With the advent of volumetric EM techniques, large connectomic datasets are being created, providing neuroscience researchers with knowledge about the full connectivity of neural circuits under study. This allows for numerical simulation of detailed, biophysical models of each neuron participating in the circuit. However, these models typically include a large number of parameters, and insight into which of these are essential for circuit function is not readily obtained. Here, we review two mathematical strategies for gaining insight into connectomics data: linear dynamical systems analysis and matrix reordering techniques. Such analytical treatment can allow us to make predictions about time constants of information processing and functional subunits in large networks.SIGNIFICANCE STATEMENT This viewpoint provides a concise overview on how to extract important insights from Connectomics data by mathematical methods. First, it explains how new dynamics and new time constants can evolve, simply through connectivity between neurons. These new time-constants can be far longer than the intrinsic membrane time-constants of the individual neurons. Second, it summarizes how structural motifs in the circuit can be discovered. Specifically, there are tools to decide whether or not a circuit is strictly feed-forward or whether feed-back connections exist. Only by reordering connectivity matrices can such motifs be made visible.
Keywords: connectomics; network dynamics; neural circuits.
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