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2015

Obstructions to convexity in neural codes

Lienkaemper, Caitlin, Shiu, Anne, Woodstock, Zev

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How does the brain encode spatial structure? One way is through hippocampal neurons called place cells, which become associated to convex regions of space known as their receptive fields: each place cell fires at a high rate precisely when the animal is in the receptive field.

The firing patterns of multiple place cells form what is known as a convex neural code.
How can we tell when a neural code is convex? To address this question, Giusti and Itskov identified a local obstruction, defined via the topology of a code's simplicial complex, and proved that convex neural codes have no local obstructions.
Curto et al.

Obstructions to convexity in neural codes · Around

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Eduard Helly · 1923
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