Neural Ideals in SageMath

TL;DR

This paper introduces a SageMath package that provides algorithms for analyzing neural codes through their algebraic neural ideals, facilitating the extraction of stimulus space features from neural data.

Contribution

It presents a novel SageMath implementation of algorithms for the canonical form of neural ideals, advancing computational tools in neural code analysis.

Findings

Algorithms for neural ideal canonical forms implemented in SageMath

Facilitates extraction of stimulus features from neural codes

Enhances computational analysis in neuroscience

Abstract

A major area in neuroscience research is the study of how the brain processes spatial information. Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem consists in determining what stimulus space features can be extracted directly from a neural code. The neural ideal is an algebraic object that encodes the full combinatorial data of a neural code. This ideal can be expressed in a canonical form that directly translates to a minimal description of the receptive field structure intrinsic to the code. In here, we describe a SageMath package that contains several algorithms related to the canonical form of a neural ideal.