Fig. 2: The cross-correlation between two spike trains can be expressed as a sum of three elements.

a Cartoon of two neurons, driven by external sources and coupled by reciprocal excitatory and inhibitory monosynaptic connections. In the example, both neurons exhibit spiking activity which deviates from a Poisson process: the excitatory neuron exhibits burst spiking, and the inhibitory neuron exhibits second-order gamma spiking activity. b The spike trains of the two neurons result from all of these (and possibly other) sources. c An example CCH created from the synthetic spike trains described in (a, b). The rSTG is 0.04, whereas the eSTG provides an inaccurate estimate (0.054; 135%). The example demonstrates that in the presence of complex dynamics, the STG cannot be estimated accurately by the “tails” method. d The CCH between two coupled spike trains, s₁ and s₂, can be expressed as a sum of three elements. The first element is the convolution of the auto-correlation histogram of the first train (ACH₁) with the STC from neuron 1 to neuron 2 (STC₂₁). The second element, denoted as “other inputs”, is equal to the cross-correlation between the uncoupled spike trains. The third element is the convolution of ACH₂ with STC₁₂. e Based on the composition (d), a decomposition procedure may recover the other inputs and the two STCs from the CCH.