Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Dou, Xu'an"'
The integrate and fire equation is a classical model for neural assemblies which can exhibit finite time blow-up. A major open problem is to understand how to continue solutions after blow-up. Here we study an approach based on random discharge model
Externí odkaz:
http://arxiv.org/abs/2409.14749
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given phase in a sui
Externí odkaz:
http://arxiv.org/abs/2404.13703
Motivated by the incompressible limit of a cell density model, we propose a free boundary tumor growth model where the pressure satisfies an obstacle problem on an evolving domain $\Omega(t)$, and the coincidence set $\Lambda(t)$ captures the emergin
Externí odkaz:
http://arxiv.org/abs/2309.00065
The voltage-conductance kinetic equation for an ensemble of neurons has been studied by many scientists and mathematicians, while its rigorous analysis is still at a premature stage. In this work, we obtain for the first time the exponential converge
Externí odkaz:
http://arxiv.org/abs/2305.03992
In neuroscience, the time elapsed since the last discharge has been used to predict the probability of the next discharge. Such predictions can be improved taking into account the last two discharge times, and possibly more. Such multi-time processes
Externí odkaz:
http://arxiv.org/abs/2304.01605
Autor:
Dou, Xu'an, Zhou, Zhennan
The nonlinear noisy leaky integrate-and-fire (NNLIF) model is a popular mean-field description of a large number of interacting neurons, which has attracted mathematicians to study from various aspects. A core property of this model is the finite tim
Externí odkaz:
http://arxiv.org/abs/2206.06972
The voltage-conductance kinetic model for the collective behavior of neurons has been studied by scientists and mathematicians for two decades, but the rigorous analysis of its solution structure has been only partially obtained in spite of plenty of
Externí odkaz:
http://arxiv.org/abs/2203.02746
The voltage-conductance equation determines the probability distribution of a stochastic process describing a fluctuation-driven neuronal network arising in the visual cortex. Its structure and degeneracy share many common features with the kinetic F
Externí odkaz:
http://arxiv.org/abs/2202.12539
Autor:
Dou, Xu'an, Zhou, Zhennan
We study a two-speed model with variant drift fields, which generalizes the Goldstein-Taylor model but the two advection fields are not necessarily in proportion. Due to the lack of a local equilibrium structure of the steady state, prevailing hypoco
Externí odkaz:
http://arxiv.org/abs/2201.12494
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients. First, we
Externí odkaz:
http://arxiv.org/abs/2007.13543