---
_id: '13165'
abstract:
- lang: eng
text: "A graph G=(V, E) is called fully regular if for every independent set I c
V, the number of vertices in V\\I that are not connected to any element of I
depends only on the size of I. A linear ordering of the vertices of G is called
successive if for every i, the first i vertices induce a connected subgraph of
G. We give an explicit formula for the number of successive vertex orderings of
a fully regular graph.\r\nAs an application of our results, we give alternative
proofs of two theorems of Stanley and Gao & Peng, determining the number of linear
edge orderings of complete graphs and complete bipartite graphs, respectively,
with the property that the first i edges induce a connected subgraph.\r\nAs another
application, we give a simple product formula for the number of linear orderings
of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for
every i, the first i hyperedges induce a connected subgraph. We found similar
formulas for complete (non-partite) 3-uniform hypergraphs and in another closely
related case, but we managed to verify them only when the number of vertices is
small."
article_number: '105776'
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Lixing
full_name: Fang, Lixing
last_name: Fang
- first_name: Hao
full_name: Huang, Hao
last_name: Huang
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Gábor
full_name: Tardos, Gábor
last_name: Tardos
- first_name: Junchi
full_name: Zuo, Junchi
last_name: Zuo
citation:
ama: Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully
regular graphs. Journal of Combinatorial Theory Series A. 2023;199(10).
doi:10.1016/j.jcta.2023.105776
apa: Fang, L., Huang, H., Pach, J., Tardos, G., & Zuo, J. (2023). Successive
vertex orderings of fully regular graphs. Journal of Combinatorial Theory.
Series A. Elsevier. https://doi.org/10.1016/j.jcta.2023.105776
chicago: Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive
Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory.
Series A. Elsevier, 2023. https://doi.org/10.1016/j.jcta.2023.105776.
ieee: L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings
of fully regular graphs,” Journal of Combinatorial Theory. Series A, vol.
199, no. 10. Elsevier, 2023.
ista: Fang L, Huang H, Pach J, Tardos G, Zuo J. 2023. Successive vertex orderings
of fully regular graphs. Journal of Combinatorial Theory. Series A. 199(10), 105776.
mla: Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.”
Journal of Combinatorial Theory. Series A, vol. 199, no. 10, 105776, Elsevier,
2023, doi:10.1016/j.jcta.2023.105776.
short: L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory.
Series A 199 (2023).
date_created: 2023-06-25T22:00:45Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2024-01-30T12:03:51Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jcta.2023.105776
external_id:
arxiv:
- '2206.13592'
file:
- access_level: open_access
checksum: 9eebc213b4182a66063a99083ff5bd04
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:03:10Z
date_updated: 2024-01-30T12:03:10Z
file_id: '14902'
file_name: 2023_JourCombinatiorialTheory_Fang.pdf
file_size: 352555
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:03:10Z
has_accepted_license: '1'
intvolume: ' 199'
issue: '10'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
publication: Journal of Combinatorial Theory. Series A
publication_identifier:
eissn:
- 1096-0899
issn:
- 0097-3165
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Successive vertex orderings of fully regular graphs
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 199
year: '2023'
...
---
_id: '14362'
abstract:
- lang: eng
text: "Motivated by recent applications to entropy theory in dynamical systems,
we generalise notions introduced by Matthews and define weakly weighted and componentwise
weakly weighted (generalised) quasi-metrics. We then systematise and extend to
full generality the correspondences between these objects and other structures
arising in theoretical computer science and dynamics. In particular, we study
the correspondences with weak partial metrics and, if the underlying space is
a semilattice, with invariant (generalised) quasi-metrics satisfying the descending
path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude
discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation
of both the known intrinsic semilattice entropy and the semigroup entropy."
article_number: '114129'
article_processing_charge: No
article_type: original
author:
- first_name: Ilaria
full_name: Castellano, Ilaria
last_name: Castellano
- first_name: Anna
full_name: Giordano Bruno, Anna
last_name: Giordano Bruno
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
citation:
ama: Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric
spaces and semilattices. Theoretical Computer Science. 2023;977. doi:10.1016/j.tcs.2023.114129
apa: Castellano, I., Giordano Bruno, A., & Zava, N. (2023). Weakly weighted
generalised quasi-metric spaces and semilattices. Theoretical Computer Science.
