| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] INRA, MaIAGE, Allee Vilvert, F-78352 Jouy En Josas - France
[2] Univ Sao Paulo, Inst Matemat & Estat, Neuromat, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | MATHEMATICS; v. 7, n. 6 JUN 2019. |
| Web of Science Citations: | 1 |
| Abstract | |
We aim to prove Poincare inequalities for a class of pure jump Markov processes inspired by the model introduced by Galves and Locherbach to describe the behavior of interacting brain neurons. In particular, we consider neurons with degenerate jumps, i.e., which lose their memory when they spike, while the probability of a spike depends on the actual position and thus the past of the whole neural system. The process studied by Galves and Locherbach is a point process counting the spike events of the system and is therefore non-Markovian. In this work, we consider a process describing the membrane potential of each neuron that contains the relevant information of the past. This allows us to work in a Markovian framework. (AU) | |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 17/15587-8 - Stochastic dynamics of neural networks |
| Grantee: | Ioannis Papageorgiou |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 16/17655-8 - Modeling and estimation of neural networks |
| Grantee: | Pierre Hodara |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |