Modeling neuronal networks as systems of interacting point processes with memory of variable length

• Grant number: 22/07386-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: July 01, 2022
• End date: July 01, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Antonio Carlos Roque da Silva Filho
• Grantee: Kádmo de Souza Laxa
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated research grant: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat, AP.CEPID
• Associated scholarship(s): 23/12335-9 - Modeling neuronal networks as systems of interacting point processes with memory of variable length: models comparison and mean-field limits, BE.EP.PD

Abstract

In this project I continue the research I developed in my PhD project and presented in my articles Laxa (2022) and Galves and Laxa (2022). Laxa (2022) studies a system of interacting point processes with memory of variable length modeling a finite but large network of spiking neurons with leakage. Associated to each neuron there are two point processes, describing its successive spiking and leakage times. We prove that the system has a metastable behavior as the population size diverges. This means that the time at which the system gets trapped by the list of null membrane potentials suitably re-scaled converges to a mean one exponential random time. Galves and Laxa (2022) studies a new model for a highly polarized social network. In this system, the point processes are marked and indicate the successive times in which a social actor express a "favorable" or "contrary" opinion on a certain subject. For this model, we prove that when the polarization coefficient diverges, the social network reaches instantaneous consensus and this consensus has a metastable behavior. The model studied in Galves and Laxa (2022) is an interesting mathematical extension of theclass of networks of spiking neurons introduced by Galves and Löcherbach (2013) and De Masi et al. (2014). One of the two main lines of research of RIDC Neuromat is the mathematical modeling and statistical analysis of neuronal networks. To contribute to the development of this direction of research on the class of models introduced by Galves and Löcherbach (2013) and De Masi et al. (2014), I intend to approach the following questions: metastability, phase transition, perfect simulation and estimation of the graph of interaction between neurons. (AU)

Scientific publications

(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)

GALVES, ANTONIO; LAXA, KADMO. Fast consensus and metastability in a highly polarized social network. Stochastic Processes and their Applications, v. 177, p. 24-pg., 2024-08-23. (13/07699-0, 22/07386-0, 23/12335-9)

LOECHERBACH, EVA; LAXA, KADMO. Propagation of Chaos and Phase Transition in a Stochastic Model for a Social Network. Journal of Statistical Physics, v. 191, n. 12, p. 34-pg., 2024-11-25. (23/12335-9, 22/07386-0)

LAXA, KADMO DE S.. Metastability in a Stochastic System of Spiking Neurons with Leakage. Journal of Statistical Physics, v. 190, n. 2, p. 31-pg., 2023-02-01. (13/07699-0, 22/07386-0)