authors are grateful for the technical and administrative support of the ILL for the installation and operation of the Stereo detector**C**: We further acknowledge the support of the CEA, the CNRS/IN2P3 and the Max Planck Society.

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**A**: (2002); Schnedermann et al**B**: (1993); Broniowski and Florkowski (2001). **C**: One should recall that collective radial expansion (specified by the radial velocity v𝑣vitalic_v) and resonance decays also affect the momentum distribution of hadrons Florkowski et al

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Selection 4

**A**: To put a number on this observation we fitted function of the form:**B**: In Figure 1 we can see that value of A is not only smaller but also that it converges to 00 with growing ϵitalic-ϵ\epsilonitalic_ϵ faster than B and C**C**: similarly to the random matrix ensembles (Fact 7)

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Selection 4

**A**: Gargaté et al**B**: (2019, 2019) used hybrid simulations (with kinetic ions and fluid electrons) to follow the instability on longer time-scales, well into the non-linear regime when saturation occurs. Their results supported a saturation mechanism similar to that described by Riquelme & Spitkovsky (2009), who used full PIC simulations: saturation occurs due to the deceleration of CRs and simultaneous acceleration of the background plasma, which reduces the CR current, an effect also seen in the earlier work of Lucek & Bell (2000).**C**: (2010); Weidl et al

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Selection 2

**A**: Regarding the accidental background, radioactivity is the primary source of the prompt signal below 3.5 MeV, where stringent background control measures are essential, as outlined in Abusleme et al**B**: (2021b)**C**: Conversely, solar neutrino ES events become the leading prompt signal above 3.5 MeV. For the prompt energy range from 3.5 to 5 MeV, the cosmogenic correlated background is significantly higher than that in the region above 5 MeV, as depicted in Fig. 1, while the signal efficiency is considerably lower between 3.5 and 5 MeV due to the multiplicity cut. Additional technical details in this regard will be reported elsewhere in the future.

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Selection 4

**A**: The absorption of the pump pulse energy results in an increase of the electron temperature (see Fig. 2(a) below) and thus an increase in the real part of the permittivity (see Fig. 4(a) below)**B**: This causes the ENZ resonance to slip away from the incoming frequencies so that the local field and the absorptivity decrease (see Fig. 5); consequently, the total absorbed energy, the maximum electron and phonon temperature increases sublinearly (rather than linearly) with the illumination intensity**C**: As shown below, this effect explains the high damage threshold of ITO. The changes of the imaginary part of the ITO permittivity are also large, and similar in nature to those occurring in noble metals (see, e.g., [21, 22]), but are secondary compared to the large ENZ resonance shift.

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Selection 4

**A**: Recently, industry research labs have been shifting towards the hexagonal architecture for their quantum computers**B**: This architecture has the advantage of reducing the number of distinct frequencies, and thus crosstalk**C**: The surface code [14] structure has been modified to a topological code with a heavy hexagonal structure [15] in order to become more suitable for these architectures. The heavy hexagonal code [15] uses a combination of degree-two and degree-three vertices in the topology, and can be considered as a hybrid of a surface code and a Bacon-Shor code [16]. This QECC reduces the distinct number of frequencies required in their realization by introducing more ancilla qubits (termed as flag qubits) for entanglement in the syndrome measurement

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Selection 3

**A**: While illustrated qualitatively in Figure 1g, this oscillatory behavior has been verified for both the NEID and HPF spectrographs, and qualitatively analogous behavior has been found for the etalon system of the ESPRESSO Schmidt et al. (2022) spectrograph. Surprisingly, it implies that the optical length of the etalon is effectively increasing and decreasing in length at different wavelength regions. This poses a clear problem for high-precision RV spectrograph calibration, as such etalon mode drifts are undetectable and thus unaccounted for unless the entire etalon spectrum is continuously compared to a high-precision and broadband absolute frequency reference (i.e., an LFC, but requiring a secondary calibrator defeats the purpose of developing the etalon as a calibrator in the first place)**B**: (2018); de Hond et al. (2017); Bohlouli-Zanjani et al. (2006); Dawel et al. (2024); Riedle et al. (1994), particularly when those modes have large spectral separation. **C**: This drift behavior also raises important considerations for experiments that utilize multiple FP cavity modes for frequency referencing in precision spectroscopy Hill et al. (2021); Wang et al. (2020); Milani et al. (2017); Arias et al

