---
_id: '9630'
abstract:
- lang: eng
  text: Various kinds of data are routinely represented as discrete probability distributions.
    Examples include text documents summarized by histograms of word occurrences and
    images represented as histograms of oriented gradients. Viewing a discrete probability
    distribution as a point in the standard simplex of the appropriate dimension,
    we can understand collections of such objects in geometric and topological terms.  Importantly,
    instead of using the standard Euclidean distance, we look into dissimilarity measures
    with information-theoretic justification, and we develop the theory needed for
    applying topological data analysis in this setting. In doing so, we emphasize
    constructions that enable the usage of existing computational topology software
    in this context.
acknowledgement: This research is partially supported by the Office of Naval Research,
  through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
  109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
  the Austrian Science Fund (FWF).
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Ziga
  full_name: Virk, Ziga
  id: 2E36B656-F248-11E8-B48F-1D18A9856A87
  last_name: Virk
- first_name: Hubert
  full_name: Wagner, Hubert
  id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
citation:
  ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
    space. <i>Journal of Computational Geometry</i>. 2020;11(2):162-182. doi:<a href="https://doi.org/10.20382/jocg.v11i2a7">10.20382/jocg.v11i2a7</a>
  apa: Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2020). Topological data analysis
    in information space. <i>Journal of Computational Geometry</i>. Carleton University.
    <a href="https://doi.org/10.20382/jocg.v11i2a7">https://doi.org/10.20382/jocg.v11i2a7</a>
  chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
    Analysis in Information Space.” <i>Journal of Computational Geometry</i>. Carleton
    University, 2020. <a href="https://doi.org/10.20382/jocg.v11i2a7">https://doi.org/10.20382/jocg.v11i2a7</a>.
  ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
    space,” <i>Journal of Computational Geometry</i>, vol. 11, no. 2. Carleton University,
    pp. 162–182, 2020.
  ista: Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information
    space. Journal of Computational Geometry. 11(2), 162–182.
  mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
    <i>Journal of Computational Geometry</i>, vol. 11, no. 2, Carleton University,
    2020, pp. 162–82, doi:<a href="https://doi.org/10.20382/jocg.v11i2a7">10.20382/jocg.v11i2a7</a>.
  short: H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11
    (2020) 162–182.
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2021-08-11T12:26:34Z
day: '14'
ddc:
- '510'
- '000'
department:
- _id: HeEd
doi: 10.20382/jocg.v11i2a7
file:
- access_level: open_access
  checksum: f02d0b2b3838e7891a6c417fc34ffdcd
  content_type: application/pdf
  creator: asandaue
  date_created: 2021-08-11T11:55:11Z
  date_updated: 2021-08-11T11:55:11Z
  file_id: '9882'
  file_name: 2020_JournalOfComputationalGeometry_Edelsbrunner.pdf
  file_size: 1449234
  relation: main_file
  success: 1
file_date_updated: 2021-08-11T11:55:11Z
has_accepted_license: '1'
intvolume: '        11'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '12'
oa: 1
oa_version: Published Version
page: 162-182
project:
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
  grant_number: I4887
  name: Discretization in Geometry and Dynamics
publication: Journal of Computational Geometry
publication_identifier:
  eissn:
  - 1920180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological data analysis in information space
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
  name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
  short: CC BY (3.0)
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 11
year: '2020'
...
---
_id: '737'
abstract:
- lang: eng
  text: We generalize Brazas’ topology on the fundamental group to the whole universal
    path space X˜ i.e., to the set of homotopy classes of all based paths. We develop
    basic properties of the new notion and provide a complete comparison of the obtained
    topology with the established topologies, in particular with the Lasso topology
    and the CO topology, i.e., the topology that is induced by the compact-open topology.
