Neural ideals and stimulus space visualization

by   Elizabeth Gross, et al.

A neural code C is a collection of binary vectors of a given length n that record the co-firing patterns of a set of neurons. Our focus is on neural codes arising from place cells, neurons that respond to geographic stimulus. In this setting, the stimulus space can be visualized as subset of R^2 covered by a collection U of convex sets such that the arrangement U forms an Euler diagram for C. There are some methods to determine whether such a convex realization U exists; however, these methods do not describe how to draw a realization. In this work, we look at the problem of algorithmically drawing Euler diagrams for neural codes using two polynomial ideals: the neural ideal, a pseudo-monomial ideal; and the neural toric ideal, a binomial ideal. In particular, we study how these objects are related to the theory of piercings in information visualization, and we show how minimal generating sets of the ideals reveal whether or not a code is 0, 1, or 2-inductively pierced.



There are no comments yet.


page 1

page 2

page 3

page 4


Algebraic signatures of convex and non-convex codes

A convex code is a binary code generated by the pattern of intersections...

Neural codes, decidability, and a new local obstruction to convexity

Given an intersection pattern of arbitrary sets in Euclidean space, is t...

An Application of Mosaic Diagrams to the Visualization of Set Relationships

We present an application of mosaic diagrams to the visualisation of set...

IDEAL: A Software Package for Analysis of Influence Diagrams

IDEAL (Influence Diagram Evaluation and Analysis in Lisp) is a software ...

Projective toric codes over hypersimplices

Let d≥ 1 be an integer, and let P be the convex hull in R^s of all integ...

The PSPACE-hardness of understanding neural circuits

In neuroscience, an important aspect of understanding the function of a ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.