Elsevier. https://doi.org/10.1016/j.tcs.2023.114129
chicago: Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted
Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science.
Elsevier, 2023. https://doi.org/10.1016/j.tcs.2023.114129.
ieee: I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised
quasi-metric spaces and semilattices,” Theoretical Computer Science, vol.
977. Elsevier, 2023.
ista: Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised
quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.
mla: Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces
and Semilattices.” Theoretical Computer Science, vol. 977, 114129, Elsevier,
2023, doi:10.1016/j.tcs.2023.114129.
short: I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977
(2023).
date_created: 2023-09-24T22:01:11Z
date_published: 2023-10-25T00:00:00Z
date_updated: 2024-01-30T13:22:04Z
day: '25'
department:
- _id: HeEd
doi: 10.1016/j.tcs.2023.114129
external_id:
arxiv:
- '2212.08424'
isi:
- '001076934000001'
intvolume: ' 977'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://doi.org/10.48550/arXiv.2212.08424 '
month: '10'
oa: 1
oa_version: Preprint
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weakly weighted generalised quasi-metric spaces and semilattices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 977
year: '2023'
...
---
_id: '13182'
abstract:
- lang: eng
text: "We characterize critical points of 1-dimensional maps paired in persistent
homology\r\ngeometrically and this way get elementary proofs of theorems about
the symmetry\r\nof persistence diagrams and the variation of such maps. In particular,
we identify\r\nbranching points and endpoints of networks as the sole source of
asymmetry and\r\nrelate the cycle basis in persistent homology with a version
of the stable marriage\r\nproblem. Our analysis provides the foundations of fast
algorithms for maintaining a\r\ncollection of sorted lists together with its persistence
diagram."
acknowledgement: Open access funding provided by Austrian Science Fund (FWF). This
project has received funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme, grant no. 788183,
from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and
from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of
this paper thank anonymous reviewers for their constructive criticism and Monika
Henzinger for detailed comments on an earlier version of this paper.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera Di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera Di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization
of the persistence of 1D maps. Journal of Applied and Computational Topology.
2023. doi:10.1007/s41468-023-00126-9
apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M.
(2023). Geometric characterization of the persistence of 1D maps. Journal of
Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00126-9
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.”
Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00126-9.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric
characterization of the persistence of 1D maps,” Journal of Applied and Computational
Topology. Springer Nature, 2023.
ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2023. Geometric
characterization of the persistence of 1D maps. Journal of Applied and Computational
Topology.
mla: Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D
Maps.” Journal of Applied and Computational Topology, Springer Nature,
2023, doi:10.1007/s41468-023-00126-9.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal
of Applied and Computational Topology (2023).
date_created: 2023-07-02T22:00:44Z
date_published: 2023-06-17T00:00:00Z
date_updated: 2024-03-20T09:36:56Z
day: '17'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s41468-023-00126-9
ec_funded: 1
file:
- access_level: open_access
checksum: 697249d5d1c61dea4410b9f021b70fce
content_type: application/pdf
creator: alisjak
date_created: 2023-07-03T09:41:05Z
date_updated: 2023-07-03T09:41:05Z
file_id: '13185'
file_name: 2023_Journal of Applied and Computational Topology_Biswas.pdf
file_size: 487355
relation: main_file
success: 1
file_date_updated: 2023-07-03T09:41:05Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Geometric characterization of the persistence of 1D maps
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14226'
abstract:
- lang: eng
text: "We introduce the notion of a Faustian interchange in a 1-parameter family
of smooth\r\nfunctions to generalize the medial axis to critical points of index
larger than 0.\r\nWe construct and implement a general purpose algorithm for approximating
such\r\ngeneralized medial axes."
alternative_title:
- ISTA Master's Thesis
article_processing_charge: No
author:
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
citation:
ama: Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:10.15479/at:ista:14226
apa: Stephenson, E. R. (2023). Generalizing medial axes with homology switches.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14226
chicago: Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.”
Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14226.
ieee: E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute
of Science and Technology Austria, 2023.
ista: Stephenson ER. 2023. Generalizing medial axes with homology switches. Institute
of Science and Technology Austria.
mla: Stephenson, Elizabeth R. Generalizing Medial Axes with Homology Switches.
Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14226.
short: E.R. Stephenson, Generalizing Medial Axes with Homology Switches, Institute
of Science and Technology Austria, 2023.
date_created: 2023-08-24T13:01:18Z
date_published: 2023-08-24T00:00:00Z
date_updated: 2024-02-26T23:30:04Z
day: '24'
ddc:
- '500'
degree_awarded: MS
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:14226
file:
- access_level: closed
checksum: 453caf851d75c3478c10ed09bd242a91
content_type: application/x-zip-compressed
creator: cchlebak
date_created: 2023-08-24T13:02:49Z
date_updated: 2024-02-26T23:30:03Z
embargo_to: open_access
file_id: '14227'
file_name: documents-export-2023-08-24.zip
file_size: 15501411
relation: source_file
- access_level: open_access
checksum: 7349d29963d6695e555e171748648d9a
content_type: application/pdf
creator: cchlebak
date_created: 2023-08-24T13:03:42Z
date_updated: 2024-02-26T23:30:03Z
embargo: 2024-02-25
file_id: '14228'
file_name: thesis_pdf_a.pdf
file_size: 6854783
relation: main_file
file_date_updated: 2024-02-26T23:30:03Z
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: '43'
publication_identifier:
issn:
- 2791-4585
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: Generalizing medial axes with homology switches
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '11428'
abstract:
- lang: eng
text: The medial axis of a set consists of the points in the ambient space without
a unique closest point on the original set. Since its introduction, the medial
axis has been used extensively in many applications as a method of computing a
topologically equivalent skeleton. Unfortunately, one limiting factor in the use
of the medial axis of a smooth manifold is that it is not necessarily topologically
stable under small perturbations of the manifold. To counter these instabilities
various prunings of the medial axis have been proposed. Here, we examine one type
of pruning, called burning. Because of the good experimental results, it was hoped
that the burning method of simplifying the medial axis would be stable. In this
work we show a simple example that dashes such hopes based on Bing’s house with
two rooms, demonstrating an isotopy of a shape where the medial axis goes from
collapsible to non-collapsible.
acknowledgement: 'Partially supported by the DFG Collaborative Research Center TRR
109, “Discretization in Geometry and Dynamics” and the European Research Council
(ERC), grant no. 788183, “Alpha Shape Theory Extended”. Erin Chambers: Supported
in part by the National Science Foundation through grants DBI-1759807, CCF-1907612,
and CCF-2106672. Mathijs Wintraecken: Supported by the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement
No. 754411. The Austrian science fund (FWF) M-3073 Acknowledgements We thank André
Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early
discussions on this work. We also thank Lu Liu, Yajie Yan and Tao Ju for sharing
code to generate the examples.'
article_processing_charge: No
author:
- first_name: Erin
full_name: Chambers, Erin
last_name: Chambers
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale:
Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. 38th International
Symposium on Computational Geometry. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2022:66:1-66:9. doi:10.4230/LIPIcs.SoCG.2022.66'
apa: 'Chambers, E., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M. (2022).
A cautionary tale: Burning the medial axis is unstable. In X. Goaoc & M. Kerber
(Eds.), 38th International Symposium on Computational Geometry (Vol. 224,
p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2022.66'
chicago: 'Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs
Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In 38th
International Symposium on Computational Geometry, edited by Xavier Goaoc
and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2022. https://doi.org/10.4230/LIPIcs.SoCG.2022.66.'
ieee: 'E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary
tale: Burning the medial axis is unstable,” in 38th International Symposium
on Computational Geometry, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.'
ista: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. 2022. A cautionary
tale: Burning the medial axis is unstable. 38th International Symposium on Computational
Geometry. SoCG: Symposium on Computational GeometryLIPIcs vol. 224, 66:1-66:9.'
mla: 'Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.”
