标题： 抑制性神经元的发放统计学带有延迟反馈。 I. 输出 ISI 概率密度 显示英文标题

标题： Firing statistics of inhibitory neuron with delayed feedback. I. Output ISI probability density

摘要： 抑制性神经元带有延迟反馈的活动是在点随机过程的框架下考虑的。 该神经元接收来自泊松流的兴奋性输入脉冲，以及来自带有延迟的反馈线的抑制性脉冲。 我们在这里研究抑制性反馈的存在如何影响输出发放统计特性。 使用绑定神经元（BN）作为模型，我们解析地推导出输出峰间间隔（ISI）概率密度、平均输出 ISI 和变异系数作为阈值为 2 的模型参数的函数的精确表达式。 使用漏电积分-发放（LIF）模型以及具有更高阈值的 BN 模型，这些统计量是数值计算得到的。 与之前研究的无反馈情况不同，这里对于 BN 和 LIF 神经元找到的 ISI 概率密度呈现双峰性，并且存在跳跃类型的不连续性。 然而，抑制性延迟反馈的存在并未显著影响输出 ISI 变异系数。 找到的 ISI 变异系数范围在 0.5 到 1 之间。 结论是，引入延迟抑制性反馈可以彻底改变神经元输出发放统计特性。 这种统计特性也不同于之前通过类似方法对具有延迟反馈的兴奋性神经元所发现的结果（Vidybida & Kravchuk, 2009）。 显示英文摘要

摘要： Activity of inhibitory neuron with delayed feedback is considered in the framework of point stochastic processes. The neuron receives excitatory input impulses from a Poisson stream, and inhibitory impulses from the feedback line with a delay. We investigate here, how does the presence of inhibitory feedback affect the output firing statistics. Using binding neuron (BN) as a model, we derive analytically the exact expressions for the output interspike intervals (ISI) probability density, mean output ISI and coefficient of variation as functions of model's parameters for the case of threshold 2. Using the leaky integrate-and-fire (LIF) model, as well as the BN model with higher thresholds, these statistical quantities are found numerically. In contrast to the previously studied situation of no feedback, the ISI probability densities found here both for BN and LIF neuron become bimodal and have discontinuity of jump type. Nevertheless, the presence of inhibitory delayed feedback was not found to affect substantially the output ISI coefficient of variation. The ISI coefficient of variation found ranges between 0.5 and 1. It is concluded that introduction of delayed inhibitory feedback can radically change neuronal output firing statistics. This statistics is as well distinct from what was found previously (Vidybida & Kravchuk, 2009) by a similar method for excitatory neuron with delayed feedback.