---
_id: '9157'
abstract:
- lang: eng
text: Representing an atom by a solid sphere in 3-dimensional Euclidean space, we
get the space-filling diagram of a molecule by taking the union. Molecular dynamics
simulates its motion subject to bonds and other forces, including the solvation
free energy. The morphometric approach [12, 17] writes the latter as a linear
combination of weighted versions of the volume, area, mean curvature, and Gaussian
curvature of the space-filling diagram. We give a formula for the derivative of
the weighted mean curvature. Together with the derivatives of the weighted volume
in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this
yields the derivative of the morphometric expression of the solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of the weighted\r\ncurvature derivatives for the purpose of improving molecular
dynamics simulations and for his continued encouragement. They also thank Patrice
Koehl for the implementation of the formulas and for his encouragement and advise
along the road. Finally, they thank two anonymous reviewers for their constructive
criticism.\r\nThis project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative
Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant
no. I02979-N35 of the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling
diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0100
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of
a space-filling diagram,” Computational and Mathematical Biophysics, vol.
8, no. 1. De Gruyter, pp. 51–67, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of
a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative
of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 51–67.
corr_author: '1'
date_created: 2021-02-17T15:13:01Z
date_published: 2020-06-20T00:00:00Z
date_updated: 2025-04-14T07:48:35Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0100
ec_funded: 1
file:
- access_level: open_access
checksum: cea41de9937d07a3b927d71ee8b4e432
content_type: application/pdf
creator: dernst
date_created: 2021-02-19T13:56:24Z
date_updated: 2021-02-19T13:56:24Z
file_id: '9171'
file_name: 2020_CompMathBiophysics_Akopyan2.pdf
file_size: 562359
relation: main_file
success: 1
file_date_updated: 2021-02-19T13:56:24Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 51-67
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Computational and Mathematical Biophysics
publication_identifier:
issn:
- 2544-7297
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: The weighted mean curvature derivative of a space-filling diagram
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: 8
year: '2020'
...
---
_id: '9249'
abstract:
- lang: eng
text: Rhombic dodecahedron is a space filling polyhedron which represents the close
packing of spheres in 3D space and the Voronoi structures of the face centered
cubic (FCC) lattice. In this paper, we describe a new coordinate system where
every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid.
In order to illustrate the interest of the new coordinate system, we propose the
characterization of 3D digital plane with its topological features, such as the
interrelation between the thickness of the digital plane and the separability
constraint we aim to obtain. We also present the characterization of 3D digital
lines and study it as the intersection of multiple digital planes. Characterization
of 3D digital sphere with relevant topological features is proposed as well along
with the 48-symmetry appearing in the new coordinate system.
acknowledgement: "This work has been partially supported by the European Research
Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation
programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109,
‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no.
I 02979-N35. "
article_processing_charge: No
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: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic
dodecahedron grid. Mathematical Morphology - Theory and Applications. 2020;4(1):143-158.
doi:10.1515/mathm-2020-0106
apa: Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital
objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and
Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106
chicago: Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital
Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and
Applications. De Gruyter, 2020. https://doi.org/10.1515/mathm-2020-0106.
ieee: R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects
in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications,
vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.
ista: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in
rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications.
4(1), 143–158.
mla: Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical
Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp.
143–58, doi:10.1515/mathm-2020-0106.
short: R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology
- Theory and Applications 4 (2020) 143–158.
corr_author: '1'
date_created: 2021-03-16T08:55:19Z
date_published: 2020-11-17T00:00:00Z
date_updated: 2025-04-14T07:48:35Z
day: '17'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/mathm-2020-0106
ec_funded: 1
file:
- access_level: open_access
checksum: 4a1043fa0548a725d464017fe2483ce0
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T08:56:37Z
date_updated: 2021-03-22T08:56:37Z
file_id: '9272'
file_name: 2020_MathMorpholTheoryAppl_Biswas.pdf
file_size: 3668725
relation: main_file
success: 1
file_date_updated: 2021-03-22T08:56:37Z
has_accepted_license: '1'
intvolume: ' 4'
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 143-158
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Mathematical Morphology - Theory and Applications
publication_identifier:
issn:
- 2353-3390
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: Digital objects in rhombic dodecahedron grid
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: 4
year: '2020'
...
---
_id: '9299'
abstract:
- lang: eng
text: We call a multigraph non-homotopic if it can be drawn in the plane in such
a way that no two edges connecting the same pair of vertices can be continuously
transformed into each other without passing through a vertex, and no loop can
be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic
multigraph on n>1 vertices can have arbitrarily many edges. We prove that the
number of crossings between the edges of a non-homotopic multigraph with n vertices
and m>4n edges is larger than cm2n for some constant c>0 , and that this
bound is tight up to a polylogarithmic factor. We also show that the lower bound
is not asymptotically sharp as n is fixed and m⟶∞ .
acknowledgement: Supported by the National Research, Development and Innovation Office,
NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional
Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant
Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant
No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full
version can be found at https://arxiv.org/abs/2006.14908.
article_processing_charge: No
arxiv: 1
author:
- 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: Géza
full_name: Tóth, Géza
last_name: Tóth
citation:
ama: 'Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th
International Symposium on Graph Drawing and Network Visualization. Vol 12590.
LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28'
apa: 'Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic
edges. In 28th International Symposium on Graph Drawing and Network Visualization
(Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28'
chicago: Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic
Edges.” In 28th International Symposium on Graph Drawing and Network Visualization,
12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28.
ieee: J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,”
in 28th International Symposium on Graph Drawing and Network Visualization,
Virtual, Online, 2020, vol. 12590, pp. 359–371.
ista: 'Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th
International Symposium on Graph Drawing and Network Visualization. GD: Graph
Drawing and Network VisualizationLNCS vol. 12590, 359–371.'
mla: Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International
Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer
Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28.
short: J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing
and Network Visualization, Springer Nature, 2020, pp. 359–371.
conference:
end_date: 2020-09-18
location: Virtual, Online
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2020-09-16
date_created: 2021-03-28T22:01:44Z
date_published: 2020-09-20T00:00:00Z
date_updated: 2025-04-15T07:16:52Z
day: '20'
department:
- _id: HeEd
doi: 10.1007/978-3-030-68766-3_28
external_id:
arxiv:
- '2006.14908'
intvolume: ' 12590'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2006.14908
month: '09'
oa: 1
oa_version: Preprint
page: 359-371
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
publication: 28th International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783030687656'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNCS
status: public
title: Crossings between non-homotopic edges
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12590
year: '2020'
...
---
_id: '74'
abstract:
- lang: eng
text: "We study the Gromov waist in the sense of t-neighborhoods for measures in
the Euclidean space, motivated by the famous theorem of Gromov about
\ the waist of radially symmetric Gaussian measures. In particular, it turns
our possible to extend Gromov’s original result to the case of not necessarily
\ radially symmetric Gaussian measure. We also provide examples of measures
having no t-neighborhood waist property, including a rather wide class\r\nof compactly
supported radially symmetric measures and their maps into the Euclidean space
of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument
\ to produce some estimates of t-neighborhoods of (weighted) volume-critical
submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic
manifolds in the complex projective space. In the appendix of this paper we provide
for reader’s convenience a more detailed explanation of the Caffarelli theorem
that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."
article_processing_charge: No
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. Gromov’s waist of non-radial Gaussian measures and radial
non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional
Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1'
apa: Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian
measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.),
Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer
Nature. https://doi.org/10.1007/978-3-030-36020-7_1
chicago: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer
Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.
ieee: A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis,
vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.
ista: 'Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis.
vol. 2256, 1–27.'
mla: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer
Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.
short: A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects
of Functional Analysis, Springer Nature, 2020, pp. 1–27.
date_created: 2018-12-11T11:44:29Z
date_published: 2020-06-21T00:00:00Z
date_updated: 2025-07-10T11:54:33Z
day: '21'
department:
- _id: HeEd
- _id: JaMa
doi: 10.1007/978-3-030-36020-7_1
ec_funded: 1
editor:
- first_name: Bo'az
full_name: Klartag, Bo'az
last_name: Klartag
- first_name: Emanuel
full_name: Milman, Emanuel
last_name: Milman
external_id:
arxiv:
- '1808.07350'
isi:
- '000557689300003'
intvolume: ' 2256'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1808.07350
month: '06'
oa: 1
oa_version: Preprint
page: 1-27
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Geometric Aspects of Functional Analysis
publication_identifier:
eisbn:
- '9783030360207'
eissn:
- 1617-9692
isbn:
- '9783030360191'
issn:
- 0075-8434
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNM
status: public
title: Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2256
year: '2020'
...
