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A Comparison Framework For Interleav...

Rutgers The State University of New Jersey - New Brunswick.

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

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics./
Author:	Levanger, Rachel.
Description:	1 online resource (187 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
Contained By:	Dissertation Abstracts International79-05B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
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. - 1 online resource (187 pages)

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

Thesis (Ph.D.)

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355552034Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics.
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100 1 $a Levanger, Rachel. $3 1182577
245 1 2 $a A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics.
264 0 $c 2017
300 $a 1 online resource (187 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
500 $a Adviser: Konstantin Mischaikow.
502 $a Thesis (Ph.D.) $c Rutgers The State University of New Jersey - New Brunswick $d 2017.
504 $a Includes bibliographical references
520 $a 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.
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Physics. $3 564049
650 4 $a Computer science. $3 573171
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0605
690 $a 0984
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Rutgers The State University of New Jersey - New Brunswick. $b Mathematics. $3 1182578
773 0 $t Dissertation Abstracts International $g 79-05B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10753105 $z click for full text (PQDT)

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