---
_id: '12764'
abstract:
- lang: eng
text: We study a new discretization of the Gaussian curvature for polyhedral surfaces.
This discrete Gaussian curvature is defined on each conical singularity of a polyhedral
surface as the quotient of the angle defect and the area of the Voronoi cell corresponding
to the singularity. We divide polyhedral surfaces into discrete conformal classes
using a generalization of discrete conformal equivalence pioneered by Feng Luo.
We subsequently show that, in every discrete conformal class, there exists a polyhedral
surface with constant discrete Gaussian curvature. We also provide explicit examples
to demonstrate that this surface is in general not unique.
acknowledgement: Open access funding provided by the Austrian Science Fund (FWF).
This research was supported by the FWF grant, Project number I4245-N35, and by the
Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID
195170736 - TRR109.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
orcid: 0000-0001-7841-0091
citation:
ama: Kourimska H. Discrete yamabe problem for polyhedral surfaces. Discrete and
Computational Geometry. 2023;70:123-153. doi:10.1007/s00454-023-00484-2
apa: Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. Discrete
and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00484-2
chicago: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete
and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00484-2.
ieee: H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” Discrete
and Computational Geometry, vol. 70. Springer Nature, pp. 123–153, 2023.
ista: Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete
and Computational Geometry. 70, 123–153.
mla: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete
and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 123–53, doi:10.1007/s00454-023-00484-2.
short: H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.
date_created: 2023-03-26T22:01:09Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-10-04T11:46:48Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00484-2
external_id:
isi:
- '000948148000001'
file:
- access_level: open_access
checksum: cdbf90ba4a7ddcb190d37b9e9d4cb9d3
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T11:46:24Z
date_updated: 2023-10-04T11:46:24Z
file_id: '14396'
file_name: 2023_DiscreteGeometry_Kourimska.pdf
file_size: 1026683
relation: main_file
success: 1
file_date_updated: 2023-10-04T11:46:24Z
has_accepted_license: '1'
intvolume: ' 70'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 123-153
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I04245
name: Algebraic Footprints of Geometric Features in Homology
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: Discrete yamabe problem for polyhedral surfaces
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: 70
year: '2023'
...
---
_id: '12709'
abstract:
- lang: eng
text: Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within
distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter
family of spaces that grow larger when r increases or k decreases, called the
multicover bifiltration. Motivated by the problem of computing the homology of
this bifiltration, we introduce two closely related combinatorial bifiltrations,
one polyhedral and the other simplicial, which are both topologically equivalent
to the multicover bifiltration and far smaller than a Čech-based model considered
in prior work of Sheehy. Our polyhedral construction is a bifiltration of the
rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using
a variant of an algorithm given by these authors as well. Using an implementation
for dimension 2 and 3, we provide experimental results. Our simplicial construction
is useful for understanding the polyhedral construction and proving its correctness.
acknowledgement: We thank the anonymous reviewers for many helpful comments and suggestions,
which led to substantial improvements of the paper. The first two authors were supported
by the Austrian Science Fund (FWF) grant number P 29984-N35 and W1230. The first
author was partly supported by an Austrian Marshall Plan Scholarship, and by the
Brummer & Partners MathDataLab. A conference version of this paper was presented
at the 37th International Symposium on Computational Geometry (SoCG 2021). Open
access funding provided by the Royal Institute of Technology.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: René
full_name: Corbet, René
last_name: Corbet
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Michael
full_name: Lesnick, Michael
last_name: Lesnick
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
citation:
ama: Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration.
Discrete and Computational Geometry. 2023;70:376-405. doi:10.1007/s00454-022-00476-8
apa: Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2023). Computing the
multicover bifiltration. Discrete and Computational Geometry. Springer
Nature. https://doi.org/10.1007/s00454-022-00476-8
chicago: Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing
the Multicover Bifiltration.” Discrete and Computational Geometry. Springer
Nature, 2023. https://doi.org/10.1007/s00454-022-00476-8.
ieee: R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover
bifiltration,” Discrete and Computational Geometry, vol. 70. Springer Nature,
pp. 376–405, 2023.
ista: Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration.
