Detecting Square Grid Structure in an Animal Neuronal Network

Abstract

An animal neural system ranges from a cluster of a few neurons to a brain of billions. At the lower range, it is possible to test each neuron for its role across a set of environmental conditions. However, the higher range requires another approach. One method is to disentangle the organization of the neuronal network. In the case of the entorhinal cortex in a rodent, a set of neuronal cells involved in spatial location activate in a regular grid-like arrangement. Therefore, it is of interest to develop methods to find these kinds of patterns in a neural network. For this study, a square grid arrangement of neurons is quantified by network metrics and then applied for identification of square grid structure in areas of the fruit fly brain. The results show several regions with contiguous clusters of square grid arrangements in the neural network, supportive of specialization in the information processing of the system.

Geometry-Based Deep Learning in the Natural Sciences

“…An example is a graph-based description of information that flows between an interconnected system of computing devices. This graph is idealized as a fully connected network [13] (Figure 1). This representation of information and its flow further applies to the artificial neural networks (ANNs) of computer science, a graph consisting of nodes and connections [14].…”

“…The cause of this limit may be referred to as a combinatorial explosion as there is a calculation at each edge, and, therefore, the number of calculations potentially exceeds that of an exponential growth rate. (Figure and legend reproduced from [13]. )…”