Nondegenerate Neural Codes and Obstructions to Closed-Convexity

DOI10.1137/21M1452147OpenAlexW3106298332MaRDI QIDQ5883278

Unnamed Author, Patrick P. K. Chan, Anne Shiu, Alexander Ruys de Perez, Katherine G. Johnston

Publication date: 30 March 2023

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.04565

zbMATH Keywords

simplicial complexconvexembedding dimensionneural code

Mathematics Subject Classification ID

Neural biology (92C20) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Combinatorial aspects of simplicial complexes (05E45)

Related Items (2)

Open, closed, and non-degenerate embedding dimensions of neural codes ⋮ Wheels: a new criterion for non-convexity of neural codes

Uses Software

• neural ideal

Cites Work

• The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes
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• Neural ideals in SageMath
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• Non-monotonicity of closed convexity in neural codes
• Classification of open and closed convex codes on five neurons
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• Algebraic signatures of convex and non-convex codes
• Convex Union Representability and Convex Codes
• Gröbner bases of neural ideals
• Neural Codes, Decidability, and a New Local Obstruction to Convexity
• Morphisms of Neural Codes
• Strengthening Relationships between Neural Ideals and Receptive Fields
• A No-Go Theorem for One-Layer Feedforward Networks
• What Makes a Neural Code Convex?

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