Discrete and Computational Geometry. 70, 376–405.
mla: Corbet, René, et al. “Computing the Multicover Bifiltration.” Discrete and
Computational Geometry, vol. 70, Springer Nature, 2023, pp. 376–405, doi:10.1007/s00454-022-00476-8.
short: R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational
Geometry 70 (2023) 376–405.
date_created: 2023-03-05T23:01:06Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2023-10-04T12:03:40Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s00454-022-00476-8
external_id:
arxiv:
- '2103.07823'
isi:
- '000936496800001'
file:
- access_level: open_access
checksum: 71ce7e59f7ee4620acc704fecca620c2
content_type: application/pdf
creator: cchlebak
date_created: 2023-03-07T14:40:14Z
date_updated: 2023-03-07T14:40:14Z
file_id: '12715'
file_name: 2023_DisCompGeo_Corbet.pdf
file_size: 1359323
relation: main_file
success: 1
file_date_updated: 2023-03-07T14:40:14Z
has_accepted_license: '1'
intvolume: ' 70'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 376-405
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '9605'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Computing the multicover bifiltration
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: 70
year: '2023'
...
---
_id: '12763'
abstract:
- lang: eng
text: 'Kleinjohann (Archiv der Mathematik 35(1):574–582, 1980; Mathematische Zeitschrift
176(3), 327–344, 1981) and Bangert (Archiv der Mathematik 38(1):54–57, 1982) extended
the reach rch(S) from subsets S of Euclidean space to the reach rchM(S) of subsets
S of Riemannian manifolds M, where M is smooth (we’ll assume at least C3). Bangert
showed that sets of positive reach in Euclidean space and Riemannian manifolds
are very similar. In this paper we introduce a slight variant of Kleinjohann’s
and Bangert’s extension and quantify the similarity between sets of positive reach
in Euclidean space and Riemannian manifolds in a new way: Given p∈M and q∈S, we
bound the local feature size (a local version of the reach) of its lifting to
the tangent space via the inverse exponential map (exp−1p(S)) at q, assuming that
rchM(S) and the geodesic distance dM(p,q) are bounded. These bounds are motivated
by the importance of the reach and local feature size to manifold learning, topological
inference, and triangulating manifolds and the fact that intrinsic approaches
circumvent the curse of dimensionality.'
acknowledgement: "We thank Eddie Aamari, David Cohen-Steiner, Isa Costantini, Fred
Chazal, Ramsay Dyer, André Lieutier, and Alef Sterk for discussion and Pierre Pansu
for encouragement. We further acknowledge the anonymous reviewers whose comments
helped improve the exposition.\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). The first author is
further 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. The second author is supported by the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411 and the Austrian science fund (FWF) M-3073."
article_processing_charge: No
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 JD, Wintraecken M. The reach of subsets of manifolds. Journal
of Applied and Computational Topology. 2023;7:619-641. doi:10.1007/s41468-023-00116-x
apa: Boissonnat, J. D., & Wintraecken, M. (2023). The reach of subsets of manifolds.
Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00116-x
chicago: Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets
of Manifolds.” Journal of Applied and Computational Topology. Springer
Nature, 2023. https://doi.org/10.1007/s41468-023-00116-x.
ieee: J. D. Boissonnat and M. Wintraecken, “The reach of subsets of manifolds,”
Journal of Applied and Computational Topology, vol. 7. Springer Nature,
pp. 619–641, 2023.
ista: Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal
of Applied and Computational Topology. 7, 619–641.
mla: Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of
Manifolds.” Journal of Applied and Computational Topology, vol. 7, Springer
Nature, 2023, pp. 619–41, doi:10.1007/s41468-023-00116-x.
short: J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology
7 (2023) 619–641.
date_created: 2023-03-26T22:01:08Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2023-10-04T12:07:18Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s41468-023-00116-x
ec_funded: 1
intvolume: ' 7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1
month: '09'
oa: 1
oa_version: Submitted Version
page: 619-641
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: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The reach of subsets of manifolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2023'
...
---
_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.
date_created: 2023-05-14T22:01:00Z
date_published: 2023-04-30T00:00:00Z
date_updated: 2023-10-10T07:34:35Z
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: '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).
date_created: 2023-06-18T22:00:45Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2023-10-10T07:37:16Z
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: Discretization in Geometry and Dynamics
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: '14557'
abstract:
- lang: eng
text: Motivated by a problem posed in [10], we investigate the closure operators
of the category SLatt of join semilattices and its subcategory SLattO of join
semilattices with bottom element. In particular, we show that there are only finitely
many closure operators of both categories, and provide a complete classification.
We use this result to deduce the known fact that epimorphisms of SLatt and SLattO
are surjective. We complement the paper with two different proofs of this result
using either generators or Isbell’s zigzag theorem.
acknowledgement: "The first and second named authors are members of GNSAGA – INdAM.\r\nThe
third named author was supported by the FWF Grant, Project number I4245–N35"
article_processing_charge: No
article_type: original
author:
- first_name: D.
full_name: Dikranjan, D.
last_name: Dikranjan
- first_name: A.
full_name: Giordano Bruno, A.
