Precision of neural timing: effects of convergence and time-windowing

We study the improvement in timing accuracy in a neural system having n identical input neurons projecting to one target neuron. The n input neurons receive the same stimulus but fire at stochastic times selected from one of four specified probability densities, f, each with standard deviation 1.0 msec. The target cell fires if and when it receives m inputs within a time window of epsilon msec. Let sigma(n,m,epsilon) denote the standard deviation of the time of firing of the target neuron (i.e. the standard deviation of the target neuron's latency relative to the arrival time of the stimulus). Mathematical analysis shows that sigma(n,m,epsilon) is a very complicated function of n, m, and epsilon. Typically, sigma(n,m,epsilon) is a non-monotone function of m and epsilon and the improvement of timing accuracy is highly dependent of the shape of the probability density for the time of firing of the input neurons. For appropriate choices of m, epsilon, and f, the standard deviation sigma(n,m,epsilon) may be as low as 1/n. Thus, depending on these variables, remarkable improvements in timing accuracy of such a stochastic system may occur.