It is shown that the Tsallis entropies are the only f -entropies satisfying the condition of composability.

We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q ↔ q−1 symmetric nonextensive entropy preserves all of the mathematical structure of thermodynamics just as in the case of non-symmetric Tsallis statistics. Basic properties and analogies with quantum groups are discussed. PACS: 05.20.-y; 0...

Image segmentation plays an important role in medical imaging applications. Therefore, accurate methods are needed for the successful segmentation of medical images for diagnosis and detection of various diseases. In this paper, we have used maximum entropy to achieve image segmentation. Maximum entropy has been calculated using Shannon, Renyi and Tsallis entropies. This work has novelty based ...

Alexandra C. Tsallis, Constantino Tsallis, Aglae C.N. de Magalhaes and Francisco A. Tamarit ∗ Instituto de Psicologia, Pos-Graduacao em Psicologia Social Rua Sao Francisco Xavier 524, 10 andar, Bloco F Universidade do Estado do Rio de Janeiro, 20559-900 Rio de Janeiro-RJ, Brazil Centro Brasileiro de Pesquisas Fisicas Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil Santa Fe Institute, 139...

A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between Tsallis entropy and the one-dimensional correlated anomalous diffusion equation is established. It is also developed explicitly a WKB-like method for second order ...

Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for Rényi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we s...

There exist two different versions of the Kullback-Leibler divergence (K-Ld) in Tsallis statistics, namely the usual generalized K-Ld and the generalized Bregman K-Ld. Problems have been encountered in trying to reconcile them. A condition for consistency between these two generalized K-Ld-forms by recourse to the additive duality of Tsallis statistics is derived. It is also shown that the usua...

The cumulative probability distribution of sparseness time interval in the Internet is studied by the method of data analysis. Round-trip time between a local host and a destination host through ten odd routers is measured using the ping command, i.e., doing an echo experiment. The data are found to be well described by q-exponential distributions, which maximize the Tsallis entropy indexed by ...

In this paper a novel feature extraction method for image processing via PCNN and Tsallis entropy is presented. We describe the mathematical model of the PCNN and the basic concept of Tsallis entropy in order to find a recognition method for isolated objects. Experiments show that the novel feature is translation and scale independent, while rotation independence is a bit weak at diagonal angle...