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Selection 1

**A**: Initially applied to precipitation nowcasting based on 2D radar images (Suman et al., 2021; Shi et al., 2017), DL-based models have recently surpassed traditional methods for longer forecast periods (Lam et al., 2022). These methods usually work with highly structured data**B**: Radar precipitation data, for example, can be organized as images and analyzed using convolutional neural networks. For 3D regular spherical grid data, graph neural networks or spherical CNNs are employed (Lam et al., 2022; Esteves et al., 2023)**C**: However, in our study, the data set is distributed sparsely in space, which hinders the use of these traditional architectures. The use of DL for modeling dynamical systems, in general, has also seen recent advancements (Li et al., 2021; Gupta & Brandstetter, 2022; Pfaff et al., 2020) but most approaches in this field typically operate on regularly-spaced data or irregular but fixed mesh.

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**A**: The first is needed to define the solution of the Wick-ordered heat equation for large times, the second is needed for the convergence to the KPZ equation. **B**: We need this in two different settings**C**: The first is for fixed drift as the size of the exceptional set tends to zero, and the second is a uniform bound as the drift increases

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Selection 2

**A**: (c-e) Snapshots of the dislocation network at strain 0.8 extracted from (c) MD, (d) old DDD and (e) new DDD.**B**: Figure 6: Evolution of stress (a) and dislocation density (b) predicted in three simulations performed under identical conditions: MD simulation (green), DDD simulation with the old kinematic rules for 3-node motion (blue) and DDD simulation with the new kinematic rules permitting additional modes of 3-node motion (red)**C**: In all three simulations uniaxial compression along the [001] axis of a BCC single crystal of tantalum was performed under a constant straining rate of 2×1082superscript1082\times 10^{8}2 × 10 start_POSTSUPERSCRIPT 8 end_POSTSUPERSCRIPT s-1

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**A**: Zumbühl, G. A. D. Briggs, M. A. Osborne, D. Sejdinovic and N. Ares, ”Deep reinforcement learning for efficient measurement of quantum devices,” npj Quantum Inf 7, 100 (2021).**B**: V. Nguyen, S. B. Orbell, D. T. Lennon, H**C**: Moon, F. Vigneau, L. C. Camenzind, L. Yu, D. M

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**A**: OTOCs in different systems Swingle et al. (2016); Zhu et al. (2016); Gärttner et al**B**: (2020); Braumüller et al. (2022); Zhao et al. (2022). OTOCs have been found to be useful for measuring entanglement entropy and the**C**: (2017); Li et al. (2017); Lewis-Swan et al. (2019); Nie et al

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Selection 1

**A**: Therefore, the atomic interference signal in Fig. 6 not only includes the fundamental frequency, but also the second harmonic signal. When the output of the fiber-optic gyroscope is compared with that of the AI gyroscopes, the open-loop dynamic range of the AI is estimated to be ∼similar-to\sim∼0.0157 rad/s, which is slightly different from the theoretical value (0.0118 rad/s). This may be due to the difference between the theoretical and measured values of the AI scale factor, such as the measurement error in atomic velocity. In addition, the sensing axes of the two gyroscopes may be not completely consistent, and the measurement may not be synchronized completely. **B**: A rotational test was performed to verify the inertial sensitivity of the AI gyroscope. The entire sensor was placed on a platform, which was floating on four pneumatic vibration isolators (I-2000, Newport, USA) and adjusted to be perpendicular to the direction of local gravitational acceleration using a tilt sensor. A fiber-optic gyroscope was fixed on the same platform to measure the rotation rate simultaneously using the same sensing axis as the AI gyroscope. The AI gyroscope was operated in open-loop mode. Figure 5 shows the signals measured with the AI gyroscope and the fiber-optic gyroscope when an external force was applied to turn the entire platform around the central axis**C**: The two AIs pick up the change in the rotation rate induced by the applied force and output two oscillating signals with frequencies of 1.25 Hz and 1.33 Hz deduced from their Fourier transform spectra, as shown in Fig. 6. The output signal from the fiber-optic gyroscope also responds to the applied force with an oscillation frequency of 1.33 Hz, which agrees well with the AI results. In addition, some umbilications appear in the peaks and troughs of the dual-AI signals that are caused by the measurement ambiguity of the interferometric sensor, as shown in Fig. 5 (green dashed circles)

