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Universal
Gröbner bases of toric ideals of combinatorial neural
codes
Melissa Beer, Robert Davis, Thomas Elgin, Matthew Hertel, Kira Laws, Rajinder Mavi, Paula Mercurio and Alexandra Newlon
Vol. 14 (2021), No. 5, 723–742
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Abstract |
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In the 1970s, O’Keefe and Dostrovsky discovered that certain neurons, called place cells, in an animal’s brain are tied to its location within its arena. A combinatorial neural code is a collection of -vectors which encode the patterns of cofiring activity among the place cells. Gross, Obatake, and Youngs have recently used techniques from toric algebra to study when a neural code is 0-, 1-, or 2-inductively pierced: a property that allows one to reconstruct a Venn diagram-like planar figure that acts as a geometric schematic for the neural cofiring patterns. This article continues their work by closely focusing on an assortment of classes of combinatorial neural codes. In particular, we identify universal Gröbner bases of the toric ideals for these codes. |
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Keywords
combinatorial neural codes, place cells
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Mathematical Subject Classification 2010
Primary: 13P25, 92B20
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Milestones
Received: 22 April 2019
Revised: 15 June 2021
Accepted: 18 June 2021
Published: 9 February 2022
Communicated by Ann N. Trenk
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Authors |
| Melissa Beer | |
| Department of Mathematics and
Computing Franklin College Franklin, IN United States |
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| Robert Davis | |
| Department of Mathematics Colgate University Hamilton, NY United States |
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| Thomas Elgin | |
| Department of Mathematics University of South Carolina Columbia, SC United States |
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| Matthew Hertel | |
| Department of Mathematics Michigan State University East Lansing, MI United States |
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| Kira Laws | |
| Department of Mathematical
Sciences Applachian State University Boone, NC United States |
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| Rajinder Mavi | |
| Department of Mathematics University of Cincinnati Cincinnati, OH United States |
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| Paula Mercurio | |
| Department of Mathematics Michigan State University Lansing, MI United States |
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| Alexandra Newlon | |
| Department of Mathematics Colgate University Hamilton, NY United States |
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