相关论文: On $n$-tuplewise IP-sensitivity and thick sensitiv…

The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with discrete spectrum. To that end, we first determine when an isomorphic maximal equicontinuous factor map of…

We introduce a functor which associates to every measure preserving system (X,B,\mu,T) a topological system (C_2(\mu),\tilde{T}) defined on the space of 2-fold couplings of \mu, called the topological lens of T. We show that often the…

We investigate sensitivity to cumulative perturbations for a few dynamical system classes of practical interest. A system is said to have bounded sensitivity to cumulative perturbations (bounded sensitivity, for short) if an additive…

This paper studies the possibility of detecting and isolating topology failures (including link failures and node failures) of a networked system from subsystem measurements, in which subsystems are of fixed high-order linear dynamics, and…

The inference of an underlying network topology from local observations of a complex system composed of interacting units is usually attempted by using statistical similarity measures, such as Cross-Correlation (CC) and Mutual Information…

In recent years, algorithmic breakthroughs in stringology, computational social choice, scheduling, etc., were achieved by applying the theory of so-called $n$-fold integer programming. An $n$-fold integer program (IP) has a highly uniform…

We demonstrate how the collective response of $N$ globally coupled bistable elements can strongly reflect the presence of very few non-identical elements in a large array of otherwise identical elements. Counter-intuitively, when there are…

Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…

Several indicators have been recently proposed for measuring various characteristics of the tuples of a dataset -- particularly, the so-called skyline tuples, i.e., those that are not dominated by other tuples. Numeric indicators are very…

Let $\boldsymbol{X}=\{X_{k}\}_{k=0}^{\infty}$ be a sequence of compact metric spaces $X_{k}$ and $\boldsymbol{T}=\{T_{k}\}_{k=0}^{\infty}$ a sequence of continuous mappings $T_{k}:X_{k} \to X_{k+1}$. The pair…

If $\pi:(X,T)\to(Z,S)$ is a topological factor map between uniquely ergodic topological dynamical systems, then $(X,T)$ is called an isomorphic extension of $(Z,S)$ if $\pi$ is also a measure-theoretic isomorphism. We consider the case when…

Some necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant (LTI) dynamics. The topology of this system is fixed but arbitrary, and every subsystem is…

A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability space. The connection among some dynamical properties on the original space and on the induced spaces are…

We investigate the connections between independence, sequence entropy, and mean sensitivity for a measure preserving system under the action of a countable infinite discrete group. We establish that every sequence entropy tuple for an…

Recently, we introduced dynamic networks with preferred degrees, showing that interesting properties are present in a single, homogeneous system as well as one with two interacting networks. While simulations are readily performed, analytic…

Let $\pi\colon T\times X\rightarrow X$ with phase map $(t,x)\mapsto tx$, denoted $(\pi,T,X)$, be a \textit{semiflow} on a compact Hausdorff space $X$ with phase semigroup $T$. If each $t\in T$ is onto, $(\pi,T,X)$ is called surjective; and…

Let us consider a pair signal-observation ((xn,yn),n 0) where the unobserved signal (xn) is a Markov chain and the observed component is such that, given the whole sequence (xn), the random variables (yn) are independent and the conditional…

We consider extensions of the notion of topological transitivity for a dynamical system $(X,f)$. In addition to chain transitivity, we define strong chain transitivity and vague transitivity. Associated with each there is a notion of…

We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical…

We show that in a topological dynamical system $(X,T)$ of positive entropy there exist proper (positively) asymptotic pairs, that is, pairs $(x,y)$ such that $x\not= y$ and $\lim_{n\to +\infty} d(T^n x,T^n y)=0$. More precisely we consider…