Cessac Bruno, Ampuero Ignacio, Cofré Rodrigo
Biovision Team, INRIA and Neuromod Institute, Université Côte d'Azur, 06902 Sophia Antipolis, France.
Departamento de Informática, Universidad Técnica Federico Santa María, Valparaíso 2340000, Chile.
Entropy (Basel). 2021 Jan 27;23(2):155. doi: 10.3390/e23020155.
We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow us to predict the influence of a weak amplitude time dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics. We illustrate our results with numerical simulations performed over a discrete time integrate and fire model.
我们基于具有无界记忆的链，为脉冲神经元网络建立了一个通用的线性响应关系。这种关系使我们能够在脉冲动力学中的记忆可以在过去任意延伸的一般情况下，从自发统计（无刺激）预测弱幅度随时间变化的外部刺激对时空脉冲相关性的影响。使用这种方法，我们展示了线性响应如何与刺激、内在神经元动力学以及网络连通性对脉冲序列统计的集体效应明确相关。我们通过在离散时间积分发放模型上进行的数值模拟来说明我们的结果。
