Zobrazeno 1 - 10
of 100
pro vyhledávání: '"Veltz, Romain"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G1, Pp 59-87 (2022)
We study a simplified model of the representation of colors in the primate primary cortical visual area V1. The model is described by an initial value problem related to a Hammerstein equation. The solutions to this problem represent the variation of
Externí odkaz:
https://doaj.org/article/20037926e0114f10aa1adb578ebf56f6
Publikováno v:
Comptes Rendus. Math\'ematique, Tome 360 (2022), pp. 59-87
We study a simplified model of the representation of colors in the primate primary cortical visual area V1. The model is described by an initial value problem related to a Hammerstein equation. The solutions to this problem represent the variation of
Externí odkaz:
http://arxiv.org/abs/2110.10040
Publikováno v:
Electronic Journal of Probability, Vol. 26 (2021)
We study a family of non-linear McKean-Vlasov SDEs driven by a Poisson measure, modelling the mean-field asymptotic of a network of generalized Integrate-and-Fire neurons. We give sufficient conditions to have periodic solutions through a Hopf bifurc
Externí odkaz:
http://arxiv.org/abs/2008.11116
Publikováno v:
SIAM Journal on Mathematical Analysis, 2020, 52(6), 5703-5747
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an infinite-dim
Externí odkaz:
http://arxiv.org/abs/1912.06205
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system, and a fin
Externí odkaz:
http://arxiv.org/abs/1906.10232
Semiconductor lasers with coherent forcing are expected to behave similarly to simple neuron models in response to external perturbations, as long as the physics describing them can be approximated by that of an overdamped pendulum with fluid torque.
Externí odkaz:
http://arxiv.org/abs/1811.06820
We address the question of color-space interactions in the brain, by proposing a neural field model of color perception with spatial context for the visual area V1 of the cortex. Our framework reconciles two opposing perceptual phenomena, known as si
Externí odkaz:
http://arxiv.org/abs/1810.12898
We study the long time behavior of the solution to some McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the asymptotic dynamic of the membrane potential of a spiking neuron in a large
Externí odkaz:
http://arxiv.org/abs/1810.08562
Publikováno v:
Annales de l'Institut Henri Poincare - Probabilites et Statistiques (2020) 56(2), pp. 1041-1071
Consider a large number $n$ of neurons, each being connected to approximately $N$ other ones, chosen at random. When a neuron spikes, which occurs randomly at some rate depending on its electric potential, its potential is set to a minimum value $v_{
Externí odkaz:
http://arxiv.org/abs/1802.04118
Autor:
Veltz, Romain
Cette thèse traite de modèles mésoscopiques de cortex appelés champs neuronaux. Les équations des champs neuronaux décrivent l'activité corticale de populations de neurones, ayant des propriétés anatomiques/fonctionnelles communes. Elles ont
Externí odkaz:
http://www.theses.fr/2011PEST1056/document