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**A**: (2020), which showed that a detection with an effective signal-to-noise ratio of 3 would be seen in five years of LIGO and Virgo operation at their design (O4) sensitivities. The results of Boersma et al**B**: This approach was performed in Boersma et al**C**: (2020) are consistent with those of Hübner et al. (2020) in terms of the number of events which were needed.

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Selection 4

**A**: The surface resistance of cold beam pipes is as well an important subject, as the anomalous skin effect can cause a large contribution to the beam driven wall losses [12], and direct cooling is not possible in many cases. In space-flight, many RF devices are exposed to varying temperatures in the range as discussed here. For these applications, it is sufficient to only know the resistive part R𝑅Ritalic_R of the surface impedance Z𝑍Zitalic_Z. **B**: Other topics to apply the geometric model are for example copper components in superconducting cavities – like power couplers**C**: It is of great importance to know exactly the thermal losses at these surfaces, which can’t be cooled efficiently in an easy way[18], and which are drifting to intermediate temperature levels depending on the operating conditions

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**A**: We found that the skewness of the distribution of genotypes coded in each chromosome is essential to determining the probability of evolving new traits. Because skewness peaked with a finite number of chromosomes (Fig**B**: 2B).**C**: 2F), there is an optimal number of chromosomes for evolving novel traits (Fig

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Selection 2

**A**: Similar to SBM, ScBM also can not model overlapping networks. The Directed Mixed Membership Stochastic Blockmodels (DiMMSB) (Qing & Wang, 2021) was proposed to address this limitation by allowing nodes to belong to multiple communities. DiMMSB can be seen as a direct extension of MMSB from un-directed un-weighted networks to bipartite un-weighted networks. To estimate memberships under DiMMSB, Qing & Wang (2021) designed a spectral algorithm with a theoretical guarantee of estimation consistency.**B**: Spectral algorithms with theoretical guarantees on consistent estimation have been designed to estimate groups of nodes under ScBM and DCScBM, see algorithms proposed in Rohe et al. (2016); Zhou & A.Amini (2019); Wang et al. (2020)**C**: For community detection of bipartite un-weighted networks, Rohe et al. (2016) proposed Stochastic co-Blockmodel (ScBM) and Degree-Corrected Stochastic co-Blockmodel (DCScBM). ScBM and DCScBM can be seen as direct extensions of SBM and DCSBM from un-directed un-weighted networks to bipartite un-weighted networks, respectively

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**A**: We have used these observations in [2] to understand the orbit structure of such systems**B**: To obtain analogous results for general two-sided automata, we first perform some shifts and reduce to a counting problem for more general coincidence sets rather than periodic points (that are coincidence sets for iterates of a map and the identity map), to which the methods from [2] can also be applied. **C**: The results can be directly translated to the setting of one-sided cellular automata; to the best of our knowledge, in this generality the results are new

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Selection 4

**A**: Within the infinite lattice [17, 18], configurations with more sites in the trap would be particularly interesting, through which one can seed diverse initial fluctuations, and investigate the correlations between the particle emission and the leads**B**: There have been various theoretical works exploring several aspects of the highly nonequilibrium phenomena [11, 12, 13, 14, 15, 16, 17, 18], from the dynamics of the stimulating process of the observed pair emission [14, 15, 16] and a unique single-particle emission [17], to the characterizations of rapid density oscillations, typical threshold behavior [18] and high-harmonic generations [12]**C**: Accordingly, if one wanted to explore the competitions among different modes in the collective emission, extended models should be employed. From the theoretical point of view, one can configure synthetic traps, condensates and couplings based upon demands, to study the properties of the resulting particle jets.

