Related papers: On the relation between topological entropy and re…
Motter et al. derived a real-valued master stability function which determines whether and to what degree a given power grid is asymptotically stable. Stright and Edrington adopted certain uniformity assumptions on a grid's components and…
In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately,…
Topological entropy is not lower semi-continous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive…
Earth and soils are indispensable elements of river environment. Dam-downstream environment and ecosystems have been severely affected by reduced or even stopped sediment supply from the upstream. Replenishing earth and soils from outside…
Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle…
Transfer entropy is capable of capturing nonlinear source-destination relations between multi-variate time series. It is a measure of association between source data that are transformed into destination data via a set of linear…
Many potential applications of reinforcement learning (RL) require guarantees that the agent will perform well in the face of disturbances to the dynamics or reward function. In this paper, we prove theoretically that maximum entropy…
A key issue in complex systems regards the relationship between topology and dynamics. In this work, we use a recently introduced network property known as steering coefficient as a means to approach this issue with respect to different…
We give an algorithm, based on the $\phi$-expansion of Parry, in order to compute the topological entropy of a class of shift spaces. The idea is the solve an inverse problem for the dynamical systems $\beta x+\alpha \mod1$.The first part…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using…
The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make…
Finite volume methods are popular tools for solving time-dependent partial differential equations, especially hyperbolic conservation laws. Over the past 40 years a popular way of enlarging their robustness was the enforcement of global or…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Previous research has shown how indirect reciprocity can promote cooperation through evolutionary game theoretic models. Most work in this field assumes a separation of time-scales: individuals' reputations equilibrate at a fast time scale…
We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…
Traditional thermodynamic trade-off relations usually apply to quantities that depend linearly on probability distributions. In contrast, many important information-theoretic measures, such as entropies, are nonlinear and therefore…
It is known that when a system interacts with its environment, the entanglement contained in the system is redistributed since parts of the system entangle with the environment. On the other hand, the entanglement of a system with its…
Transfer entropy (TE) is an attractive model-free method to detect causality and infer structural connectivity of general digital systems. However it relies on high dimensions used in its definition to clearly remove the memory effect and…