Numerical Evidence Research Articles

Monitored fermions with conserved U(1) charge

We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and timescales. We focus on a multiflavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) nonlinear sigma model (NLσM) coupled to fluctuating hydrodynamics. Contrary to the case of noninteracting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NLσM and also discuss higher-dimensional generalizations. Published by the American Physical Society 2024

Non-Myopic Beam Scheduling for Multiple Smart-Target Tracking in Phased Array Radar Networks

This paper addresses beam scheduling for tracking multiple smart targets in phased array radar networks, aiming to mitigate the performance degradation in previous myopic scheduling methods and enhance the tracking performance, which is measured by a discounted cost objective related to the tracking error covariance (TEC) of the targets. The scheduling problem is formulated as a restless multi-armed bandit problem, where each bandit process is associated with a target and its TEC states evolve with different transition rules for different actions, i.e., either the target is tracked or not. However, non-linear measurement functions necessitate the inclusion of dynamic state information for updating future multi-step TEC states. To compute the marginal productivity (MP) index, the unscented sampling method is employed to predict dynamic and TEC states. Consequently, an unscented sampling-based MP (US-MP) index policy is proposed for selecting targets to track at each time step, which can be applicable to large networks with a realistic number of targets. Numerical evidence presents that the bandit model with the scalar Kalman filter satisfies sufficient conditions for indexability based upon partial conservation laws and extensive simulations validate the effectiveness of the proposed US-MP policy in practical scenarios with TEC states.

The existence of real nine-dimensional manifolds which include classical one-parameter families of triply periodic minimal surfaces

Triply periodic minimal surfaces have been studied in many fields of natural science, and in particular, many one-parameter families of triply periodic minimal surfaces of genus three have been considered. In 1990s, the moduli theory of triply periodic minimal surfaces established by C. Arezzo and G. P. Pirola [1], [14], and they studied a relationship between the nullity of a minimal surface and the differential of its real period map from the viewpoint of complex geometry. The present paper develops their theory in terms of a real differential geometric aspect, and, by applying the classical transversal property to the real period map, we obtain the numerical evidence for the existence of real nine-dimensional manifolds of triply periodic minimal surfaces which include such one-parameter families. For each case that the transversal property fails, we give values of parameters from which new one-parameter families of triply periodic minimal surfaces issue.

A GENERAL LIMIT THEORY FOR NONLINEAR FUNCTIONALS OF NONSTATIONARY TIME SERIES

New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root, or fractional processes. The limit theory is unusually general in that it covers both parametric and nonparametric regressions. Self-normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals interesting strong bimodality in the finite sample distributions of conventional self-normalized statistics similar to the bimodality that can arise in t-ratio statistics based on heavy tailed data. Bimodal behavior in these statistics is due to the presence of long memory innovations and is shown to persist for very large sample sizes even though the limit theory is Gaussian when the long memory innovations are stationary. Bimodality is shown to occur even in the limit theory when the long memory innovations are nonstationary. To address these complications, new self-normalized versions of the test statistics are introduced that deliver improved approximations that can be used for inference.

An approximate solution of multi-term fractional telegraph equation with quadratic B-spline basis functions

This paper introduces the Galerkin Method for the approximate solution ofMulti-term Fractional Telegraph Equations (MFTE). The Galerkin Method (GM)is one of the most popular techniques for the solution of Partial Differential Equations (PDEs), and it uses the idea of mapping a solution onto a set of basis functions and then seeking the residual error through minimization. In GM, the weight and basis functions are the same, and as such, the basis functions are selected appropriately to satisfy the given conditions imposed. In this paper, the quadratic B-spline functions are adopted as shape and test functions for resolving the approximate solution of MFTE. Here, the Caputo fractional derivative takes care of the fractional part, and the Gauss-Mamadu-Njoseh quadrature scheme handles numerical integration. Numerical illustrations are examined for single-term and two-term MFTE, respectively, with numerical evidence measured usingL2 and L∞ error norms. Consequently, the resulting numerical evidence, as presented in Tables and Figures, shows the accuracy and reliability of the method. Also, the study examined and presented relevant theorems of convergence and error analyses of method. MAPLE 18 was used for all computational frameworks in this research.

