| Texto completo | |
| Autor(es): |
Nascimento, A. M. B.
Número total de Autores: 1
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| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Statistical Physics; v. 188, n. 1, p. 12-pg., 2022-07-01. |
| Resumo | |
We consider a stochastic model describing the spiking activity of a countable set of neurons spatially organized into a homogeneous tree of degree d, d >= 2; the degree of a neuron is just the number of connections it has. Roughly, the model is as follows. Each neuron is represented by its membrane potential, which takes non-negative integer values. Neurons spike at Poisson rate 1, provided they have strictly positive membrane potential. When a spike occurs, the potential of the spiking neuron changes to 0, and all neurons connected to it receive a positive amount of potential. Moreover, between successive spikes and without receiving any spiking inputs from other neurons, each neuron's potential behaves independently as a pure death process with death rate gamma >= 0. In this article, we show that if the number d of connections is large enough, then the process exhibits at least two phase transitions depending on the choice of rate gamma: For large values of gamma, the neural spiking activity almost surely goes extinct; For small values of gamma, a fixed neuron spikes infinitely many times with a positive probability, and for "intermediate" values of gamma, the system has a positive probability of always presenting spiking activity, but, individually, each neuron eventually stops spiking and remains at rest forever. (AU) | |
| Processo FAPESP: | 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat |
| Beneficiário: | Oswaldo Baffa Filho |
| Modalidade de apoio: | Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs |