# Daniel Johanne Collin: Brains and Bugs - Two Applications of Persistent Homology in the Life Sciences

**Time: **
Tue 2021-06-01 09.30 - 10.30

**Location: **
Meeting ID: 697 4204 2109

**Respondent: **
Daniel Johanne Collin

### Abstract

Persistent homology is a way of giving a topological summary of a data set. In this thesis we give an introduction to persistent homology, including a proof of its algebraic decomposition as a finitely generated graded module with respect to a polynomial ring with a field as its underlying ring. This proof is constructive and yields an algorithm for computing persistent homology in a practical sense.

In order to provide examples of the practical applications of persistent homology, we present two case studies. In the first case study, we investigate the relationship between size and persistent homology of the bumblebee Bombus terrestris. We find that the difference in size between samples is in some ways highly correlated to differences in persistent homology. In the second case study, we analyze the persistent homology of a synthetic model of the striatum, a part of the basal ganglia in the brain. Here we find that the synthetic model differs in size and complexity from a number of control models when viewed through the lens of persistent homology and the accompanying theory.

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