38th International Symposium on Computational Geometry, edited by Xavier
Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2022, p. 66:1-66:9, doi:10.4230/LIPIcs.SoCG.2022.66.'
short: E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc,
M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.
conference:
end_date: 2022-06-10
location: Berlin, Germany
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2022-06-07
date_created: 2022-06-01T14:18:04Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-02-21T09:50:52Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2022.66
ec_funded: 1
editor:
- first_name: Xavier
full_name: Goaoc, Xavier
last_name: Goaoc
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
file:
- access_level: open_access
checksum: b25ce40fade4ebc0bcaae176db4f5f1f
content_type: application/pdf
creator: dernst
date_created: 2022-06-07T07:58:30Z
date_updated: 2022-06-07T07:58:30Z
file_id: '11437'
file_name: 2022_LIPICs_Chambers.pdf
file_size: 17580705
relation: main_file
success: 1
file_date_updated: 2022-06-07T07:58:30Z
has_accepted_license: '1'
intvolume: ' 224'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 66:1-66:9
project:
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 38th International Symposium on Computational Geometry
publication_identifier:
isbn:
- 978-3-95977-227-3
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
series_title: LIPIcs
status: public
title: 'A cautionary tale: Burning the medial axis is unstable'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 224
year: '2022'
...
---
_id: '11429'
abstract:
- lang: eng
text: "This book constitutes the refereed proceedings of the 18th International
Symposium on Web and Wireless Geographical Information Systems, W2GIS 2022, held
in Konstanz, Germany, in April 2022.\r\nThe 7 full papers presented together with
6 short papers in the volume were carefully reviewed and selected from 16 submissions.
\ The papers cover topics that range from mobile GIS and Location-Based Services
to Spatial Information Retrieval and Wireless Sensor Networks."
alternative_title:
- LNCS
article_processing_charge: No
citation:
ama: 'Karimipour F, Storandt S, eds. Web and Wireless Geographical Information
Systems. Vol 13238. 1st ed. Cham: Springer Nature; 2022. doi:10.1007/978-3-031-06245-2'
apa: 'Karimipour, F., & Storandt, S. (Eds.). (2022). Web and Wireless Geographical
Information Systems (1st ed., Vol. 13238). Cham: Springer Nature. https://doi.org/10.1007/978-3-031-06245-2'
chicago: 'Karimipour, Farid, and Sabine Storandt, eds. Web and Wireless Geographical
Information Systems. 1st ed. Vol. 13238. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-031-06245-2.'
ieee: 'F. Karimipour and S. Storandt, Eds., Web and Wireless Geographical Information
Systems, 1st ed., vol. 13238. Cham: Springer Nature, 2022.'
ista: 'Karimipour F, Storandt S eds. 2022. Web and Wireless Geographical Information
Systems 1st ed., Cham: Springer Nature, 153p.'
mla: Karimipour, Farid, and Sabine Storandt, editors. Web and Wireless Geographical
Information Systems. 1st ed., vol. 13238, Springer Nature, 2022, doi:10.1007/978-3-031-06245-2.
short: F. Karimipour, S. Storandt, eds., Web and Wireless Geographical Information
Systems, 1st ed., Springer Nature, Cham, 2022.
date_created: 2022-06-02T05:40:53Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2022-06-02T05:56:22Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-031-06245-2
edition: '1'
editor:
- first_name: Farid
full_name: Karimipour, Farid
id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425
last_name: Karimipour
orcid: 0000-0001-6746-4174
- first_name: Sabine
full_name: Storandt, Sabine
last_name: Storandt
intvolume: ' 13238'
language:
- iso: eng
month: '05'
oa_version: None
page: '153'
place: Cham
publication_identifier:
eisbn:
- '9783031062452'
eissn:
- 1611-3349
isbn:
- '9783031062445'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Web and Wireless Geographical Information Systems
type: book_editor
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 13238
year: '2022'
...
