The research of geometric means of matrices is attracting more and more attention from scholars since it has very important applications in mathematics and physics, especially in the von Neuman entropy involving the quantum physics and statistical thermal physical. There are many achievements on the entropy, among which the entropy uncertainty relation, the generalization of the Heisenberg unce...

In recent decades, different definitions of conditional Rényi entropy (CRE) have been introduced. Thus, Arimoto proposed a definition that found an application in information theory, Jizba and Arimitsu proposed a definition that found an application in time series analysis and Renner-Wolf, Hayashi and Cachin proposed definitions that are suitable for cryptographic applications. However, there i...

Rényi entropy is an information-theoretic measure of randomness which is fundamental to several applications. Several estimators of Rényi entropy based on k-nearest neighbor (kNN) based distances have been proposed in literature. For d-dimensional densities f , the variance of these Rényi entropy estimators of f decay as O(M), whereM is the sample size drawn from f . On the other hand, the bias...

We discuss a basic thermodynamic properties of systems with multifractal structure. This is possible by extending the notion of Gibbs–Shannon’s entropy into more general framework Rényi’s information entropy. We show a connection of Rényi’s parameter q with the multifractal singularity spectrum f (α) and clarify a relationship with the Tsallis–Havrda–Charvat entropy. Finally, we generalize Hage...

We present a computational algorithm for isotrigon texture discrimination. The aim of this method consists in discriminating isotrigon textures against a binary random background. The extension of the method to the problem of multitexture discrimination is considered as well. The method relies on the fact that the information content of time or space-frequency representations of signals, includ...

We consider the problem of approximating the empirical Shannon entropy of a highfrequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is the Rényi entropy that depends on a constant α. This quantity can be estimated efficiently and unbiasedly from a low-dimensional synopsis called an α-stable da...