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Random walks with strongly correlated memory and applications to biology

Grant number: 18/15308-4
Support type:Regular Research Grants
Duration: December 01, 2018 - November 30, 2021
Field of knowledge:Physical Sciences and Mathematics - Physics
Cooperation agreement: University of Manchester
Mobility Program: SPRINT - Projetos de pesquisa - Mobilidade
Principal Investigator:Marco Antonio Alves da Silva
Grantee:Marco Antonio Alves da Silva
Principal investigator abroad: Sergei Fedotov
Institution abroad: University of Manchester, England
Home Institution: Faculdade de Ciências Farmacêuticas de Ribeirão Preto (FCFRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
Associated research grant:16/03918-7 - Characterization and memory effects in stochastic processes, AP.R

Abstract

The main purposes of this project are the development of new models of non-linear non-Markovian discrete and continuous time random walks with strong memory dependence in terms of long range time-memory correlations and their application to biological problems. Specifically, we will focus on systems with full and damaged memory, the latter being those in which the recent memory has been erased. We will apply newly developed random walk models to explain observed phenomena of anomalous sub- and super-diffusive transport inside living cells. The question of mapping non-Markovian processes in Markovian processes will be explored both in 1D and 2D. We will tackle the emergence of Lévy distributions from random walk processes with strong memory dependence and explore non-linear cooperative effects and emergence behaviour arising from interactions of random walkers with memory. (AU)