---
_id: '12960'
abstract:
- lang: eng
text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension
and codimension, i.e., submanifolds of Rd defined as the zero set of some multivariate
multivalued smooth function f:Rd→Rd−n, where n is the intrinsic dimension of the
manifold. A natural way to approximate a smooth isomanifold M=f−1(0) is to consider
its piecewise linear (PL) approximation M^\r\n based on a triangulation T of the
ambient space Rd. In this paper, we describe a simple algorithm to trace isomanifolds
from a given starting point. The algorithm works for arbitrary dimensions n and
d, and any precision D. Our main result is that, when f (or M) has bounded complexity,
the complexity of the algorithm is polynomial in d and δ=1/D (and unavoidably
exponential in n). Since it is known that for δ=Ω(d2.5), M^ is O(D2)-close and
isotopic to M\r\n, our algorithm produces a faithful PL-approximation of isomanifolds
of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality
reduction techniques, the dependency on d in the size of M^ can be completely
removed with high probability. We also show that the algorithm can handle isomanifolds
with boundary and, more generally, isostratifolds. The algorithm for isomanifolds
with boundary has been implemented and experimental results are reported, showing
that it is practical and can handle cases that are far ahead of the state-of-the-art. "
acknowledgement: The authors have received funding from the European Research Council
under the European Union's ERC grant greement 339025 GUDHI (Algorithmic Foundations
of Geometric Un-derstanding in Higher Dimensions). The first author was supported by the French government,through
the 3IA C\^ote d'Azur Investments in the Future project managed by the National
ResearchAgency (ANR) with the reference ANR-19-P3IA-0002. The third author was
supported by the Eu-ropean Union's Horizon 2020 research and innovation programme
under the Marie Sk\lodowska-Curiegrant agreement 754411 and the FWF (Austrian Science
Fund) grant M 3073.
article_processing_charge: No
article_type: original
author:
- first_name: Jean Daniel
full_name: Boissonnat, Jean Daniel
last_name: Boissonnat
- first_name: Siargey
full_name: Kachanovich, Siargey
last_name: Kachanovich
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Boissonnat JD, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in
time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal
on Computing. 2023;52(2):452-486. doi:10.1137/21M1412918
apa: Boissonnat, J. D., Kachanovich, S., & Wintraecken, M. (2023). Tracing isomanifolds
in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM
Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1412918
chicago: Boissonnat, Jean Daniel, Siargey Kachanovich, and Mathijs Wintraecken.
“Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn
Triangulations.” SIAM Journal on Computing. Society for Industrial and
Applied Mathematics, 2023. https://doi.org/10.1137/21M1412918.
ieee: J. D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds
in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations,”
SIAM Journal on Computing, vol. 52, no. 2. Society for Industrial and Applied
Mathematics, pp. 452–486, 2023.
ista: Boissonnat JD, Kachanovich S, Wintraecken M. 2023. Tracing isomanifolds in
Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM
Journal on Computing. 52(2), 452–486.
mla: Boissonnat, Jean Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial
in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing,
vol. 52, no. 2, Society for Industrial and Applied Mathematics, 2023, pp. 452–86,
doi:10.1137/21M1412918.
short: J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing
52 (2023) 452–486.
corr_author: '1'
date_created: 2023-05-14T22:01:00Z
date_published: 2023-04-30T00:00:00Z
date_updated: 2025-04-15T06:54:46Z
day: '30'
department:
- _id: HeEd
doi: 10.1137/21M1412918
ec_funded: 1
external_id:
isi:
- '001013183000012'
intvolume: ' 52'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1
month: '04'
oa: 1
oa_version: Submitted Version
page: 452-486
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
publication: SIAM Journal on Computing
publication_identifier:
eissn:
- 1095-7111
issn:
- 0097-5397
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
record:
- id: '9441'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn
triangulations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 52
year: '2023'
...
---
_id: '13048'
abstract:
- lang: eng
text: In this paper we introduce a pruning of the medial axis called the (λ,α)-medial
axis (axλα). We prove that the (λ,α)-medial axis of a set K is stable in a Gromov-Hausdorff
sense under weak assumptions. More formally we prove that if K and K′ are close
in the Hausdorff (dH) sense then the (λ,α)-medial axes of K and K′ are close as
metric spaces, that is the Gromov-Hausdorff distance (dGH) between the two is
1/4-Hölder in the sense that dGH (axλα(K),axλα(K′)) ≲ dH(K,K′)1/4. The Hausdorff
distance between the two medial axes is also bounded, by dH (axλα(K),λα(K′)) ≲
dH(K,K′)1/2. These quantified stability results provide guarantees for practical
computations of medial axes from approximations. Moreover, they provide key ingredients
for studying the computability of the medial axis in the context of computable
analysis.
acknowledgement: "We are greatly indebted to Erin Chambers for posing a number of
questions that eventually led to this paper. We would also like to thank the other
organizers of the workshop on ‘Algorithms\r\nfor the medial axis’. We are also indebted
to Tatiana Ezubova for helping with the search for and translation of Russian literature.
The second author thanks all members of the Edelsbrunner and Datashape groups for
the atmosphere in which the research was conducted.\r\nThe research leading to these
results has received funding from the European Research Council (ERC) under the
European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement
No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions).
