Interacting processes with variable range memory in neurobiological models

• Grant number: 15/11579-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2015
• End date: November 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Pablo Augusto Ferrari
• Grantee: Aline Duarte de Oliveira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat, AP.CEPID

Abstract

We consider non Markovian stochastic processes describing the time evolution of a countable system of neurons in both discrete and continuous time. The evolutionof the process can be informally described as follows. For each neuron the rate (incontinuous time) or the probability (in discrete time) of spiking depends on the time evolution of the entire system after its last spike time. When a neuron spikes, its membrane potential is immediately reset to a resting value. Simultaneously, the membrane potential of the neurons which are influenced by it receive an additional value. This reset of potential in the spiking neuron acts as a renewal event making the stochastic chains with memory of variable length good candidates to model a single neuron. The goal of this project is continue the study and development of these classes of stochastic processes aiming the rigorous mathematical description of the brain activity. To this end, we propose a set of new steps to be studied in the classes presented here.