5 papers · 1 filter
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…
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…
Dowker Duality for Relations of Categories
Morten Brun, Marius Gårdsmann Fosse, Lars M. Salbu
We propose a categorification of the Dowker duality theorem for relations. Dowker's theorem states that the Dowker complex of a relation of sets and $Y…
The Rectangle Complex of a Relation
Morten Brun, Lars M. Salbu
We construct a simplicial complex, the rectangle complex of a relation R, and show that it is homotopy equivalent to the Dowker complex of R. This results in a short and conceptual…
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…