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dc.contributor.advisorBlumberg, Andrew J.
dc.contributor.advisorBen-Zvi, David, 1974-
dc.creatorGrindstaff, Gillian Roxanne
dc.date.accessioned2021-09-14T23:27:21Z
dc.date.available2021-09-14T23:27:21Z
dc.date.created2021-08
dc.date.issued2021-08-13
dc.date.submittedAugust 2021
dc.identifier.urihttps://hdl.handle.net/2152/87742
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/14686
dc.description.abstractA 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.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectPhylogenetics
dc.subjectSupertree
dc.subjectModuli space
dc.subjectManifold learning
dc.subjectNonlinear dimensionality reduction
dc.subjectStratified manifold
dc.subjectTopological data analysis
dc.titleGeometric data analysis for phylogenetic trees and non-contractible manifolds
dc.typeThesis
dc.date.updated2021-09-14T23:27:21Z
dc.contributor.committeeMemberBowen, Lewis
dc.contributor.committeeMemberOwen, Megan
dc.contributor.committeeMemberTran, Ngoc M
dc.description.departmentMathematics
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
dc.creator.orcid0000-0002-3993-1510
dc.type.materialtext


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