In this work, Fault Induced Delayed Voltage Recovery (FIDVR) phenomenon has been characterized as the loss of Entropy in the voltage time series. The relationship between entropy and the voltage recovery rate has been established. It is shown that, the entropy can be an estimate of the recovery rate. Furthermore, the entropy computation has been done entirely from the statistical properties of ...

We investigate the complexity of computing entropy of various Markovian models including Markov Chains (MCs), Interval Markov Chains (IMCs) and Markov Decision Processes (MDPs). We consider both entropy and entropy rate for general MCs, and study two algorithmic questions, i.e., entropy approximation problem and entropy threshold problem. The former asks for an approximation of the entropy/entr...

A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uni...

We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length. Second, on this basis, we give an elementary alternative proof of the equality between the permutation entropy rate and ...

Statistical entropy was introduced by Shannon as a basic concept in information theory, measuring the average missing information on a random source. Extended into an entropy rate, it gives bounds in coding and compression theorems. I here present how statistical entropy and entropy rate relate to other notions of entropy, relevant either to probability theory (entropy of a discrete probability...

The Shannon lower bound is one of the few lower bounds on the rate-distortion function that holds for a large class of sources. In this paper, it is demonstrated that its gap to the rate-distortion function vanishes as the allowed distortion tends to zero for all sources that have a finite differential entropy and whose integer parts have a finite entropy. Conversely, it is demonstrated that if...

Csiszár’s forward -cutoff rate (given a fixed 0) for a discrete source is defined as the smallest number such that for every , there exists a sequence of fixed-length codes of rate with probability of error asymptotically vanishing as . For a discrete memoryless source (DMS), the forward -cutoff rate is shown by Csiszár [6] to be equal to the source Rényi entropy. An analogous concept of revers...

{The performance of optimum vector quantizers subject to a conditional entropy constraint is studied in this paper. This new class of vector quantizers was originally suggested by Chou and Lookabaugh. A locally optimal design of this kind of vector quantizer can be accomplished through a generalization of the well known entropy-constrained vector quantizer (ECVQ) algorithm. This generalization ...

This paper deals with the discrimination between suffering foetuses and normal foetuses by means of a multi-scale similarity entropy. Sample entropy and similarity entropy are evaluated in multi-scale analysis on foetal heart rate signals. Without multi-scale analysis, our results show that only the similarity entropy differentiate suffering foetuses to normal foetuses. Furthermore with the mul...