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: Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of
categories of semilattices. Quaestiones Mathematicae. 2023;46(S1):191-221.
doi:10.2989/16073606.2023.2247731
apa: Dikranjan, D., Giordano Bruno, A., & Zava, N. (2023). Epimorphisms and
closure operators of categories of semilattices. Quaestiones Mathematicae.
Taylor & Francis. https://doi.org/10.2989/16073606.2023.2247731
chicago: Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure
Operators of Categories of Semilattices.” Quaestiones Mathematicae. Taylor
& Francis, 2023. https://doi.org/10.2989/16073606.2023.2247731.
ieee: D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators
of categories of semilattices,” Quaestiones Mathematicae, vol. 46, no.
S1. Taylor & Francis, pp. 191–221, 2023.
ista: Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators
of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221.
mla: Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of
Semilattices.” Quaestiones Mathematicae, vol. 46, no. S1, Taylor &
Francis, 2023, pp. 191–221, doi:10.2989/16073606.2023.2247731.
short: D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023)
191–221.
date_created: 2023-11-19T23:00:55Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-11-20T09:24:48Z
day: '01'
department:
- _id: HeEd
doi: 10.2989/16073606.2023.2247731
intvolume: ' 46'
issue: S1
language:
- iso: eng
month: '11'
oa_version: None
page: 191-221
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I04245
name: Algebraic Footprints of Geometric Features in Homology
publication: Quaestiones Mathematicae
publication_identifier:
eissn:
- 1727-933X
issn:
- 1607-3606
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Epimorphisms and closure operators of categories of semilattices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 46
year: '2023'
...
---
_id: '14345'
abstract:
- lang: eng
text: For a locally finite set in R2, the order-k Brillouin tessellations form an
infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely
dense and generic, then the corresponding infinite sequences of minimum and maximum
angles are both monotonic in k. As an example, a stationary Poisson point process
in R2 is locally finite, coarsely dense, and generic with probability one. For
such a set, the distributions of angles in the Voronoi tessellations, Delaunay
mosaics, and Brillouin tessellations are independent of the order and can be derived
from the formula for angles in order-1 Delaunay mosaics given by Miles (Math.
Biosci. 6, 85–127 (1970)).
acknowledgement: Work by all authors but A. Garber is supported by the European Research
Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund
(FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109,
Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially
supported by the Alexander von Humboldt Foundation.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Alexey
full_name: Garber, Alexey
last_name: Garber
- first_name: Mohadese
full_name: Ghafari, Mohadese
last_name: Ghafari
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher
order Brillouin tessellations and related tilings in the plane. Discrete and
Computational Geometry. 2023. doi:10.1007/s00454-023-00566-1
apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2023).
On angles in higher order Brillouin tessellations and related tilings in the plane.
Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00566-1
chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and
Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related
Tilings in the Plane.” Discrete and Computational Geometry. Springer Nature,
2023. https://doi.org/10.1007/s00454-023-00566-1.
ieee: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles
in higher order Brillouin tessellations and related tilings in the plane,” Discrete
and Computational Geometry. Springer Nature, 2023.
ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2023. On angles
in higher order Brillouin tessellations and related tilings in the plane. Discrete
and Computational Geometry.
mla: Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations
and Related Tilings in the Plane.” Discrete and Computational Geometry,
Springer Nature, 2023, doi:10.1007/s00454-023-00566-1.
short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete
and Computational Geometry (2023).
date_created: 2023-09-17T22:01:10Z
date_published: 2023-09-07T00:00:00Z
date_updated: 2023-12-13T12:25:06Z
day: '07'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00566-1
ec_funded: 1
external_id:
arxiv:
- '2204.01076'
isi:
- '001060727600004'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-023-00566-1
month: '09'
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: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On angles in higher order Brillouin tessellations and related tilings in the
plane
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14464'
abstract:
- lang: eng
text: 'Given a triangle Δ, we study the problem of determining the smallest enclosing
and largest embedded isosceles triangles of Δ with respect to area and perimeter.