---
_id: '7554'
abstract:
- lang: eng
text: Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional
weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation.
Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the
smallest empty circumscribed sphere whose center lies in the $k$-plane gives a
generalized discrete Morse function. Assuming the Voronoi tessellation is generated
by a Poisson point process in ${R}^n$, we study the expected number of simplices
in the $k$-dimensional weighted Delaunay mosaic as well as the expected number
of intervals of the Morse function, both as functions of a radius threshold. As
a by-product, we obtain a new proof for the expected number of connected components
(clumps) in a line section of a circular Boolean model in ${R}^n$.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of
Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726
apa: Edelsbrunner, H., & Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics.
Theory of Probability and Its Applications. SIAM. https://doi.org/10.1137/S0040585X97T989726
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay
Mosaics.” Theory of Probability and Its Applications. SIAM, 2020. https://doi.org/10.1137/S0040585X97T989726.
ieee: H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” Theory
of Probability and its Applications, vol. 64, no. 4. SIAM, pp. 595–614, 2020.
ista: Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory
of Probability and its Applications. 64(4), 595–614.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.”
Theory of Probability and Its Applications, vol. 64, no. 4, SIAM, 2020,
pp. 595–614, doi:10.1137/S0040585X97T989726.
short: H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications
64 (2020) 595–614.
date_created: 2020-03-01T23:00:39Z
date_published: 2020-02-13T00:00:00Z
date_updated: 2025-07-10T11:54:44Z
day: '13'
department:
- _id: HeEd
doi: 10.1137/S0040585X97T989726
ec_funded: 1
external_id:
arxiv:
- '1705.08735'
isi:
- '000551393100007'
intvolume: ' 64'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.08735
month: '02'
oa: 1
oa_version: Preprint
page: 595-614
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Theory of Probability and its Applications
publication_identifier:
eissn:
- 1095-7219
issn:
- 0040-585X
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weighted Poisson–Delaunay mosaics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 64
year: '2020'
...
---
_id: '7567'
abstract:
- lang: eng
text: Coxeter triangulations are triangulations of Euclidean space based on a single
simplex. By this we mean that given an individual simplex we can recover the entire
triangulation of Euclidean space by inductively reflecting in the faces of the
simplex. In this paper we establish that the quality of the simplices in all Coxeter
triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate
the Delaunay property for these triangulations. Moreover, we consider an extension
of the Delaunay property, namely protection, which is a measure of non-degeneracy
of a Delaunay triangulation. In particular, one family of Coxeter triangulations
achieves the protection O(1/d2). We conjecture that both bounds are optimal for
triangulations in Euclidean space.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Aruni
full_name: Choudhary, Aruni
last_name: Choudhary
- 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: Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good
quality. Mathematics in Computer Science. 2020;14:141-176. doi:10.1007/s11786-020-00461-5
apa: Choudhary, A., Kachanovich, S., & Wintraecken, M. (2020). Coxeter triangulations
have good quality. Mathematics in Computer Science. Springer Nature. https://doi.org/10.1007/s11786-020-00461-5
chicago: Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter
Triangulations Have Good Quality.” Mathematics in Computer Science. Springer
Nature, 2020. https://doi.org/10.1007/s11786-020-00461-5.
ieee: A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations
have good quality,” Mathematics in Computer Science, vol. 14. Springer
Nature, pp. 141–176, 2020.
ista: Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have
good quality. Mathematics in Computer Science. 14, 141–176.
