Related papers: On the relation between topological entropy and re…

Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare…

Nature is full of random networks of complex topology describing such apparently disparate systems as biological, economical or informatical ones. Their most characteristic feature is the apparent scale-free character of interconnections…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…

A crucial challenge in decentralized systems is state estimation in the presence of unknown inputs, particularly within heterogeneous sensor networks with dynamic topologies. While numerous consensus algorithms have been introduced, they…

Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…

Network dynamics offers critical insights into the behavior and evolution of complex systems. Here, we focus on the topological dynamics of networks to explore a unique process for reducing the average distance: topological compression. The…

We show why the amount of information communicated between the past and future--the excess entropy--is not in general the amount of information stored in the present--the statistical complexity. This is a puzzle, and a long-standing one,…

A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…

Recent crises have shown that the knowledge of the structure of input-output networks at the firm level is crucial when studying economic resilience from the microscopic point of view of firms that rewire their connections under supply and…

We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…

When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is…

Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…

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…

Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…

The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore,…

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…

The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…

Maximum entropy (MaxEnt) RL maximizes a combination of the original task reward and an entropy reward. It is believed that the regularization imposed by entropy, on both policy improvement and policy evaluation, together contributes to good…

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…