This problem was initially posed by Nandakumar [17, 22] and was first studied
by Kiss, Pach, and Somlai [13], who showed that if Δ′ is the smallest area isosceles
triangle containing Δ, then Δ′ and Δ share a side and an angle. In the present
paper, we prove that for any triangle Δ, every maximum area isosceles triangle
embedded in Δ and every maximum perimeter isosceles triangle embedded in Δ shares
a side and an angle with Δ. Somewhat surprisingly, the case of minimum perimeter
enclosing triangles is different: there are infinite families of triangles Δ whose
minimum perimeter isosceles containers do not share a side and an angle with Δ.'
article_processing_charge: No
article_type: original
author:
- first_name: Áron
full_name: Ambrus, Áron
last_name: Ambrus
- first_name: Mónika
full_name: Csikós, Mónika
last_name: Csikós
- first_name: Gergely
full_name: Kiss, Gergely
last_name: Kiss
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Gábor
full_name: Somlai, Gábor
last_name: Somlai
citation:
ama: Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. Optimal embedded and enclosing
isosceles triangles. International Journal of Foundations of Computer Science.
2023;34(7):737-760. doi:10.1142/S012905412342008X
apa: Ambrus, Á., Csikós, M., Kiss, G., Pach, J., & Somlai, G. (2023). Optimal
embedded and enclosing isosceles triangles. International Journal of Foundations
of Computer Science. World Scientific Publishing. https://doi.org/10.1142/S012905412342008X
chicago: Ambrus, Áron, Mónika Csikós, Gergely Kiss, János Pach, and Gábor Somlai.
“Optimal Embedded and Enclosing Isosceles Triangles.” International Journal
of Foundations of Computer Science. World Scientific Publishing, 2023. https://doi.org/10.1142/S012905412342008X.
ieee: Á. Ambrus, M. Csikós, G. Kiss, J. Pach, and G. Somlai, “Optimal embedded and
enclosing isosceles triangles,” International Journal of Foundations of Computer
Science, vol. 34, no. 7. World Scientific Publishing, pp. 737–760, 2023.
ista: Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. 2023. Optimal embedded and enclosing
isosceles triangles. International Journal of Foundations of Computer Science.
34(7), 737–760.
mla: Ambrus, Áron, et al. “Optimal Embedded and Enclosing Isosceles Triangles.”
International Journal of Foundations of Computer Science, vol. 34, no.
7, World Scientific Publishing, 2023, pp. 737–60, doi:10.1142/S012905412342008X.
short: Á. Ambrus, M. Csikós, G. Kiss, J. Pach, G. Somlai, International Journal
of Foundations of Computer Science 34 (2023) 737–760.
date_created: 2023-10-29T23:01:18Z
date_published: 2023-10-05T00:00:00Z
date_updated: 2023-12-13T13:04:55Z
day: '05'
department:
- _id: HeEd
doi: 10.1142/S012905412342008X
external_id:
arxiv:
- '2205.11637'
isi:
- '001080874400001'
intvolume: ' 34'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2205.11637
month: '10'
oa: 1
oa_version: Preprint
page: 737-760
publication: International Journal of Foundations of Computer Science
publication_identifier:
eissn:
- 1793-6373
issn:
- 0129-0541
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal embedded and enclosing isosceles triangles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2023'
...
---
_id: '12833'
abstract:
- lang: eng
text: 'The input to the token swapping problem is a graph with vertices v1, v2,
. . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal
is to get token i to vertex vi for all i= 1, . . . , n using a minimum number
of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token
swapping on a tree, also known as “sorting with a transposition tree,” is not
known to be in P nor NP-complete. We present some partial results: 1. An optimum
swap sequence may need to perform a swap on a leaf vertex that has the correct
token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that
fixes happy leaves—as all known approximation algorithms for the problem do—has
approximation factor at least 4/3. Furthermore, the two best-known 2-approximation
algorithms have approximation factor exactly 2. 3. A generalized problem—weighted
coloured token swapping—is NP-complete on trees, but solvable in polynomial time
on paths and stars. In this version, tokens and vertices have colours, and colours
have weights. The goal is to get every token to a vertex of the same colour, and
the cost of a swap is the sum of the weights of the two tokens involved.'
acknowledgement: "This work was begun at the University of Waterloo and was partially
supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n"
article_number: '9'
article_processing_charge: No
article_type: original
author:
- first_name: Ahmad
full_name: Biniaz, Ahmad
last_name: Biniaz
- first_name: Kshitij
full_name: Jain, Kshitij
last_name: Jain
- first_name: Anna
full_name: Lubiw, Anna
last_name: Lubiw
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tillmann
full_name: Miltzow, Tillmann
last_name: Miltzow
- first_name: Debajyoti
full_name: Mondal, Debajyoti
last_name: Mondal
- first_name: Anurag Murty
full_name: Naredla, Anurag Murty
last_name: Naredla
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Alexi
full_name: Turcotte, Alexi
last_name: Turcotte
citation:
ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics
and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383
apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte,
A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer
Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383
chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow,
Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token
Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science.
EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383.
ieee: A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics
and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023.
ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec
J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical
Computer Science. 24(2), 9.
mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and
Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383.
short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla,
J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science
24 (2023).
date_created: 2023-04-16T22:01:08Z
date_published: 2023-01-18T00:00:00Z
date_updated: 2024-01-04T12:42:09Z
day: '18'
ddc:
- '000'
department:
- _id: KrCh
- _id: HeEd
- _id: UlWa
doi: 10.46298/DMTCS.8383
external_id:
arxiv:
- '1903.06981'
file:
- access_level: open_access
checksum: 439102ea4f6e2aeefd7107dfb9ccf532
content_type: application/pdf
creator: dernst
date_created: 2023-04-17T08:10:28Z
date_updated: 2023-04-17T08:10:28Z
file_id: '12844'
file_name: 2022_DMTCS_Biniaz.pdf
file_size: 2072197
relation: main_file
success: 1
file_date_updated: 2023-04-17T08:10:28Z
has_accepted_license: '1'
intvolume: ' 24'
issue: '2'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
publication: Discrete Mathematics and Theoretical Computer Science
publication_identifier:
eissn:
- 1365-8050
issn:
- 1462-7264
publication_status: published
publisher: EPI Sciences
quality_controlled: '1'
related_material:
record:
- id: '7950'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: 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: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '14739'
abstract:
- lang: eng
text: Attempts to incorporate topological information in supervised learning tasks
have resulted in the creation of several techniques for vectorizing persistent
homology barcodes. In this paper, we study thirteen such methods. Besides describing
an organizational framework for these methods, we comprehensively benchmark them
against three well-known classification tasks. Surprisingly, we discover that
the best-performing method is a simple vectorization, which consists only of a
few elementary summary statistics. Finally, we provide a convenient web application
which has been designed to facilitate exploration and experimentation with various
vectorization methods.
acknowledgement: "The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel
Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia
e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part
by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028.
The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la
Universidad de Sevilla para la recualificacion del sistema universitario español,
2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda
was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR
under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON
developers, for their work and their support. We are also grateful to Streamlit
for providing extra resources to deploy the web app\r\nonline on Streamlit community
cloud. We thank the anonymous referees for their helpful suggestions."
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Dashti
full_name: Ali, Dashti
last_name: Ali
- first_name: Aras
full_name: Asaad, Aras
last_name: Asaad
- first_name: Maria-Jose
full_name: Jimenez, Maria-Jose
last_name: Jimenez
- first_name: Vidit
full_name: Nanda, Vidit
last_name: Nanda
- first_name: Eduardo
full_name: Paluzo-Hidalgo, Eduardo
last_name: Paluzo-Hidalgo
- first_name: Manuel
full_name: Soriano Trigueros, Manuel
id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
last_name: Soriano Trigueros
orcid: 0000-0003-2449-1433
citation:
ama: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M.
A survey of vectorization methods in topological data analysis. IEEE Transactions
on Pattern Analysis and Machine Intelligence. 2023;45(12):14069-14080. doi:10.1109/tpami.2023.3308391
apa: Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., & Soriano
Trigueros, M. (2023). A survey of vectorization methods in topological data analysis.
IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2023.3308391
chicago: Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo,
and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological
Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence.
IEEE, 2023. https://doi.org/10.1109/tpami.2023.3308391.
ieee: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano
Trigueros, “A survey of vectorization methods in topological data analysis,” IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12.
IEEE, pp. 14069–14080, 2023.
ista: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros
M. 2023. A survey of vectorization methods in topological data analysis. IEEE
Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.
mla: Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data
Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:10.1109/tpami.2023.3308391.
short: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano
Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023)
14069–14080.
date_created: 2024-01-08T09:59:46Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-08T10:11:46Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1109/tpami.2023.3308391
file:
- access_level: open_access
checksum: 465c28ef0b151b4b1fb47977ed5581ab
content_type: application/pdf
creator: dernst
date_created: 2024-01-08T10:09:14Z
date_updated: 2024-01-08T10:09:14Z
file_id: '14740'
file_name: 2023_IEEEToP_Ali.pdf
file_size: 2370988
relation: main_file
success: 1
file_date_updated: 2024-01-08T10:09:14Z
has_accepted_license: '1'
intvolume: ' 45'
issue: '12'
keyword:
- Applied Mathematics
- Artificial Intelligence
- Computational Theory and Mathematics
- Computer Vision and Pattern Recognition
- Software
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 14069-14080
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: IEEE
quality_controlled: '1'
status: public
title: A survey of vectorization methods in topological data analysis
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: 45
year: '2023'
...