Macroscopic thermodynamics of equilibrium characterized by power-law canonical distributions

Macroscopic thermodynamics of equilibrium is constructed for systems obeying power-law canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is complementary to the Gibbs theorem for the celebrated exponential canonical distributions of systems in contact with a heat bath. Thereby, a thermodynamic basis is provided for power-law phenomena ubiquitous in nature.Comment: 12 page

Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Renyi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.Comment: 20 pages, no figures, the disappeared "primes" on the distributions are added. Also, Eq. (65) is correcte

Support Vector Machines in Analysis of Top Quark Production

Multivariate data analysis techniques have the potential to improve physics analyses in many ways. The common classification problem of signal/background discrimination is one example. The Support Vector Machine learning algorithm is a relatively new way to solve pattern recognition problems and has several advantages over methods such as neural networks. The SVM approach is described and compared to a conventional analysis for the case of identifying top quark signal events in the dilepton decay channel amidst a large number of background events.Comment: 8 pages, 8 figures, to be published in the proceedings of the "Advanced Statistical Techniques in Particle Physics" conference in Durham, UK (March, 2002

The CPTPP and Digital Trade: Embracing E-Commerce Opportunities for SMEs in Japan and Canada

One of the most innovative features of the CPTPP is its material on digital trade, especially its chapter on e-commerce which contains a number of provisions aimed at enhancing this vital sector of the economy by eliminating distortive trade barriers such as restrictions on data transfer and data localization requirements. Such provisions should be important to the CPTPP’s two largest parties: Canada and Japan, both of which are highly advanced economies seeking to enhance their digital trade capacity across the Pacific Rim. This paper explores the main features of the CPTPP concerning digital trade from the perspective of Small and Medium Sized Enterprises (SMEs) in Canada and Japan. Such businesses have a poor track record of e-commerce uptake and may be disadvantaged relative to their larger competitors which enjoy dominance in the online marketplace. Whether or not the CPTPP will assist these businesses while striking the right balance between an open internet and safeguarding of issues such as privacy is a matter of some debate

Geometry of escort distributions

Given an original distribution, its statistical and probabilistic attributs may be scanned by the associated escort distribution introduced by Beck and Schlogl and employed in the formulation of nonextensive statistical mechanics. Here, the geometric structure of the one-parameter family of the escort distributions is studied based on the Kullback-Leibler divergence and the relevant Fisher metric. It is shown that the Fisher metric is given in terms of the generalized bit-variance, which measures fluctuations of the crowding index of a multifractal. The Cramer-Rao inequality leads to the fundamental limit for precision of statistical estimate of the order of the escort distribution. It is also quantitatively discussed how inappropriate it is to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics.Comment: 12 pages, no figure