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.
Zigzag Persistence
2 Pith papers cite this work, alongside 264 external citations. Polarity classification is still indexing.
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Interleaving-distance confidence regions for Reeb graphs are obtained from PL proximity-graph estimators, with Mapper treated as a controlled visualization coarsening and extended persistence bounded by twice the interleaving distance.
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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.
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Building confidence regions for Reeb graphs using the interleaving distance
Interleaving-distance confidence regions for Reeb graphs are obtained from PL proximity-graph estimators, with Mapper treated as a controlled visualization coarsening and extended persistence bounded by twice the interleaving distance.