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Interacting processes with variable range memory in neurobiological models

Grant number: 16/17791-9
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): December 01, 2016
Effective date (End): December 31, 2017
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 evolution of the process can be informally described as follows. For each neuron the rate (in continuous time) or theprobability (in discrete time) of spiking depends on the time evolution of the entire system after its last spiking 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. This project intent to continue the study of theses sort of classes of stochastic processes by means of rigorous mathematical description of the brain activity. To this end, we propose a set of new problems to be studied in the classes presented here. (AU)

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Scientific publications (5)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
DUARTE, ALINE; LOCHERBACH, EVA; OST, GUILHERME. Stability, convergence to equilibrium and simulation of non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels. ESAIM-PROBABILITY AND STATISTICS, v. 23, p. 770-796, . (16/17791-9, 13/07699-0, 16/17789-4)
CHEVALLIER, J.; DUARTE, A.; LOCHERBACH, E.; OST, G.. Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels. Stochastic Processes and their Applications, v. 129, n. 1, p. 1-27, . (13/07699-0, 16/17791-9, 16/17789-4)
HERNANDEZ, NOSLEN; DUARTE, ALINE; OST, GUILHERME; FRAIMAN, RICARDO; GALVES, ANTONIO; VARGAS, CLAUDIA D.. Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data. SCIENTIFIC REPORTS, v. 11, n. 1, . (16/22053-7, 13/07699-0, 16/17791-9, 16/17789-4)
DUARTE, ALINE; FRAIMAN, RICARDO; GALVES, ANTONIO; OST, GUILHERME; VARGAS, CLAUDIA D.. Retrieving a Context Tree from EEG Data. MATHEMATICS, v. 7, n. 5, . (16/17791-9, 13/07699-0, 16/17789-4)
DUARTE, ALINE; GALVES, ANTONIO; LOCHERBACH, EVA; OST, GUILHERME. Estimating the interaction graph of stochastic neural dynamics. BERNOULLI, v. 25, n. 1, p. 771-792, . (16/17791-9, 13/07699-0, 16/17789-4)

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