相关论文: Generalized Farey trees, transfer Operators and ph…

We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.

We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…

Flocking phase transitions found in models of polar active matter are paradigmatic examples of active phase transitions in soft matter. An interesting specialization of flocking models concerns a ``topological'' vs ``metric'' choice by…

The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…

Thermalization is one of the most important phenomena in statistical physics. Often, the transition probabilities between different states in the phase space is or can be approximated by constants. In this case, the system can be described…

The structure of functional graphs of nonlinear systems provides one of the most intuitive methods for analyzing their properties in digital domain. The generalized Tent map is particularly suitable for studying the degradation of dynamic…

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…

We consider a particular example of interplay between statistical models related to CFT on one hand, and to the spectral properties of ODE, known as ODE/IS correspondence, on the other hand. We focus at the representation of wave functions…

We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an…

In this article we give several characterizations for various transitivity properties for linear operators. We define a general form of `Hypercyclicity Criterion' using a Furstenberg family $\mathcal{F}$ to characterize…

We propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian…

A perturbed family of interval exchange maps (FIEMs) provides a natural two-\linebreak{}dimensional area-preserving extension of interval exchange maps, with each IEM parameterized by an action variable $y$. Such families arise, for…

We develop a theory of generalized characters of local systems in $\infty$-categories, which extends classical character theory for group representations and, in particular, the induced character formula. A key aspect of our approach is…

While General Fractional Calculus has successfully expanded the scope of memory operators beyond power-laws, standard formulations remain predominantly restricted to the half-line via Riemann-Liouville or Caputo definitions. This constraint…

The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by…

Distributions of triplets in some genetic sequences are examined and found to be well described by a 2-parameter Markov process with a sparse transition matrix. The variances of all the relevant parameters are not large, indicating that…

Inspired by the success of foundation models in applications such as ChatGPT, as graph data has been ubiquitous, one can envision the far-reaching impacts that can be brought by Graph Foundation Models (GFMs) with broader applications in…

We consider the random iteration of finitely many expanding $\mathcal{C}^{1+\epsilon}$ diffeomorphisms on the real line without a common fixed point. We derive the spectral gap property of the associated transition operator acting on…

The Transformed-Transformer family of distributions are the resulting family of distributions as transformed from a random variable $T$ through another transformer random variable $X$ using a weight function $\omega$ of the cumulative…