Cover refinements enable a near-linear-size approximation to the Vietoris-Rips filtration with unconditional log-3 interleaving that preserves persistent homology.
Ripser: efficient Computation of Vietoris–Rips Persistence Barcodes
10 Pith papers cite this work. Polarity classification is still indexing.
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STRAND treats persistence diagrams as survival data to derive a calibrated two-sample test, interpretable effect sizes, and a 1-Wasserstein-stable feature vector from one representation.
RedZeD presents a new theoretical framework and algorithm for faster persistent homology computation on Vietoris-Rips filtrations.
SMIXAE is a new mixture-of-autoencoders architecture that learns multidimensional manifolds directly from transformer activations, recovering known structures and identifying novel ones in Gemma 2 2B and 9B models.
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.
A graph encoding of connected-component dynamics enables direct extraction of H0 and H1 zigzag barcodes for binary video, bypassing cubical complexes and achieving linear-time scaling via Dey-Hou decomposition.
Proves Cheeger inequalities for persistent up p-Laplacians on complex inclusions, with reductions for pseudomanifolds and comparisons to graph cases.
The authors combine topological data analysis and multi-objective Bayesian inference to achieve practical parameter identifiability and identify simpler rules in an agent-based model of zebrafish patterns.
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.
citing papers explorer
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It's All About Covers: Persistent Homology of Cover Refinements
Cover refinements enable a near-linear-size approximation to the Vietoris-Rips filtration with unconditional log-3 interleaving that preserves persistent homology.
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A continuum of K\"unneth theorems for persistence modules
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.
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From Frames to Features: Scalable Zigzag Persistence for Binary Video
A graph encoding of connected-component dynamics enables direct extraction of H0 and H1 zigzag barcodes for binary video, bypassing cubical complexes and achieving linear-time scaling via Dey-Hou decomposition.
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Cheeger Inequalities for the Persistent Laplacian
Proves Cheeger inequalities for persistent up p-Laplacians on complex inclusions, with reductions for pseudomanifolds and comparisons to graph cases.
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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.