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math.AT2026
On the Hausdorff stability of barcodes over posets
Mujtaba Ali, Tom Needham, Anastasios Stefanou +1
The Isometry Theorem of Chazal et al. and Lesnick is a fundamental result in persistence theory, which states that the interleaving distance between two one-parameter persistence m…
math.AT2025
Doughnut or Mickey Mouse? Detecting Toroidal Structure in Data through Persistent Cup-Length
Ekaterina S. Ivshina, Galit Anikeeva, Ling Zhou
Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies bas…
math.AT2025
Persistence and Topological Complexity
Facundo Mémoli, Ling Zhou
Topological complexity is a homotopy invariant that measures the minimal number of continuous rules required for motion planning in a space. In this work, we introduce persistent a…