NeuroMat/NeuroMod webinars 2020

Amidst difficulties associated with the COVID-19 pandemics worldwide, in a context in which universities are closed and scientific missions are prohibited, we must do our best to keep scientific life alive. The series of webinars "Mathematics and Neurobiology Intertwined", presented on this page, bears the distinctive feature of bonding efforts and teams to move science forward.

A note on perfect simulation for Exponential Random Graph Models

Andressa Cerqueira, Aurélien Garivier and Florencia Leonardi

In this paper, we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling from the past method of Propp and Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the monotonicity of the ERGM for a subset of the parametric space. We also obtain an upper bound on the running time of the algorithm that depends on the mixing time of the Markov chain.

Modified log-Sobolev inequality for a compact PJMP with degenerate jumps

Ioannis Papageorgiou

We study the modified log-Sobolev inequality for a class of pure jump Markov processes that describe the interactions between brain neurons. In particular, we focus on a finite and compact process with degenerate jumps inspired by the model introduced by Galves and Löcherbach. As a result, we obtain concentration properties for empirical approximations of the process.

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