Miracle-dz/UniFAR-FTUs huggingface dataset:
On correlation function of high moments of large Wigner random matrices

Abstract. We consider the Wigner ensemble of Hermitian n-dimensional random matrices with elements and study the asymptotic behavior of the expression in the limit such that and are the values of the order . Assuming that the random variables have a symmetric probability distribution such that all of its moments are of the sub-gaussian form, we prove that the limit of exists and does not depend on the particular values of , . The proof is based on a combination of the arguments by Ya. Sinai and A. Soshnikov with the detailed study of a moment analog of the Green's function representation of the Inverse Participation Ratio (IPR) considered for Gaussian Unitary Invariant Ensemble of random matrices (GUE).
Equivariant cohomology Chern numbers determine equivariant unitary bordism for torus groups

This paper shows that the integral equivariant cohomology Chern numbers completely determine the equivariant geometric unitary bordism classes of closed unitary $G$-manifolds, which gives an affirmative answer to the conjecture posed by Guillemin--Ginzburg--Karshon in [20, Remark H.5, $\S3$, Appendix H], where $G$ is a torus. As a further application, we also obtain a satisfactory solution of [20, Question (A), $\S1.1$, Appendix H] on unitary Hamiltonian $G$-manifolds. Our key ingredients in the proof are the universal toric genus defined by Buchstaber--Panov--Ray and the Kronecker pairing of bordism and cobordism. Our approach heavily exploits Quillen's geometric interpretation of homotopic unitary cobordism theory. Moreover, this method can also be applied to the study of $({\Bbb Z}_2)^k$-equivariant unoriented bordism and can still derive the classical result of tom Dieck.
Variational Calculation of Laplace transforms via Entropy on Wiener Space and some Applications

Let (W,H,μ) be the classical Wiener space where H is the Cameron-Martin space which consists of the primitives of the elements of L2([0, 1], dt)⊗ IR, we denote by La(μ,H) the equivalence classes w.r. t. dt× dμ whose Lebesgue densities s → u̇(s,w) are almost surely adapted to the canonical Brownian filtration. If f is a Wiener functional s.t. 1 E[e−f ] edμ is of finite relative entropy w.r. t. μ, we prove that J⋆ = inf (
Lower bounds to the spectral gap of Davies generators

We construct lower bounds to the spectral gap of a family of Lindblad generators known as Davies maps. These maps describe the thermalization of quantum systems weakly coupled to a heat bath. The steady state of these systems is given by the Gibbs distribution with respect to the system Hamiltonian. The bounds can be evaluated explicitly, when the eigenbasis and the spectrum of the Hamiltonian is known. A crucial assumption is that the spectrum of the Hamiltonian is non-degenerate. Furthermore, we provide a counterexample to the conjecture, that the convergence rate is always determined by the gap of the associated Pauli master equation. We conclude that the full dynamics of the Lindblad generator has to be considered. Finally, we present several physical example systems for which the bound to the spectral gap is evaluated.
Generalized Lyubeznik numbers

Abstract Given a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers but captures finer information. These generalized Lyubeznik numbers are defined in terms of D-modules and are proved well defined using a generalization of the classical version of Kashiwara’s equivalence for smooth varieties; we also give a definition for finitely generated K-algebras. These new invariants are indicators of F-singularities in characteristic p > 0 and have close connections with characteristic cycle multiplicities in characteristic zero. We characterize the generalized Lyubeznik numbers associated to monomial ideals and compute examples of those associated to determinantal ideals.
A Novel Robust Grey Model for Forecasting Chinese Electricity Demand

The grey model, which is abbreviated as GM (1, 1), has been widely applied in the fields of decision and prediction, particularly in the prediction of time series with few observations, referred to as the poor information and small sample in the literature related to grey model. Previous studies focus on improving the accuracy of prediction but pay less attention to the robustness of the grey model to outliers, which often occur in practice due to an incorrect record by chance or an accidental failure in equipment. To fill that void, we develop a robust grey model, whose structural parameters are obtained from the least trim squares, to forecast Chinese electricity demand. Also, we use the last value in the first-order accumulative generating time series as the initial value, according to the new information priority criterion. We name the novel grey model, proposed in this paper, the novel robust grey model integrating the new information priority criterion, which could be abbreviated as NIPC-GM (1, 1). In addition, we introduce a novel approach, that is, the bootstrapping test, to investigate the robustness against outliers for the novel robust grey model and the classical grey model, respectively. Using the data on Chinese electricity demand from 2011 to 2021, we find that not only does the novel robust grey model integrating the new information priority criterion have a better robustness to outliers than the classical grey model, but it also has a higher accuracy of prediction than the classical grey model. Finally, we apply the novel robust grey model integrating the new information priority criterion to forecasting the future values in Chinese electricity demand during the period 2022 to 2025. We see that Chinese electricity demand would continue to rise in the next four years.
Predictions for the Cosmogenic Neutrino Flux in Light of New Data from the Pierre Auger Observatory

