A parameterized family of tensor products on persistence modules produces Künneth short exact sequences and universal coefficient theorems usable for persistent homology of filtered CW complexes and product spaces.
Cohen-Steiner, H
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A normal form for curved differentials guarantees (4n-2)-complex structures from n-nilpotent curvature and gives Lipschitz control on persistent homology barcodes.
MS-COOT uses co-optimal transport on hypergraph representations of Morse-Smale complexes to enable explicit region-to-region matching for identifying structural events such as splitting and merging.
Proves Cheeger inequalities for persistent up p-Laplacians on complex inclusions, with reductions for pseudomanifolds and comparisons to graph cases.
Introduces variance-based TSI for persistence barcodes, defines scale-invariant cvTSI as an affine function of Rényi-2 collision probability, and shows complementary behavior to entropy on synthetic and time-series data.
Random slicing for subsampling combined with Nadaraya-Watson smoothing enables faster and improved persistence-based topological optimization of point clouds in 2D and 3D.
A standardized pipeline converts time series to graphs, computes persistence diagrams, and extracts features that classify UCR benchmarks, with diffusion distance outperforming shortest-path metrics and performance varying by graph type.
Two persistent homology pipelines quantify regional thinning and pairwise structural similarity in T1 MRI, separating AD from CN subjects at ROC-AUC 0.895 and tracking longitudinal change without template registration.
HOLE applies persistent homology to latent embeddings in neural networks and uses visualizations such as cluster flow diagrams to reveal patterns of class separation, feature disentanglement, and robustness.
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Persistent Homology of Time Series through Complex Networks
A standardized pipeline converts time series to graphs, computes persistence diagrams, and extracts features that classify UCR benchmarks, with diffusion distance outperforming shortest-path metrics and performance varying by graph type.