Graduation Year


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science



Reader 1

Mohamed Omar

Reader 2

Dagan Karp

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2017 Caitlin R Lienkaemper


How does the brain encode the spatial structure of the external world?

A partial answer comes through place cells, hippocampal neurons which

become associated to approximately convex regions of the world known

as their place fields. When an organism is in the place field of some place

cell, that cell will fire at an increased rate. A neural code describes the set

of firing patterns observed in a set of neurons in terms of which subsets

fire together and which do not. If the neurons the code describes are place

cells, then the neural code gives some information about the relationships

between the place fields–for instance, two place fields intersect if and only if

their associated place cells fire together. Since place fields are convex, we are

interested in determining which neural codes can be realized with convex

sets and in finding convex sets which generate a given neural code when

taken as place fields. To this end, we study algebraic invariants associated

to neural codes, such as neural ideals and toric ideals. We work with a

special class of convex codes, known as inductively pierced codes, and seek

to identify these codes through the Gröbner bases of their toric ideals.