5 citations · 9 across the 5 of their papers we have counts for
5 papers
A synchronization-capturing multi-scale solver to the noisy integrate-and-fire neuron networks
Ziyu Du, Yantong Xie, Zhennan Zhou
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 simul…
Frozen Gaussian Sampling: A Mesh-free Monte Carlo Method For Approximating Semiclassical Schrödinger Equations
Yantong Xie, Zhennan Zhou
In this paper, we develop a Monte Carlo algorithm named the Frozen Gaussian Sampling (FGS) to solve the semiclassical Schrödinger equation based on the frozen Gaussian approximatio…
Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
Jian-Guo Liu, Ziheng Wang, Yantong Xie +2
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once th…
Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
Jian-Guo Liu, Ziheng Wang, Yantong Xie +2
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once th…
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
Jingwei Hu, Jian-Guo Liu, Yantong Xie +1
In this work, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at…