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
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
years
2026 3verdicts
UNVERDICTED 3roles
background 1polarities
support 1representative citing papers
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.
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.
citing papers explorer
-
Canopies: A Generalization of Vines and Vineyards for Parameterized Persistence
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.
-
Computing Homomorphisms of Poset Representations with Applications to Multiparameter Persistence
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.
-
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.