On the inviscid instability of the 2-D Taylor–Green vortex

We consider Euler flows on two-dimensional (2-D) periodic domain and are interested in the stability, both linear and nonlinear, of a simple equilibrium given by the 2-D Taylor–Green vortex. As the first main result, numerical evidence is provided for the fact that such flows possess unstable eigenvalues embedded in the band of the essential spectrum of the linearized operator. However, the unstable eigenfunction is discontinuous at the hyperbolic stagnation points of the base flow and its regularity is consistent with the prediction of Lin (Intl Math. Res. Not., vol. 2004, issue 41, 2004, pp. 2147–2178). This eigenfunction gives rise to an exponential transient growth with the rate given by the real part of the eigenvalue followed by passage to a nonlinear instability. As the second main result, we illustrate a fundamentally different, non-modal, growth mechanism involving a continuous family of uncorrelated functions, instead of an eigenfunction of the linearized operator. Constructed by solving a suitable partial differential equation (PDE) optimization problem, the resulting flows saturate the known estimates on the growth of the semigroup related to the essential spectrum of the linearized Euler operator as the numerical resolution is refined. These findings are contrasted with the results of earlier studies of a similar problem conducted in a slightly viscous setting where only the modal growth of instabilities was observed. This highlights the special stability properties of equilibria in inviscid flows.

Magnetic reconnection in magnetohydrodynamics

We provide examples of periodic solutions (in both 2 and 3 dimension) of the magnetohydrodynamics equations such that the topology of the magnetic lines changes during the evolution. This phenomenon, known as magnetic reconnection, is relevant for physicists, in particular in the study of highly conducting plasmas. Although numerical and experimental evidences exist, analytical examples of magnetic reconnection were not known.

Numerical and Experimental Evidence of Extreme Events in a Sprott‐Like Model

Numerical and Experimental Evidence of Extreme Events in a Sprott‐Like Model

The influence of timescales and data injection schemes for reservoir computing using spin-VCSELs

Reservoir computing with photonic systems promises fast and energy efficient computations. Vertical emitting semiconductor lasers with two spin-polarized charge-carrier populations (spin-VCSEL), are good candidates for high-speed reservoir computing. With our work, we highlight the role of the internal dynamic coupling on the prediction performance. We present numerical evidence for the critical impact of different data injection schemes and internal timescales. A central finding is that the internal dynamics of all dynamical degrees of freedom can only be utilized if an appropriate perturbation via the input is chosen as data injection scheme. If the data is encoded via an optical phase difference, the internal spin-polarized carrier dynamics is not addressed but instead a faster data injection rate is possible. We find strong correlations of the prediction performance with the system response time and the underlying delay-induced bifurcation structure, which allows to transfer the results to other physical reservoir computing systems.

Abstract 4137296: Single-cell Atlas of Human Epicardial Adipose Tissue Reveals Aging IL4R + Naive B cell Contributing To Atrial Fibrillation

Background: Numerous recent evidence suggested a role of epicardial adipose tissue (EAT), the visceral fat depot of the heart, in the development of Atrial Fibrillation (AF). However, the cellular and molecular mechanisms underlying the association remain elusive. Methods: We performed single-nucleus RNA sequencing on eleven EAT samples collected from 2 groups of subjects: patients with nonvalvular AF undergoing coronary bypass surgery for severe CAD (n=7), and a control group of patients without concomitant AF (n=4). Comparative analyses were performed between the groups, including cellular compositional analysis, cell type–resolved transcriptomic changes, and functional analysis. Results: Unsupervised clustering of 92734 nuclei identified 11 clusters, encompassing all known cell types in the adipose tissue. Pseudobulk differential expression analysis between the AF and control groups revealed pronounced differences in a select subset of genes located on the X and Y chromosomes, including XIST and TSIX. Subsequent pathway analysis identified that the most significantly impacted pathways were those associated with immune cell functions. Meanwhile, differences in cellular composition and transcriptomic profiles, particularly concerning B cells, were observed between normal and AF conditions, highlighting distinct immune cell dynamics. Comparison of pathways across different B cell states revealed the enrichment of distinct pathways within each state, including those involved in cellular senescence, antigen processing and presentation, and programmed cell death signatures. Notably, aging IL4R + naive B cell and inflammatory ITGB1 + memory B cell were identified as important regulators potentially involved in functional changes of EAT and AF pathogenesis. Conclusions: We built a complete single-nucleus transcriptomic atlas of human EAT in normal and AF conditions. Our study lays the foundation for developing novel therapeutic strategies for treating AF by targeting and modifying B cell functions within EAT.

