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Statistical properties of superimposed stationary spike trains

机译：叠加式固定秒杀列车的统计特性

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摘要

The Poisson process is an often employed model for the activity of neuronal populations. It is known, though, that superpositions of realistic, non-Poisson spike trains are not in general Poisson processes, not even for large numbers of superimposed processes. Here we construct superimposed spike trains from intracellular in vivo recordings from rat neocortex neurons and compare their statistics to specific point process models. The constructed superimposed spike trains reveal strong deviations from the Poisson model. We find that superpositions of model spike trains that take the effective refractoriness of the neurons into account yield a much better description. A minimal model of this kind is the Poisson process with dead-time (PPD). For this process, and for superpositions thereof, we obtain analytical expressions for some second-order statistical quantities—like the count variability, inter-spike interval (ISI) variability and ISI correlations— and demonstrate the match with the in vivo data. We conclude that effective refractoriness is the key property that shapes the statistical properties of the superposition spike trains. We present new, efficient algorithms to generate superpositions of PPDs and of gamma processes that can be used to provide more realistic background input in simulations of networks of spiking neurons. Using these generators, we show in simulations that neurons which receive superimposed spike trains as input are highly sensitive for the statistical effects induced by neuronal refractoriness.
机译：泊松过程是神经元种群活动的常用模型。但是，众所周知，现实的非泊松峰值序列的叠加在一般的泊松过程中并不存在，即使对于大量的叠加过程也是如此。在这里，我们从大鼠新皮层神经元的细胞内体内记录中构建叠加的尖峰序列，并将其统计数据与特定的点过程模型进行比较。构造的叠加尖峰序列显示出与泊松模型的强烈偏差。我们发现，考虑了神经元的有效耐火度的模型峰值序列的叠加产生了更好的描述。带有停滞时间（PPD）的泊松过程是这种类型的最小模型。对于此过程及其叠加，我们获得了一些二阶统计量的解析表达式，例如计数变异性，峰间间隔（ISI）变异性和ISI相关性，并证明了与体内数据的匹配性。我们得出结论，有效的耐火度是影响叠加峰值序列统计特性的关键特性。我们提出了新的高效算法来生成PPD和伽马过程的叠加，可用于在尖峰神经元网络的仿真中提供更现实的背景输入。使用这些生成器，我们在仿真中表明，接收叠加的尖峰序列作为输入的神经元对神经元耐火性引起的统计效应高度敏感。

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