Titlebook: Topological Methods in Data Analysis and Visualization III; Theory, Algorithms, Peer-Timo Bremer,Ingrid Hotz,Ronald Peikert Conference pro

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1612-3786 l techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine..978-3-319-38165-7978-3-319-04099-8Series ISSN 1612-3786 Series E-ISSN 2197-666X

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Measuring the Distance Between Merge Trees, one needs a notion of a distance between merge trees, which we define. We provide examples of using our merge tree distance and compare this new measure to other ways used to characterize topological similarity (bottleneck distance for persistence diagrams) and numerical difference (..-norm of the difference between functions).

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Topological Methods in Data Analysis and Visualization III978-3-319-04099-8Series ISSN 1612-3786 Series E-ISSN 2197-666X

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Simplification of Morse Decompositions Using Morse Set Mergerse sets to be merged can be picked based on a variety of criteria. For example, one can allow only pairs whose merger results in a topologically simple Morse set to be selected, and give preference to mergers leading to small Morse sets.