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."
article_processing_charge: No
arxiv: 1
author:
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Lieutier A, Wintraecken M. Hausdorff and Gromov-Hausdorff stable subsets of
the medial axis. In: Proceedings of the 55th Annual ACM Symposium on Theory
of Computing. Association for Computing Machinery; 2023:1768-1776. doi:10.1145/3564246.3585113'
apa: 'Lieutier, A., & Wintraecken, M. (2023). Hausdorff and Gromov-Hausdorff
stable subsets of the medial axis. In Proceedings of the 55th Annual ACM Symposium
on Theory of Computing (pp. 1768–1776). Orlando, FL, United States: Association
for Computing Machinery. https://doi.org/10.1145/3564246.3585113'
chicago: Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff
Stable Subsets of the Medial Axis.” In Proceedings of the 55th Annual ACM Symposium
on Theory of Computing, 1768–76. Association for Computing Machinery, 2023.
https://doi.org/10.1145/3564246.3585113.
ieee: A. Lieutier and M. Wintraecken, “Hausdorff and Gromov-Hausdorff stable subsets
of the medial axis,” in Proceedings of the 55th Annual ACM Symposium on Theory
of Computing, Orlando, FL, United States, 2023, pp. 1768–1776.
ista: 'Lieutier A, Wintraecken M. 2023. Hausdorff and Gromov-Hausdorff stable subsets
of the medial axis. Proceedings of the 55th Annual ACM Symposium on Theory of
Computing. STOC: Symposium on Theory of Computing, 1768–1776.'
mla: Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable
Subsets of the Medial Axis.” Proceedings of the 55th Annual ACM Symposium on
Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–76,
doi:10.1145/3564246.3585113.
short: A. Lieutier, M. Wintraecken, in:, Proceedings of the 55th Annual ACM Symposium
on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–1776.
conference:
end_date: 2023-06-23
location: Orlando, FL, United States
name: 'STOC: Symposium on Theory of Computing'
start_date: 2023-06-20
corr_author: '1'
date_created: 2023-05-22T08:02:02Z
date_published: 2023-06-02T00:00:00Z
date_updated: 2025-09-09T12:26:49Z
day: '02'
department:
- _id: HeEd
doi: 10.1145/3564246.3585113
ec_funded: 1
external_id:
arxiv:
- '2303.04014'
isi:
- '001064640700143'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2303.04014
month: '06'
oa: 1
oa_version: Preprint
page: 1768-1776
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
publication: Proceedings of the 55th Annual ACM Symposium on Theory of Computing
publication_identifier:
isbn:
- '9781450399135'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hausdorff and Gromov-Hausdorff stable subsets of the medial axis
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2023'
...
---
_id: '13134'
abstract:
- lang: eng
text: We propose a characterization of discrete analytical spheres, planes and lines
in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently
proposed alternative compact coordinate system, in which each integer triplet
addresses some voxel in the grid. We define spheres and planes through double
Diophantine inequalities and investigate their relevant topological features,
such as functionality or the interrelation between the thickness of the objects
and their connectivity and separation properties. We define lines as the intersection
of planes. The number of the planes (up to six) is equal to the number of the
pairs of faces of a BCC voxel that are parallel to the line.
acknowledgement: The first author has been partially supported by the Ministry of
Science, Technological Development and Innovation of the Republic of Serbia through
the project no. 451-03-47/2023-01/200156. The fourth author is funded by the DFG
Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’,
Austrian Science Fund (FWF), grant no. I 02979-N35.
article_number: '109693'
article_processing_charge: No
article_type: original
author:
- first_name: Lidija
full_name: Čomić, Lidija
last_name: Čomić
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical
objects in the body-centered cubic grid. Pattern Recognition. 2023;142(10).
doi:10.1016/j.patcog.2023.109693
apa: Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., & Andres, E. (2023).
Discrete analytical objects in the body-centered cubic grid. Pattern Recognition.
Elsevier. https://doi.org/10.1016/j.patcog.2023.109693
chicago: Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and
Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern
Recognition. Elsevier, 2023. https://doi.org/10.1016/j.patcog.2023.109693.
ieee: L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete
analytical objects in the body-centered cubic grid,” Pattern Recognition,
vol. 142, no. 10. Elsevier, 2023.
ista: Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. 2023. Discrete analytical
objects in the body-centered cubic grid. Pattern Recognition. 142(10), 109693.
mla: Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic
Grid.” Pattern Recognition, vol. 142, no. 10, 109693, Elsevier, 2023, doi:10.1016/j.patcog.2023.109693.
short: L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition
142 (2023).
corr_author: '1'
date_created: 2023-06-18T22:00:45Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2025-04-15T07:45:32Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.patcog.2023.109693
external_id:
isi:
- '001013526000001'
intvolume: ' 142'
isi: 1
issue: '10'
language:
- iso: eng
month: '10'
oa_version: None
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
publication: Pattern Recognition
publication_identifier:
issn:
- 0031-3203
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete analytical objects in the body-centered cubic grid
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 142
year: '2023'
...
---
_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
arxiv: 1
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).
corr_author: '1'
date_created: 2023-06-25T22:00:45Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2025-09-09T12:30:39Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jcta.2023.105776
external_id:
arxiv:
- '2206.13592'
isi:
- '001144487800001'
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'
isi: 1
issue: '10'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 199
year: '2023'
...
---
OA_place: publisher
_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.
corr_author: '1'
date_created: 2023-08-24T13:01:18Z
date_published: 2023-08-24T00:00:00Z
date_updated: 2026-04-07T14:02:30Z
day: '24'
ddc:
- '500'
degree_awarded: MS
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:14226
file:
- access_level: closed
checksum: 453caf851d75c3478c10ed09bd242a91
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creator: cchlebak
date_created: 2023-08-24T13:02:49Z
date_updated: 2024-02-26T23:30:03Z
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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: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2023'
...
