arXiv subjects

K. Topolski

Publications and source records attributed to K. Topolski.

6 recordsLinked to original sources

arXiv2014

Hyperbolic statistics and entropy loss in the description of gene distributions

Zipf's law implies the statistical distributions of hyperbolic type, which can describe the properties of stability and entropy loss in linguistics. We present the information theory from which follows that if the system is described by distributions of hyperbolic type it leads to the possibility of entropy loss. We present the number of repetitions of genes in tne genomes for some bacteria, as Borelia burgdorferi and Escherichia coli. Distributions of repetitions of genes in genome appears to be represented by distributions of hyperbolic type.

physics.bio-ph↗

arXiv2012

Some remarks about the domain statistics in the Ising model

In this paper we describe a relation between the Zipf law and statistical distributions for the Fortuin-Kasteleyn clusters in the Ising model.It has been shown,that histograms for fixed domain masses present the right-skewed distributions.

cond-mat.stat-mech↗

arXiv2009

Hausdorff dimension and hierarchical system dynamics

We show that Hausdorff dimension may be used to distinguish different dynamics of therelaxation in hierarchical systems. We examine the hierarchical systems following the temperature-dependent power-law decay and the Kohlrausch law. For our purposes, we consider a Lévy stochastic processes on p-adic integer numbers.

cond-mat.stat-mech↗

arXiv2009

Statistical description of domains in the Potts model

The Zipf power law and its connection with the inhomogeneity of the system is investigated. We describe the statistical distributions of the domain masses in the Potts model near the temperature-induced phase transition. We found that the statistical distribution near the critical point is described by the power law form with a long tail, while beyond the critical point the power law tail is suppressed.

cond-mat.stat-mech↗

arXiv2008

Statistical description of magnetic domains in the Ising model

We use the Mandelbrot-Zipfs power law for the description of the inhomogenity of the spin system. We describe the statistical distributions of the domain's masses in the Ising model near the phase transition induced by the temperature. The statistical distribution near the critical point appears to be of the Pareto type.

cond-mat.stat-mech↗

arXiv2005

Random walk on p-$adics in glassy systems

We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical glassy systems. For our purposes, we specify the Markov stochastic process considered by S. Albeverio and W. Karwowski. As a result we have obtained a random walk on p-adic integer numbers, which provide the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.

cond-mat.dis-nn↗