Identification of patterns of neuronal connectivity--partial spectra, partial coherence, and neuronal interactions.

The cross-correlation histogram has provided the primary tool for inferring the structure of common inputs to pairs of neurones. While this technique has produced useful results it not clear how it may be extended to complex networks. In this report we introduce a linear model for point process systems. The finite Fourier transform of this model leads to a regression type analysis of the relations between spike trains. An advantage of this approach is that the full range of techniques for multivariate regression analyses becomes available for spike train analysis. The two main parameters used for the identification of neural networks are the coherence and partial coherences. The coherence defines a bounded measure of association between two spike trains and plays the role of a squared correlation coefficient defined at each frequency lambda. The partial coherences, analogous to the partial correlations of multiple regression analysis, allow an assessment of how any number of putative input processes may influence the relation between any two output processes. In many cases analytic solutions may be found for coherences and partial coherences for simple neural networks, and in combination with simulations may be used to test hypotheses concerning proposed networks inferred from spike train analyses.