Dynamic effects and information quantifiers of statistical memory of MEG's signals at photosensitive epilepsy.

The time series analysis of magnetoencephalographic (MEG) signals is very important both for basic brain research and for medical diagnosis and treatment. Here we discuss the crucial role of statistical memory effects (ME) in human brain functioning with photosensitive epilepsy (PSE). We study two independent statistical memory quantifiers that reflect the dynamical characteristics of neuromagnetic brain responses on a flickering stimulus of different colored combinations from a group of control subjects, which are contrasted with those from a patient with PSE. We analyze the frequency dependence of two memory measures for the neuromagnetic signals. The strong memory and the accompanying transition to a regular and robust regime of the signals' chaotic behavior in the separate areas are characteristic for a patient with PSE. This particularly interesting observation most likely identifies the regions of the protective mechanism in a human organism against occurrence of PSE.

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.

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 (EQ's) and technogenic explosions (TE's). EQ's 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 TE's from the weak EQ's. 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 Earth's core (IV). The estimation of states I, II, and III has been made on the particular examples of Turkey (1999) EQ's, state IV has been taken as an example of Earth's 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 TE's from weak EQ's, have been developed.

Stochastic dynamics of time correlation in complex systems with discrete time

In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy S(i)(t) where i=0,1,2,3,ellipsis, as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,ellipsis). The set of functions S(i)(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,ellipsis) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function S(i)(t) for time correlation (i=0) and time memory (i=1,2,3,ellipsis). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG's shows convincing evidence for a non-Markovian phenomemena associated with a peculiarities in short- and long-range scaling. This method may be of use in distinguishing healthy from pathologic data sets based in differences in these non-Markovian properties.