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pro vyhledávání: '"Quininao, Cristobal"'
We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the stro
Externí odkaz:
http://arxiv.org/abs/2310.02809
We investigate the dynamics of a limit of interacting FitzHugh-Nagumo neurons in the regime of large interaction coefficients. We consider the dynamics described by a mean-field model given by a nonlinear evolution partial differential equation repre
Externí odkaz:
http://arxiv.org/abs/1804.06758
For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works [7, 8, 6], w
Externí odkaz:
http://arxiv.org/abs/1802.02893
Autor:
Quininao, Cristobal
Ce travail est consacré à l’étude de quelques questions issues de la modélisation des systèmes biologiques en combinant des outils analytiques et probabilistes. Dans la première partie, nous nous intéressons à la dérivation des équations
Externí odkaz:
http://www.theses.fr/2015PA066152/document
We investigate existence and uniqueness of solutions of a McKean-Vlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation is hypoelliptic, nonlocal and has unbounded coefficients. We prove exis
Externí odkaz:
http://arxiv.org/abs/1503.00492
Autor:
Quiñinao, Cristóbal
We introduce a microscopic spiking network consistent with the age-structured/renewal equation proposed by Pakdaman, Perthame and Salort. It is a jump process interacting through a global activity variable with random delays. We show the well-posedne
Externí odkaz:
http://arxiv.org/abs/1503.00115
We analyze an inhomogeneous system of coupled reaction-diffusion equations representing the dynamics of gene expression during differentiation of nerve cells. The outcome of this developmental phase is the formation of distinct functional areas separ
Externí odkaz:
http://arxiv.org/abs/1408.2091
Autor:
Quininao, Cristobal, Touboul, Jonathan
Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these random archi
Externí odkaz:
http://arxiv.org/abs/1306.5175
Autor:
Godinho, David, Quininao, Cristobal
This paper deals with a sub-critical Keller-Segel equation. Starting from the stochastic particle system associated with it, we show well-posedness results and the propagation of chaos property. More precisely, we show that the empirical measure of t
Externí odkaz:
http://arxiv.org/abs/1306.3831
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