This week, "Agência FAPESP" website featured an article about the RIDC NeuroMat series of online seminars on mathematics and neurobiology, NeuroMat/NeuroMod webinars 2020 - mathematics and neurobiology intertwined.
The webinars are part of a partnership with theInstitute for Modeling in Neuroscience and Cognition of Université Côte d'Azur (NeuroMod), France. The virtual meetings will take place every two weeks, from April 16 to June 25, 2020, via Google Meet at meet.google.com/xdz-rqup-dze.
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.
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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