An application of neighbourhoods in digraphs to the classification of binary dynamics

TL;DR

This paper introduces a topological and graph-theoretic method leveraging neighborhoods in digraphs to analyze binary dynamics, demonstrated on neural activity data from the Blue Brain Project's rat cortical tissue reconstruction.

Contribution

It presents a novel approach for extracting information from binary dynamics on graphs using neighborhoods, applicable to neural activity analysis.

Findings

Effective extraction of information from binary neural activity patterns.

Application demonstrated on Blue Brain Project data.

Method shows potential for analyzing complex neural dynamics.

Abstract

A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produced by the neurons at an instant of time is a binary state on the encoding graph. Allowing time to vary and recording the spiking patterns of the neurons in the network produces an example of binary dynamics on the encoding graph, namely a one-parameter family of binary states on it. The central object of study in this article is the closed neighbourhood of a vertex $v$ in a graph $\mathcal{G}$, namely the subgraph of $\mathcal{G}$ that is induced by $v$ and all its neighbours in $\mathcal{G}$. We present a topological/graph theoretic method for extracting information out of binary dynamics on a graph, based on a selection of a relatively small number of vertices and their neighbourhoods. As a test case we demonstrate an application of the method to binary dynamics that arises from sample activity on the Blue Brain Project reconstruction of cortical tissue of a rat.