Vol. 12, No. 5, 2019

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Author Index Coming Soon Other MSP Journals
Sparse neural codes and convexity

R. Amzi Jeffs, Mohamed Omar, Natchanon Suaysom, Aleina Wachtel and Nora Youngs

Vol. 12 (2019), No. 5, 737–754
Abstract

Determining how the brain stores information is one of the most pressing problems in neuroscience. In many instances, the collection of stimuli for a given neuron can be modeled by a convex set in ${ℝ}^{d}$. Combinatorial objects known as neural codes can then be used to extract features of the space covered by these convex regions. We apply results from convex geometry to determine which neural codes can be realized by arrangements of open convex sets. We restrict our attention primarily to sparse codes in low dimensions. We find that intersection-completeness characterizes realizable 2-sparse codes, and show that any realizable 2-sparse code has embedding dimension at most $3$. Furthermore, we prove that in ${ℝ}^{2}$ and ${ℝ}^{3}$, realizations of 2-sparse codes using closed sets are equivalent to those with open sets, and this allows us to provide some preliminary results on distinguishing which 2-sparse codes have embedding dimension at most $2$.

We have not been able to recognize your IP address 3.239.119.61 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

Keywords
neural code, sparse, convexity
Mathematical Subject Classification 2010
Primary: 05C62, 52A10, 92B20