Year: 2026
Type: preprint
Abstract: We introduce the notion of birth and death cochains as generalized versions of birth and death simplices in persistent cohomology. We show that birth and death cochains (unlike birth and death simplices) are always unique for a given persistent cohomology class. We use birth and death cochains to define birth and death content as generalizations of birth and death times. We then demonstrate the advantages of using that birth and death content as loss functions on a variety of topological optimization tasks with point clouds, time series and scalar fields. We close with a novel application of topological optimization to a dataset of arctic ice images.
Source: arXiv (Cornell University)
Authors: Weighill, Thomas, Zhou, Ling
Institutions: University of North Carolina at Greensboro, Duke University
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7141275554
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