Renat M. Yulmetyev

Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis

The basic scientific point of this paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature. One example of such kinds of signals is presented by seismograms containing recordings of earthquakes (EQs) and technogenic explosions (TEs). EQs are among the most dramatic phenomena in nature. We propose here a discrete stochastic model for possible solution of a problem of strong EQ forecasting and differentiation of TEs from the weak EQs. Theoretical analysis is performed by two independent methods: by using statistical theory of discrete non-Markov stochastic processes [Phys. Rev. E 62, 6178 (2000)] and the local Hurst exponent. The following Earth states have been considered among them: before (Ib) and during (I) strong EQ, during weak EQ (II) and during TE (III), and in a calm state of Earths core (IV). The estimation of states I, II, and III has been made on the particular examples of Turkey (1999) EQs, state IV has been taken as an example of Earths state before underground TE. Time recordings of seismic signals of the first four dynamic orthogonal collective variables, six various planes of phase portrait of four-dimensional phase space of orthogonal variables and the local Hurst exponent have been calculated for the dynamic analysis of states of systems I-IV. The analysis of statistical properties of seismic time series I-IV has been realized with the help of a set of discrete time-dependent functions (time correlation function and first three memory functions), their power spectra, and the first three points in the statistical spectrum of non-Markovity parameters. In all systems studied we have found a bizarre combination of the following spectral characteristics: the fractal frequency spectra adjustable by phenomena of usual and restricted self-organized criticality, spectra of white and color noises and unusual alternation of Markov and non-Markov effects of long-range memory, detected earlier [J. Phys. A 27, 5363 (1994)] only for hydrodynamic systems. Our research demonstrates that discrete non-Markov stochastic processes and long-range memory effects play a crucial role in the behavior of seismic systems I-IV. The approaches, permitting us to obtain an algorithm of strong EQ forecasting and to differentiate TEs from weak EQs, have been developed.

Physical criterion of the degree of non-Markovity of relaxation processes in liquids

Abstract The microscopic parameter characterizing the degree of non-Markovity of irreversible processes is introduced. It is shown that the structure relaxation process in liquids is essentially non-Markovian in a wide range of wave vectors excluding the region near the first maximum of the static structure factor.

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 Parkinsons 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.

Analysis of biomedical signals by flicker-noise spectroscopy: Identification of photosensitive epilepsy using magnetoencephalograms

The flicker-noise spectroscopy (FNS) approach is used to determine the dynamic characteristics of neuromagnetic responses by analyzing the magnetoencephalographic (MEG) signals recorded as the response of a group of control human subjects and a patient with photosensitive epilepsy (PSE) to equiluminant flickering stimuli of different color combinations. Parameters characterizing the analyzed stochastic biomedical signals for different frequency bands are identified. It is shown that the classification of the parameters of analyzed MEG responses with respect to different frequency bands makes it possible to separate the contribution of the chaotic component from the overall complex dynamics of the signals. It is demonstrated that the chaotic component can be adequately described by the anomalous diffusion approximation in the case of control subjects. On the other hand, the chaotic component for the patient is characterized by a large number of high-frequency resonances. This implies that healthy organisms can suppress the perturbations brought about by the flickering stimuli and reorganize themselves. The organisms affected by photosensitive epilepsy no longer have this ability. This result also gives a way to simulate the separate stages of the brain cortex activity in vivo. The examples illustrating the use of the “FNS device” for identifying even the slightest individual differences in the activity of human brains using their responses to external standard stimuli show a unique possibility to develop the “individual medicine” of the future.

Analysis of the dynamics of liquid aluminium: recurrent relation approach

By use of the recurrent relation approach (RRA) we study the microscopic dynamics of liquid aluminium at T = 973 K and develop a theoretical model which satisfies all the corresponding sum rules. The investigation covers the inelastic features as well as the crossover of our theory into the hydrodynamical and the free-particle regimes. A comparison between our theoretical results with those following from a generalized hydrodynamical approach is also presented. In addition to this we report the results of our molecular dynamics simulations for liquid aluminium, which are also discussed and compared to experimental data. The results obtained reveal (i) that the microscopical dynamics of density fluctuations is defined mainly by the first four even frequency moments of the dynamic structure factor, and (ii) the inherent relation of the high-frequency collective excitations observed in experimental spectra of dynamic structure factor S(k,ω) with the two-, three- and four-particle correlations.

Collective dynamics in liquid aluminum near the melting temperature: Theory and computer simulation

The microscopic collective dynamics of liquid aluminum near the melting temperature has been studied using two independent methods: first, using a theoretical approach developed in terms of the Zwanzig-Mori formalism and based on Bogolyubov’s idea of reduced description of relaxation processes in liquids; second, using molecular dynamics simulation. The X-ray inelastic scattering spectra obtained with the theoretical approach and computer simulation are compared with experimental data. The high-frequency acoustic excitations that appear on microscopic spatial scales in liquid aluminum are found to be mainly caused by two-, three-, and four-particle interactions.

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 (Phys. Rev. E 62 (5) (2000) 6178, Phys. Rev. E 64 (2001) 066132, Phys. Rev. E 65 (2002) 046107, Physica A 303 (2002) 427). 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 olds), young people (from 21 up to 29 year olds), 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 Parkinsons disease. We have found out distinct differences between the five submitted groups. On this basis we offer a new method of diagnostics and forecasting Parkinsons disease.

New evidence for the idea of timescale invariance of relaxation processes in simple liquids: The case of molten sodium

The idea of the timescale invariance of relaxation processes in liquids (Yulmetyevetal 2001Phys. Rev. E64 057101; 2002JETPLett.76 147) is used to analyse the short-wave collectiv ee xcitation in liquid sodium, as recently measured by means of very-high-energy-resolution inelastic x-ray scattering (Scopigno et al 2002 Phys. Rev. E 65 031205). The dynamic structure factor, S(Q ,ω ), calculated on the basis of this idea is in very good agreement with the experimental data in the wavevector range from 1.5 to 14. 6n m −1 ,w here pronounced collective excitations exist. The frequency dependence of the non∗

Time-scale invariance of relaxation processes of density fluctuation in slow neutron scattering in liquid cesium.

The realization of the idea of time-scale invariance for relaxation processes in liquids has been performed by the memory functions formalism. The best agreement with experimental data for the dynamic structure factor S(k,omega) of liquid cesium near melting point in the range of wave vectors (0.4 A(-1) < or = k < or = 2.55 A(-1)) is found with the assumption of concurrence of relaxation scales for memory functions of third and fourth orders. Spatial dispersion of the first four points in the spectrum of the statistical parameter of non-Markovity epsilon(i)(k,omega) at i=1,2,3,4 has allowed us to reveal the non-Markov nature of collective excitations in liquid cesium, connected with long-range memory effect.

Intensity approximation of random fluctuation in complex systems

The Markov and non-Markov processes in complex systems are examined with the help of dynamical information Shannon entropy method. Here we consider the essential role of two mutually independent channels of entropy involving creation of correlation and annihilation of correlation. The developed method has been used to analyze the intensity fluctuation of the complex systems of various nature: in psychology (to analyze numerical and pattern short-time human memory, to study the effect of stress on the parameters of the dynamical taping-test) and in cardiology (to analyze the random dynamics of RR-intervals in human ECGs and to diagnose various diseases of human cardiovascular systems). The received results show that the application of intensity approximation allows to improve essentially the diagnostics of parameters in the evolution of human dynamic states.