8 papers
Encoding the Euler Characteristic Transform
Nello Blaser, Odin Hoff Gardaa, Lars M. Salbu +2
The Euler Characteristic Curve (ECC) records the Euler characteristic of a linearly embedded cell complex as a function of filtration height in a given direction, and the Euler Cha…
Reeb Graph of Sample Thickenings
Håvard Bakke Bjerkevik, Nello Blaser, Lars M. Salbu
We consider the Reeb graph of a thickening of points sampled from an unknown space. Our main contribution is a framework to transfer reconstruction results similar to the well-know…
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…
The Parameterized Complexity of Finding Minimum Bounded Chains
Nello Blaser, Morten Brun, Lars M. Salbu +1
Finding the smallest -chain with a specific -boundary in a simplicial complex is known as the \textsc{Minimum Bounded Chain} (MBC) problem. The MBC problem is NP-…