---
_id: '11545'
abstract:
- lang: eng
text: "We classify contravariant pairings between standard Whittaker modules and
Verma modules over a complex semisimple Lie algebra. These contravariant pairings
are useful in extending several classical techniques for category O to the Miličić–Soergel
category N . We introduce a class of costandard modules which generalize dual
Verma modules, and describe canonical maps from standard to costandard modules
in terms of contravariant pairings.\r\nWe show that costandard modules have unique
irreducible submodules and share the same composition factors as the corresponding
standard Whittaker modules. We show that costandard modules give an algebraic
characterization of the global sections of costandard twisted Harish-Chandra sheaves
on the associated flag variety, which are defined using holonomic duality of D-modules.
We prove that with these costandard modules, blocks of category\r\nN have the
structure of highest weight categories and we establish a BGG reciprocity theorem
for N ."
acknowledgement: We thank Catharina Stroppel and Jens Niklas Eberhardt for interesting
discussions. The first author acknowledges the support of the European Union's Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 754411. The second author is supported by the National Science Foundation Award
No. 1803059 and the Australian Research Council grant DP170101579.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Anna
full_name: Romanov, Anna
last_name: Romanov
citation:
ama: Brown A, Romanov A. Contravariant pairings between standard Whittaker modules
and Verma modules. Journal of Algebra. 2022;609(11):145-179. doi:10.1016/j.jalgebra.2022.06.017
apa: Brown, A., & Romanov, A. (2022). Contravariant pairings between standard
Whittaker modules and Verma modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2022.06.017
chicago: Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard
Whittaker Modules and Verma Modules.” Journal of Algebra. Elsevier, 2022.
https://doi.org/10.1016/j.jalgebra.2022.06.017.
ieee: A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker
modules and Verma modules,” Journal of Algebra, vol. 609, no. 11. Elsevier,
pp. 145–179, 2022.
ista: Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker
modules and Verma modules. Journal of Algebra. 609(11), 145–179.
mla: Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker
Modules and Verma Modules.” Journal of Algebra, vol. 609, no. 11, Elsevier,
2022, pp. 145–79, doi:10.1016/j.jalgebra.2022.06.017.
short: A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.
corr_author: '1'
date_created: 2022-07-08T11:40:07Z
date_published: 2022-11-01T00:00:00Z
date_updated: 2025-04-14T07:43:58Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jalgebra.2022.06.017
ec_funded: 1
external_id:
isi:
- '000861841100004'
file:
- access_level: open_access
checksum: 82abaee3d7837f703e499a9ecbb25b7c
content_type: application/pdf
creator: dernst
date_created: 2023-02-02T07:32:48Z
date_updated: 2023-02-02T07:32:48Z
file_id: '12473'
file_name: 2022_JournalAlgebra_Brown.pdf
file_size: 582962
relation: main_file
success: 1
file_date_updated: 2023-02-02T07:32:48Z
has_accepted_license: '1'
intvolume: ' 609'
isi: 1
issue: '11'
keyword:
- Algebra and Number Theory
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 145-179
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Algebra
publication_identifier:
issn:
- 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Contravariant pairings between standard Whittaker modules and Verma modules
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: 609
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.
corr_author: '1'
date_created: 2023-01-16T10:07:21Z
date_published: 2022-05-28T00:00:00Z
date_updated: 2024-10-09T21:03:58Z
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: '10608'
abstract:
- lang: eng
text: We consider infinite-dimensional properties in coarse geometry for hyperspaces
consisting of finite subsets of metric spaces with the Hausdorff metric. We see
that several infinite-dimensional properties are preserved by taking the hyperspace
of subsets with at most n points. On the other hand, we prove that, if a metric
space contains a sequence of long intervals coarsely, then its hyperspace of finite
subsets is not coarsely embeddable into any uniformly convex Banach space. As
a corollary, the hyperspace of finite subsets of the real line is not coarsely
embeddable into any uniformly convex Banach space. It is also shown that every
(not necessarily bounded geometry) metric space with straight finite decomposition
complexity has metric sparsification property.
acknowledgement: We would like to thank the referees for their careful reading and
the comments that improved our work. The third named author would like to thank
the Division of Mathematics, Physics and Earth Sciences of the Graduate School of
Science and Engineering of Ehime University and the second named author for hosting
his visit in June 2018. Open access funding provided by Institute of Science and
Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Thomas
full_name: Weighill, Thomas
last_name: Weighill
- first_name: Takamitsu
full_name: Yamauchi, Takamitsu
last_name: Yamauchi
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
citation:
ama: Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics. 2022;8(1):335-355.
doi:10.1007/s40879-021-00515-3
apa: Weighill, T., Yamauchi, T., & Zava, N. (2022). Coarse infinite-dimensionality
of hyperspaces of finite subsets. European Journal of Mathematics. Springer
Nature. https://doi.org/10.1007/s40879-021-00515-3
chicago: Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality
of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer
Nature, 2022. https://doi.org/10.1007/s40879-021-00515-3.
ieee: T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of
hyperspaces of finite subsets,” European Journal of Mathematics, vol. 8,
no. 1. Springer Nature, pp. 335–355, 2022.
ista: Weighill T, Yamauchi T, Zava N. 2022. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics. 8(1), 335–355.
mla: Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of
Finite Subsets.” European Journal of Mathematics, vol. 8, no. 1, Springer
Nature, 2022, pp. 335–55, doi:10.1007/s40879-021-00515-3.
short: T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics 8 (2022)
335–355.
date_created: 2022-01-09T23:01:27Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2024-05-22T11:10:22Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s40879-021-00515-3
file:
- access_level: open_access
checksum: ce35cbb2d8c889dc7750719972634ed4
content_type: application/pdf
creator: kschuh
date_created: 2024-05-22T11:10:10Z
date_updated: 2024-05-22T11:10:10Z
file_id: '17036'
file_name: 2022_EuJournalMath_Weighill.pdf
file_size: 371515
relation: main_file
success: 1
file_date_updated: 2024-05-22T11:10:10Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 335-355
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coarse infinite-dimensionality of hyperspaces of finite subsets
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2022'
...
