The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the channel capacity by maximization of the Tsallis entropy within a given condition of code length. As a result, we obtained a simple relational expression betw...

Mutual information is one of the mostly used measures for evaluating image similarity. In this paper, we investigate the application of three different Tsallis-based generalizations of mutual information to analyze the similarity between scanned documents. These three generalizations derive from the Kullback–Leibler distance, the difference between entropy and conditional entropy, and the Jense...

In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.

We prove a tight uniform continuity bound for a family of entropies which includes the von Neumann entropy, the Tsallis entropy and the α-Rényi entropy, Sα, for α ∈ (0, 1). We establish necessary and sufficient conditions for equality in the continuity bound and prove that these conditions are the same for every member of the family. Our result builds on recent work in which we constructed a st...

The Tsallis measure of mutual information is combined with the simultaneous perturbation stochastic approximation algorithm to register images. It is shown that Tsallis entropy can improve registration accuracy and speed of convergence, compared with Shannon entropy, in the calculation of mutual information. Simulation results show that the new algorithm achieves up to seven times faster conver...

The purpose of this note is to argue that degree of nonextensivity as given by the Tsallis distribution obtained from maximum entropy principle has a different origin than the nonextensivity inferred from pseudo-additive property of Tsallis entropy. PACS: 05.20.-y, 05.30.-d

In density estimation task, maximum entropy model (Maxent) can effectively use reliable prior information via certain constraints, i.e., linear constraints without empirical parameters. However, reliable prior information is often insufficient, and the selection of uncertain constraints becomes necessary but poses considerable implementation complexity. Improper setting of uncertain constraints...

We have calculated the Tsallis entropy and Fisher information matrix (entropy) of spatially correlated nonextensive systems, by using an analytic non-Gaussian distribution obtained by the maximum entropy method. The effects of the correlated variability on the Fisher information matrix are shown to be different from those on the Tsallis entropy. The Fisher information is increased (decreased) b...

Several previous results valid for one-dimensional nonlinear Fokker-Planck equations are generalized to N-dimensions. A general nonlinear N-dimensional FokkerPlanck equation is derived directly from a master equation, by considering nonlinearities in the transition rates. Using nonlinear Fokker-Planck equations, the H-theorem is proved; for that, an important relation involving these equations ...

Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy is equally suitable to describe those systems with powerlaw behaviour, where the use of the Tsallis entropy is relevant. We discuss a specific class of dynam...