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Algorithms and hardness results in c...

Chen, Chao.

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Algorithms and hardness results in computational homology.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Algorithms and hardness results in computational homology./
作者:	Chen, Chao.
面頁冊數:	108 p.
附註:	Source: Dissertation Abstracts International, Volume: 70-12, Section: B, page: 7660.
Contained By:	Dissertation Abstracts International70-12B.
標題:	Computer Science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3385638
ISBN:	9781109515138

Algorithms and hardness results in computational homology.
Chen, Chao.

Algorithms and hardness results in computational homology. - 108 p.

Source: Dissertation Abstracts International, Volume: 70-12, Section: B, page: 7660.

Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 2009.

In this thesis, we address various issues concerning characterizing topological features in computation.

ISBN: 9781109515138Subjects--Topical Terms:

626642
Computer Science.

Algorithms and hardness results in computational homology.
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245 1 0 $a Algorithms and hardness results in computational homology.
300 $a 108 p.
500 $a Source: Dissertation Abstracts International, Volume: 70-12, Section: B, page: 7660.
500 $a Adviser: Daniel Freedman.
502 $a Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 2009.
520 $a In this thesis, we address various issues concerning characterizing topological features in computation.
520 $a First, we define metrics on homology classes. This definition uses the discrete metric and the induced geodesic distance. A polynomial algorithm is provided to compute these measure. Besides, this work leads to the definition and algorithm of a canonical basis of the homology group, namely, the optimal homology basis. A straightforward algorithm and an improved algorithm are given.
520 $a Second, we discuss the problem of homology localization, namely, localizing a homology class with a cycle which is concise in geometry. This problem is posed as an optimization problem. Different objective function is discussed. For the volume function, we show that the problem is NP-hard to approximate within constant factor. Other objective functions are also discussed, namely, the diameter and the radius.
520 $a Third, we study the problem of enriching persistent homology. The objective is to reveal structural relationship between persistent homology classes by computing canonical representative cycles. Various definitions are provided basing on an extension of persistent homology. However, it has been proven that these definitions are not stable with regard to the change of filter function.
520 $a Fourth, we apply computation topology method in ribosome drug docking problem. More specifically, we compute the pockets/cavities relating to the drug docking sites. Interesting insights about ribosome are revealed by our work. However, the results are not specific enough for studying drug docking sites.
590 $a School code: 0185.
650 4 $a Computer Science. $3 626642
690 $a 0984
710 2 $a Rensselaer Polytechnic Institute. $3 1019062
773 0 $t Dissertation Abstracts International $g 70-12B.
790 1 0 $a Freedman, Daniel, $e advisor
790 $a 0185
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3385638