### Article

## On the mixing time in the Wang-Landau algorithm

We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the mixing time of the Markov chain. We estimate numerically the dependence of the mixing time on the lattice size, and extract the mixing exponent.

This article concerns the problem of predicting the size of company's customer base in case of solving the task of managing its clients. The author purposes a new approach to segment-oriented predicting the size of clients based on adopting the Staroverov's employees moving model. Besides the article includes the limitations of using this model and its modification for each type of relations of the client and the company.

The aim of this work is to analyze a circle of questions related to the notion of recurrence in general general Markov chains. Being well known in two very different subfields of random systems: lattice random walks and ergodic theory of continuous selfmaps, the recurrence property is next to being neglected in general theory of Markov chains (perhaps except for a few notable exceptions which we will discuss in detail).

We use a Markov chains models for the analysis of Russian stock market. First problem studied in the paper is the multiperiod portfolio optimization. We show that known approaches applied for the Russian stock market produce the phenomena of non stability and propose a new methods in order to smooth it. The second problem addressed in the paper is a structural changes on the Russian stock market after the financial crisis of 2008.We propose a hidden Markov chains model to analyse a structural changes and apply it for the Russian stock market.

The celebrated Nagel–Schreckenberg model allows to study a reasonably large class of one-dimensional traffic flow models with parallel updates. Unfortunately further generalizations of this construction turn out to be not especially fruitful. Namely, numerical simulations of such generalizations did not demonstrate stable behavior qualitatively different from the original model, and more to the point their mathematical treatment is still not available even up to nowadays. I'll discuss several features of these models which partially explain the failure of both numerical and mathematical attempts to study generalizations of the Nagel–Schreckenberg model.

The textbook has passed practical tests and written on the basis of the readable authors for many years. Presented in textbook materials give students orientation in the solution of many practical problems in a number of areas, constitute the initial level to obtain a broader and deeper education in the field of probability theory. The book provides an overview of the theory of stochastic processes, detailed material on the theory of Markov processes with discrete time (Markov chains) and continuous-time. In addition to the solved problems for each Chapter of the textbook suggested problems to solve and theoretical questions to test the quality of the learning material.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.