mla: Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” Mathematics
in Computer Science, vol. 14, Springer Nature, 2020, pp. 141–76, doi:10.1007/s11786-020-00461-5.
short: A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science
14 (2020) 141–176.
corr_author: '1'
date_created: 2020-03-05T13:30:18Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2025-04-14T07:44:03Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s11786-020-00461-5
ec_funded: 1
file:
- access_level: open_access
checksum: 1d145f3ab50ccee735983cb89236e609
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T10:18:02Z
date_updated: 2020-11-20T10:18:02Z
file_id: '8783'
file_name: 2020_MathCompScie_Choudhary.pdf
file_size: 872275
relation: main_file
success: 1
file_date_updated: 2020-11-20T10:18:02Z
has_accepted_license: '1'
intvolume: ' 14'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 141-176
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Mathematics in Computer Science
publication_identifier:
eissn:
- 1661-8289
issn:
- 1661-8270
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coxeter triangulations have good quality
tmp:
image: /images/cc_by.png
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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: 14
year: '2020'
...
---
_id: '9630'
abstract:
- lang: eng
text: Various kinds of data are routinely represented as discrete probability distributions.
Examples include text documents summarized by histograms of word occurrences and
images represented as histograms of oriented gradients. Viewing a discrete probability
distribution as a point in the standard simplex of the appropriate dimension,
we can understand collections of such objects in geometric and topological terms. Importantly,
instead of using the standard Euclidean distance, we look into dissimilarity measures
with information-theoretic justification, and we develop the theory needed for
applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable the usage of existing computational topology software
in this context.
acknowledgement: This research is partially supported by the Office of Naval Research,
through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
the Austrian Science Fund (FWF).
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0009-0009-9111-8429
citation:
ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7
apa: Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis
in information space. Journal of Computational Geometry. Carleton University.
https://doi.org/10.20382/jocg.v11i2a7
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
Analysis in Information Space.” Journal of Computational Geometry. Carleton
University, 2020. https://doi.org/10.20382/jocg.v11i2a7.
ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University,
pp. 162–182, 2020.
ista: Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information
space. Journal of Computational Geometry. 11(2), 162–182.
mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
Journal of Computational Geometry, vol. 11, no. 2, Carleton University,
2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.
short: H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11
(2020) 162–182.
corr_author: '1'
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2026-04-02T14:35:31Z
day: '14'
ddc:
- '510'
- '000'
department:
- _id: HeEd
doi: 10.20382/jocg.v11i2a7
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content_type: application/pdf
creator: asandaue
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date_updated: 2021-08-11T11:55:11Z
file_id: '9882'
file_name: 2020_JournalOfComputationalGeometry_Edelsbrunner.pdf
file_size: 1449234
relation: main_file
success: 1
file_date_updated: 2021-08-11T11:55:11Z
has_accepted_license: '1'
intvolume: ' 11'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '12'
oa: 1
oa_version: Published Version
page: 162-182
project:
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
publication: Journal of Computational Geometry
publication_identifier:
eissn:
- 1920-180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological data analysis in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 11
year: '2020'
...
---
_id: '8135'
abstract:
- lang: eng
text: Discrete Morse theory has recently lead to new developments in the theory
of random geometric complexes. This article surveys the methods and results obtained
with this new approach, and discusses some of its shortcomings. It uses simulations
to illustrate the results and to form conjectures, getting numerical estimates
for combinatorial, topological, and geometric properties of weighted and unweighted
Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes
contained in the mosaics.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreements No 78818 Alpha and No 638176). It is also partially supported
by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and
Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).
alternative_title:
- Abel Symposia
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
- first_name: Peter
full_name: Synak, Peter
id: 331776E2-F248-11E8-B48F-1D18A9856A87
last_name: Synak
citation:
ama: 'Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay
mosaics and related complexes experimentally. In: Topological Data Analysis.
Vol 15. Springer Nature; 2020:181-218. doi:10.1007/978-3-030-43408-3_8'
apa: Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). Radius
functions on Poisson–Delaunay mosaics and related complexes experimentally. In
Topological Data Analysis (Vol. 15, pp. 181–218). Springer Nature. https://doi.org/10.1007/978-3-030-43408-3_8
chicago: Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak.
“Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.”
In Topological Data Analysis, 15:181–218. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-43408-3_8.
ieee: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions
on Poisson–Delaunay mosaics and related complexes experimentally,” in Topological
Data Analysis, 2020, vol. 15, pp. 181–218.
ista: Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on
Poisson–Delaunay mosaics and related complexes experimentally. Topological Data
Analysis. , Abel Symposia, vol. 15, 181–218.
mla: Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics
and Related Complexes Experimentally.” Topological Data Analysis, vol.
15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8.
short: H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data
Analysis, Springer Nature, 2020, pp. 181–218.
date_created: 2020-07-19T22:00:59Z
date_published: 2020-06-22T00:00:00Z
date_updated: 2026-04-07T12:35:47Z
day: '22'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/978-3-030-43408-3_8
ec_funded: 1
external_id:
isi:
- '001321861000008'
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checksum: 7b5e0de10675d787a2ddb2091370b8d8
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creator: dernst
date_created: 2020-10-08T08:56:14Z
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file_name: 2020-B-01-PoissonExperimentalSurvey.pdf
file_size: 2207071
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success: 1
file_date_updated: 2020-10-08T08:56:14Z
has_accepted_license: '1'
intvolume: ' 15'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 181-218
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2533E772-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '638176'
name: 'Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large
Scales'
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Topological Data Analysis
publication_identifier:
eissn:
- 2197-8549
isbn:
- '9783030434076'
issn:
- 2193-2808
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '19630'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Radius functions on Poisson–Delaunay mosaics and related complexes experimentally
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 15
year: '2020'
...
---
_id: '8703'
abstract:
- lang: eng
text: 'Even though Delaunay originally introduced his famous triangulations in the
case of infinite point sets with translational periodicity, a software that computes
such triangulations in the general case is not yet available, to the best of our
knowledge. Combining and generalizing previous work, we present a practical algorithm
for computing such triangulations. The algorithm has been implemented and experiments
show that its performance is as good as the one of the CGAL package, which is
restricted to cubic periodicity. '
alternative_title:
- LIPIcs
article_number: '75'
article_processing_charge: No
author:
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
- first_name: Mael
full_name: Rouxel-Labbé, Mael
last_name: Rouxel-Labbé
- first_name: Monique
full_name: Teillaud, Monique
last_name: Teillaud
citation:
ama: 'Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay
triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75'
apa: 'Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL
periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms
(Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für
Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75'
chicago: Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing
CGAL Periodic Delaunay Triangulations.” In 28th Annual European Symposium on
Algorithms, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
https://doi.org/10.4230/LIPIcs.ESA.2020.75.
ieee: G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic
Delaunay triangulations,” in 28th Annual European Symposium on Algorithms,
Virtual, Online; Pisa, Italy, 2020, vol. 173.
ista: 'Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay
triangulations. 28th Annual European Symposium on Algorithms. ESA: European Symposium
on Algorithms, LIPIcs, vol. 173, 75.'
mla: Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.”
28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75.
short: G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium
on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
conference:
end_date: 2020-09-09
location: Virtual, Online; Pisa, Italy
name: 'ESA: European Symposium on Algorithms'
start_date: 2020-09-07
corr_author: '1'
date_created: 2020-10-25T23:01:18Z
date_published: 2020-08-26T00:00:00Z
date_updated: 2026-04-08T07:01:29Z
day: '26'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.ESA.2020.75
ec_funded: 1
file:
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checksum: fe0f7c49a99ed870c671b911e10d5496
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creator: cziletti
date_created: 2020-10-27T14:31:52Z
date_updated: 2020-10-27T14:31:52Z
file_id: '8712'
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file_size: 733291
relation: main_file
success: 1
file_date_updated: 2020-10-27T14:31:52Z
has_accepted_license: '1'
intvolume: ' 173'
language:
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month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: 28th Annual European Symposium on Algorithms
publication_identifier:
isbn:
- '9783959771627'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Generalizing CGAL periodic Delaunay triangulations
tmp:
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legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 173
year: '2020'
...
