2018/07/06 by Molly Hoch, Hoch, Molly, Samuel Muthiah +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Medicine · #Cholinesterase and Neurodegenerative Diseases #Commutative Algebra and Its Applications #Digital Image Processing Techniques #FOS: Biological sciences #Neurons and Cognition (q-bio.NC) #Topological and Geometric Data Analysis #q-bio.NC
paper · pdf · doi:10.48550/arxiv.1807.02390
arxiv created 2018/07/06 · openalex publication_date 2018/07/06 · arxiv updated 2018/07/09 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
Neural codes are binary codes in \0,1\n; here we focus on the ones which represent the firing patterns of a type of neurons called place cells. There is much interest in determining which neural codes can be realized by a collection of convex sets. However, drawing representations of these convex sets, particularly as the number of neurons in a code increases, can be very difficult. Nevertheless, for a class of codes that are said to be k-inductively pierced for k=0,1,2 there is an algorithm for drawing Euler diagrams. Here we use the toric ideal of a code to show sufficient conditions for a code to be 1- or 2-inductively pierced, so that we may use the existing algorithm to draw realizations of such codes.