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Selection 3

**A**: Data are available from the authors upon reasonable request and with the permission of [third party]. **B**: Restrictions apply to the availability of these data, which were used under license for this study**C**: The data that support the findings of this study are available from [third party]

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Selection 2

**A**: Acknowledgment: We thank C. H. Keitel, K. Z. Hatsagortsyan, P. Zhang, and I. P**B**: Ivanov for helpful discussions. We are grateful to Q. Zhao for his help during the revision of our manuscript. This work is supported by the National Natural Science Foundation of China (Grants No. 11874295, No. 12022506, No. U2267204, No**C**: 11905169, No. 12275209, No. 12147176, No. 12135001, No. 11825502, No. 11921006, and No. U2241281), the Foundation of Science and Technology on Plasma Physics Laboratory (No. JCKYS2021212008), and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSY014).

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Selection 2

**A**: It implements the hypothetical Wilsonian perspective that the coarse-grained perturbative description should determine the complete non-perturbative description at any scale. Therefore, assuming that S~~𝑆\tilde{S}over~ start_ARG italic_S end_ARG and the inter-system couplings can be derived from S𝑆Sitalic_S, we can state that the coarse-grained descriptions of the two subsystems are related,222In Banerjee:2017ozx , a derivation of the semi-holographic procedure was proposed by noting that the perturbative series has renormalons which forbid Borel resummation, and this can be cured by considering non-perturbative contributions**B**: The mutual effective metric coupling thus leads to a full energy-momentum tensor (6) which can be obtained ultra-locally from the subsystem energy-momentum tensors alone, and does not require any further microscopic input. This ensures that a coarse-grained hydrodynamic description of the full energy-momentum tensor in terms of those of the subsystems**C**: A physical observable, such as the full energy-momentum tensor, which receives contributions from both sectors, should be a function of the perturbative coupling with a finite radius of convergence, provided that the intersystem couplings are appropriate functions of the perturbative couplings. This was illustrated in a toy bi-holographic set-up. and the full hydrodynamic description can be constructed in terms of the subsystem hydrodynamic variables. A detailed description will follow soon.

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Selection 4

**A**: When the shock front reaches the tropopause, then the escaping neutral H-atom flux is no longer limited by diffusion but is directly coupled to the winds and circulation within the troposphere of the planetary body, and greatly enhanced**B**: Then, the depth that this shock front eats into the planet body depends on the incoming photon flux level**C**: This transition may be paralleled with a phase transition from an entropy-limited regime to an energy-limited regime.

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Selection 1

**A**: The physical effects discussed below also occur in other lattices with NNN hopping, including the 1D chain and 3D simple cubic lattice**B**: The square U⁢V𝑈𝑉UVitalic_U italic_V model serves as a convenient proxy for all hyper-cubic U⁢V𝑈𝑉UVitalic_U italic_V models**C**: The non-interacting (one particle) dispersion of Eq. (4) is

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Selection 3

**A**: Following similar projection methods as described in §3.3, we take our velocity magnitude v𝑣vitalic_v, and randomly sample two angular components for latitudinal and longitudinal velocity components999We assume a Maxwellian distribution for PBH velocities as a computational shortcut, but use mean speeds following the Eddington inversion results from Lacroix et al**B**: However, we do not expect this simplifying assumption to be a dominant source of uncertainty in our analysis.. The longitudinal component is sampled uniformly between [0, 2⁢π2𝜋2\pi2 italic_π], while the latitudinal component is sampled uniformly on the unit sphere (i.e., uniform in cos⁡(latitude)latitude\cos({\rm latitude})roman_cos ( roman_latitude ) between [−11-1- 1, 1111]).**C**: (2018) (which assumes velocities deviate from the truncated Maxwellian of the SHM)