The Pierre Auger Observatory (PAO) has measured the spectrum and composition of the ultrahigh energy cosmic rays with unprecedented precision. We use these measurements to constrain their spectrum and composition as injected from their sources and, in turn, use these results to estimate the spectrum of cosmogenic neutrinos generated in their propagation through intergalactic space. We find that the PAO spectrum and elongation rate measurements can be well fitted if the injected cosmic rays consist entirely of nuclei with masses in the intermediate (carbon, nitrogen, or oxygen) to heavy (iron, silicon) range. A mixture of protons and heavier species is also acceptable but (on the basis of existing hadronic interaction models) injection of pure light nuclei (protons, helium) results in unacceptable fits to the new elongation rate data. The expected spectrum of cosmogenic neutrinos can vary considerably, depending on the precise spectrum and chemical composition injected from the cosmic ray sources. In the models where heavy nuclei dominate the cosmic ray spectrum and few dissociated protons exceed GZK energies, the cosmogenic neutrino flux can be suppressed by up to 2 orders of magnitude relative to the all-proton prediction, making its detection beyond the reach of current and planned neutrino telescopes.more » Other models consistent with the data, however, are proton-dominated with only a small (1%-10%) admixture of heavy nuclei and predict an associated cosmogenic flux within the reach of upcoming experiments. Thus a detection or nondetection of cosmogenic neutrinos can assist in discriminating between these possibilities. « less
FREQUENCY-DEPENDENT DAMPING IN PROPAGATING SLOW MAGNETO-ACOUSTIC WAVES

Propagating slow magneto-acoustic waves are often observed in polar plumes and active region fan loops. The observed periodicities of these waves range from a few minutes to a few tens of minutes and their amplitudes were found to decay rapidly as they travel along the supporting structure. Previously, thermal conduction, compressive viscosity, radiation, density stratification, and area divergence were identified to be some of the causes for change in the slow wave amplitude. Our recent studies indicate that the observed damping in these waves is frequency-dependent. We used imaging data from the Solar Dynamics Observatory/Atmospheric Imaging Assembly to study this dependence in detail and for the first time via observations we attempted to deduce a quantitative relation between the damping length and frequency of these oscillations. We developed a new analysis method to obtain this relation. The observed frequency dependence does not seem to agree with the current linear wave theory and it was found that the waves observed in the polar regions show a different dependence from those observed in the on-disk loop structures despite the similarity in their properties.
Microlensing pulsars: Microlensing pulsars

We investigate the possibilities that pulsars act as the lens in gravitational microlensing events towards the galactic bulge or a spiral arm. Our estimation is based on expectant survey and observations of FAST (Five hundred meter Aperture Spherical Telescope) and SKA (Square Kilometer Array), and two different models of pulsar distribution are used. We find that the lensing rate is > 1 event/decade, being high enough to search the real events. Therefore, the microlensing observations focusing on pulsars identified by FAST or SKA in the future are meaningful. As an independent determination of pulsar mass, a future detection of microlensing pulsars should be significant in the history of studying pulsars, especially in constraining the state of matter (either hadronic or quark matter) at supra-nuclear densities. The observations of such events by using advanced optical facilities (e.g., the James Webb Space Telescope and the Thirty Meter Telescope) in future are highly suggested.
Distributed Dynamic Event-Triggered Secure Model Predictive Control of Vehicle Platoon Against DoS Attacks

This paper studies the distributed dynamic event-triggered model predictive control (MPC) of vehicle platoon systems subject to denial-of-service (DoS) attacks and external disturbances. We develop a novel DoS-attack-aware event-triggered mechanism for each vehicle to determine whether the MPC problem should be solved or not at each sampling time instant. If the MPC problem is solved, the constructed vehicular beacon information will be transmitted to its neighbouring vehicles through the vehicular ad-hoc network (VANET). In the DoS-attack-aware event-triggered condition, the dynamic threshold adjusts adaptively according to DoS attack durations, local vehicular data, and beacon information from its neighbours. Then, an exponential-type robustness constraint is introduced in the MPC problem to deal with external disturbances. Subsequently, sufficient conditions are given to guarantee the recursive feasibility of the MPC algorithm and closed-loop platoon system stability. Finally, extensive simulation examples are provided to illustrate the effectiveness of the proposed algorithm in terms of communication efficiency and platoon resilience control performance.
An implicit scheme for solving the anisotropic diffusion of heat and cosmic rays in the RAMSES code

