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Methods and applications of topological data analysis

Author: Jennifer Novak Kloke; G Carlsson; Steve Kerckhoff; Rafe Mazzeo; Stanford University. Department of Mathematics.
Publisher: 2010.
Dissertation: Ph. D. Stanford University 2010
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : English
Database:WorldCat
Summary:
The focus of this dissertation is the development of methods for topological analysis as well as the application of topological tools to real world problems. The first half of the dissertation focuses on an algorithm for de-noising high-dimensional data for topological data analysis. This method significantly extends the applicability of many topological data analysis methods. In particular, this method extends the  Read more...
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Details

Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jennifer Novak Kloke; G Carlsson; Steve Kerckhoff; Rafe Mazzeo; Stanford University. Department of Mathematics.
OCLC Number: 652792734
Notes: Submitted to the Department of Mathematics.
Description: 1 online resource
Responsibility: Jennifer Novak Kloke.

Abstract:

The focus of this dissertation is the development of methods for topological analysis as well as the application of topological tools to real world problems. The first half of the dissertation focuses on an algorithm for de-noising high-dimensional data for topological data analysis. This method significantly extends the applicability of many topological data analysis methods. In particular, this method extends the use of persistent homology, a generalized notion of homology for discrete data points, to data sets that were previously inaccessible because of noise. The second half of this dissertation focuses on a method for using topology to simplify complex chemical structures and to define a metric to quantify similarity for use in screening large databases of chemical compounds. This method has shown very promising initial results in locating new materials for efficiently separating carbon dioxide from the exhaust of coal-burning power plants.

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