---
OA_place: publisher
_id: '7944'
abstract:
- lang: eng
text: "This thesis considers two examples of reconfiguration problems: flipping
edges in edge-labelled triangulations of planar point sets and swapping labelled
tokens placed on vertices of a graph. In both cases the studied structures – all
the triangulations of a given point set or all token placements on a given graph
– can be thought of as vertices of the so-called reconfiguration graph, in which
two vertices are adjacent if the corresponding structures differ by a single elementary
operation – by a flip of a diagonal in a triangulation or by a swap of tokens
on adjacent vertices, respectively. We study the reconfiguration of one instance
of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor
triangulations of point sets in which each edge has a unique label and a flip
transfers the label from the removed edge to the new edge, we prove a polynomial-time
testable condition, called the Orbit Theorem, that characterizes when two triangulations
of the same point set lie in the same connected component of the reconfiguration
graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot.
We additionally provide a polynomial time algorithm that computes a reconfiguring
flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties
of a certain high-dimensional cell complex that has the usual reconfiguration
graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph,
we make partial progress on the problem of finding shortest reconfiguration sequences.
We disprove the so-called Happy Leaf Conjecture and demonstrate the importance
of swapping tokens that are already placed at the correct vertices. We also prove
that a generalization of the problem to weighted coloured token swapping is NP-hard
on trees but solvable in polynomial time on paths and stars."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
citation:
ama: Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944
apa: Masárová, Z. (2020). Reconfiguration problems. Institute of Science
and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944
chicago: Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and
Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944.
ieee: Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology
Austria, 2020.
ista: Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology
Austria.
mla: Masárová, Zuzana. Reconfiguration Problems. Institute of Science and
Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.
short: Z. Masárová, Reconfiguration Problems, Institute of Science and Technology
Austria, 2020.
corr_author: '1'
date_created: 2020-06-08T00:49:46Z
date_published: 2020-06-09T00:00:00Z
date_updated: 2026-04-08T07:23:01Z
day: '09'
ddc:
- '516'
- '514'
degree_awarded: PhD
department:
- _id: HeEd
- _id: UlWa
doi: 10.15479/AT:ISTA:7944
file:
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content_type: application/zip
creator: zmasarov
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file_size: 32184006
relation: source_file
file_date_updated: 2020-07-14T12:48:05Z
has_accepted_license: '1'
keyword:
- reconfiguration
- reconfiguration graph
- triangulations
- flip
- constrained triangulations
- shellability
- piecewise-linear balls
- token swapping
- trees
- coloured weighted token swapping
language:
- iso: eng
license: https://creativecommons.org/licenses/by-sa/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: '160'
publication_identifier:
isbn:
- 978-3-99078-005-3
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '7950'
relation: part_of_dissertation
status: public
- id: '5986'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: Reconfiguration problems
tmp:
image: /images/cc_by_sa.png
legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode
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short: CC BY-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
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...
---
OA_place: publisher
_id: '7460'
abstract:
- lang: eng
text: "Many methods for the reconstruction of shapes from sets of points produce
ordered simplicial complexes, which are collections of vertices, edges, triangles,
and their higher-dimensional analogues, called simplices, in which every simplex
gets assigned a real value measuring its size. This thesis studies ordered simplicial
complexes, with a focus on their topology, which reflects the connectedness of
the represented shapes and the presence of holes. We are interested both in understanding
better the structure of these complexes, as well as in developing algorithms for
applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure
for a simplex is the radius of the smallest empty circumsphere. Based on it, we
revisit Alpha and Wrap complexes and experimentally determine their probabilistic
properties for random data. Also, we prove the existence of tri-partitions, propose
algorithms to open and close holes, and extend the concepts from Euclidean to
Bregman geometries."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
citation:
ama: Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460
apa: Ölsböck, K. (2020). The hole system of triangulated shapes. Institute
of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460
chicago: Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute
of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.
ieee: K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science
and Technology Austria, 2020.
ista: Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science
and Technology Austria.
