Canonical forms of neural ideals

TL;DR

This paper introduces a simple criterion and an improved algorithm for determining and computing the canonical form of neural ideals, which encode neuronal firing patterns as pseudomonomial ideals in polynomial rings.

Contribution

It provides a straightforward criterion and a more efficient algorithm for obtaining the canonical form of neural ideals, enhancing analysis of neuronal firing data.

Findings

Established a simple criterion for neural ideal canonical form

Developed an improved algorithm for computing the canonical form

Facilitated more efficient analysis of neuronal firing patterns

Abstract

Neural ideals, originally defined in arXiv:1212.4201, give a way of translating information about the firing pattern of a set of neurons into a pseudomonomial ideal in a polynomial ring. We give a simple criterion for determining whether a neural ideal is in canonical form, along with an improved algorithm for computing the canonical form of a neural ideal.