Polarization of neural codes

zbMath1443.13007arXiv1802.01251MaRDI QIDQ4971333

Hamid Kulosman, Katie Christensen

Publication date: 12 October 2020

Full work available at URL: https://arxiv.org/abs/1802.01251

zbMATH Keywords

monomial idealpolarizationcanonical formminimal prime idealpartial wordneural codemotifssquare-free monomial idealneural idealinactive neuronspartial motifpartial neural codepseudomonomial ideal

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Other types of codes (94B60) Polynomials over commutative rings (13B25) Ideals and multiplicative ideal theory in commutative rings (13A15) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Cites Work

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• The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes
• Homomorphisms preserving neural ideals
• Neural Codes, Decidability, and a New Local Obstruction to Convexity
• Polarization of neural rings
• Morphisms of Neural Codes
• Polarization and spreading of monomial ideals
• What Makes a Neural Code Convex?

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