---
_id: '10754'
abstract:
- lang: eng
text: Targeting dysregulated Ca2+ signaling in cancer cells is an emerging chemotherapy
approach. We previously reported that store-operated Ca2+ entry (SOCE) blockers,
such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine
kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted
therapy for patients with EGFR mutation-positive cancers. While preclinical studies
and clinical trials have shown that afatinib has benefits for esophageal cancer
patients, it is not known whether a combination of afatinib and RP4010 could achieve
better anticancer effects. Since TKI can alter intracellular Ca2+ dynamics through
EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect
of afatinib and RP4010 on intracellular Ca2+ oscillations in KYSE-150, a human
esophageal squamous cell carcinoma cell line, using both experimental and mathematical
simulations. Our mathematical simulation of Ca2+ oscillations could fit well with
experimental data responding to afatinib or RP4010, both separately or in combination.
Guided by simulation, we were able to identify a proper ratio of afatinib and
RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect
evidence by experimental measurement of intracellular Ca2+ and cell proliferation.
This intracellular Ca2+ dynamic-based mathematical simulation approach could be
useful for a rapid and cost-effective evaluation of combined targeting therapy
drugs.
acknowledgement: "This work was partially supported by grants from National Institutes
of Health (NIH) (R01 CA185055, S10OD0252300) and The University of Texas System
STARs Award (to Z.P.),\r\nThe University of Texas at Arlington Interdisciplinary
Research Program (to B.C., H.V.K. and Z.P.). "
article_number: '1763'
article_processing_charge: Yes
article_type: original
author:
- first_name: Yan
full_name: Chang, Yan
last_name: Chang
- first_name: Marah
full_name: Funk, Marah
last_name: Funk
- first_name: Souvik
full_name: Roy, Souvik
last_name: Roy
- 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: Sangyong
full_name: Choi, Sangyong
last_name: Choi
- first_name: Hristo V.
full_name: Kojouharov, Hristo V.
last_name: Kojouharov
- first_name: Benito
full_name: Chen, Benito
last_name: Chen
- first_name: Zui
full_name: Pan, Zui
last_name: Pan
citation:
ama: Chang Y, Funk M, Roy S, et al. Developing a mathematical model of intracellular
Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010
in esophageal cancer. International Journal of Molecular Sciences. 2022;23(3).
doi:10.3390/ijms23031763
apa: Chang, Y., Funk, M., Roy, S., Stephenson, E. R., Choi, S., Kojouharov, H. V.,
… Pan, Z. (2022). Developing a mathematical model of intracellular Calcium dynamics
for evaluating combined anticancer effects of afatinib and RP4010 in esophageal
cancer. International Journal of Molecular Sciences. MDPI. https://doi.org/10.3390/ijms23031763
chicago: Chang, Yan, Marah Funk, Souvik Roy, Elizabeth R Stephenson, Sangyong Choi,
Hristo V. Kojouharov, Benito Chen, and Zui Pan. “Developing a Mathematical Model
of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of
Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular
Sciences. MDPI, 2022. https://doi.org/10.3390/ijms23031763.
ieee: Y. Chang et al., “Developing a mathematical model of intracellular
Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010
in esophageal cancer,” International Journal of Molecular Sciences, vol.
23, no. 3. MDPI, 2022.
ista: Chang Y, Funk M, Roy S, Stephenson ER, Choi S, Kojouharov HV, Chen B, Pan
Z. 2022. Developing a mathematical model of intracellular Calcium dynamics for
evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer.
International Journal of Molecular Sciences. 23(3), 1763.
mla: Chang, Yan, et al. “Developing a Mathematical Model of Intracellular Calcium
Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in
Esophageal Cancer.” International Journal of Molecular Sciences, vol. 23,
no. 3, 1763, MDPI, 2022, doi:10.3390/ijms23031763.
short: Y. Chang, M. Funk, S. Roy, E.R. Stephenson, S. Choi, H.V. Kojouharov, B.
Chen, Z. Pan, International Journal of Molecular Sciences 23 (2022).
date_created: 2022-02-13T23:01:35Z
date_published: 2022-02-01T00:00:00Z
date_updated: 2025-06-11T13:46:46Z
day: '01'
ddc:
- '510'
- '576'
department:
- _id: HeEd
doi: 10.3390/ijms23031763
external_id:
isi:
- '000754773500001'
pmid:
- '35163685'
file:
- access_level: open_access
checksum: 8890ad20c54e90dc58ad5ea97c902998
content_type: application/pdf
creator: dernst
date_created: 2022-02-14T07:46:30Z
date_updated: 2022-02-14T07:46:30Z
file_id: '10756'
file_name: 2022_IJMS_Chang.pdf
file_size: 24416183
relation: main_file
success: 1
file_date_updated: 2022-02-14T07:46:30Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
pmid: 1
publication: International Journal of Molecular Sciences
publication_identifier:
eissn:
- 1422-0067
issn:
- 1661-6596
publication_status: published
publisher: MDPI
quality_controlled: '1'
scopus_import: '1'
status: public
title: Developing a mathematical model of intracellular Calcium dynamics for evaluating
combined anticancer effects of afatinib and RP4010 in esophageal cancer
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: 23
year: '2022'
...
