Complex Dynamics of Epileptic Brain and Turbulence :From Time Series to Information Flow

Anvari, Mehrnaz | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47665 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rahimi Tabar, Mohammad Reza; Karimipour, Vahid
  7. Abstract:
  8. Complex systems are composed of a large number of subsystems behaving in a collective manner. In such systems, which are usually far from equilibrium, collective behavior arises due to self-organization and results in the formation of temporal, spatial, spatio-temporal and functional structures. The dynamics of order parameters in complex systems are generally non-stationary and can interact with each other in nonlinear manner. As a result, the analysis of the behavior of complex systems must be based on the assessment of the nonlinear interactions, as well as the determination of the characteristics and the strength of the fluctuating forces. This leads to the problem of retrieving a stochastic dynamical system from data.Much efforts have been devoted to address the question of how to describe a dynamical system by a suitable analysis of the experimental data. The answer to this question can yield important information on the dynamical properties of the system under consideration. The problem of dynamical noise, i.e., fluctuations that interfere with the dynamical evolution, has been addressed recently in much detail.There are two possible approaches to investigate the dynamics of complex systems. In the first approach, the stochastic behavior of order parameters are assumed to belongs to continuous stochastic process. In this approach the drift and diffusion coefficients of a Kolmogorov equation (also called the Fokker-Planck equation) can be estimated by a parameter-free manner. The drift and diffusion coefficients then define a stochastic process that can be described by a Langevin equation.The second approach is based on the information theory. In this approach using the causality concept one can figure out that how subsystems interact with each other. In this view the stochastic behaviors of subsystems can be explained by the flow of information between them.In this thesis, we investigate the dynamical properties of two well-known complex systems, epileptic brain and turbulent flow, using the methods developed in stochastic processes and information theory.We show that the dynamics of epileptic brain can be described by a stochastic dynamics including the jumps and their dynamics does not follow a continuous diffusive process. Indeed jumps in stochastic processes can be considered as extreme events which are discontinuous events with some distributed amplitudes. With respect to heavy tail statistics both volatility (diffusion coefficient) and jumps could have similar impact. Disentangling the effects caused by the volatility from the effects caused by jumps is a main problem in detailed understanding of stochastic dynamics of complex systems. We introduce a nonparametric method to address this general problem and disintegrate the stochastic behavior of epileptic brain dynamics into its deterministic trend (drift), stochastic diffusive contribution (volatility) and short-term jumpy dynamics, and determine the jump amplitude variance. Our empirical study shows that during the seizure-free interval the dynamics of the seizure-generating brain region appears to be a stochastic process with non-vanishing jump rate and is characterized by small mean diffusion and small mean jump amplitudes. From point of view of the information theory, we study the information flow in length scales of three-dimensional turbulence in the inertial range. We show the direction of information flow is from large to small length scales in the inertial range similar to the known energy 405 cascade picture of turbulence. Such analysis yields valuable information to understanding of the extreme events of complex dynamical systems
  9. Keywords:
  10. Turbulence ; Epilepsy ; Information Theory ; Jump-Diffusion Model ; Complex System ; Time Series

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