On open and closed convex codes

DOI10.1007/s00454-018-00050-1zbMath1407.92031DBLPjournals/dcg/CruzGIK19arXiv1609.03502OpenAlexW2522272220WikidataQ90396535 ScholiaQ90396535MaRDI QIDQ1715995

Vladimir Itskov, Bill Kronholm, Joshua Cruz, Chad Giusti

Publication date: 29 January 2019

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.03502

zbMATH Keywords

combinatorial codesembedding dimensionneural codesclosed convexconvex codesintersection-complete codesopen convex

Mathematics Subject Classification ID

Neural biology (92C20) General convexity (52A99)

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Cites Work

• The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes
• Obstructions to convexity in neural codes
• Characterization of f-vectors of families of convex sets in \({\mathbb{R}}^ d\). I: Necessity of Eckhoff's conditions
• Characterization of f-vectors of families of convex sets in \({\mathbb{R}}^ d\). II: Sufficiency of Eckhoff's conditions
• Every binary code can be realized by convex sets
• $d$-representability of simplicial complexes of fixed dimension
• A No-Go Theorem for One-Layer Feedforward Networks
• What Makes a Neural Code Convex?
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