Vectorial phase-space analysis for detecting dynamical interactions in firing patterns of biological neural networks

A vectorial statistical phase-space analysis is introduced to detect temporally correlated firing patterns in a network of n neurons. The cross-interval vector is used to establish temporal correlation between firing intervals between neurons. The resultant vectorial sum computed from these individual cross-interval vectors establishes a statistical average measure of the cross correlation among all n neurons. Thus, an n-tuple correlation among all n neurons in the network can be computed. The normalized resultant vectors not only capture an O(n³) combinatorial correlation but also reduce the combinatorics to an O (n) vectorial statistic. This vectorial phase-space analysis provides a description of the temporal correlation relationships among different neurons from the trajectories of the cross-interval vectors