4 papers · 1 filter
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…
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…
On the bottleneck stability of rank decompositions of multi-parameter persistence modules
Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot +1
A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations -- often referred to as multi-paramet…
Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions
Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot
In this paper, we introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally…