标题： 神经传导延迟的极值统计学 显示英文标题

标题： Extreme value statistics of nerve transmission delay

摘要： 神经传导延迟是神经科学中的一个重要课题。 在神经元的树突上发出或接收的尖峰信号从轴突传输到突触前细胞。 尖峰信号在突触处引发化学反应，其中突触前细胞将神经递质传递给突触后细胞，并通过离子通道的化学反应过程再生电信号并传递给相邻神经元。 在将复杂的生理反应过程描述为随机过程的背景下，本研究旨在表明尖峰信号的最大时间间隔分布遵循极值顺序统计量。 通过考虑泄漏积分-放电模型的时间常数的统计方差，该模型是尖峰信号的确定性时间演化模型，我们使尖峰信号的时间间隔具有随机性。 当时间常数服从指数分布函数时，尖峰信号的时间间隔也服从指数分布。 在这种情况下，我们的理论和仿真结果证实，最大时间间隔的直方图遵循Gumbel分布，这是三种极值统计中的一种。 我们还确认，当尖峰信号的时间间隔服从帕累托分布时，最大时间间隔的直方图遵循Fréchet分布。 这些发现证实，神经传导延迟可以使用极值统计来描述，因此可以作为传输延迟的新指标。 显示英文摘要

摘要： Nerve transmission delay is an important topic in neuroscience. Spike signals fired or received at the dendrites of a neuron travel from the axon to the presynaptic cell. The spike signal triggers a chemical reaction at the synapse, wherein a presynaptic cell transfers neurotransmitters to the postsynaptic cell, and regenerates electrical signals by a chemical reaction process through ion channels and transmits it to neighboring neurons. In the context of describing the complex physiological reaction process as a stochastic process, this study aimed to show that the distribution of the maximum time interval of spike signals follows extreme order statistics. By considering the statistical variance in the time constant of the Leaky Integrate-and-Fire model, which is a deterministic time evolution model of spike signals, we enabled randomness in the time interval of spike signals. When the time constant follows an exponential distribution function, the time interval of the spike signal also follows an exponential distribution. In this case, our theory and simulations confirmed that the histogram of the maximum time interval follows the Gumbel distribution, which is one of the three types of extreme value statistics. We also confirmed that the histogram of the maximum time interval follows a Fr\'{e}chet distribution when the time interval of the spike signal follows a Pareto distribution. These findings confirm that nerve transmission delay can be described using extreme value statistics and could, therefore, be used as a new indicator for transmission delay.