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Continual learning aims to acquire new tasks while preserving performance on previously learned ones, but most methods struggle with catastrophic forgetting. Existing approaches typically treat all layers uniformly, often trading stability…
The entropies of molecules in solution are routinely calculated using gas phase formulae. It is assumed that, because implicit solvation models are fitted to reproduce free energies, this is sufficient for modeling reactions in solution.…
Machine learning models must continuously self-adjust themselves for novel data distribution in the open world. As the predominant principle, entropy minimization (EM) has been proven to be a simple yet effective cornerstone in existing…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…
Brenier and Grenier [SIAM J. Numer. Anal., 1998] proved that sticky particle dynamics with a large number of particles allow to approximate the entropy solution to scalar one-dimensional conservation laws with monotonic initial data. In…
Fluctuating entropy production is studied for a set of linearly coupled complex fields. The general result is applied to non-equilibrium fluctuating hydrodynamic equations for coarse-grained fields (density, temperature and velocity), in…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
Given a one-dimensional dynamical system we study its cover time, which quantifies the rate at which orbits become dense in the state space. Using transfer operator tools for dynamical systems with holes and inducing techniques, for a wide…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
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…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
Maximal repetition of a string is the maximal length of a repeated substring. This paper investigates maximal repetition of strings drawn from stochastic processes. Strengthening previous results, two new bounds for the almost sure growth…
We demonstrate that the shallow water moment equations satisfy an auxiliary entropy conservation law, where the entropy function corresponds to the total energy. Additionally, we show that the classical Newtonian slip friction and Manning…
The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we…
We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical…
Motivated by the notion of intermediate dimensions introduced by Falconer et al., we introduce a continuum of topological entropies that are intermediate between the (Bowen) topological entropy and the lower and upper capacity topological…
This paper is a first step in the study of the recurrence behavior in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the…
This paper has a flaw in an argument that uses the weak-* convergence of measures. The paper was replaced by "Entropy and Its Variational Principle for Locally Compact Metrizable Systems", by the same authors.