國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

A Comparison Framework For Interleav...

Levanger, Rachel.

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics.
作者:	Levanger, Rachel.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, 2017
面頁冊數:	187 p.
附註:	Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
附註:	Adviser: Konstantin Mischaikow.
Contained By:	Dissertation Abstracts International79-05B(E).
標題:	Mathematics.
電子資源:	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.
LDR:02015nmm a2200325 4500 001 523985
005 20180517120326.5
008 180709s2017 ||||||||||||||||| ||eng d
020 $a 9780355552034
035 $a (MiAaPQ)AAI10753105
035 $a (MiAaPQ)rutgersnb:7974
035 $a AAI10753105
040 $a MiAaPQ $c MiAaPQ
100 1 $a Levanger, Rachel. $3 795515
245 1 2 $a A Comparison Framework For Interleaved Persistence Modules and Applications of Persistent Homology to Problems in Fluid Dynamics.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 187 p.
500 $a Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
500 $a Adviser: Konstantin Mischaikow.
502 $a Thesis (Ph.D.)--Rutgers The State University of New Jersey - New Brunswick, 2017.
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.
590 $a School code: 0190.
650 4 $a Mathematics. $3 184409
650 4 $a Physics. $3 179414
650 4 $a Computer science. $3 199325
690 $a 0405
690 $a 0605
690 $a 0984
710 2 $a Rutgers The State University of New Jersey - New Brunswick. $b Mathematics. $3 708790
773 0 $t Dissertation Abstracts International $g 79-05B(E).
790 $a 0190
791 $a Ph.D.
792 $a 2017
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10753105