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

This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less…

We study the problem of controlling a partially observed Markov decision process (POMDP) to either aid or hinder the estimation of its state trajectory. We encode the estimation objectives via the smoother entropy, which is the conditional…

In this paper, we show through examples, how the existing definitions of information transfer, namely directed information and transfer entropy fail to capture true causal interaction between states in control dynamical system. We propose a…

In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…

Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct…

Reinforcement learning for large language models faces a fundamental trade-off between sample efficiency and asymptotic performance: strictly on-policy methods discard trajectories after a single update, while off-policy reuse introduces…

We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mappings. By introducing varying metrics, we simplify the analysis…

Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…

For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…

The entropy production rate (EPR), a key measure of thermodynamic irreversibility in stochastic thermodynamics, is difficult to determine directly in experiments, motivating lower-bound-based estimation from observations. However, a…

Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a…

Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…

The recursive property of entropy is well known in information theory; however, the concept is underutilized in thermodynamics, despite being the field where the concept of entropy originated. The zentropy approach is built on this idea,…

Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve…

This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

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…

The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…

A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…

Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…