Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 4 of 4 for “"persistence diagrams"”.
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Homological Illusions of Persistence and Stability
… of points in the extended plane called persistence diagram.</p><p>We start with the question of ridding the function of topological noise as suggested by its persistence diagram. We give an algorithm for hierarchically finding such epsilon-simplifications on 2-manifolds as well as answer …
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Topics in applied topology
… mature theory with well-defined invariants like persistence diagrams, many real-world phenomena are inherently characterized by multiple interacting parameters. On the theoretical front, this thesis investigates biparameter persistent homology, a more expressive but significantly more challenging …
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Structural features of persistent homology and their algorithmic transformations
… cycle representatives that are associated to persistence diagrams. A common background to the subject covers several aspects: schemes to process input data (embedding it in a low-dimensional manifold), categorical descriptions of persistence objects, and algorithms by which the barcode …
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Generalized Rank Invariant : Structure, Möbius Inversion, and Persistence Diagram
… Unlike the one-parameter case, multiparameter persistence modules lack a complete discrete invariant analogous to barcodes, and their classification requires tools that can capture subtle interactions across the indexing poset. In this thesis we develop and study a generalized rank invariant …