---
_id: '11440'
abstract:
- lang: eng
text: To compute the persistent homology of a grayscale digital image one needs
to build a simplicial or cubical complex from it. For cubical complexes, the two
commonly used constructions (corresponding to direct and indirect digital adjacencies)
can give different results for the same image. The two constructions are almost
dual to each other, and we use this relationship to extend and modify the cubical
complexes to become dual filtered cell complexes. We derive a general relationship
between the persistent homology of two dual filtered cell complexes, and also
establish how various modifications to a filtered complex change the persistence
diagram. Applying these results to images, we derive a method to transform the
persistence diagram computed using one type of cubical complex into a persistence
diagram for the other construction. This means software for computing persistent
homology from images can now be easily adapted to produce results for either of
the two cubical complex constructions without additional low-level code implementation.
acknowledgement: This project started during the Women in Computational Topology workshop
held in Canberra in July of 2019. All authors are very grateful for its organisation
and the financial support for the workshop from the Mathematical Sciences Institute
at ANU, the US National Science Foundation through the award CCF-1841455, the Australian
Mathematical Sciences Institute and the Association for Women in Mathematics. AG
is supported by the Swiss National Science Foundation grant CRSII5_177237. TH is
supported by the European Research Council (ERC) Horizon 2020 project “Alpha Shape
Theory Extended” No. 788183. KM is supported by the ERC Horizon 2020 research and
innovation programme under the Marie Sklodowska-Curie grant agreement No. 859860.
VR was supported by Australian Research Council Future Fellowship FT140100604 during
the early stages of this project.
alternative_title:
- Association for Women in Mathematics Series
article_processing_charge: No
author:
- first_name: Bea
full_name: Bleile, Bea
last_name: Bleile
- first_name: Adélie
full_name: Garin, Adélie
last_name: Garin
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Kelly
full_name: Maggs, Kelly
last_name: Maggs
- first_name: Vanessa
full_name: Robins, Vanessa
last_name: Robins
citation:
ama: 'Bleile B, Garin A, Heiss T, Maggs K, Robins V. The persistent homology of
dual digital image constructions. In: Gasparovic E, Robins V, Turner K, eds. Research
in Computational Topology 2. Vol 30. 1st ed. AWMS. Cham: Springer Nature;
2022:1-26. doi:10.1007/978-3-030-95519-9_1'
apa: 'Bleile, B., Garin, A., Heiss, T., Maggs, K., & Robins, V. (2022). The
persistent homology of dual digital image constructions. In E. Gasparovic, V.
Robins, & K. Turner (Eds.), Research in Computational Topology 2 (1st
ed., Vol. 30, pp. 1–26). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-95519-9_1'
chicago: 'Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins.
“The Persistent Homology of Dual Digital Image Constructions.” In Research
in Computational Topology 2, edited by Ellen Gasparovic, Vanessa Robins, and
Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-030-95519-9_1.'
ieee: 'B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology
of dual digital image constructions,” in Research in Computational Topology
2, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer
Nature, 2022, pp. 1–26.'
ista: 'Bleile B, Garin A, Heiss T, Maggs K, Robins V. 2022.The persistent homology
of dual digital image constructions. In: Research in Computational Topology 2.
Association for Women in Mathematics Series, vol. 30, 1–26.'
mla: Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.”
Research in Computational Topology 2, edited by Ellen Gasparovic et al.,
1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:10.1007/978-3-030-95519-9_1.
short: B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V.
Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer
Nature, Cham, 2022, pp. 1–26.
date_created: 2022-06-07T08:21:11Z
date_published: 2022-01-27T00:00:00Z
date_updated: 2022-06-07T08:32:42Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-030-95519-9_1
ec_funded: 1
edition: '1'
editor:
- first_name: Ellen
full_name: Gasparovic, Ellen
last_name: Gasparovic
- first_name: Vanessa
full_name: Robins, Vanessa
last_name: Robins
- first_name: Katharine
full_name: Turner, Katharine
last_name: Turner
external_id:
arxiv:
- '2102.11397'
intvolume: ' 30'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2102.11397'
month: '01'
oa: 1
oa_version: Preprint
page: 1-26
place: Cham
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: Research in Computational Topology 2
publication_identifier:
eisbn:
- '9783030955199'
isbn:
- '9783030955182'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: AWMS
status: public
title: The persistent homology of dual digital image constructions
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2022'
...
