Towards the Modeling of Neuronal Firing by Gaussian Processes

Delayed feedback causes non-Markovian behavior of neuronal firing statistics

The instantaneous state of a neural network consists of both the degree of excitation of each neuron, the network is composed of, and positions of impulses in communication lines between neurons. In neurophysiological experiments, the neuronal firing moments are registered, but not the state of communication lines. But future spiking moments depend essentially on the past positions of impulses in the lines. This suggests, that the sequence of intervals between firing moments (interspike intervals, ISIs) in the network could be non-Markovian. In this paper, we address this question for a simple…

用于长时间神经元状态分布和放电率的有限状态马尔可夫代理模型

Finite-state Markovian surrogates for long-time neuronal state distributions and firing rates

该研究构建有限状态马尔可夫代理模型，结合两种闭合方式，在LIF、EIF等神经元模型上实现无需逐尖峰模拟的长时间状态分布和放电率估计，性能良好。

Use of an Hourglass Model in Neuronal Coding

We study a system of interacting renewal processes which is a model for neuronal activity. We show that the system possesses an exponentially large number (with respect to the number of neurons in the network) of limiting configurations of the "firing neurons". These we call patterns. Furthermore, under certain conditions of symmetry we find an algorithm to control limiting patterns by means of the connection parameters.

带跳跃的雅可比过程作为神经元模型：首次通过时间分析

Jacobi processes with jumps as neuronal models: a first passage time analysis

该研究提出带向下跳跃的马尔可夫雅可比过程作为神经元模型，通过分析其首次通过时间研究峰峰间期，推导拉普拉斯变换与期望闭式解，并开展神经元放电率数值研究。

Scaling limit of a generalized contact process

We derive macroscopic equations for a generalized contact process that is inspired by a neuronal integrate and fire model on the lattice $\mathbb{Z}^d$. The states at each lattice site can take values in $0,\ldots,k$. These can be interpreted as neuronal membrane potential, with the state $k$ corresponding to a firing threshold. In the terminology of the contact processes, which we shall use in this paper, the state $k$ corresponds to the individual being infectious (all other states are noninfectious). In order to reach the firing threshold, or to become infectious, the site must progress seq…

Approximation of the first passage time density of a Wiener process to an exponentially decaying threshold by two-piecewise linear threshold. Application to neuronal spiking activity

The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal spiking activity. Since analytical expressions of the first passage time density are not available, we propose to approximate the curved boundary by means of a continuous two-piecewise linear threshold. Explicit expressions for the first passage time density towards the new boundary are provided. Then we introduce different approximating linear threshold and descr…