Title

Convexity of Neural Codes

Graduation Year

2016

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Mohamed Omar

Reader 2

Nora Youngs

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

2016 Robert A Jeffs

Abstract

An important task in neuroscience is stimulus reconstruction: given activity in the brain, what stimulus could have caused it? We build on previous literature which uses neural codes to approach this problem mathematically. A neural code is a collection of binary vectors that record concurrent firing of neurons in the brain. We consider neural codes arising from place cells, which are neurons that track an animal's position in space. We examine algebraic objects associated to neural codes, and completely characterize a certain class of maps between these objects. Furthermore, we show that such maps have natural geometric implications related to the receptive fields of place cells. Lastly we describe several purely geometric results related to neural codes.