Discrete Time Crystals in Unbounded Potentials.

Discrete time crystalline phases have attracted significant theoretical and experimental attention in the last few years. Such systems require a seemingly impossible combination of nonadiabatic driving and a finite-entropy long-time state, which, surprisingly, is possible in nonergodic systems. Previous works have often relied on disorder for the required nonergodicity; here, we describe the construction of a discrete time crystal (DTC) phase in nondisordered, nonintegrable Ising-type systems. After discussing the conditions for interacting and periodically driven systems to display such phases in general, we propose a concrete model and then provide approximate analytical arguments and direct numerical evidence that it satisfies the conditions and displays a DTC phase robust to local periodic perturbations.

The Role of Predictive Analytics in Disease Prevention : A Technical Overview

This article explores the transformative potential of predictive analytics in healthcare, focusing on its applications in disease prevention and public health management. It examines the power of data integration from diverse sources, the use of predictive modeling for risk stratification, and the broader implications for public health surveillance and chronic disease management. The article also discusses the significant growth of AI in the healthcare market and highlights successful implementations of predictive analytics across various medical domains. Additionally, it addresses the key challenges in implementing these technologies, including data privacy concerns, integration issues, model accuracy, and ethical considerations. Through numerous case studies and statistical evidence, the article demonstrates how predictive analytics is revolutionizing healthcare by enabling more accurate, personalized, and proactive approaches to disease prevention and management.

Building 1D lattice models with $G$-graded fusion category

We construct a family of one-dimensional (1D) quantum lattice models based on GG-graded unitary fusion category \mathcal{C}_G𝒞G. This family realize an interpolation between the anyon-chain models and edge models of 2D symmetry-protected topological states, and can be thought of as edge models of 2D symmetry-enriched topological states. The models display a set of unconventional global symmetries that are characterized by the input category \mathcal{C}_G𝒞G. While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the models to the extent that the low-energy physics has a large likelihood to be gapless.

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

Floquet theory and stability analysis for Hamiltonian PDEs

Abstract We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs, including the generalized KdV and BBM equations (third order), the nonlinear Schrödinger and Boussinesq equations (fourth order), and the Kawahara equation (fifth order). Our analysis reveals that the characteristic polynomial of the monodromy matrix inherits symmetry from the underlying PDE, enabling us to determine the essential spectrum along the imaginary axis and bifurcations of the spectrum away from the axis, employing the Floquet discriminant. We present numerical evidence to support our analytical findings.

Defining Stable Phases of Open Quantum Systems

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors of the non-Hermitian operators that generate the dynamics, i.e., quantum channels (Markov chains). However, since these operators are non-Hermitian, their spectra are an unreliable guide to dynamical relaxation timescales or to stability against perturbations. We propose an alternative dynamical criterion for a steady state to be in a stable phase, which we name uniformity: Informally, our criterion amounts to requiring that, under sufficiently small local perturbations of the dynamics, the unperturbed and perturbed steady states are related to one another by a finite-time dissipative evolution. We show that this criterion implies many of the properties one would want from any reasonable definition of a phase. We prove that uniformity is satisfied in a canonical classical cellular automaton, and we provide numerical evidence that the gap determines the relaxation rate between nearby steady states in the same phase, a situation we conjecture holds generically whenever uniformity is satisfied. We further conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability. Published by the American Physical Society 2024

Between Living and Non-living: Materiality of the Placentain Ming China.

