Related papers: Persistent Entropy as a Detector of Phase Transiti…
Multi-stream sequential change detection involves simultaneously monitoring many streams of data and trying to detect when their distributions change, if at all. Here, we theoretically study multiple testing issues that arise from detecting…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of non-equilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are…
When presented with a data stream of two statistically dependent variables, predicting the future of one of the variables (the target stream) can benefit from information about both its history and the history of the other variable (the…
Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of…
We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most…
A plug-in estimator of entropy is the entropy of the distribution where probabilities of symbols or blocks have been replaced with their relative frequencies in the sample. Consistency and asymptotic unbiasedness of the plug-in estimator…
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…
We introduce bipartite projected ensembles (BPEs) for quantum many-body wave functions, which consist of pure states supported on two local subsystems, with each state associated with the outcome of a projective measurement of the…
Stochastic HYPE is a novel process algebra that models stochastic, instantaneous and continuous behaviour. It develops the flow-based approach of the hybrid process algebra HYPE by replacing non-urgent events with events with…
Brain connectivity characterizes interactions between different regions of a brain network during resting-state or performance of a cognitive task. In studying brain signals such as electroencephalograms (EEG), one formal approach to…
In the regime of change-point detection, a nonparametric framework based on scan statistics utilizing graphs representing similarities among observations is gaining attention due to its flexibility and good performances for high-dimensional…
We investigate the critical behavior of continuous phase transitions in the context of Ginzburg Landau models with a double well effective potential. In particular, we show that the recently proposed configurational entropy, a measure of…
Entanglement entropy (EE) of a state is a measure of correlation or entanglement between two parts of a composite system and it may show appreciable change when the ground state (GS) undergoes a qualitative change in a quantum phase…
We define an entropy for a quantum field theory by combining quantum fluctuations, scaling and the maximum entropy concept. This entropy has different behavior in asymptotically free and non--asymptotically free theories. We find that the…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
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…
In this paper we propose a new approach for sequential monitoring of a parameter of a $d$-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a…