27 citations · 97 across the 19 of their papers we have counts for
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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…
Relative persistent homology
Nello Blaser, Morten Brun
The alpha complex efficiently computes persistent homology of a point cloud in Euclidean space when the dimension is low. Given a subset of , relative persistent hom…
Sparse Nerves in Practice
Nello Blaser, Morten Brun
Topological data analysis combines machine learning with methods from algebraic topology. Persistent homology, a method to characterize topological features occurring in data at mu…
Sparse Filtered Nerves
Nello Blaser, Morten Brun
Given a point cloud in Euclidean space and a positive parameter we can consider the -neighborhood of consisting of points at distance less than to . H…