In this paper we apply an evolving stochastic method to construct simple and effective Artificial Neural Networks, based on the theory of Tsallis statistical mechanics. Our aim is to establish an automatic process for building a smaller network with high classification performance. We aim to assess the utility of the method based on statistical mechanics for the estimation of transparent coatin...

We provide evidence that the small-scale statistics of the acceleration of a test particle in high-Reynolds number Lagrangian turbulence is correctly described by Tsallis statistics with entropic index q = 3 2 . We present theoretical arguments why Tsallis statistics can naturally arise in Lagrangian turbulence and why at the smallest scales q = 32 is relevant. A generalized Heisenberg-Yaglom f...

Special Edition “2015 UN/Japan Workshop on Space Weather” 157 Pathway Model and Nonextensive Statistical Mechanics A.M. Mathai, H.J. Haubold , C. Tsallis 5 1 Department of Mathematics and Statistics, McGill University, Quebec, Canada 2 Centre for Mathematical and Statistical Sciences, Kerala, India 3 Office for Outer Space Affairs, United Nations, Vienna, Austria 4 Centro Brasileiro de Pesquisa...

During the last decades, many attempts have beenmade in order to explain and formalize mathematically a large set of phenomena that, at a first glance, are not well described by traditional theories. Among those attempts one finds the whole theory of self-organized criticality and some statistical theories. In recent years, a popular approach has been a Daróczy-like entropy [2] and its correspo...

We consider a generalized statistical mechanics model for the creation process of cosmic rays which takes into account local temperature fluctuations. This model yields Tsallis statistics for the cosmic ray spectrum. It predicts an entropic index q given by q = 11/9 at largest energies (equivalent to a spectral index of α = 5/2), and an effective temperature given by 59TH , where kTH ≈ 180 MeV ...

Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a qdeformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the Tsallis entropy depends on the deformation parameter and must be redefined to recover the usual thermodynamic relations. The notions of variance and covarianc...

Additive deformations of statistical systems arise in various areas of physics. Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved. This paper investigates ways in which deformed algebraic operations lead to distinctive central limit theory. We establish some general central limit results that are applicable to a range of examp...

The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius' inequality is shown to hold in the range q in (0, 2]. This restriction on the range of the entropic index, q, is purely quantum mechanical and there exists n...

The nonadditive entropy introduced by Tsallis in 1988 has been used different fields and generalizes the Boltzmann extending possibilities of application statistical methods developed context Mechanics. Here we investigate one last points theory that still are under discussion: source term nonextensive transport equation. Based on a simple system, show nonadditivity is direct consequence phase ...