---
_id: '10773'
abstract:
- lang: eng
text: The Voronoi tessellation in Rd is defined by locally minimizing the power
distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined
by locally maximizing the negative power distance to other such points. We prove
that the average of the two piecewise quadratic functions is piecewise linear,
and that all three functions have the same critical points and values. Discretizing
the two piecewise quadratic functions, we get the alpha shapes as sublevel sets
of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel
sets of the discrete function on the Voronoi tessellation. For the same non-critical
value, the corresponding shapes are disjoint, separated by a narrow channel that
contains no critical points but the entire level set of the piecewise linear function.
acknowledgement: Open access funding provided by the Institute of Science and Technology
(IST Austria).
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
last_name: Saghafian
citation:
ama: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous
and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete
and Computational Geometry. 2022;67:811-842. doi:10.1007/s00454-022-00371-2
apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M.
(2022). Continuous and discrete radius functions on Voronoi tessellations and
Delaunay mosaics. Discrete and Computational Geometry. Springer Nature.
https://doi.org/10.1007/s00454-022-00371-2
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations
and Delaunay Mosaics.” Discrete and Computational Geometry. Springer Nature,
2022. https://doi.org/10.1007/s00454-022-00371-2.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous
and discrete radius functions on Voronoi tessellations and Delaunay mosaics,”
Discrete and Computational Geometry, vol. 67. Springer Nature, pp. 811–842,
2022.
ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2022. Continuous
and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete
and Computational Geometry. 67, 811–842.
mla: Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi
Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry,
vol. 67, Springer Nature, 2022, pp. 811–42, doi:10.1007/s00454-022-00371-2.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete
and Computational Geometry 67 (2022) 811–842.
corr_author: '1'
date_created: 2022-02-20T23:01:34Z
date_published: 2022-04-01T00:00:00Z
date_updated: 2024-10-09T21:01:38Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-022-00371-2
external_id:
isi:
- '000752175300002'
file:
- access_level: open_access
checksum: 9383d3b70561bacee905e335dc922680
content_type: application/pdf
creator: dernst
date_created: 2022-08-02T06:07:55Z
date_updated: 2022-08-02T06:07:55Z
file_id: '11718'
file_name: 2022_DiscreteCompGeometry_Biswas.pdf
file_size: 2518111
relation: main_file
success: 1
file_date_updated: 2022-08-02T06:07:55Z
has_accepted_license: '1'
intvolume: ' 67'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 811-842
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Continuous and discrete radius functions on Voronoi tessellations and Delaunay
mosaics
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: 67
year: '2022'
...
---
_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
corr_author: '1'
date_created: 2022-06-01T14:18:04Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2025-04-14T07:43:57Z
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.
corr_author: '1'
date_created: 2022-06-02T05:40:53Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2024-10-09T21:02:30Z
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: '10413'
abstract:
- lang: eng
text: Motivated by the recent introduction of the intrinsic semilattice entropy,
we study generalized quasi-metric semilattices and their categories. We investigate
the relationship between these objects and generalized semivaluations, extending
Nakamura and Schellekens' approach. Finally, we use this correspondence to compare
the intrinsic semilattice entropy and the semigroup entropy induced in particular
situations, like sets, torsion abelian groups and vector spaces.
acknowledgement: Dedicated to the memory of Hans-Peter Künzi.
article_number: '107916'
article_processing_charge: No
article_type: original
author:
- first_name: Dikran
full_name: Dikranjan, Dikran
last_name: Dikranjan
- first_name: Anna
full_name: Giordano Bruno, Anna
last_name: Giordano Bruno
- first_name: Hans Peter
full_name: Künzi, Hans Peter
last_name: Künzi
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
- first_name: Daniele
full_name: Toller, Daniele
last_name: Toller
citation:
ama: Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric
semilattices. Topology and its Applications. 2022;309. doi:10.1016/j.topol.2021.107916
apa: Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., & Toller, D.
(2022). Generalized quasi-metric semilattices. Topology and Its Applications.
Elsevier. https://doi.org/10.1016/j.topol.2021.107916
chicago: Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava,
and Daniele Toller. “Generalized Quasi-Metric Semilattices.” Topology and Its
Applications. Elsevier, 2022. https://doi.org/10.1016/j.topol.2021.107916.
ieee: D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized
quasi-metric semilattices,” Topology and its Applications, vol. 309. Elsevier,
2022.
ista: Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized
quasi-metric semilattices. Topology and its Applications. 309, 107916.
mla: Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” Topology
and Its Applications, vol. 309, 107916, Elsevier, 2022, doi:10.1016/j.topol.2021.107916.
short: D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology
and Its Applications 309 (2022).
corr_author: '1'
date_created: 2021-12-05T23:01:44Z
date_published: 2022-03-15T00:00:00Z
date_updated: 2024-10-09T21:01:16Z
day: '15'
department:
- _id: HeEd
doi: 10.1016/j.topol.2021.107916
external_id:
isi:
- '000791838800012'
intvolume: ' 309'
isi: 1
language:
- iso: eng
month: '03'
oa_version: None
publication: Topology and its Applications
publication_identifier:
issn:
- 0166-8641
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Generalized quasi-metric semilattices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 309
year: '2022'
...