Astrophysical plasmas are subject to a tight connection between magnetic fields and the diffusion of particles, which leads to an anisotropic transport of energy. Under the fluid assumption, this effect can be reduced to an advection-diffusion equation augmenting the equations of magnetohydrodynamics. We introduce a new method for solving the anisotropic diffusion equation using an implicit finite-volume method with adaptive mesh refinement and adaptive time-stepping in the RAMSES code. We apply this numerical solver to the diffusion of cosmic ray energy, and diffusion of heat carried by electrons, which couple to the ion temperature. We test this new implementation against several numerical experiments and apply it to a simple supernova explosion with a uniform magnetic field.
Research on task offloading strategy of mobile edge computing in 5G environment

With the wide application of 5G technology, more and more computing-intensive tasks and delay-sensitive tasks need to be calculated and processed on user equipment, but limited by the computing power and storage capacity of user equipment, these tasks cannot be efficient processing. The emergence of mobile edge computing (MEC) makes it possible. In this paper, we consider task offloading on Small Cell Network (SCN) structures unique to 5G. Under this network structure, a computational offloading strategy for joint optimization of forward and backward links is designed and implemented. Considering the front-end link and the backward link comprehensively, a computational offloading strategy model aiming at minimizing the total energy cost is established under the premise of delay limitation. Then, the objective function that needs to be optimized for energy is established according to the model, and the objective function is optimized by the improved artificial fish swarm algorithm. Finally, through the simulation of the algorithm, the performance of the improved algorithm is proved.
Deep Attention Aware Feature Learning for Data Association in Multiple Source Localization

The letter addresses the problem of data association for multiple source localization in a distributed sensor network. To increase the efficiency of localization, we present a learning methodology to generate highly distinctive measurement features for data association. We propose an attention-based graph neural network that exploits the relationship among the phases from the Short Time Fourier transform and the estimated measurements to generate highly descriptive features for each of the detected source signals. The methodology is free from any selective threshold and processes each of the measurements to detect and enrich the similar and distinguishable aspects of the measurements. These aspects are then aggregated in feature representations for each source measurement. The generated features can then be employed with any data association method to segregate the measurements belonging to the same source. It is observed in experimental evaluation that the proposed features employed with state-of-the-art association frameworks yield lower association and localization errors.
Distributed Network of Adaptive and Self-Reconfigurable Active Vision Systems

The performance of a computer vision system depends on the accuracy of visual information extracted by the sensors and the system’s visual-processing capabilities. To derive optimum information from the sensed data, the system must be capable of identifying objects of interest (OOIs) and activities in the scene. Active vision systems intend to capture OOIs with the highest possible resolution to extract the optimum visual information by calibrating the configuration spaces of the cameras. As the data processing and reconfiguration of cameras are interdependent, it becomes very challenging for advanced active vision systems to perform in real time. Due to limited computational resources, model-based asymmetric active vision systems only work in known conditions and fail miserably in unforeseen conditions. Symmetric/asymmetric systems employing artificial intelligence, while they manage to tackle unforeseen environments, require iterative training and thus are not reliable for real-time applications. Thus, the contemporary symmetric/asymmetric reconfiguration systems proposed to obtain optimum configuration spaces of sensors for accurate activity tracking and scene understanding may not be adequate to tackle unforeseen conditions in real time. To address this problem, this article presents an adaptive self-reconfiguration (ASR) framework for active vision systems operating co-operatively in a distributed blockchain network. The ASR framework enables active vision systems to share their derived learning about an activity or an unforeseen environment, which learning can be utilized by other active vision systems in the network, thus lowering the time needed for learning and adaptation to new conditions. Further, as the learning duration is reduced, the duration of the reconfiguration of the cameras is also reduced, yielding better performance in terms of understanding of a scene. The ASR framework enables resource and data sharing in a distributed network of active vision systems and outperforms state-of-the-art active vision systems in terms of accuracy and latency, making it ideal for real-time applications.
Möbius disjointness for homogeneous dynamics

We prove Sarnak's Mobius disjointness conjecture for all unipotent translations on homogeneous spaces of real connected Lie groups. Namely, we show that if $G$ is any such group, $\Gamma\subset G$ a lattice, and $u\in G$ an Ad-unipotent element, then for every $x\in\Gamma\backslash G$ and every continuous, bounded function $f$ on $\Gamma\backslash G$, the sequence $f(xu^{n})$ cannot correlate with the Mobius function on average.
Gravitational collapse of charged dust cloud in the Lovelock gravity

We study the effect of charge on gravitational collapse of inhomogeneous dust cloud in the Einstein, Gauss-Bonnet and Lovelock gravity. Dynamics of the collapsing shell is analyzed. The conditions for the occurrence of bounce during collapse are given. We also show that shell crossing occurs inevitably if the shell near the center is weakly charged.
Introduction to finite $W$-algebras

These are notes of lectures given at UN Encuentro 2016 at the Colombia National University. We begin with the definition of infinite $W$-algebras. Then we explain the motivation for the definition if finite $W$-algebras. Then we present basic facts about the structure and representations of finite $W$-algebras. In these lectures we follow the historical development of the subject.
AN INTRODUCTION TO WELL-POSEDNESS AND FREE-EVOLUTION

These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of evolution partial differential equations. I show how strong hyperbolicity guarantees well-posedness of the initial value problem. Symmetric hyperbolic systems are shown to render the initial boundary value problem well-posed with maximally dissipative boundary conditions. I discuss the Laplace–Fourier method for analyzing the initial boundary value problem. Finally, I state how these notions extend to systems that are first-order in time and second-order in space. In the second lecture I discuss the effect that the gauge freedom of electromagnetism has on the PDE status of the initial value problem. I focus on gauge choices, strong-hyperbolicity and the construction of constraint preserving boundary conditions. I show that strongly hyperbolic pure gauges can be used to build strongly hyperbolic formulations. I examine which of these formulations is additionally symmetric hyperbolic and finally demonstrate that the system can be made boundary stable.
Nonlinear charge and energy dynamics of an adiabatically driven interacting quantum dot

Javier I. Romero, Pablo Roura-Bas, Armando A. Aligia, and Liliana Arrachea International Center for Advanced Studies, ECyT-UNSAM, Campus Miguelete, 25 de Mayo y Francia, 1650 Buenos Aires, Argentina Dpto de Fı́sica, Centro Atómico Constituyentes, Comisión Nacional de Energı́a Atómica, CONICET, Buenos Aires, Argentina Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energı́a Atómica, CONICET, 8400 Bariloche, Argentina (Dated: September 19, 2018)
On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions

We supply a detailed proof of the result by P.S. Green and T. H$\ddot{\text{u}}$bsch that all complete intersection Calabi--Yau 3-folds in product of projective spaces are connected through projective conifold transitions (known as the standard web). We also introduce a subclass of small transitions which we call primitive small transitions and study such subclass. More precisely, given a small projective resolution $\pi : \widehat{X} \rightarrow X$ of a Calabi--Yau 3-fold $X$, we show that if the natural closed immersion $Def(\widehat{X}) \hookrightarrow Def(X)$ is an isomorphism then $X$ has only ODPs as singularities.
Differential Inequalities for Distance Comparison

Comparison of $1$-dimensional distance functions is a basic tool in Alexandrov geometry and it is used to characterize spaces with curvature bounded above or below. For the zero curvature bound there is a differential inequality which enables one to check this comparison directly on a given smooth $1$-dimensional distance function. In this note we give a generalization of this property to arbitrary curvature bounds.
Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus

We study convergence to equilibrium for the kinetic Fokker-Planck equation on the torus. Solving the stochastic differential equation, we show exponential convergence in the Monge-Kantorovich-Wasserstein $\mathcal{W}_2$ distance. Finally, we investigate if such a coupling can be obtained by a co-adapted coupling, and show that then the bound must depend on the square root of the initial distance.
Repr\'esentations modulo $p$ de $\mathrm{GL}(m,D)$, $D$ alg\`ebre \`a division sur un corps local

Soutenue le 22 novembre 2013 devant le jury composé de : M. Ioan Badulescu Université Montpellier II Examinateur M. Laurent Berger E.N. S. de Lyon Examinateur M. Elmar Grosse-Klönne Humboldt-Universität zu Berlin Examinateur M. Guy Henniart Université Paris-Sud 11 Rapporteur Mme Ariane Mézard Université Pierre et Marie Curie 6 Examinatrice M. Vincent Sécherre Université de Versailles Saint-Quentin Examinateur Mme Marie-France Vignéras Université Paris Diderot 7 Directrice de thèse
Error bounds on the probabilistically optimal problem solving strategy

We consider a simple optimal probabilistic problem solving strategy that searches through potential solution candidates in a specific order. We are interested in what impact has interchanging the order of two solution candidates with respect to this optimal strategy on the problem solving effectivity (i.e., the solution candidates examined as well as time spent before solving the problem). Such interchange can happen in the applications with only partial information available. We derive bounds on these errors in general as well as in three special systems in which we impose some restrictions on the solution candidates.