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dc.contributor.advisor Edelsbrunner, Herbert en_US
dc.contributor.author Patel, Amit en_US
dc.date.accessioned 2010-05-10T20:17:15Z
dc.date.available 2010-05-10T20:17:15Z
dc.date.issued 2010 en_US
dc.identifier.uri http://hdl.handle.net/10161/2447
dc.description Dissertation en_US
dc.description.abstract <p>We study how the preimages of a mapping f : X &rarr Y between manifolds vary under perturbations. First, we consider the preimage of a single point and track the history of its connected component as this point varies in Y. This information is compactly represented in a structure that is the generalization of the Reeb graph we call the Reeb space. We study its local and global properties and provide an algorithm for its construction. Using homology, we then consider higher dimensional connectivity of the preimage. We develop a theory quantifying the stability of each homology class under perturbations of the mapping f . This number called robustness is given to each homology class in the preimage. The robustness of a class is the magnitude of the perturbation necessary to remove it from the preimage. The generality of this theory allows for many applications. We apply this theory to quantify the stability of contours, fixed points, periodic orbits, and more.</p> en_US
dc.format.extent 755071 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.subject Computer Science en_US
dc.subject fixed points en_US
dc.subject homology en_US
dc.subject manifolds en_US
dc.subject persistence en_US
dc.subject stability en_US
dc.subject transversality en_US
dc.title Reeb Spaces and the Robustness of Preimages en_US
dc.type Dissertation en_US
dc.department Computer Science en_US

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