---
_id: '17084'
abstract:
- lang: eng
text: 'Given a graph where every vertex has exactly one labeled token, how can we
most quickly execute a given permutation on the tokens? In (sequential) token
swapping, the goal is to use the shortest possible sequence of swaps, each of
which exchanges the tokens at the two endpoints of an edge of the graph. In parallel
token swapping, the goal is to use the fewest rounds, each of which consists of
one or more swaps on the edges of a matching. We prove that both of these problems
remain NP-hard when the graph is restricted to be a tree. These token swapping
problems have been studied by disparate groups of researchers in discrete mathematics,
theoretical computer science, robot motion planning, game theory, and engineering.
Previous work establishes NP-completeness on general graphs (for both problems),
constant-factor approximation algorithms, and some poly-time exact algorithms
for simple graph classes such as cliques, stars, paths, and cycles. Sequential
and parallel token swapping on trees were first studied over thirty years ago
(as "sorting with a transposition tree") and over twenty-five years ago (as "routing
permutations via matchings"), yet their complexities were previously unknown.
We also show limitations on approximation of sequential token swapping on trees:
we identify a broad class of algorithms that encompass all three known polynomial-time
algorithms that achieve the best known approximation factor (which is 2) and show
that no such algorithm can achieve an approximation factor less than 2.'
acknowledgement: "g Anna Lubiw: Supported by the Natural Sciences and Engineering
Research Council of\r\nCanada (NSERC). Jayson Lynch: Supported by the Natural Sciences
and Engineering Research Council of Canada (NSERC). Zuzana Masárová: Supported by
Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. Virginia Vassilevska
Williams: Supported by an NSF CAREER Award, NSF Grants CCF-1528078, CCF-1514339
and CCF-1909429, a BSF Grant BSF:2012338, a Google Research Fellowship and a Sloan
Research Fellowship.\r\nNicole Wein: Supported by a grant to DIMACS from the Simons
Foundation (820931). This work was done while the author was at MIT.\r\nThis research
was initiated at the 34th Bellairs Winter Workshop on Computational Geometry, co-organized
by Erik Demaine and Godfried Toussaint, held on March 22–29,\r\n2019 in Holetown,
Barbados. We thank the other participants of that workshop for providing a\r\nstimulating
research environment."
alternative_title:
- LIPIcs
article_number: '3'
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Erik D.
full_name: Demaine, Erik D.
last_name: Demaine
- first_name: Matias
full_name: Korman, Matias
last_name: Korman
- first_name: Anna
full_name: Lubiw, Anna
last_name: Lubiw
- first_name: Jayson
full_name: Lynch, Jayson
last_name: Lynch
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Mikhail
full_name: Rudoy, Mikhail
last_name: Rudoy
- first_name: Virginia
full_name: Vassilevska Williams, Virginia
last_name: Vassilevska Williams
- first_name: Nicole
full_name: Wein, Nicole
last_name: Wein
citation:
ama: 'Aichholzer O, Demaine ED, Korman M, et al. Hardness of token swapping on trees.
In: 30th Annual European Symposium on Algorithms. Vol 244. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2022. doi:10.4230/LIPIcs.ESA.2022.3'
apa: 'Aichholzer, O., Demaine, E. D., Korman, M., Lubiw, A., Lynch, J., Masárová,
Z., … Wein, N. (2022). Hardness of token swapping on trees. In 30th Annual
European Symposium on Algorithms (Vol. 244). Berlin/Potsdam, Germany: Schloss
Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2022.3'
chicago: Aichholzer, Oswin, Erik D. Demaine, Matias Korman, Anna Lubiw, Jayson Lynch,
Zuzana Masárová, Mikhail Rudoy, Virginia Vassilevska Williams, and Nicole Wein.
“Hardness of Token Swapping on Trees.” In 30th Annual European Symposium on
Algorithms, Vol. 244. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.
https://doi.org/10.4230/LIPIcs.ESA.2022.3.
ieee: O. Aichholzer et al., “Hardness of token swapping on trees,” in 30th
Annual European Symposium on Algorithms, Berlin/Potsdam, Germany, 2022, vol.
244.
ista: 'Aichholzer O, Demaine ED, Korman M, Lubiw A, Lynch J, Masárová Z, Rudoy M,
Vassilevska Williams V, Wein N. 2022. Hardness of token swapping on trees. 30th
Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms,
LIPIcs, vol. 244, 3.'
mla: Aichholzer, Oswin, et al. “Hardness of Token Swapping on Trees.” 30th Annual
European Symposium on Algorithms, vol. 244, 3, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2022, doi:10.4230/LIPIcs.ESA.2022.3.
short: O. Aichholzer, E.D. Demaine, M. Korman, A. Lubiw, J. Lynch, Z. Masárová,
M. Rudoy, V. Vassilevska Williams, N. Wein, in:, 30th Annual European Symposium
on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.
conference:
end_date: 2022-09-09
location: Berlin/Potsdam, Germany
name: 'ESA: European Symposium on Algorithms'
start_date: 2022-09-05
corr_author: '1'
date_created: 2024-05-29T06:27:16Z
date_published: 2022-09-01T00:00:00Z
date_updated: 2025-04-15T07:16:56Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
- _id: UlWa
doi: 10.4230/LIPIcs.ESA.2022.3
external_id:
arxiv:
- '2103.06707'
file:
- access_level: open_access
checksum: a1fbd3e7baad510fbcb998cf4a7d9f7f
content_type: application/pdf
creator: dernst
date_created: 2024-08-12T08:51:44Z
date_updated: 2024-08-12T08:51:44Z
file_id: '17420'
file_name: 2022_LIPIcS_Aichholzer.pdf
file_size: 1406071
relation: main_file
success: 1
file_date_updated: 2024-08-12T08:51:44Z
has_accepted_license: '1'
intvolume: ' 244'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: 30th Annual European Symposium on Algorithms
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hardness of token swapping on trees
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 244
year: '2022'
...
