For any fixed c ≥ 1, there exist finite metric spaces whose Vietoris-Rips filtration cannot be c-approximated by any finitely presented construction of linear size; for c < √2, exponential size is required.
Persistence stability for geo- metric complexes.Geometriae Dedicata, 173(1), 2014
2 Pith papers cite this work. Polarity classification is still indexing.
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Introduces a new solvability theory for multiple fractional cohomological equations of Type II to establish effective higher-order mixing with partial regularity in the semisimple setting.
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Lower Bounds for Approximating the Vietoris-Rips Filtration
For any fixed c ≥ 1, there exist finite metric spaces whose Vietoris-Rips filtration cannot be c-approximated by any finitely presented construction of linear size; for c < √2, exponential size is required.
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Multiple mixing and multiple fractional cohomological equation: semisimple setting
Introduces a new solvability theory for multiple fractional cohomological equations of Type II to establish effective higher-order mixing with partial regularity in the semisimple setting.