arXiv:physics/0611285v1 physics.med-ph 29 Nov 2006 STRONG MEMORY IN TIME SERIES OF HUMAN MAGNETOENCEPHALOGRAMS CAN IDENTIFY PHOTOSENSITIVE EPILEPSY R. M. Yulmetyev,D. G. Yulmetyeva, and E. V. Khusaenova Department of Physics, Kazan State University, Kremlevskaya Street, 18 Kazan, 420008 Russia and Department of Physics, Kazan State Pedagogical University, Mezhlauk Street, 1 Kazan, 420021 Russia P. H anggi Department of Physics,University of Augsburg, Universit atsstrasse 1, D-86135 Augsburg, Germany S. Shimojo Division of Biology, CalTech, Pasadena, CA 91125 USA J. Bhattacharya Comission for Scientifi c Visualisation, Austrian Academy of Sciences, Tech Gate, Vienna A - 1220, Austria and Department of Psychology, Goldsmits College, University of London, New Cross , London, SE14 6NW UK To discuss the salient role of the statistical memory eff ects in the human brain functioning we have analyzed a set of stochastic memory quantifi ers that refl ects the dynamical characteristics of neuromagnetic brain responses to a fl ickering stimulus of diff erent color combinations from a group of control subjects which is contrasted with those from a patient with photosensitive epilepsy (PSE). We have discovered the emergence of strong memory and the accompanying transition to a regular and robust regime of chaotic behavior of the signals in the separate areas for a patient with PSE. This fi nding most likely identifi es the regions of the location the protective mechanism in a human organism against occurrence of PSE. PACS numbers: 05. 45. Tp; 87. 19. La; 89. 75. -k Increasing attention has been paid recently to the study of statistical memory eff ects in random processes that originate from nature by means of nonequilibrium statistical physics. The role of memory has its roots in natural sciences since 1906 when the famous Russian mathematician Markov wrote his fi rst paper on the theory of Markov Random Processes (MRP) 1. His theory is based on the notion of an instant loss of memory from the prehistory (memoryless property) of random processes. In contrast, there are an abundance of physical phenomena and processes which can be characterized by statistical memory eff ects: kinetic and relaxation processes in gases 2 and plasma 3, condensed matter physics (liquids 4, solids 5, and superconductivity 6), astrophysics 7, nuclear physics 8, quantum 9 and classical 10 physics, to name only a few. At present, we can make use of a variety of statistical Electronic address: rmytheory.kazan-spu.ru 2 methods for the analysis of the memory eff ects in diverse physical systems. Typical such schemes are Zwanzig-Moris kinetic equations 11, generalized master equations and corresponding statistical quantifi ers 12, Lees recurrence relation method 13, the generalized Langevin equation (GLE) 14, etc. In this paper we shall demonstrate that the presence of statistical memory eff ects is of salient importance for the functioning of healthy physiological systems. Particularly, it can imply that the presence of large memory times scales in the stochastic dynamics of discrete time series can characterize pathological (or catastrophical) violation of salutary dynamic states of the human brain. As an example, we will demonstrate here that the emergence of strong memory time scales in the chaotic behavior of neuromagnetic responses of human brain as recorded by MEG is accompanied by the likely initiation and the existence of PSE. First consider a simplifi ed version of the Markov processes.Let us introduce the conditional probability K1(x1,t1|x2,t2) that x is found in the range (x2,x2+ dx2) at x2, if x had the value x1at t1.For the Markov random process the conditional probability that x lies in the range (xn,xn+ dxn) at tngiven that x had the values x1,x2,.xn1at times t1,t2,tn1depends only on xn1is as follows: Kn1(x1,t1;x2,t2;.xn1,tn1|xn,tn) = K1(xn1,tn1|xn,tn). The equation states that, given the state of a Markov process at some times tn1 1 one can observe a complex dynamics characterized by short-ranged temporal memory scales. In the limit these processes assume a -like memory with , . When , 1 one deals with a situation with moderate memory strength, and the case with both , 1 typically constitutes a more regular and robust process possessing strong memory features. 0200400600 0.5 0 0.5 1 M0 0200400600 0.5 0 0.5 1 M1 0200400600 0.5 0 0.5 1 M2 0200400600 0.5 0 0.5 1 M0 0200400600 0.5 0 0.5 1 M1 0200400600 0.5 0 0.5 1 M2 t/ t/ t/ t/ t/ t/ Figure 1: Time dependence of TCF M0 (t)(i = 0) and fi rst two subordinate MFs Mi(t),i = 1,2 for a healthy subject (No. 6) (blue) and for a patient (red) with PSE for the SQUIDs number n = 10, = 0,2 ms. The drastic distinctions of Mi(t) in a healthy person as compared to a patient with PSE is clearly detectable. They consist in the appearance of signifi cant long-ranged oscillations in a healthy subject and the suppression of high