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Reconstruction of Jump-diffusion Model from Epileptic Brain Signal and Pyramidal Neurons Potential in an Electric Fish

Shafaee, Yasaman | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55229 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rahimi Tabar, Mohammad Reza
  7. Abstract:
  8. Complex systems involve a large number of degrees of freedom and consist of many components. Interactions of these components with each other, or with an external force, play a significant role in the collective behavior of the complex system.We come across complex systems in many different fields of study including neuroscience, climatology, studying stock markets, etc. The non-linearity of the interactions between their components is what they have in common. Interesting macro-scale properties can be observed in a complex system, as a result of the collective behavior of the system components. We usually focus on studying a group of components in a system, rather than a single component, to study these properties.We usually gain a valid perspective of the system dynamic by studying these macro-scale properties.Langevin equation is usually used for modelling fluctuations in complex systems. By using such an equation, a deterministic factor (drift term) and a stochastic factor (diffusion term) can be considered for the fluctuations in time series measured in a complex system. However, there are cases such as studying electroencephalogram signals recorded from the epileptic brain, in which we are dealing with discontinuous stochastic processes. In these cases, large fluctuations are observed in the system. The Langevin equation cannot model these fluctuations. As a result, we need to add a term to the Langevin equation and use it in a more
    general form. This correcting term is the jump term and includes characteristics related to the large fluctuations in the time series. In this thesis, reconstruction of the jump-diffusion model is performed for studying the brain dynamics of epilepsy patients and the local field potential of membrane voltage fluctuations in pyramidal neurons in an electric fish
  9. Keywords:
  10. Electroencphalogram Signal ; Langevin Equation ; Stochastic Process ; Epilepsy ; Jump-Diffusion Model ; Complex System

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