We consider a small closed physical systems. It has xed energy and if the energy is a power of its generale coordinates then the distribution of any single coordinate will follow a distribution that maximizes Tsallis entropy. For many aspects of entropy can be discussed for such small systems with out going to the thermodynamical limit. By letting the number of degrees of freedom tend to in nit...

As a novel data mining approach, a wavelet entropy algorithm is used to perform entropy statistics on wavelet coefficients (or reconstructed signals) at various wavelet scales on the basis of wavelet decomposition and entropy statistic theory. Shannon wavelet energy entropy, one kind of wavelet entropy algorithm, has been taken into consideration and utilized in many areas since it came into be...

In statistical physics, Boltzmann-Shannon entropy provides good understanding for the equilibrium states of a number of phenomena. In statistics, the entropy corresponds to the maximum likelihood method, in which Kullback-Leibler divergence connects Boltzmann-Shannon entropy and the expected log-likelihood function. The maximum likelihood estimation has been supported for the optimal performanc...

We prove characterization theorems for relative entropy (also known as Kullback–Leibler divergence), q-logarithmic entropy (also known as Tsallis entropy), and q-logarithmic relative entropy. All three have been characterized axiomatically before, but we show that earlier proofs can be simplified considerably, at the same time relaxing some of the hypotheses.

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptot...

We present a first physical application of Tsallis’ generalized entropy to the thermodynamics of self-gravitating systems. The stellar system confined in a spherical cavity of radius re exhibits an instability, so-called gravothermal catastrophe, which has been originally investigated by Antonov (Vest.Leningrad Gros.Univ. 7 (1962) 135) and Lynden-Bell & Wood (Mon.Not.R.Astron.Soc. 138 (1968) 49...

The construction of efficient and effective decision trees remains a key topic in machine learning because of their simplicity and flexibility. A lot of heuristic algorithms have been proposed to construct near-optimal decision trees. Most of them, however, are greedy algorithms which have the drawback of obtaining only local optimums. Besides, common split criteria, e.g. Shannon entropy, Gain ...

We present a first physical application of Tsallis’ generalized entropy to the thermodynamics of self-gravitating systems. The stellar system confined in a spherical cavity of radius re exhibits an instability, so-called gravothermal catastrophe, which has been originally investigated by Antonov (Vest.Leningrad Gros.Univ. 7 (1962) 135) and Lynden-Bell & Wood (Mon.Not.R.Astron.Soc. 138 (1968) 49...

In this paper, we study the stability under convolution of the maximizing distributions of the Tsallis entropy under energy constraint (called hereafter Tsallis distributions). These distributions are shown to obey three important properties: a stochastic representation property, an orthogonal invariance property and a duality property. As a consequence of these properties, the behaviour of Tsa...