72 citations · 181 across the 18 of their papers we have counts for
23 papers
Cheeger Inequalities for the Persistent Laplacian
Magnus Bakke Botnan, Rui Dong
We study Cheeger-type inequalities for persistent Laplacians associated with inclusions of simplicial complexes . We introduce a persistent…
Extremal Betti Numbers and Persistence in Flag Complexes
Lies Beers, Magnus Bakke Botnan
We investigate several problems concerning extremal Betti numbers and persistence in filtrations of flag complexes. For graphs on vertices, we show that is maximal…
On the additive image of 0th persistent homology
Ulrich Bauer, Magnus Bakke Botnan, Steffen Oppermann +1
For a finite category and a finite field, we study the additive image of the functor $\operatorname{H}_0(-,F) \colon \operatorname{rep}(X, \mathbf{Top}) \to \operatorname{r…
The persistent Laplacian of non-branching complexes
Magnus Bakke Botnan, Rui Dong
Non-branching matrices are real matrices with entries in , where each row contains at most two non-zero entries. Such matrices naturally arise in the study of Laplacian…
Computing -presentation distances is hard
Håvard Bakke Bjerkevik, Magnus Bakke Botnan
Recently, -presentation distances for were introduced for merge trees and multiparameter persistence modules as more sensitive variations of the respective int…
Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures
David Loiseaux, Luis Scoccola, Mathieu Carrière +2
Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g.,…