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Selection 1

**A**: Red: analysis of PSR J0030+0451 from Riley et al. (2019). Green: latest analysis of HESS J1731-347 from Doroshenko et al. (2022). Orange error bars: analysis of 3XMM J185246.6+003317 from de Lima et al. (2022).**B**: Blue: analysis of PSR J0740+6620 from NICER and XMM-Newton data from Miller et al. (2021). Magenta: analysis of 4U 1702-429 from Nättilä et al. (2017)**C**: Figure 1: Mass-radius relation of QSs from Bombaci et al. (2021) (solid red), Ferrer et al. (2015) (solid blue) and Traversi et al. (2022) (solid black) with observational constraints at 68% of confidence level (dotted) and at 90% (dashed)

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Selection 1

**A**: Therefore, there is no additional data to the boundary observables and the boundary data is trivial**B**: the factor of 1/2⁢m12𝑚1/2m1 / 2 italic_m in (43)) are not sufficient to capture the interactions in the bulk and reconstruct the EFT. **C**: In other words, the prefactors of the delta functions (e.g

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Selection 3

**A**: In computing language, the Margolus-Levitin’s theorem on the maximum rate at which a quantum system can evolve through distinct states, translates into a theoretical upper limit on the number of operations that can be performed in a unit time. Lloyd applied Margolus–Levitin’s results to derive an upper bound for the computation speed of any system and argued that the maximum rate is actually attained by black holes compution **B**: The saturation of the Lloyd’s bound by black holes has been then rigorously demonstrated using quantum complexity and its relation to fidelity qc1 ; qc2 . If black holes can contain hairs, e.g**C**: quantum fields in equilibrium with the black hole, neither infalling nor escaping to infinity, such configurations would conceptually represent the fastest achievable quantum computers. In the presence of modifications of quantum mechanics (e.g. induced by quantum gravitational effects), the corresponding bounds would be even lower due to the increased quantum speed limit.

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Selection 4

**A**: The action of the algebraic torus ℂ*superscriptℂ\mathbb{C}^{*}blackboard_C start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT is quotient out by the equivalence relation**B**: As one can note the CY condition is automatically implemented by the fact that the vectors are coplanar**C**: and a possible solution is Q=(1,−1,1,−1)𝑄1111Q=(1,-1,1,-1)italic_Q = ( 1 , - 1 , 1 , - 1 )

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Selection 1

**A**: The non-linear memory signal from eccentric binary orbits was calculated at 3-PN order in [33] and the 3-PN calculation for eccentric orbits including the tail contributions is done in [35]. **B**: The non-linear memory signal, for binaries in a quasi-circular orbit, already occurs at the 0-PN order [18, 29]**C**: In [30, 32] the non-linear memory for the quasi-circular orbit was computed at the 3-PN (Post-Newtonian) order

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Selection 4

**A**: The variation of this action gives equation of motion and a boundary term which depends on the normal derivative of the boundary metric. To solve the variational principle one usually adds Gibbons Hawking term and various counter terms such that in the end total variation of the action is only proportional to the boundary component and not its derivative**B**: We expect the variational problem that gives rise to chiral symmetry algebra in NU gauge to hold for these gauges as well. We leave a comparison of these boundary terms with that of standard Gibbon-Hawking term and other counterterms for future work. The derivation of finding boundary terms for locally AdS4 follows identically to Gupta:2021cwo and therefore we use only the final answer here. The boundary action that we add to Einstein-Hilbert action is,**C**: This is the usual procedure when one works in FG gauge. As we are working in NU gauge, we use the boundary terms that we found in Gupta:2021cwo for the case of asymptotically locally flat spacetimes in NU gauge.666Normally the boundary action for AdSd+1 gravity in Fefferman-Graham gauge Balasubramanian:1999re ; Brown:1992br or the gauge used to describe ‘boosted black brane’ Bhattacharyya:2007vjd is invariant under d𝑑ditalic_d-dimensional boundary preserving diffeomorphisms unlike the boundary terms used here in context of NU gauge

