This article extends the non-extensive entropy of Tsallis and uses this entropy to model an energy producing system in an absorbing heat bath. This modified non-extensive entropy is superficially identical to the one proposed by Tsallis, but also incorporates a “hidden” parameter that provides greater flexibility for modeling energy constraints. This modified non-extensive entropy also leads to...

A concept of entropy production associated with continuous topolog-ical evolution is deduced (without statistics) from the fact that Cartan-Hilbert 1-form of Action defines a non-equilibrium symplectic system of Pfaff Topological dimension 2n+2. The differential entropy, dS, is composed of the interior product of the non-canonical components of momentum with the components of the differential v...

A comprehensive research of Electroencephalography (EEG) is carried out on Empirical Mode Decomposition (EMD) and Discrete Wavelet Transform (DWT) domains. In this scenario, the hybrid feature extraction is performed by utilizing entropy features like Shannon entropy, log-energy entropy and Renyi entropy. Generally, the entropy measures are effective in evaluation of non-linear interrelation an...

A non-malleable extractor is a seeded extractor with a very strong guarantee – the output of a non-malleable extractor obtained using a typical seed is close to uniform even conditioned on the output obtained using any other seed. The first contribution of this paper consists of two new and improved constructions of non-malleable extractors: We construct a non-malleable extractor with seed-leng...

Binary Low Density Parity Check (LDPC) codes have been shown to have near Shan-non limit performance when decoded using a probabilistic decoding algorithm. The analogous codes deened over nite elds GF(q) of order q > 2 show signiicantly improved performance. We present the results of Monte Carlo simulations of the decoding of innnite LDPC Codes which can be used to obtain good constructions for...

Based on the non-standard analysis by Robinson, a new definition of the entropy of general distributions is given as a straightforward extension of Shannon's discrete entropy. The newly defined entropy has natural properties such as positiveness and invariance under transformations unlike Shannon's continuous entropy. In the light of this new definition, the meaning of Shannon's continuous entr...

We propose entropy functions based on fractional calculus. We show that this new entropy has the same properties than the Shannon entropy except that of additivity, therefore making this entropy non-extensive. We show that this entropy function satisfies the Lesche and thermodynamic stability criteria.

The information entropy, as a measurement of the average amount of information contained in an information system, is used in the classification of objects and the analysis of information systems. The information entropy of a partition is non-increasing when the partition is refined, and is related to rough sets by Wong and Ziarko. The partitions and information entropy have some graph-theoreti...

The aim of this paper is to present an axiomatization of a generalization of Shannon’s entropy starting from partitions of finite sets. The proposed axiomatization yields as special cases the Havrda-Charvat entropy, and thus, provides axiomatizations for the Shannon entropy, the Gini index, and for other types of entropy used in classification and data mining. Keywords—Shannon entropy, Gini ind...