Strongly maximal intersection-complete neural codes on grids are convex

TL;DR

This paper establishes an intrinsic condition under which neural codes can be represented as convex regions in space, providing bounds on the minimal dimension needed for such convex realizations.

Contribution

It introduces a new intrinsic condition for neural codes to be convex and derives bounds on the minimal embedding dimension.

Findings

The intrinsic condition guarantees convex realizability of neural codes.

A bound on the minimal dimension for convex realization is provided.

The results connect combinatorial neural codes with geometric convexity.

Abstract

The brain encodes spacial structure through a combinatorial code of neural activity. Experiments suggest such codes correspond to convex areas of the subject's environment. We present an intrinsic condition that implies a neural code may correspond to a convex space and give a bound on the minimal dimension underlying such a realization.