An efficient algorithm for continuous time cross correlogram of spike trains

We propose an efficient algorithm to compute the smoothed correlogram for the detection of temporal relationship between two spike trains. Unlike the conventional histogram-based correlogram estimations, the proposed algorithm operates on continuous time and does not bin either the spike train nor the correlogram. Hence it can be more precise in detecting the effective delay between two recording sites. Moreover, it can take advantage of the higher temporal resolution of the spike times provided by the current recording methods. The Laplacian kernel for smoothing enables efficient computation of the algorithm. We also provide the basic statistics of the estimator and a guideline for choosing the kernel size. This new technique is demonstrated by estimating the effective delays in a neuronal network from synthetic data and recordings of dissociated cortical tissue.