Related papers: Dynamical Complexity Of Short and Noisy Time Serie…
A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear…
In this chapter we present a new approach to the study of manifestations of chaos in real complex system. Recently we have achieved the following result. In real complex systems the informational measure of chaotic chatacter (IMC) can serve…
We show how the Shannon entropy function can be used as a basis to set up complexity measures weighting the economic efficiency of countries and the specialization of products beyond bare diversification. This entropy function guarantees…
We address the problem of estimating the parameters of a time-homogeneous Markov chain given only noisy, aggregate data. This arises when a population of individuals behave independently according to a Markov chain, but individual sample…
Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing the return time entropy of a Markov chain, subject to a graph topology with travel times and stationary distribution. The return time entropy…
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
To improve the robustness of transformer neural networks used for temporal-dynamics prediction of chaotic systems, we propose a novel attention mechanism called easy attention which we demonstrate in time-series reconstruction and…
A large number of biological systems - from bacteria to sheep - can be described as ensembles of self-propelled agents (active particles) with a complex internal dynamic that controls the agent's behavior: resting, moving slow, moving fast,…
Shannon entropy ($S$), Fisher information ($I$) and a measure equivalent to Fisher-Shannon complexity $(C_{IS})$ of a ro-vibrational state of diatomic molecules (O$_2$, O$_2^+$, NO, NO$^+$) with generalized Kratzer potential is analyzed.…
This paper studies cross-domain lossy compression through the lens of minimum entropy coupling (MEC) with rate and classification constraints. In this setting, an encoder observes samples from a degraded source domain, while the decoder is…
In this note we study contractivity of monotone systems and exponential convergence of positive systems using non-Euclidean norms. We first introduce the notion of conic matrix measure as a framework to study stability of monotone and…
Lightweight Temporal Compression (LTC) is among the lossy stream compression methods that provide the highest compression rate for the lowest CPU and memory consumption. As such, it is well suited to compress data streams in…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
Shannon entropy in position ($S_{\rvec}$) and momentum ($S_{\pvec}$) spaces, along with their sum ($S_t$) are presented for unit-normalized densities of He, Li$^+$ and Be$^{2+}$ ions, spatially confined at the center of an impenetrable…
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some…
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
Chaotic time series forecasting has been far less understood despite its tremendous potential in theory and real-world applications. Traditional statistical/ML methods are inefficient to capture chaos in nonlinear dynamical systems,…
Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…