Related papers: Time-restricted sensitivity and entropy
The study is devoted to definition of generalized metrical and topological (informational entropy) characteristics of neural signals via their well-known theoretical models. We have shown that time dependence of action potential of neurons…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
Let $(X,T)$ be a topological dynamical system. We define the measure-theoretical lower and upper entropies $\underline{h}_\mu(T)$, $\bar{h}_\mu(T)$ for any $\mu\in M(X)$, where $M(X)$ denotes the collection of all Borel probability measures…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
In this paper, we study the Feldman-Katok metric in random dynamical systems and establish corresponding fiber topological entropy formula, Brin-Katok local entropy formula and fiber Katok entropy formula by replacing Bowen metric with…
We establish abstract local limit theorems for hitting times and return-times of suitable sequences (A_{l}) of asymptotically rare events in ergodic probability preserving dynamical systems, including versions for tuples of consecutive…
This paper studies local asymptotic relationship between two scalar estimates. We define sensitivity of a target estimate to a control estimate to be the directional derivative of the target functional with respect to the gradient direction…
We study the receptive metric entropy for semigroup actions on probability spaces, inspired by a similar notion of topological entropy introduced by Hofmann and Stoyanov. We analyze its basic properties and its relation with the classical…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of…
For sensory networks, we determine the rate with which they acquire information about the changing external conditions. Comparing this rate with the thermodynamic entropy production that quantifies the cost of maintaining the network, we…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…