Modeling study of criticality in neural networks

• Grant number: 14/17850-0
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: November 01, 2014
• End date: April 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Jose Antonio Brum
• Grantee: Elohim Fonseca dos Reis
• Supervisor: Thierry Mora
• Host Institution: Instituto de Física Gleb Wataghin (IFGW). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: École Normale Supérieure, Paris (ENS), France
• Associated to the scholarship: 13/25361-6 - Criticality on neural networks, BP.MS

Abstract

Neurons encode information in the form of short action potentials or spikes and, considering a population of neurons, the combination of spikes and silences forms a neural "codeword". The elements, or "bits", of that codeword are usually correlated to each other, meaning that the behavior of the network is not well described by the sum of its parts. This has led to the suggestion that statistical mechanics could be used to study these systems. In this way, the state of a neuron can be mapped to a classical Ising spin, with an "up" state being a spike and "down" state being a silence, so that the collective activity of neural populations may be described by the Ising model with pairwise coupling. Although many studies that have used the analogy between Ising models and neurons have focused on the statistical distribution of codewords in a given time window, no regard was made for the temporal dynamics of the neurons. This project is devoted to generalizing the Ising model approach to temporal sequences of spikes and silences, adding time as an extra "dimension" in the system. These models will be fit to the collective activity of retinal ganglion cells. The analogy with statistical mechanics can be further pursued by studying the thermodynamic properties of the system. The specific heat will be calculated as well asother thermodynamic quantities that can serve as signatures of criticality, and the question of criticality in the context of dynamical systems will be revisited. Time-reversibility of the neural activity and possible violations of detailed balance in the system will also be studied. (AU)