1 citations · 1 across the 10 of their papers we have counts for
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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…
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…
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…
Persistent cohomology operations and Gromov-Hausdorff estimates
Anibal M. Medina-Mardones, Ling Zhou
We establish the foundations of the theory of persistent cohomology operations, derive decomposition formulas for wedge sums and products, and prove their Gromov-Hausdorff stabilit…
Persistent Sullivan Minimal Models of Metric Spaces
Ling Zhou
We extend classical tools from rational homotopy theory to topological data analysis by introducing persistent Sullivan minimal models of persistent topological spaces. Our main re…