Non-Markov stochastic dynamics of real epidemic process of respiratory infections

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.Comment: 18 pages, 8figs, 1 table

Stratification of the phase clouds and statistical effects of the non-Markovity in chaotic time series of human gait for healthy people and Parkinson patients

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. 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 71 to 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.Comment: 15 pages, 5 figs, 3 Table

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres

Structure of Zinc Coating on Steels Formed by Diffusion Saturation in Nitrogen-Containing Atmosphere

Diffusion technique of metallization is applied for receiving of zinc coatings on low-carbon steel with transitional zone. Structure of diffusion zinc layers after saturation of 09Mn2Si steel in ammonia at different temperatures is examined. Effects on saturation temperature on thickness of diffusion layers are discovered. Process at 600⁰C forms diffusion layers with high strengthening level and with smooth microhardness profiles. Elements (Fe, Zn, N) spectrums are analyzed, and phase composition of zinc coating and of transitional zone is determined

Surface Strengthening of High-Alloyed Martensitic Steel by Staged Nitriding

Gas nitriding processes with cyclical rotation of ammonia and ammonia/air atmospheres are suggested for surface strengthening of martensitic Cr-Ni-W-Mo-V steel. One-, two-, and three-staged processes were studied differing by gas atmospheres at the final stage of processes. Microstructure and phase composition of received diffusion layers were examined. Results of microhardness, wear and impact toughness tests are discussed in correspondence with the layers structure