Directed and weighted graphs were constructed from the inferred neuronal spike trains. Following Teller et al. (27, 28), we used a formalism grounded on time delays to determine the strength of functional couplings among neurons. For each detected sequence of coherent activity, the weight of the functional links among all pairs of firing neurons was established as a decaying function of their time delay in activation. The analysis was then extended to all observed sequences, and the final value of the functional connection wij between neurons (i, j) was established as the sum of all computed weights. The significance of functional links was assessed through a random model wSij in which the number of firings per neuron was preserved, and a z score was introduced in the form ofEmbedded Image(4)where 〈wSij is the mean weight for 500 surrogates of the random model and Embedded Image is the corresponding SD. Values with Wij < 0 correspond to links that are less connected than those in the surrogates and were set to 0. The final matrix W = {Wij} (weighed and directed) provided the normalized weights between all the functionally connected neurons.

We verified (fig. S9) that the effective connectivity matrices derived using time delays were similar to those obtained with other approaches such as transfer entropy (6, 37). Both approaches shared 80% of the strongest links, procured identical communities, and exhibited very similar measures. In addition, we also verified that important network measures such as the global efficiency were robust to more restrictive thresholds in the z score (fig. S10).

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