L-fuzzy simplicial homology generalizes simplicial homology to L-fuzzy subcomplexes by assigning values from a completely distributive lattice L to simplices and deriving associated homology modules.
Morse theory for chromatic de- launay triangulations
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Mixup barcodes and summary statistics (total mixup, total percentage mixup) are defined to capture geometric-topological interactions between point sets and applied to assess class disentanglement in embeddings.
The paper surveys algebraic properties of poset representations and their stability under the interleaving distance in persistence theory.
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L-fuzzy simplicial homology
L-fuzzy simplicial homology generalizes simplicial homology to L-fuzzy subcomplexes by assigning values from a completely distributive lattice L to simplices and deriving associated homology modules.
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Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds
Mixup barcodes and summary statistics (total mixup, total percentage mixup) are defined to capture geometric-topological interactions between point sets and applied to assess class disentanglement in embeddings.
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An Algebraic Introduction to Persistence
The paper surveys algebraic properties of poset representations and their stability under the interleaving distance in persistence theory.