Data-Based Reconstruction of Jump-Diffusion Processes Using Statistical Moments with Application to Studying Dynamics of Bacteria Trapped in Optical Tweezers and Neuron Membrane Voltage

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Parvandi, Zohreh | 2024

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 56944 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Seyed Reihani, Nader; Rahimi Tabar, Mohammad Reza
Abstract:
Reconstruction of stochastic dynamical equations from measured timeseries of complex systems plays a crucial role in retrieving dynamic information and studying macroscopic states of such systems. This method which has been pursued for decades is practical in diverse fields like physics, biology, ecology, economics, social science, neuroscience and so on. To obtain stochastic dynamic equation, we have to calculate Kramers-Moyal coefficients from Markovian processes measured time series. We aim to propose new method for deriving these coefficients which is more accurate than two current methods, namely the histogram and kernel methods. In this dissertation, we studied dynamic equations of jump-diffusion process of bacteria trapped in optical tweezers while adding alcohol and potential fluctuations of neuronal membrane
Keywords:
Jump-Diffusion Model ; Kramers-Moyal Coefficient ; Stochastic Process ; Optical Tweezer ; Membrane Potential