Functional dissection of Neuron Network by Identification Method for Non-linear Signal Processing in Informational Engineering

研究了一种感觉神经元的功能解剖方法及其揭示的脉冲密度编码特性。作为一个非线性信号处理系统，用Wiener分析方法研究了板球中风敏感机械感受器神经元在高斯白噪声刺激下的棘波训练活动。从系统中提取的二阶Wiener核与相应的一阶(线性)核的直积成正比。因此，该系统等价于静态非线性元件跟随其时域脉冲响应与一阶核成正比的线性动态元件的级联。静态非线性元件表示脉冲频率调制器，其尖峰放电的概率仅取决于其输入的瞬时幅度，即无记忆。利用Hermite多项式进行适当的展开，得到了脉冲发射概率随输入幅度的变化曲线。静态非线性元件的输入也是高斯过程，因为系统输入的高斯白噪声是线性卷积的。高斯权下Hermite多项式的正交性允许确定展开系数，并提供神经元的尖峰放电特性曲线。通过一阶核线性卷积，由系统的观测实际输出与估计输入的多项式值之间的内积计算系统的系数。还描述了目前的系统识别方法所揭示的神经生理特性。

A method for functional dissection of sensory neuron and pulse-density encoding properties revealed by the method are studied. Spike train activities of wind sensitive mechanoreceptor neurons in cricket, in response to a Gaussian white noise stimulus, have been studied by the Wiener's analysis as a non-linear signal processing system. The 2nd order wiener kernel extracted from the system was proportional to the direct product of corresponding 1st order (linear) kernels. The system is, therefore equivalent to the cascade of a static non-linear element following the linear dynamic element whose time-domain impulse response is proportional to the 1st order kernel. The static non-linear element represents a pulse frequency modulator whose probability of spike discharge depends solely on the instantaneous amplitude of its input, i.e. memoryless. The curve of spike firing probability as a function of input amplitude was expressed by an appropriate expansion with Hermite polynominals. The input of the static non-linear element is also a Gaussian process, because of linear convolution of the Gaussian white noise of the system input. The orthogonality of the Hermite polynominals under Gaussian weight permits the determination of the coefficients of the expansion, and provides a curve of the spike firing characteristics of the neuron. The coefficients were calculated from the inner product between the observed actual outputs of the system and the polynominal values of the estimated input by linear convolution with 1st order kernel. Neurophysiological properties revealed by the present method of system identification are also described.