Breakthroughs in modeling systems of interacting neurons: NeuroMat's second report of activities

The CEPID NeuroMat submitted its Second Report of Activities on July, 28th, which shows consistent advances in the development of a new class of stochastic processes to model systems of interacting neurons, as introduced by Antonio Galves and Eva Löcherbach, in 2013. This document is required by the São Paulo Research Foundation (FAPESP), the funding entity of the Research, Innovation and Dissemination Center for Neuromathematics (CEPID NeuroMat), and presented detailed accounts of scientific, dissemination and technology-transfer activities. A link to the report is available here.

NeuroMat’s scientific production from July, 2014 to July, 2015 has summed up to 24 published or accepted articles as well as 24 submitted papers. Twenty-one papers under preparation and 14 communications in scientific meetings were also reported as scientific achievements. The first report of activities, that was submitted in 2014, listed 17 published or accepted papers, 14 submitted papers, 7 papers under preparation, and 3 communications in scientific meetings.

NeuroMat’s scientific sprout has been associated to a growing network around Neuromathematics. At least two characteristics of this network are worth emphasizing. Firstly, it rests upon global ties amongst scientists and universities. As it reads on the report, "This network brings together scientists from universities in Europe —France (3), Italy (3), Netherlands (3), United Kingdom (1)—, Latin America —Argentina (3), Brazil (8), Uruguay (1)— and the United States (8).” Secondly, NeuroMat has contributed to the continuing training of young researchers in the field of Neuromathematics. This training is crucial to broadening and deepening the achievements around a theory of the brain, so the report claims. As an illustration of this training, NeuroMat highlights 2 concluded postdoctoral fellows, 5 ongoing postdoctoral fellows, 3 concluded PhD dissertations, 1 concluded Master dissertation, 13 PhD dissertations in progress, and 5 Master dissertations in progress.

Illustration of FAPESP's NeuroMat global network of scienti?fic, institutional affi?liations.

Research findings

There were three main general advances in the development of a new class of stochastic processes to model systems of interacting neurons, according to the report. Firstly, NeuroMat researchers have contributed to the issue of hydrodynamic limits, "a crucial and unavoidable step to understand the time evolution of mesoscopic and macroscopic behavior of the system,” so it is claimed in the document. This has been mostly achieved on four papers: "Hydrodynamic limit for interacting neurons", "On a toy model of interacting neurons”, "Modeling networks of spiking neurons as interacting processes with memory of variable length”, and "Hydrodynamic limits for interacting neurons with spatial dependency”.

Secondly, NeuroMat researchers have continued working on the long time behavior and stability issues of the process in order to be able to predict and classify different behaviors as a function of the parameters. This has been achieved in some of the aforementioned pieces and "A model for neural activity in the absence of external stimuli”.

Lastly, perfect simulation methods, that are related to the issue of long time behavior, were extended to the continuous frame. This extension was done on papers "Hawkes processes with variable length memory and an infinite number of components” and "A stochastic system with infinite interacting components to model the time evolution of the membrane potentials of a population of neurons".

The forthcoming NeuroMat High-Performance Computational Center, at the University of São Paulo, campus Ribeirão Preto, is meant to speed and level up research on modeling and simulating systems of interacting neurons. This project is under the coordination of NeuroMat PI Antonio Carlos Roque.

A major emphasis in the report is put on the work around "Retrieving a hidden context tree model from EEG signals,” an unpublished draft, where the conjecture that the brain assigns models to external stimuli by a procedure which is reminiscent of statistical model selection is addressed. According to the report, "The experimental protocol consists in exposing volunteers to rhythmic sequences of beats generated by a random source while the EEG signal is recorded. The research question is whether or not the brain is able to identify the context tree which characterizes the random source producing the stimuli.” This work may be considered an innovative perspective on the issue, to the extent that it introduced a new experimental protocol using context-tree random sources, it depended on translating the problem of structure identification by the brain as a context tree selection procedure, and it contributed to overcome the challenge of testing hypotheses in infinite dimensional spaces.

NeuroMat’s report of activities also brings achievements of the dissemination and technology-transfer teams. Excerpts on the report of these achievements will be posted on NeuroMat’s Facebook page.

“Random Graphs in the Brain"

A major following step in the development of the model introduced by Galves and Löcherbach in 2013 is the organization of the workshop “Random Graphs in the Brain,” from November 23-7, at the NeuroMat center at the University of São Paulo. This event is coordinated by NeuroMat team members C. Pouzat, A. Galves and C. Vargas, along with R. van der Hofstad. The workshop, that should a favorite of the 2015 international schedule of scientific activities associated to Neuromathematics, tackles a crucial open question in science: how to deal with features characterizing a graph of interactions between regions in the brain in several scales.

This workshop will bring and connect scientists from several fields, considering that progress in understanding the brain is slowed down by a deficit of clear understanding of how the results of the different disciplines involved are obtained. On the one hand, a mathematician has almost no idea of how recordings from synaptically connected neurons in brain slices are performed and has therefore no intuition for the kind of artifacts they generate and for the precision of the measurements they provide. On the other hand, an experimentalist often fails to grasp that the definiteness on which mathematician are so insistent is the very condition needed to start mathematical work, which is by proving theorems.

More information on the NeuroMat workshop “Random Graphs in the Brain” will be posted on a special page on the event at the NeuroMat webpage.

This piece is part of NeuroMat's Newsletter #18. Read more here

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