---
_id: '12307'
abstract:
- lang: eng
text: Point-set topology is among the most abstract branches of mathematics in that
it lacks tangible notions of distance, length, magnitude, order, and size. There
is no shape, no geometry, no algebra, and no direction. Everything we are used
to visualizing is gone. In the teaching and learning of mathematics, this can
present a conundrum. Yet, this very property makes point set topology perfect
for teaching and learning abstract mathematical concepts. It clears our minds
of preconceived intuitions and expectations and forces us to think in new and
creative ways. In this paper, we present guided investigations into topology through
questions and thinking strategies that open up fascinating problems. They are
intended for faculty who already teach or are thinking about teaching a class
in topology or abstract mathematical reasoning for undergraduates. They can be
used to build simple to challenging projects in topology, proofs, honors programs,
and research experiences.
article_processing_charge: No
article_type: original
author:
- first_name: Barbara A.
full_name: Shipman, Barbara A.
last_name: Shipman
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
citation:
ama: Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS.
2022;32(5):593-609. doi:10.1080/10511970.2021.1872750
apa: Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the
lens of limits. PRIMUS. Taylor & Francis. https://doi.org/10.1080/10511970.2021.1872750
chicago: Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through
the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. https://doi.org/10.1080/10511970.2021.1872750.
ieee: B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of
limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022.
ista: Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits.
PRIMUS. 32(5), 593–609.
mla: Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through
the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022,
pp. 593–609, doi:10.1080/10511970.2021.1872750.
short: B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.
date_created: 2023-01-16T10:07:21Z
date_published: 2022-05-28T00:00:00Z
date_updated: 2023-01-30T13:02:30Z
day: '28'
department:
- _id: HeEd
- _id: GradSch
doi: 10.1080/10511970.2021.1872750
intvolume: ' 32'
issue: '5'
keyword:
- Education
- General Mathematics
language:
- iso: eng
month: '05'
oa_version: None
page: 593-609
publication: PRIMUS
publication_identifier:
eissn:
- 1935-4053
issn:
- 1051-1970
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tangible topology through the lens of limits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 32
year: '2022'
...
---
_id: '11938'
abstract:
- lang: eng
text: A matching is compatible to two or more labeled point sets of size n with
labels {1, . . . , n} if its straight-line drawing on each of these point sets
is crossing-free. We study the maximum number of edges in a matching compatible
to two or more labeled point sets in general position in the plane. We show that
for any two labeled sets of n points in convex position there exists a compatible
matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets
we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound,
we use probabilistic arguments to show that for any ℓ given sets of n points there
exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1))
edges. Finally, we show that Θ(log n) copies of any set of n points are necessary
and sufficient for the existence of labelings of these point sets such that any
compatible matching consists only of a single edge.
acknowledgement: 'A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411.
Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative
DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported
by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by
ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23
(RiSE).'
article_processing_charge: No
article_type: original
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Irene
full_name: Parada, Irene
last_name: Parada
- first_name: Daniel
full_name: Perz, Daniel
last_name: Perz
- first_name: Alexander
full_name: Pilz, Alexander
last_name: Pilz
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings.
Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591
apa: Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D.,
Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph
Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591
chicago: Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada,
Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible
Matchings.” Journal of Graph Algorithms and Applications. Brown University,
2022. https://doi.org/10.7155/jgaa.00591.
ieee: O. Aichholzer et al., “On compatible matchings,” Journal of Graph
Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240,
2022.
ista: Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec
J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and
Applications. 26(2), 225–240.
mla: Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms
and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591.
short: O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz,
J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022)
225–240.
