Network reconstruction using time-delayed spike-train cross-correlation with limited information and classification according to spectral properties

Abstract

We begin by reconstructing the entire network using time-delayed spike-train correlation, and we determine the time required before an adequate reconstruction becomes possible and compare this to time spans employed by experimentalists. We then sample the reconstruction matrix randomly and use the tool of matrix completion to fill in the rest of the network. To more closely mimic experimental settings, we next examine a small subnetwork of the network and determine how much information we can deduce about the whole network from this small piece. An examination of the spectral properties of connectivity matrices forms a major part of this analysis, and we formulate a metric which classifies the complex architectural network structure. Our results have practical implications for network science and computational neuroscience.

The extent of the relation between architectural and functional connectivity in the cerebral cortex is a question which has attracted much attention in recent years. Neuroscientists frequently use the functional connectivity of neurons, i.e. the measures of causality or correlations between the neuronal activities of certain parts of a network, to infer the architectural connectivity of the network, which indicates the locations of underlying synaptic connections between neurons. Architectural connectivity can be used in the modeling of neuronal processing and in the forming of conjectures about the nature of the neural code. These two types of connectivity are by no means identical, and typically no one-to-one correspondence or mapping exists from one to the other. In particular, certain standard measures of functional connectivity, such as simple correlations, give rise to an undirected network, while synaptic architectural connectivity is always directed. Nevertheless, architectural connectivity can often be inferred from functional connectivity, and this work is one attempt to determine how to do so. Our work focuses on mimicking experimental constraints and thus addresses the question of how to infer information about a complex architecture given only limited information about neuronal dynamics.