In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes [31]- [34]. The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year oulds), young people (from 21 up to 29 year oulds), elderly persons (from 71to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused by Parkinson's disease. We have found out distinct differencies between the five submitted groups. On this basis we offer a new method of diagnostics and forecasting Parkinson's disease.
The study of social networks and especially of the stochastic dynamics of the diseases spread in human population has recently attracted considerable attention in statistical physics. In this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections (ARTI) by means of the theory of discrete non-Markov stochastic processes. We use the results of our last theory (Phys. Rev. E 65, 046107 (2002)) to study statistical memory effects, long -range correlation and discreteness in real data series, describing the epidemic dynamics of human ARTI infections and grippe. We have carried out the comparative analysis of the data of the two infections (grippe and ARTI) in one of the industrial districts of Kazan, one of the largest cities of Russia. The experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders, the phase portraits of the four first dynamic variables, the three first points of the statistical non-Markov parameter and the locally averaged kinetic and relaxation parameters. The received results give an opportunity to provide strict quantitative description of the regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory. They also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network.The functioning of network-organized statistical systems essentially depends on the nature of interaction between their elements. It is especially due to the effect of disease-causing contacts and topology of networks. This reason as well as the variety of the displayed nonlinear behavior have made this problem the subject of several studies by fundamental methods of statistical physics. To analyse the epidemic and disease dynamics complexity, it is necessary to understand the basic principles and notions of its distribution in long-time memory social media.Here we consider the problem from a theoretical and practical viewpoint and present the quantitative evidence confirming the existence of stochastic longrange memory and robust chaos in a real time series of respiratory infections of human upper respiratory track. We also discuss the implications of discrete non-Markov stochastic processes in real social complex systems from the point of view of the recent theory (Phys. Rev. E 65, 046107 (2002)).
In this paper, the non-Markov statistical processes and long-range memory e ects in human sensorimotor coordination are investigated. The theoretical basis of this study is the statistical theory of non-stationary discrete non-Markov processes in complex systems (Phys. Rev. E 62, 6178 (2000)). The human sensorimotor coordination was experimentally studied by means of standard dynamical tapping test on the group of 32 young peoples with tap numbers up to 400. This test was carried out separately for the right and the left hand according to the degree of domination of each brain hemisphere. The numerical analysis of the experimental results was made with the help of power spectra of the initial time correlation function, the memory functions of low orders and the ÿrst three points of the statistical spectrum of non-Markovity parameter. Our observations demonstrate, that with the regard to results of the standard dynamic tapping-test it is possible to divide all examinees into ÿve di erent dynamic types. We have introduced the con ict coe cient to estimate quantitatively the order-disorder e ects underlying life systems. The last one re ects the existence of disbalance between the nervous and the motor human coordination. The suggested classiÿcation of the neurophysiological activity represents the dynamic generalization of the well-known neuropsychological types and provides the new approach in a modern neuropsychology.
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