Geometric data analysis for phylogenetic trees and non-contractible manifolds
| dc.contributor.advisor | Blumberg, Andrew J. | |
| dc.contributor.advisor | Ben-Zvi, David, 1974- | |
| dc.contributor.committeeMember | Bowen, Lewis | |
| dc.contributor.committeeMember | Owen, Megan | |
| dc.contributor.committeeMember | Tran, Ngoc M | |
| dc.creator | Grindstaff, Gillian Roxanne | |
| dc.creator.orcid | 0000-0002-3993-1510 | |
| dc.date.accessioned | 2021-09-14T23:27:21Z | |
| dc.date.available | 2021-09-14T23:27:21Z | |
| dc.date.created | 2021-08 | |
| dc.date.issued | 2021-08-13 | |
| dc.date.submitted | August 2021 | |
| dc.date.updated | 2021-09-14T23:27:21Z | |
| dc.description.abstract | A phylogenetic tree is an acyclic graph with distinctly labeled leaves, whose internal edges have a positive weight. Given a set {1,2,...,n} of n leaves, the collection of all phylogenetic trees with this leaf set can be assembled into a metric cube complex known as phylogenetic tree space, or Billera-Holmes-Vogtmann tree space, after [9]. In Chapter 2, we show that the isometry group of this space is the symmetric group S [subscript n]. This fact is relevant to the analysis of some statistical tests of phylogenetic trees, such as those introduced in [11]. In Chapter 3, co-authored with Megan Owen, we give a rigorous framework for comparing trees in different moduli spaces of phylogenetic trees, and apply this to define extension spaces of trees, a conservative split-based supertree construction method, and two measures of compatibility between tree fragments. In Chapter 4, we discuss some techniques in manifold learning, and outline a new topologically-constrained nonlinear dimensionality reduction algorithm, which quickly reduces a nerve complex build on local tangent space approximations to produce a small number of manifold charts, visualized by a collection of least squares alignments of contractible components. We also give a method to optimize tangent space alignment on a sphere, and a template for using local tensor decomposition of higher-order moments to extend this technique to intersecting and stratified manifolds. | |
| dc.description.department | Mathematics | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | https://hdl.handle.net/2152/87742 | |
| dc.identifier.uri | http://dx.doi.org/10.26153/tsw/14686 | |
| dc.language.iso | en | |
| dc.subject | Phylogenetics | |
| dc.subject | Supertree | |
| dc.subject | Moduli space | |
| dc.subject | Manifold learning | |
| dc.subject | Nonlinear dimensionality reduction | |
| dc.subject | Stratified manifold | |
| dc.subject | Topological data analysis | |
| dc.title | Geometric data analysis for phylogenetic trees and non-contractible manifolds | |
| dc.type | Thesis | |
| dc.type.material | text | |
| thesis.degree.department | Mathematics | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | The University of Texas at Austin | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy |