随机神经轴突方程中信号传输的可靠性
Reliability of signal transmission in stochastic nerve axon equations
摘要：
我们介绍了一种方法，用于计算概率的自发活动和传播失败的动作电位在空间扩展，基于电导的神经元模型受到通道噪声，基于膜电位的统计特性。我们比较不同的估计器的检测质量，计算成本和鲁棒性，并提出沿轴突的膜电位的积分作为一个适当的估计，以检测自发活动和传播失败。执行模型简化，我们实现了一个简化的解析表达式的基础上的线性化在静息电位（分别）。移动动作电位（traveling action potential）这允许近似的概率自发活动和传播失败的一维线性随机微分方程的（经典）命中概率。质量的近似相对于噪声幅度进行了讨论和说明与空间扩展的霍奇金-赫胥黎的数值结果。
英文摘要：
We introduce a method for computing probabilities for spontaneous activity and propagation fail- ure of the action potential in spatially extended, conductance-based neuronal models subject to channel noise, based on statistical properties of the membrane potential. We compare different estimators with respect to the quality of detection, computational costs and robustness and propose the integral of the membrane potential along the axon as an appropriate estimator to detect both spontaneous activity and propagation failure. Performing a model reduction we achieve a simplified analytical expression based on the linearization at the resting potential (resp. the traveling action potential). This allows to approximate the probabilities for spontaneous activity and propagation failure in terms of (classical) hitting probabilities of one-dimensional linear stochastic differential equations. The quality of the approximation with respect to the noise amplitude is discussed and illustrated with numerical results for the spatially extended Hodgkin-Huxley.
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