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A Comparison Framework For Interleav...

Levanger, Rachel.

A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics.
Author:	Levanger, Rachel.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2017
Description:	187 p.
Notes:	Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
Notes:	Adviser: Konstantin Mischaikow.
Contained By:	Dissertation Abstracts International79-05B(E).
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10753105
ISBN:	9780355552034

A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics.
Levanger, Rachel.

A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 187 p.

Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.

Thesis (Ph.D.)--Rutgers The State University of New Jersey - New Brunswick, 2017.

We prove an algebraic stability theorem for interleaved persistence modules that is more general than any formulations currently in the literature. We show how this generalization leads to a framework that may be used to compare persistence modules locally, enabling the computation of non-uniform error bounds for persistence diagrams. We give several examples of how to use this comparison framework, and also address an open problem on non-uniform sublevel set filtrations.

ISBN: 9780355552034Subjects--Topical Terms:

184409
Mathematics.

A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics.
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520 $a We also give two applications of persistent homology to problems in fluid dynamics. Our first application examines the structure of the dynamics of a time-evolving system on a two-dimensional domain, where we give examples for studying fixed points and periodic orbits. Our second application uses persistent homology in conjunction with techniques in computer vision to study pattern defects in the spiral defect chaos regime of Rayleigh-Benard convection.
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