The neural dynamics generating sensory, motor, and cognitive functions are commonly
understood through field theories for neural population activity. Classic neural field theories …

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 …

The neural dynamics generating sensory, motor, and cognitive functions are commonly
understood through field theories for neural population activity. Classic neural field theories …

We prove that a single-layer neural network trained with the online actor critic algorithm
converges in distribution to a random ordinary differential equation (ODE) as the number of …

The noisy leaky integrate-and-fire (NLIF) model describes the voltage configurations of
neuron networks with an interacting many-particles system at a microscopic level. When …

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 …

In this work, we consider the Fokker-Planck equation of the Nonlinear Noisy Leaky Integrate-
and-Fire (NNLIF) model for neuron networks. Due to the firing events of neurons at the …

In this work, we are concerned with a Fokker--Planck equation related to the nonlinear noisy
leaky integrate-and-fire model for biological neural networks which are structured by the …

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 …

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 …