Analytical Description of Hadron-Hadron Scattering via Principle of Minimum Distance in Space of States

In this paper an analytical description of the hadron-hadron scattering is presented by using PMD-SQS-optimum principle in which the differential cross sections in the forward and backward c.m. angles are considered fixed from the experimental data. Experimental tests of the PMD-SQS-optimal predictions, obained by using the available phase shifts, as well as from direct experimental data, are presented. It is shown that the actual experimental data for the differential cross sections of all principal hadron-hadron [nucleon-nucleon, antiproton-proton, mezon-nucleon] scatterings at all energies higher than 2 GeV, can be well systematized by PMD-SQS predictions.Comment: 18 pages, 10 figure

Convergence rate of Tsallis entropic regularized optimal transport

In this paper, we consider Tsallis entropic regularized optimal transport and discuss the convergence rate as the regularization parameter $\varepsilon$ goes to $0$. In particular, we establish the convergence rate of the Tsallis entropic regularized optimal transport using the quantization and shadow arguments developed by Eckstein--Nutz. We compare this to the convergence rate of the entropic regularized optimal transport with Kullback--Leibler (KL) divergence and show that KL is the fastest convergence rate in terms of Tsallis relative entropy.Comment: 21 page

Neural complexity -- Statistical-mechanical approach of human electroencephalograms

The brain is a complex system whose understanding enables potentially deeper approaches to mental phenomena. Dynamics of wide classes of complex systems have been satisfactorily described within $q$-statistics, a current generalization of Boltzmann-Gibbs (BG) statistics. Here, we study human electroencephalograms of typical human adults (EEG), very specifically their inter-occurrence times across an arbitrarily chosen threshold of the signal (observed, for instance, at the midparietal location in scalp). The distributions of these inter-occurrence times differ from those usually emerging within BG statistical mechanics. They are instead well approached within the $q$-statistical theory, based on non-additive entropies characterized by the index $q$. The present method points towards a suitable tool for quantitatively accessing brain complexity, thus potentially opening useful studies of the properties of both typical and altered brain physiology