    It turns out that the new topology is the finest topology contained in the CO
    topology, for which the action of the fundamental group on the universal path
    space is a continuous group action.
article_processing_charge: No
author:
- first_name: Ziga
  full_name: Virk, Ziga
  id: 2E36B656-F248-11E8-B48F-1D18A9856A87
  last_name: Virk
- first_name: Andreas
  full_name: Zastrow, Andreas
  last_name: Zastrow
citation:
  ama: Virk Z, Zastrow A. A new topology on the universal path space. <i>Topology
    and its Applications</i>. 2017;231:186-196. doi:<a href="https://doi.org/10.1016/j.topol.2017.09.015">10.1016/j.topol.2017.09.015</a>
  apa: Virk, Z., &#38; Zastrow, A. (2017). A new topology on the universal path space.
    <i>Topology and Its Applications</i>. Elsevier. <a href="https://doi.org/10.1016/j.topol.2017.09.015">https://doi.org/10.1016/j.topol.2017.09.015</a>
  chicago: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path
    Space.” <i>Topology and Its Applications</i>. Elsevier, 2017. <a href="https://doi.org/10.1016/j.topol.2017.09.015">https://doi.org/10.1016/j.topol.2017.09.015</a>.
  ieee: Z. Virk and A. Zastrow, “A new topology on the universal path space,” <i>Topology
    and its Applications</i>, vol. 231. Elsevier, pp. 186–196, 2017.
  ista: Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology
    and its Applications. 231, 186–196.
  mla: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.”
    <i>Topology and Its Applications</i>, vol. 231, Elsevier, 2017, pp. 186–96, doi:<a
    href="https://doi.org/10.1016/j.topol.2017.09.015">10.1016/j.topol.2017.09.015</a>.
  short: Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.
date_created: 2018-12-11T11:48:14Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:53:01Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2017.09.015
external_id:
  isi:
  - '000413889100012'
intvolume: '       231'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 186 - 196
publication: Topology and its Applications
publication_identifier:
  issn:
  - '01668641'
publication_status: published
publisher: Elsevier
publist_id: '6930'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A new topology on the universal path space
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 231
year: '2017'
...
---
_id: '521'
abstract:
- lang: eng
  text: Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y
    induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful
    in showing that the classical dimension raising theorems hold in large scale;
    that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and
    Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely
    n-to-1 maps, which include the natural quotient maps via a finite group action,
    and prove that they preserve the asymptotic dimension.
author:
- first_name: Kyle
  full_name: Austin, Kyle
  last_name: Austin
- first_name: Ziga
  full_name: Virk, Ziga
  id: 2E36B656-F248-11E8-B48F-1D18A9856A87
  last_name: Virk
citation:
  ama: Austin K, Virk Z. Higson compactification and dimension raising. <i>Topology
    and its Applications</i>. 2017;215:45-57. doi:<a href="https://doi.org/10.1016/j.topol.2016.10.005">10.1016/j.topol.2016.10.005</a>
  apa: Austin, K., &#38; Virk, Z. (2017). Higson compactification and dimension raising.
    <i>Topology and Its Applications</i>. Elsevier. <a href="https://doi.org/10.1016/j.topol.2016.10.005">https://doi.org/10.1016/j.topol.2016.10.005</a>
  chicago: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
    <i>Topology and Its Applications</i>. Elsevier, 2017. <a href="https://doi.org/10.1016/j.topol.2016.10.005">https://doi.org/10.1016/j.topol.2016.10.005</a>.
  ieee: K. Austin and Z. Virk, “Higson compactification and dimension raising,” <i>Topology
    and its Applications</i>, vol. 215. Elsevier, pp. 45–57, 2017.
  ista: Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology
    and its Applications. 215, 45–57.
  mla: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
    <i>Topology and Its Applications</i>, vol. 215, Elsevier, 2017, pp. 45–57, doi:<a
    href="https://doi.org/10.1016/j.topol.2016.10.005">10.1016/j.topol.2016.10.005</a>.
  short: K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.
date_created: 2018-12-11T11:46:56Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:01:21Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2016.10.005
intvolume: '       215'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1608.03954v1
month: '01'
oa: 1
oa_version: Submitted Version
page: 45 - 57
publication: Topology and its Applications
publication_identifier:
  issn:
  - '01668641'
publication_status: published
publisher: Elsevier
publist_id: '7299'
quality_controlled: '1'
status: public
title: Higson compactification and dimension raising
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 215
year: '2017'
...