date_created: 2022-08-21T22:01:56Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-02-23T13:54:21Z
day: '01'
ddc:
- '000'
department:
- _id: UlWa
- _id: HeEd
- _id: KrCh
doi: 10.7155/jgaa.00591
ec_funded: 1
external_id:
arxiv:
- '2101.03928'
file:
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checksum: dc6e255e3558faff924fd9e370886c11
content_type: application/pdf
creator: dernst
date_created: 2022-08-22T06:42:42Z
date_updated: 2022-08-22T06:42:42Z
file_id: '11940'
file_name: 2022_JourGraphAlgorithmsApplic_Aichholzer.pdf
file_size: 694538
relation: main_file
success: 1
file_date_updated: 2022-08-22T06:42:42Z
has_accepted_license: '1'
intvolume: ' 26'
issue: '2'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 225-240
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
publication: Journal of Graph Algorithms and Applications
publication_identifier:
issn:
- 1526-1719
publication_status: published
publisher: Brown University
quality_controlled: '1'
related_material:
record:
- id: '9296'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: On compatible matchings
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 26
year: '2022'
...
---
_id: '9649'
abstract:
- lang: eng
text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension
and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued
smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an
isomanifold is to consider its Piecewise-Linear (PL) approximation based on a
triangulation T of the ambient space Rd. In this paper, we give conditions under
which the PL-approximation of an isomanifold is topologically equivalent to the
isomanifold. The conditions are easy to satisfy in the sense that they can always
be met by taking a sufficiently\r\nfine triangulation T . This contrasts with
previous results on the triangulation of manifolds where, in arbitrary dimensions,
delicate perturbations are needed to guarantee topological correctness, which
leads to strong limitations in practice. We further give a bound on the Fréchet
distance between the original isomanifold and its PL-approximation. Finally we
show analogous results for the PL-approximation of an isomanifold with boundary."
acknowledgement: "First and foremost, we acknowledge Siargey Kachanovich for discussions.
We thank Herbert Edelsbrunner and all members of his group, all former and current
members of the Datashape team (formerly known as Geometrica), and André Lieutier
for encouragement. We further thank the reviewers of Foundations of Computational
Mathematics and the reviewers and program committee of the Symposium on Computational
Geometry for their feedback, which improved the exposition.\r\nThis work was funded
by the European Research Council under the European Union’s ERC Grant Agreement
number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher
Dimensions). This work was also supported by the French government, through the
3IA Côte d’Azur Investments in the Future project managed by the National Research
Agency (ANR) with the reference number ANR-19-P3IA-0002. Mathijs Wintraecken also
received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement no. 754411."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations
of isomanifolds. Foundations of Computational Mathematics . 2022;22:967-1012.
doi:10.1007/s10208-021-09520-0
apa: Boissonnat, J.-D., & Wintraecken, M. (2022). The topological correctness
of PL approximations of isomanifolds. Foundations of Computational Mathematics
. Springer Nature. https://doi.org/10.1007/s10208-021-09520-0
chicago: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics
. Springer Nature, 2022. https://doi.org/10.1007/s10208-021-09520-0.
ieee: J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations
of isomanifolds,” Foundations of Computational Mathematics , vol. 22. Springer
Nature, pp. 967–1012, 2022.
ista: Boissonnat J-D, Wintraecken M. 2022. The topological correctness of PL approximations
of isomanifolds. Foundations of Computational Mathematics . 22, 967–1012.
mla: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics
, vol. 22, Springer Nature, 2022, pp. 967–1012, doi:10.1007/s10208-021-09520-0.
short: J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics 22
(2022) 967–1012.
date_created: 2021-07-14T06:44:53Z
date_published: 2022-01-01T00:00:00Z
date_updated: 2023-08-02T06:49:17Z
day: '01'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s10208-021-09520-0
ec_funded: 1
external_id:
isi:
- '000673039600001'
file:
- access_level: open_access
checksum: f1d372ec3c08ec22e84f8e93e1126b8c
content_type: application/pdf
creator: mwintrae
date_created: 2021-07-14T06:44:36Z
date_updated: 2021-07-14T06:44:36Z
file_id: '9650'
file_name: Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf
file_size: 1455699
relation: main_file
file_date_updated: 2021-07-14T06:44:36Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '0'
oa: 1
oa_version: Published Version
page: 967-1012
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 'Foundations of Computational Mathematics '
publication_identifier:
eissn:
- 1615-3383
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '7952'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The topological correctness of PL approximations of isomanifolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
year: '2022'
...