Every binary code can be realized by convex sets

DOI10.1016/j.aam.2018.04.004zbMath1391.94843arXiv1711.03185OpenAlexW2962728869MaRDI QIDQ1637597

Samuel Muthiah, Megan Franke

Publication date: 8 June 2018

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.03185

zbMATH Keywords

convexHelly's theorembinary codeneural code

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Neural biology (92C20) Simplicial sets and complexes in algebraic topology (55U10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Combinatorial aspects of simplicial complexes (05E45)

Related Items (8)

Non-monotonicity of closed convexity in neural codes ⋮ Signless normalized Laplacian for hypergraphs ⋮ Minimal embedding dimensions of connected neural codes ⋮ Planar Convex Codes are Decidable ⋮ On open and closed convex codes ⋮ Neural Codes, Decidability, and a New Local Obstruction to Convexity ⋮ Neural codes and the factor complex ⋮ Embedding dimension phenomena in intersection complete codes

Cites Work

• The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes
• Obstructions to convexity in neural codes
• On open and closed convex codes
• Intersection Patterns of Convex Sets via Simplicial Complexes: A Survey
• What Makes a Neural Code Convex?

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