---
_id: '8135'
abstract:
- lang: eng
  text: Discrete Morse theory has recently lead to new developments in the theory
    of random geometric complexes. This article surveys the methods and results obtained
    with this new approach, and discusses some of its shortcomings. It uses simulations
    to illustrate the results and to form conjectures, getting numerical estimates
    for combinatorial, topological, and geometric properties of weighted and unweighted
    Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes
    contained in the mosaics.
acknowledgement: This project has received funding from the European Research Council
  (ERC) under the European Union’s Horizon 2020 research and innovation programme
  (grant agreements No 78818 Alpha and No 638176). It is also partially supported
  by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and
  Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).
alternative_title:
- Abel Symposia
article_processing_charge: No
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Anton
  full_name: Nikitenko, Anton
  id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
  last_name: Nikitenko
  orcid: 0000-0002-0659-3201
- first_name: Katharina
  full_name: Ölsböck, Katharina
  id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
  last_name: Ölsböck
  orcid: 0000-0002-4672-8297
- first_name: Peter
  full_name: Synak, Peter
  id: 331776E2-F248-11E8-B48F-1D18A9856A87
  last_name: Synak
citation:
  ama: 'Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay
    mosaics and related complexes experimentally. In: <i>Topological Data Analysis</i>.
    Vol 15. Springer Nature; 2020:181-218. doi:<a href="https://doi.org/10.1007/978-3-030-43408-3_8">10.1007/978-3-030-43408-3_8</a>'
  apa: Edelsbrunner, H., Nikitenko, A., Ölsböck, K., &#38; Synak, P. (2020). Radius
    functions on Poisson–Delaunay mosaics and related complexes experimentally. In
    <i>Topological Data Analysis</i> (Vol. 15, pp. 181–218). Springer Nature. <a href="https://doi.org/10.1007/978-3-030-43408-3_8">https://doi.org/10.1007/978-3-030-43408-3_8</a>
  chicago: Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak.
    “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.”
    In <i>Topological Data Analysis</i>, 15:181–218. Springer Nature, 2020. <a href="https://doi.org/10.1007/978-3-030-43408-3_8">https://doi.org/10.1007/978-3-030-43408-3_8</a>.
  ieee: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions
    on Poisson–Delaunay mosaics and related complexes experimentally,” in <i>Topological
    Data Analysis</i>, 2020, vol. 15, pp. 181–218.
  ista: Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on
    Poisson–Delaunay mosaics and related complexes experimentally. Topological Data
    Analysis. , Abel Symposia, vol. 15, 181–218.
  mla: Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics
    and Related Complexes Experimentally.” <i>Topological Data Analysis</i>, vol.
    15, Springer Nature, 2020, pp. 181–218, doi:<a href="https://doi.org/10.1007/978-3-030-43408-3_8">10.1007/978-3-030-43408-3_8</a>.
  short: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data
    Analysis, Springer Nature, 2020, pp. 181–218.
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2026-04-07T12:35:47Z
day: '22'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/978-3-030-43408-3_8
ec_funded: 1
external_id:
  isi:
  - '001321861000008'
file:
- access_level: open_access
  checksum: 7b5e0de10675d787a2ddb2091370b8d8
  content_type: application/pdf
  creator: dernst
  date_created: 2020-10-08T08:56:14Z
  date_updated: 2020-10-08T08:56:14Z
  file_id: '8628'
  file_name: 2020-B-01-PoissonExperimentalSurvey.pdf
  file_size: 2207071
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  success: 1
file_date_updated: 2020-10-08T08:56:14Z
has_accepted_license: '1'
intvolume: '        15'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 181-218
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 2533E772-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '638176'
  name: 'Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large
    Scales'
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I02979-N35
  name: Persistence and stability of geometric complexes
publication: Topological Data Analysis
publication_identifier:
  eissn:
  - 2197-8549
  isbn:
  - '9783030434076'
  issn:
  - 2193-2808
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '19630'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Radius functions on Poisson–Delaunay mosaics and related complexes experimentally
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 15
year: '2020'
...