A maximum entropy framework based on Tsallis entropy is proposed to depict long tail behavior of queue lengths in broadband networks. Queue length expression as measured in terms of number of packets involves Hurwitz-zeta function. When the entropy parameter q in Tsallis entropy is less than unity, the distribution of packets yields power law behavior. In the limit q tending to unity, Tsallis e...

In this paper we utilize the Tsallis relative entropy, a generalization of the Kullback–Leibler entropy in the frame work of non-extensive thermodynamics to analyze the properties of anomalous diffusion processes. Anomalous (super-) diffusive behavior can be described by fractional diffusion equations, where the second order space derivative is extended to fractional order α ∈ (1, 2). They repr...

There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this misconception is explained and it is shown that a long tail distribution exists in equilibrium thermodynamics for more than a century.

We revisit Tsallis Maximum Entropy Solutions to the Vlasov-Poisson Equation describing gravitational N -body systems. We review their main characteristics and discuss their relationship with other applications of Tsallis statistics to systems with long range interactions. In the following considerations we shall be dealing with a D-dimensional space so as to be in a position to investigate poss...

Decision making is still an open issue in the application of Dempster-Shafer evidence theory. A lot of works have been presented for it. In the transferable belief model (TBM), pignistic probabilities based on the basic probability assignments are used for decision making. In this paper, multiscale probability transformation of basic probability assignment based on the belief function and the p...

The fractal and self-similarity properties are revealed in many complex networks. In order to show the influence of different part in the complex networks to the information dimension, we have proposed a new information dimension based on Tsallis entropy namely Tsallis information dimension. The Tsallis information dimension can show the fractal property from different perspective by set differ...

flow-rate measurement in rivers under different conditions is required for river management purposes including water resources planning, pollution prevention, and flood control. this study proposed a new discharge estimation method by using a mean velocity derived from a 2d velocity distribution formula based on tsallis entropy concept. this procedure is done based on several factors which refl...

This memo contains proofs that the Shannon entropy is the limiting case of both the Renyi entropy and the Tsallis entropy, or information. These results are also confirmed experimentally. We conclude with some general observations on the utility of entropy measures. A brief summary of the origins of the concept of physical entropy are provided in an appendix.

The Boltzmann–Gibbs and Tsallis entropies are essential concepts in statistical physics, which have found multiple applications in many engineering and science areas. In particular, we focus our interest on their applications to image processing through information theory. We present in this article a novel numeric method to calculate the Tsallis entropic index q characteristic to a given image...