Gröbner Bases of Convex Neural Code Ideals (Research)

DOI10.1007/978-3-030-42687-3_8zbMath1440.13115OpenAlexW3043434019MaRDI QIDQ5118667

Qingzhong Liang, Jingzhen Hu, Molly Honecker, Kaitlyn Phillipson, Elena S. Dimitrova

Publication date: 26 August 2020

Published in: Advances in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-42687-3_8

Mathematics Subject Classification ID

Neural biology (92C20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Uses Software

• neural ideal

Cites Work

• The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes
• Obstructions to convexity in neural codes
• The Hilbert zonotope and a polynomial time algorithm for universal Gröbner bases.
• Neural ideals in SageMath
• On open and closed convex codes
• Geometric characterization of data sets with unique reduced Gröbner bases
• Classification of open and closed convex codes on five neurons
• Algebraic signatures of convex and non-convex codes
• Small Gröbner fans of ideals of points
• Gröbner bases of neural ideals
• Ideals, Varieties, and Algorithms
• What Makes a Neural Code Convex?

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