This study explores materiality and material cultures of human placenta in Ming China (1368-1644), for it perfectly displays Chinese ambiguous attitudes towards the human body parts between living and non-living. For a long time, the Chinese had widely applied human body parts in medical treatments and ritual healings. Numerous evidences in relation to their collection, production, efficacy and application are widely recorded in medical works, in particular those found in materia medica. In the sixteenth century, the Bencao gangmu (Systemic Materia Medica, 1596) illustrates thirty-five "human body drugs." Of those, the placenta was believed effective for curing illnesses, nourishing the body and prolonging life. The questions to be answered include: how is the placenta perceived in medical and religious discourses? What is its "materiality" and "efficacy" when it becomes a drug? What ethical issues and moral concerns are involved with eating the placenta? Last but not least, how was the placenta ritually buried after childbirth in premodern China? In so doing, this essay aims to provide a better understanding of the placenta situated in both material and cosmological worlds. It helps us rethink the multiple relations of human body part to part, part to whole, and body to body.

Complete asymmetric polarization conversion at zero-eigenvalue exceptional points of non-Hermitian metasurfaces

Abstract Non-Hermitian systems can be tuned to exhibit exceptional points, where both eigenvalues and eigenstates coalesce concurrently. The inherent adaptability of photonic non-Hermitian systems in configuring gain and loss has allowed us to observe a plethora of counterintuitive phenomena, largely as a consequence of the eigenspace reduction at these exceptional points. In this work, we propose a non-Hermitian metasurface that, through the incorporation of gain, enables complete asymmetric polarization conversion at an exceptional point with a zero eigenvalue. Specifically, we provide numerical evidence for this concept by designing a non-Hermitian metasurface that facilitates polarization conversion from right to left circular polarization, while preventing conversion in the reverse direction and co-polarized transmission. Furthermore, our investigation reveals that this specific form of complete asymmetric polarization conversion results in maximum circular dichroism in transmission, thereby eliminating the need for external chirality or three-dimensional helical structures. This non-Hermitian technique offers an intriguing approach to designing polarization-sensitive optical devices and systems, further expanding their functionalities and capabilities.

AdS4 holography and the Hilbert scheme

We elucidate a holographic relationship between the enumerative geometry of the Hilbert scheme of N points in the plane ℂ2, with N large, and the entropy of certain magnetically charged black holes with AdS4 asymptotics. Specifically, we demonstrate how the entropy functional arises from the asymptotics of ’t Hooft and Wilson line operators in a 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 gauge theory. The gauge-Bethe correspondence allows us to interpret this calculation in terms of the enumerative geometry of the Hilbert scheme and thereby conjecture that the entropy is saturated by expectation values of certain natural operators in the quantum K-theory ring acting on the localised K-theory of the Hilbert scheme. We give numerical evidence that the large N limit is saturated by contributions from a certain vacuum/fixed point on the Hilbert scheme, associated to a particular triangular-shaped Young diagram, by evolving solutions to the Bethe equations numerically at finite (but large) N towards the classical limit. We thus conjecture a concrete geometric holographic dual of the so-called gravitational/Cardy block.

Dirac spectral density in Nf=2+1 QCD at T=230 MeV

We compute the renormalized Dirac spectral density in Nf=2+1 QCD at physical quark masses, temperature T=230 MeV, and system size Ls=3.4 fm. To that end, we perform a pointwise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of the Dirac operator describing dynamical quarks. We also provide numerical evidence that a component of this peak, which becomes dominant in the thermodynamic limit, is due to a nontrivial accumulation of near-zero modes. Features of this structure are consistent with those previously attributed to the recently proposed IR phase of thermal QCD. Our results (i) provide the only complete first-principles evidence that these IR features exist and are physical, (ii) improve the upper bound for IR phase transition temperature TIR so that the new window is 200<TIR<230 MeV, and (iii) are consistent with the nonrestoration of anomalous UA(1) symmetry (chiral limit) below T=230 MeV. Published by the American Physical Society 2024