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  1. ; ; ; ; ( , Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Mulzer, Wolfgang ; Phillips, Jeff M (Ed.)
    Given a map f:X → M from a topological space X to a metric space M, a decorated Reeb space consists of the Reeb space, together with an attribution function whose values recover geometric information lost during the construction of the Reeb space. For example, when M = ℝ is the real line, the Reeb space is the well-known Reeb graph, and the attributions may consist of persistence diagrams summarizing the level set topology of f. In this paper, we introduce decorated Reeb spaces in various flavors and prove that our constructions are Gromov-Hausdorff stable. We also provide results on approximating decorated Reeb spaces from finite samples and leverage these to develop a computational framework for applying these constructions to point cloud data. 
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  2. ; ; ; ; ; ; ; ; ; ; et al ( , Proceedings of the 41st International Conference on Machine Learning (ICML), 2024.)
    Free, publicly-accessible full text available July 21, 2025
  3. ; ; ; ; ; ; ; ; ; ; et al ( , Proceedings of the 41st International Conference on Machine Learning (ICML))
    Free, publicly-accessible full text available July 21, 2025
  4. ; ; ; ; ; ; ; ; ; ; et al ( , ICML: https://openreview.net/pdf?id=Nl3RG5XWAt)
    Free, publicly-accessible full text available June 24, 2025
  5. ; ; ; ; ; ; ; ; ; ; et al ( , International Conference on Machine Learning 2024 (ICML).)
    Free, publicly-accessible full text available July 1, 2025
  6. ; ; ; ; ( , Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML))
  7. ; ; ; ; ( , Journal of applied and computational topology)
    Full Text Available 
  8. ; ( , Theory and applications of categories)
    In this paper we prove an equivalence theorem originally observed by Robert MacPherson. On one side of the equivalence is the category of cosheaves that are constructible with respect to a locally cone-like stratification. Our constructibility condition is new and only requires that certain inclusions of open sets are sent to isomorphisms. On the other side of the equivalence is the category of functors from the entrance path category, which has points for objects and certain homotopy classes of paths for morphisms. When our constructible cosheaves are valued in Set we prove an additional equivalence with the category of stratified coverings. 
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    Accepted Manuscript Full Text Available
  9. ; ; ; ; ; ; ; ( , Journal of Applied and Computational Topology)
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