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arXiv 1810.09520q-bio.NCcs.LG
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线性Hawkes网络中尖峰时刻的传播

Propagation of spiking moments in linear Hawkes networks

Universitat Pompeu Fabra(庞培法布拉大学);Institute of Neuroinformatics and Neuroscience Center Zurich, University of Zurich/ETH Zurich(苏黎世大学/苏黎世联邦理工学院苏黎世神经信息学与神经科学中心);University of Bern(伯尔尼大学)

Matthieu Gilson, Jean-Pascal Pfister

摘要:

本文给出了线性Hawkes过程循环连通网络中尖峰活动高阶矩的精确数学表达式。它扩展了以前的研究,探讨了由确定性强度函数驱动的(线性)霍克斯网络的情况下,由外部输入(率函数或脉冲序列)与任意相关结构的刺激的情况下。我们的方法描述了时空滤波引起的传入和经常性的连接(与任意的突触反应内核),使用运营商的输入时刻。这种代数观点提供了关于网络成分如何塑造矩和累积量的输入-输出映射的直觉。我们还表明,使用数值模拟,我们的研究结果适用于神经元与自我抑制实施的耐火性,提供相应的负反馈,每个神经元只轻微改变其平均放电概率。

英文摘要:

The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently-connected network of linear Hawkes processes. It extends previous studies that have explored the case of a (linear) Hawkes network driven by deterministic intensity functions to the case of a stimulation by external inputs (rate functions or spike trains) with arbitrary correlation structure. Our approach describes the spatio-temporal filtering induced by the afferent and recurrent connectivities (with arbitrary synaptic response kernels) using operators acting on the input moments. This algebraic viewpoint provides intuition about how the network ingredients shape the input-output mapping for moments, as well as cumulants. We also show using numerical simulation that our results hold for neurons with refractoriness implemented by self-inhibition, provided the corresponding negative feedback for each neuron only mildly alters its mean firing probability.

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