The quality of an image affects its utility and image quality assessment has been a hot research topic for many years. One widely used measure for image quality assessment is Shannon entropy, which has a well-established information-theoretic basis. The value of this entropy can be interpreted as the amount of information. However, Shannon entropy is badly adapted to information measurement in ...

In this paper, we derive the exact analytical expressions for the Shannon entropy of generalized orderstatistics from Pareto-type and related distributions.

The main purpose of this manuscript is to present some new estimations the Jensen gap in a discrete sense along with their applications. proposed for are provided help notion 6-convex functions. Some numerical experiments performed determine significance and correctness intended estimates. Several outcomes results discussed Hölder inequality power quasi-arithmetic means. Furthermore, applicatio...

Recently, a new type of set, called random permutation set (RPS), is proposed by considering all the permutations elements in certain set. For measuring uncertainty RPS, entropy RPS presented. However, maximum principle has not been discussed. To address this issue, paper presents RPS. The analytical solution and its PMF condition are proven Besides, numerical examples used to illustrate entrop...

An overview of the Bose-Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to oneand two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the oneand two-body properties of the Bose gas are derived using Jastrow-type correlation function. ...

We provide a method that approximates the Bayes error rate and the Shannon entropy with high probability. The Bayes error rate approximation makes possible to build a classifier that polynomially approaches Bayes error rate. The Shannon entropy approximation provides provable performance guarantees for learning trees and Bayesian networks from continuous variables. Our results rely on some reas...

Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation of the tomographic entropy to Shannon entropy and von Neumann entropy is elucidated.

We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs [1] and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A.A. Brudno [2]. On the other hand, using the quantu...

Recurrence plots were introduced to quantify the recurrence properties of chaotic dynamics. Hereafter, the recurrence quantification analysis was introduced to transform graphical interpretations into statistical analysis. In this spirit, a new definition for the Shannon entropy was recently introduced in order to have a measure correlated with the largest Lyapunov exponent. Recurrence plots an...