자료유형  

 학위논문

Control Number  

0016932763

International Standard Book Number  

9798379843601

Dewey Decimal Classification Number  

512.942

Main Entry-Personal Name  

Karisani, Negin.

Publication, Distribution, etc. (Imprint  

[S.l.] : Purdue University., 2022

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2022

Physical Description  

1 online resource(137 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 85-01, Section: B.

General Note  

Advisor: Basu, Saugata.

Dissertation Note  

Thesis (Ph.D.)--Purdue University, 2022.

Restrictions on Access Note  

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

Summary, Etc.  

요약Applied topology is a rapidly growing discipline aiming at using ideas coming from algebraic topology to solve problems in the real world, including analyzing point cloud data, shape analysis, etc. Semi-algebraic geometry deals with studying properties of semi-algebraic sets that are subsets of Rnand defined in terms of polynomial inequalities. Semi-algebraic sets are ubiquitous in applications in areas such as modeling, motion planning, etc. Developing efficient algorithms for computing topological invariants of semi-algebraic sets is a rich and well-developed field. However, applied topology has thrown up new invariants-such as persistent homology and barcodes-which give us new ways of looking at the topology of semi-algebraic sets. In this thesis, we investigate the interplay between these two areas. We aim to develop new efficient algorithms for computing topological invariants of semialgebraic sets, such as persistent homology, and to develop new mathematical tools to make such algorithms possible.

Subject Added Entry-Topical Term  

Polynomials.

Subject Added Entry-Topical Term  

Theorems.

Subject Added Entry-Topical Term  

Geometry.

Subject Added Entry-Topical Term  

Bar codes.

Subject Added Entry-Topical Term  

Linear algebra.

Subject Added Entry-Topical Term  

Mathematics.

Added Entry-Corporate Name  

Purdue University.

Host Item Entry  

Dissertations Abstracts International. 85-01B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:643764