---
_id: '7791'
abstract:
- lang: eng
text: Extending a result of Milena Radnovic and Serge Tabachnikov, we establish
conditionsfor two different non-symmetric norms to define the same billiard reflection
law.
acknowledgement: AA was supported by European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818
Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4
and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169.
Open access funding provided by Institute of Science and Technology (IST Austria).
The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful
discussions.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. When different norms lead to same billiard trajectories?
European Journal of Mathematics. 2022;8(4):1309-1312. doi:10.1007/s40879-020-00405-0
apa: Akopyan, A., & Karasev, R. (2022). When different norms lead to same billiard
trajectories? European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00405-0
chicago: Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same
Billiard Trajectories?” European Journal of Mathematics. Springer Nature,
2022. https://doi.org/10.1007/s40879-020-00405-0.
ieee: A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,”
European Journal of Mathematics, vol. 8, no. 4. Springer Nature, pp. 1309–1312,
2022.
ista: Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories?
European Journal of Mathematics. 8(4), 1309–1312.
mla: Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard
Trajectories?” European Journal of Mathematics, vol. 8, no. 4, Springer
Nature, 2022, pp. 1309–12, doi:10.1007/s40879-020-00405-0.
short: A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.
corr_author: '1'
date_created: 2020-05-03T22:00:48Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2025-04-14T07:48:36Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s40879-020-00405-0
ec_funded: 1
external_id:
arxiv:
- '1912.12685'
file:
- access_level: open_access
checksum: f53e71fd03744075adcd0b8fc1b8423d
content_type: application/pdf
creator: dernst
date_created: 2020-05-04T10:33:42Z
date_updated: 2020-07-14T12:48:03Z
file_id: '7796'
file_name: 2020_EuropMathematics_Akopyan.pdf
file_size: 263926
relation: main_file
file_date_updated: 2020-07-14T12:48:03Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1309 - 1312
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: When different norms lead to same billiard trajectories?
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2022'
...
---
_id: '8538'
abstract:
- lang: eng
text: We prove some recent experimental observations of Dan Reznik concerning periodic
billiard orbits in ellipses. For example, the sum of cosines of the angles of
a periodic billiard polygon remains constant in the 1-parameter family of such
polygons (that exist due to the Poncelet porism). In our proofs, we use geometric
and complex analytic methods.
acknowledgement: " This paper would not be written if not for Dan Reznik’s curiosity
and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller
for interesting discussions. It is a pleasure to thank the Mathematical Institute
of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy
for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality.
AA was supported by European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported
by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR
191."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Richard
full_name: Schwartz, Richard
last_name: Schwartz
- first_name: Serge
full_name: Tabachnikov, Serge
last_name: Tabachnikov
citation:
ama: Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. European
Journal of Mathematics. 2022;8(4):1313-1327. doi:10.1007/s40879-020-00426-9
apa: Akopyan, A., Schwartz, R., & Tabachnikov, S. (2022). Billiards in ellipses
revisited. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00426-9
chicago: Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in
Ellipses Revisited.” European Journal of Mathematics. Springer Nature,
2022. https://doi.org/10.1007/s40879-020-00426-9.
ieee: A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,”
European Journal of Mathematics, vol. 8, no. 4. Springer Nature, pp. 1313–1327,
2022.
ista: Akopyan A, Schwartz R, Tabachnikov S. 2022. Billiards in ellipses revisited.
European Journal of Mathematics. 8(4), 1313–1327.
mla: Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal
of Mathematics, vol. 8, no. 4, Springer Nature, 2022, pp. 1313–27, doi:10.1007/s40879-020-00426-9.
short: A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics
8 (2022) 1313–1327.
date_created: 2020-09-20T22:01:38Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2025-04-14T07:48:34Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s40879-020-00426-9
ec_funded: 1
external_id:
arxiv:
- '2001.02934'
intvolume: ' 8'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2001.02934
month: '12'
oa: 1
oa_version: Preprint
page: 1313-1327
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Billiards in ellipses revisited
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 8
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.
corr_author: '1'
date_created: 2021-07-14T06:44:53Z
date_published: 2022-01-01T00:00:00Z
date_updated: 2025-04-22T13:45:18Z
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:
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month: '01'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
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
arxiv: 1
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: 2026-04-07T12:54:09Z
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'
related_material:
record:
- id: '18667'
relation: dissertation_contains
status: public
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: '10828'
abstract:
- lang: eng
text: Digital images enable quantitative analysis of material properties at micro
and macro length scales, but choosing an appropriate resolution when acquiring
the image is challenging. A high resolution means longer image acquisition and
larger data requirements for a given sample, but if the resolution is too low,
significant information may be lost. This paper studies the impact of changes
in resolution on persistent homology, a tool from topological data analysis that
provides a signature of structure in an image across all length scales. Given
prior information about a function, the geometry of an object, or its density
distribution at a given resolution, we provide methods to select the coarsest
resolution yielding results within an acceptable tolerance. We present numerical
case studies for an illustrative synthetic example and samples from porous materials
where the theoretical bounds are unknown.
