News
| Nov 07, 2019
This week "Agência FAPESP" website featured an article about the new RIDC NeuroMat podcast, specially addressing the publication of the second episode of the program. The aim of the podcast is to spread the research developed by NeuroMat, at the interface between neurobiology and mathematics.
The program addresses three main themes: the neuronal spiking systems model developed by the CEPID NeuroMat team; the statistical framework needed to rigorously address the “statistical brain” conjecture; and the processes of construction and production of the state-of-the science in Brazil right now.
The NeuroMat dissemination team has launched a series of short videos on which young researchers describe briefly questions they tackle and their ongoing work. As of now, four videos were distributed with junior NeuroMat researchers Fernando Araujo Najman, Fernanda Torres, Arthur Lopes da Silva Valencio, and Luiggi Lustosa.
Morgan André
We consider a countably infinite system of spiking neurons. In this model each neuron has a membrane potential which takes value in the non-negative integers. Each neuron is also associated with two point processes. The first one is a Poisson process of some parameter γ, representing the \textit{leak times}, that is the times at which the membrane potential of the neuron is spontaneously reset to 0. The second point process, which represents the \textit{spiking times}, has a non-constant rate which depends on the membrane potential of the neuron at time t. This model was previously proven to present a phase transition with respect to the parameter γ. It was also proven that the renormalized time of extinction of a finite version of the system converges in law toward an exponential random variable when the number of neurons goes to infinity, which indicates a metastable behavior. Here we prove a result which is in some sense the symmetrical of this last result: we prove that when γ>1 (super-critical) the renormalized time of extinction converges in probability to 1.
News
| Oct 23, 2019
This month on "Jornal da USP" website, there was a report about the NeuroMat podcast, "A Matemática do Cérebro", developed by the NeuroMat Dissemination Team and by Antonio Galves, NeuroMat coordinator, and Eduardo Vicente, professor from the Department of Film, Radio and TV (CTR) of ECA/USP.
The article covered the first two episodes of the podcast. It also talked about CEPID NeuroMat's work and how the epidodes were created to talk about the research developed at the center, with the interface between neurobiology and mathematics.
Morgan André
In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This model has a parameter γ, corresponding to the rate of the leaking times of the neurons and, as the title says, it was proven there to present a phase transition phenomenon with respect to this γ. Here we prove that this model also exhibit a metastable behavior. By this we mean that if γ is small enough, then the re-normalized time of extinction converges toward an exponential random variable of mean 1 as the number of neurons goes to infinity.
