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Invariants and Metrics for Multipara...

Thomas, Ashleigh Linnea.

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Invariants and Metrics for Multiparameter Persistent Homology.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Invariants and Metrics for Multiparameter Persistent Homology./
Author:	Thomas, Ashleigh Linnea.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	125 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
Contained By:	Dissertations Abstracts International80-12B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13808305
ISBN:	9781392195710

Invariants and Metrics for Multiparameter Persistent Homology.
Thomas, Ashleigh Linnea.

Invariants and Metrics for Multiparameter Persistent Homology. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 125 p.

Source: Dissertations Abstracts International, Volume: 80-12, Section: B.

Thesis (Ph.D.)--Duke University, 2019.

This item must not be sold to any third party vendors.

This dissertation is about building fundamental techniques for comparing data via a geometric and topological data analysis method called multiparameter persistent homology. The techniques used are largely algebraic. A new summary statistic, called the multirank function, is introduced as a measure of persistence output that detects relationships between important features of the data being analyzed. Also introduced is a technique for modifying existing metrics on the space of persistence outputs. Existing metrics can return infinite distances, which do not give as much information as a finite distance; the proposed modification gives fewer such situations. The final chapter of this dissertation details work in a long-term biology research project. Persistence is used to study the relationship between continuous morphological variation and rates of topologically abnormal morphologies in populations of fruit flies. Some preliminary computations showing proof of concept are included. Future plans involve using theoretical contributions from this dissertation for final analysis of the fly data.The distance modification is joint work with Ezra Miller and the biology application is joint with Surabhi Beriwal, Ezra Miller, and biologists at the Houle Lab at Florida State University.

ISBN: 9781392195710Subjects--Topical Terms:

1669109
Applied Mathematics.

Invariants and Metrics for Multiparameter Persistent Homology.
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500 $a Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Miller, Ezra.
502 $a Thesis (Ph.D.)--Duke University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a This dissertation is about building fundamental techniques for comparing data via a geometric and topological data analysis method called multiparameter persistent homology. The techniques used are largely algebraic. A new summary statistic, called the multirank function, is introduced as a measure of persistence output that detects relationships between important features of the data being analyzed. Also introduced is a technique for modifying existing metrics on the space of persistence outputs. Existing metrics can return infinite distances, which do not give as much information as a finite distance; the proposed modification gives fewer such situations. The final chapter of this dissertation details work in a long-term biology research project. Persistence is used to study the relationship between continuous morphological variation and rates of topologically abnormal morphologies in populations of fruit flies. Some preliminary computations showing proof of concept are included. Future plans involve using theoretical contributions from this dissertation for final analysis of the fly data.The distance modification is joint work with Ezra Miller and the biology application is joint with Surabhi Beriwal, Ezra Miller, and biologists at the Houle Lab at Florida State University.
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