---
res:
bibo_abstract:
- Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r consists
of all points in Rd that have k or more points of X within distance r. We consider
two filtrations—one in scale obtained by fixing k and increasing r, and the other
in depth obtained by fixing r and decreasing k—and we compute the persistence
diagrams of both. While standard methods suffice for the filtration in scale,
we need novel geometric and topological concepts for the filtration in depth.
In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal integer
slices are the order-k Delaunay mosaics of X, and construct a zigzag module of
Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Edelsbrunner, Herbert
foaf_surname: Edelsbrunner
foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9823-6833
- foaf_Person:
foaf_givenName: Georg F
foaf_name: Osang, Georg F
foaf_surname: Osang
foaf_workInfoHomepage: http://www.librecat.org/personId=464B40D6-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.1007/s00454-021-00281-9
dct_date: 2021^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/01795376
- http://id.crossref.org/issn/14320444
dct_language: eng
dct_publisher: Springer Nature@
dct_title: The multi-cover persistence of Euclidean balls@
...