相关论文: Statistical properties of uniformly hyperbolic map…
I give a concise introduction to some essential concepts of statistical mechanics: 1. Probability theory (constrained distributions, concentration theorem, frequency estimation, hypothesis testing); 2. Macroscopic systems in equilibrium…
In this letter we study how deterministic features presented by a system can be used to perform direct transport in a {\it quasi}-symmetric potential and weak dissipative system. We show that the presence of nonhyperbolic regions around…
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
The purpose of this text is: 1) to clarify the foundations of the broad histogram method, stressing the conceptual differences between it and reweighting procedures in general; 2) to propose a very simple microcanonical dynamic rule, yet to…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
The aim of this work is to try to bridge over theoretical immunology and disordered statistical mechanics. Our long term hope is to contribute to the development of a quantitative theoretical immunology from which practical applications may…
We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability…
An account is given of the methods of working of Experimental High Energy Particle Physics, from the viewpoint of statisticians and others unfamiliar with the field. Current statistical problems, techniques, and hot topics are introduced…
This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…
We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We present a scaling theory for the singular…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
The supersymmetry method has proven to be a very powerful tool of study of the statistical properties of energy levels and eigenfunctions in disordered and chaotic systems. The aim of these lectures is to present a tutorial introduction to…
When dealing with control systems, it is useful and even necessary to assess the performance of underlying transfer functions. The functions may or may not be linear, may or may not be even monotonic. In addition, they may have structural…
The present communication addresses a set of observations, obeying both deterministic as well as statistical formal requirements, and serving to operate within the framework of the dynamical systems theory, with a certain emphasis placed on…
For free-probability Voiculescu transforms, analogous to hyperbolic characteristic functions, we show how to get their representing measures in an integral form. For that purpose, it is enough to know those transforms only on the imaginary…
We reelaborate on the basic properties of lossless multilayers by using bilinear transformations. We study some interesting properties of the multilayer transfer function in the unit disk, showing that hyperbolic geometry turns out to be an…
This article is devoted to the study of the historic set of ergodic averages in some nonuniformly hyperbolic systems. In particular, our results hold for the robust classes of multidimensional nonuniformly expanding local diffeomorphisms…