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math.AT2025
Monoidal Rips: Stable Multiparameter Filtrations of Directed Networks
Nello Blaser, Morten Brun, Odin Hoff Gardaa +1
We introduce the monoidal Rips filtration, a filtered simplicial set for weighted directed graphs and other lattice-valued networks. Our construction generalizes the Vietoris-Rips…
math.AT2024
Core Bifiltration
Nello Blaser, Morten Brun, Odin Hoff Gardaa +1
The motivation of this paper is to recognize a geometric shape from a noisy sample in the form of a point cloud. Inspired by the HDBSCAN clustering algorithm, we introduce the core…
math.AT2021
Determining homology of an unknown space from a sample
Morten Brun, Belén García Pascual, Lars M. Salbu
The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euc…