| Grant number: | 16/17655-8 |
| Support type: | Scholarships in Brazil - Post-Doctorate |
| Effective date (Start): | October 01, 2016 |
| Effective date (End): | June 30, 2018 |
| Field of knowledge: | Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics |
| Principal Investigator: | Jefferson Antonio Galves |
| Grantee: | Pierre Hodara |
| Home Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Associated research grant: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat, AP.CEPID |
Abstract The starting point of my PhD work is the article "Infinite systems of interacting chains with memory of variable length - a stochastic model for biological neural nets" [1] by Antonio Galves and Eva Locherbach. In this article, the authors propose a model for biological neural nets in discrete time. In collaboration with Eva Locherbach, I proposed an extension to the continuous time framework of this model. We obtained in [2] the existence andunicity of a stationnary version of the process under two diferent sets of assumption corresponding to two dierent models of Hawkes processes. A model with saturation thresholds, and a model of cascade of spike trains. As in [1] we give a graphical construction of the stationnary version. I am now working, in collaboration with Nathalie Krell and Eva Locherbach on the non-parametric estimation of the spiking rate in systems of interacting neurons. This work should lead to a submission of an article on ArXiv within the next few weeks. Our model takes place in a Markovian framework, and the process describing the activity of the neural network is a Piecewise Deterministic Markov Process (PDMP). The spiking rate is thengiven by the jump rate of our PDMP for which we built a Kernel estimator with the optimal convergence speed for the error in L2. Both of these studies can take place in the framework of the NeuroMat mission and research program. They raise open issues that I would like to work on during my postdoctoral research. (AU) | |