Canopies generalize vines and vineyards by tracking simplex pairs in filtered chain complexes instead of persistence diagram points, with proofs of homeomorphism and applications to multiplicity and monodromy.
Topological Persistence and Simplification
5 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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New algorithms compute Hom spaces for poset representations in O(n^4 (thick(Y) + thick(Omega^1 Y))^2) time using a uniqueness result for lifts, plus a classical O(n^3 thick(Y)^3) method, both improving on O(n^6) and strengthening AIDA for multiparameter persistence.
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.
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.
Studies changes in geometric properties of conv(W · a) for finite Coxeter groups W, with focus on persistent simplices, triangulations, and subdivisions.
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The Topological Stability Index: A Variance-Based Measure for Persistence Barcodes
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.