On open and closed convex codes

Understand

Neural codes serve as a language for neurons in the brain.

• Convex codes, which arise from the pattern of intersections of convex sets in Euclidean space, are of particular relevance to neuroscience.
• Not every code is convex, however, and the combinatorial properties of a code that determine its convexity are still poorly understood.
• Here we find that a code that can be realized by a collection of open convex sets may or may not be realizable by closed convex sets, and vice versa, establishing that open convex and closed convex codes are distinct classes.