标题： 神经元脉冲网络的自洽矩动力学 显示英文标题

标题： Self-consistent moment dynamics for networks of spiking neurons

摘要： 一种新的方法用于矩闭合问题，以推导出膜电位分布在一群脉冲神经元中的矩的动力学的低维定律。 通过密度方程的谱展开，我们推导出矩之间的递归和非线性关系，例如平均电位和种群发放率。 找到的自洽动力学依赖于演化算子的主要特征值，这些特征值与单个神经元的脉冲间隔分布的矩密切相关。 与以往的尝试相反，我们的系统既可以应用于噪声主导的区域，也可以应用于漂移主导的区域，并且适用于弱耦合和强耦合的种群。 我们展示了该理论在漏电积分-发放神经元网络情况下的适用性，推导出了封闭的解析表达式。 将模式分解截断到前几个更相关的矩，能够有效地描述种群动力学，无论是非平衡状态还是对强烈变化输入的响应。 显示英文摘要

摘要： A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we derive the recursive and nonlinear relation between the moments, such as the mean potential, and the population firing rates. The self-consistent dynamics found relies on the dominant eigenvalues of the evolution operator, tightly related to the moments of the single-neuron inter-spike interval distribution. Contrary to previous attempts our system can be applied both in noise- and drift-dominated regime, and both for weakly and strongly coupled population. We demonstrate the applicability of the theory for the case of a network of leaky integrate-and-fire neurons deriving closed analytical expressions. Truncating the mode decomposition to the first few more relevant moments, results to effectively describe the population dynamics both out-of-equilibrium and in response to strongly-varying inputs.