article_processing_charge: No
arxiv: 1
author:
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Sarah
full_name: Tymochko, Sarah
last_name: Tymochko
- first_name: Brittany
full_name: Story, Brittany
last_name: Story
- first_name: Adélie
full_name: Garin, Adélie
last_name: Garin
- first_name: Hoa
full_name: Bui, Hoa
last_name: Bui
- first_name: Bea
full_name: Bleile, Bea
last_name: Bleile
- first_name: Vanessa
full_name: Robins, Vanessa
last_name: Robins
citation:
ama: 'Heiss T, Tymochko S, Story B, et al. The impact of changes in resolution on
the persistent homology of images. In: 2021 IEEE International Conference on
Big Data. IEEE; 2022:3824-3834. doi:10.1109/BigData52589.2021.9671483'
apa: 'Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., &
Robins, V. (2022). The impact of changes in resolution on the persistent homology
of images. In 2021 IEEE International Conference on Big Data (pp. 3824–3834).
Orlando, FL, United States; Virtuell: IEEE. https://doi.org/10.1109/BigData52589.2021.9671483'
chicago: Heiss, Teresa, Sarah Tymochko, Brittany Story, Adélie Garin, Hoa Bui, Bea
Bleile, and Vanessa Robins. “The Impact of Changes in Resolution on the Persistent
Homology of Images.” In 2021 IEEE International Conference on Big Data,
3824–34. IEEE, 2022. https://doi.org/10.1109/BigData52589.2021.9671483.
ieee: T. Heiss et al., “The impact of changes in resolution on the persistent
homology of images,” in 2021 IEEE International Conference on Big Data,
Orlando, FL, United States; Virtuell, 2022, pp. 3824–3834.
ista: 'Heiss T, Tymochko S, Story B, Garin A, Bui H, Bleile B, Robins V. 2022. The
impact of changes in resolution on the persistent homology of images. 2021 IEEE
International Conference on Big Data. Big Data: International Conference on Big
Data, 3824–3834.'
mla: Heiss, Teresa, et al. “The Impact of Changes in Resolution on the Persistent
Homology of Images.” 2021 IEEE International Conference on Big Data, IEEE,
2022, pp. 3824–34, doi:10.1109/BigData52589.2021.9671483.
short: T. Heiss, S. Tymochko, B. Story, A. Garin, H. Bui, B. Bleile, V. Robins,
in:, 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–3834.
conference:
end_date: 2021-12-18
location: Orlando, FL, United States; Virtuell
name: 'Big Data: International Conference on Big Data'
start_date: 2021-12-15
date_created: 2022-03-06T23:01:53Z
date_published: 2022-01-13T00:00:00Z
date_updated: 2026-04-07T12:54:09Z
day: '13'
department:
- _id: HeEd
doi: 10.1109/BigData52589.2021.9671483
external_id:
arxiv:
- '2111.05663'
isi:
- '000800559503126'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2111.05663
month: '01'
oa: 1
oa_version: Preprint
page: 3824-3834
publication: 2021 IEEE International Conference on Big Data
publication_identifier:
isbn:
- '9781665439022'
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
record:
- id: '18667'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: The impact of changes in resolution on the persistent homology of images
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2022'
...
---
_id: '11660'
abstract:
- lang: eng
text: 'We characterize critical points of 1-dimensional maps paired in persistent
homology geometrically and this way get elementary proofs of theorems about the
symmetry of persistence diagrams and the variation of such maps. In particular,
we identify branching points and endpoints of networks as the sole source of asymmetry
and relate the cycle basis in persistent homology with a version of the stable
marriage problem. Our analysis provides the foundations of fast algorithms for
maintaining collections of interrelated sorted lists together with their persistence
diagrams. '
acknowledgement: '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. '
alternative_title:
- LIPIcs
article_processing_charge: No
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
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to
the persistence of 1D maps. I: Geometric characterization of critical point pairs.
LIPIcs.'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization
of critical point pairs. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik.'
chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “A Window to the Persistence of 1D Maps. I: Geometric Characterization
of Critical Point Pairs.” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, n.d.'
ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “A
window to the persistence of 1D maps. I: Geometric characterization of critical
point pairs,” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.'
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window
to the persistence of 1D maps. I: Geometric characterization of critical point
pairs. LIPIcs.'
mla: 'Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric
Characterization of Critical Point Pairs.” LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik.'
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs
(n.d.).
corr_author: '1'
date_created: 2022-07-27T09:31:15Z
date_published: 2022-07-25T00:00:00Z
date_updated: 2026-04-07T12:58:47Z
day: '25'
ddc:
- '510'
department:
- _id: GradSch
- _id: HeEd
ec_funded: 1
file:
- access_level: open_access
checksum: 95903f9d1649e8e437a967b6f2f64730
content_type: application/pdf
creator: scultrer
date_created: 2022-07-27T09:30:30Z
date_updated: 2022-07-27T09:30:30Z
file_id: '11661'
file_name: window 1.pdf
file_size: 564836
relation: main_file
file_date_updated: 2022-07-27T09:30:30Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Submitted Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: LIPIcs
publication_status: submitted
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
status: public
title: 'A window to the persistence of 1D maps. I: Geometric characterization of critical
point pairs'
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: '2022'
...