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Selection 4

**A**: The immediate model-building challenge is that we are asking for effects derived from thermal equilibrium to result in a far-out-of-equilibrium configuration. Further, this asymmetry in abundances must remain as the symmetry-breaking scalar later rolls back to the origin and the sectors become exactly degenerate at low temperatures.**B**: The idea is to use the high-temperature ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT-breaking phase to set up an initial asymmetry in the energy densities of the SM and mirror sectors**C**: Here we present a minimal module to effect the asymmetric reheating of a degenerate mirror sector via inverse symmetry breaking

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Selection 4

**A**: The polynomial decay of the fractional charge correlation also characterises the delocalisation, and the polynomial lower and upper bounds were established in [25, 26]. In the localised phase, the Debye screening (cf**B**: [11, 52] for the lattice sine-Gordon model and [8] for the DG model) induces exponential decay of the truncated charge correlation**C**: The same type of result was studied for the dimer model in [45, 19].

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Selection 1

**A**: The observation of bi-stability and the single superconducting qubit coupling to the Kittel mode are interesting developments in this field [23, 24]**B**: Li et al**C**: illustrated how to create tripartite entanglement in a system of microwave cavity photons entangled to the magnon and phonon modes of a YIG sphere in a magnomechanical cavity [25]. This study was followed by an investigation of magnon-magnon entanglement between two YIG spheres in cavity magnomechanics [26].

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Selection 3

**A**: The transport current I𝐼Iitalic_I has been applied in this direction, after cutting the sample into rectangular shape; this resulted in approximate orientation of the I𝐼Iitalic_I (to within 10-20 deg) with one of the main in-plane axes. **B**: For magnetization and transport measurements the crystals were cleaved, with cleavage plane always perpendicular to the c𝑐citalic_c-axis**C**: The in-plane shape was slightly elongated in the direction of one of the in-plane main crystallographic axes, as confirmed by X-ray examination

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Selection 1

**A**: To date, our knowledge about this matter is restricted, and it is recommended from a practical standpoint that the terms of drift and diffusion should be maintained when applying the equation**B**: Although this approximation is widely practised and has shown some level of precision, more rigorous mathematical examination and extensive numerical testing are crucial to confirm and improve this approximation. Furthermore, it might be beneficial to investigate under what conditions an infinite-order jet can be effectively represented by a finite-order jet, considering that the kinetic equation is an outcoming of an infinite-order jet. **C**: Utilizing the infinite-order kinetic equation in real-world scenarios presents a formidable challenge

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Selection 4

**A**: The routine use of DKI in the clinic has nonetheless lagged due the inability to robustly estimate the kurtosis metric (Veraart et al., 2011a; Tabesh et al., 2010; Kuder et al., 2011; Henriques et al., 2021). A known requirement for estimating kurtosis in DKI is to restrict the maximum b-value to 2000 s/mm2 ssuperscriptmm2\text{ s}/\text{mm}^{2}s / mm start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-3000 s/mm2 ssuperscriptmm2\text{ s}/\text{mm}^{2}s / mm start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT for brain studies (Jensen et al., 2005; Jensen and Helpern, 2010; Poot et al., 2010), with the optimal maximum b-value found to be dependent on tissue type (Poot et al., 2010)**B**: This suggests that the traditional kurtosis model is less accurate at representing the diffusion signal at large b-values. Moreover, multiple b-shell, multiple direction high quality DW-MRI data can take many minutes to acquire, which poses challenges for clinical imaging protocols involving a multitude of MRI contrasts already taking tens of minutes to execute**C**: Reduction of DKI data acquisition times through parallel imaging, optimisation of b-shells and directions have been investigated (Zong et al., 2021; Heidemann et al., 2010; Zelinski et al., 2008), and DW-MRI data necessary for DKI analysis has been shown to supersede the data required for DTI (Veraart et al., 2011b). Therefore, an optimised DKI protocol can potentially replace clinical DTI data acquisitions without adversely affecting the estimation of DTI metrics.

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Selection 1