Related papers: On the relation between topological entropy and re…
In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
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…
State entropy regularization has empirically shown better exploration and sample complexity in reinforcement learning (RL). However, its theoretical guarantees have not been studied. In this paper, we show that state entropy regularization…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
Stochastic and soft optimal policies resulting from entropy-regularized Markov decision processes (ER-MDP) are desirable for exploration and imitation learning applications. Motivated by the fact that such policies are sensitive with…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However,…
Stochastic restoration algorithms allow to explore the space of solutions that correspond to the degraded input. In this paper we reveal additional fundamental advantages of stochastic methods over deterministic ones, which further motivate…
In this article the problem of reconstructing the pattern of connection between agents from partial empirical data in a macro-economic model is addressed, given a set of behavioral equations. This systemic point of view puts the focus on…
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…
We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically,…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…
Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…
Designing effective recovery strategies for damaged networked systems is critical to the resilience of built, human and natural systems. However, progress has been limited by the inability to bring together distinct philosophies, such as…
For continuous-space diffusion processes, there is a strong connection between conservative forces and entropy production. For a given time evolution of the system's state, the entropy production is minimized when the system is driven by a…
We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties,…