mla: Ölsböck, Katharina. The Hole System of Triangulated Shapes. Institute
of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7460.
short: K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science
and Technology Austria, 2020.
corr_author: '1'
date_created: 2020-02-06T14:56:53Z
date_published: 2020-02-10T00:00:00Z
date_updated: 2026-04-08T07:23:21Z
day: '10'
ddc:
- '514'
degree_awarded: PhD
department:
- _id: HeEd
- _id: GradSch
doi: 10.15479/AT:ISTA:7460
file:
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date_updated: 2020-07-14T12:47:58Z
file_id: '7461'
file_name: thesis_ist-final_noack.pdf
file_size: 76195184
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content_type: application/x-zip-compressed
creator: koelsboe
date_created: 2020-02-06T14:52:45Z
date_updated: 2020-07-14T12:47:58Z
description: latex source files, figures
file_id: '7462'
file_name: latex-files.zip
file_size: 122103715
relation: source_file
file_date_updated: 2020-07-14T12:47:58Z
has_accepted_license: '1'
keyword:
- shape reconstruction
- hole manipulation
- ordered complexes
- Alpha complex
- Wrap complex
- computational topology
- Bregman geometry
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '02'
oa: 1
oa_version: Published Version
page: '155'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '6608'
relation: part_of_dissertation
status: public
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: The hole system of triangulated shapes
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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2020'
...
---
_id: '6050'
abstract:
- lang: eng
text: 'We answer a question of David Hilbert: given two circles it is not possible
in general to construct their centers using only a straightedge. On the other
hand, we give infinitely many families of pairs of circles for which such construction
is possible. '
article_processing_charge: No
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: Fedorov, Roman
last_name: Fedorov
citation:
ama: Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of
the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240
apa: Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge.
Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240
chicago: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.”
Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240.
ieee: A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings
of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.
ista: Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings
of the American Mathematical Society. 147, 91–102.
mla: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.”
Proceedings of the American Mathematical Society, vol. 147, AMS, 2019,
pp. 91–102, doi:10.1090/proc/14240.
short: A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society
147 (2019) 91–102.
date_created: 2019-02-24T22:59:19Z
date_published: 2019-01-01T00:00:00Z
date_updated: 2023-08-24T14:48:59Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/14240
external_id:
arxiv:
- '1709.02562'
isi:
- '000450363900008'
intvolume: ' 147'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1709.02562
month: '01'
oa: 1
oa_version: Preprint
page: 91-102
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: AMS
quality_controlled: '1'
scopus_import: '1'
status: public
title: Two circles and only a straightedge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 147
year: '2019'
...
---
_id: '6515'
abstract:
- lang: eng
text: We give non-degeneracy criteria for Riemannian simplices based on simplices
in spaces of constant sectional curvature. It extends previous work on Riemannian
simplices, where we developed Riemannian simplices with respect to Euclidean reference
simplices. The criteria we give in this article are in terms of quality measures
for spaces of constant curvature that we develop here. We see that simplices in
spaces that have nearly constant curvature, are already non-degenerate under very
weak quality demands. This is of importance because it allows for sampling of
Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature.
author:
- first_name: Ramsay
full_name: Dyer, Ramsay
last_name: Dyer
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature.
Journal of Computational Geometry . 2019;10(1):223–256. doi:10.20382/jocg.v10i1a9
apa: Dyer, R., Vegter, G., & Wintraecken, M. (2019). Simplices modelled on spaces
of constant curvature. Journal of Computational Geometry . Carleton University.
https://doi.org/10.20382/jocg.v10i1a9
chicago: Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled
on Spaces of Constant Curvature.” Journal of Computational Geometry . Carleton
University, 2019. https://doi.org/10.20382/jocg.v10i1a9.
ieee: R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant
curvature,” Journal of Computational Geometry , vol. 10, no. 1. Carleton
University, pp. 223–256, 2019.
ista: Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant
curvature. Journal of Computational Geometry . 10(1), 223–256.
mla: Dyer, Ramsay, et al. “Simplices Modelled on Spaces of Constant Curvature.”
Journal of Computational Geometry , vol. 10, no. 1, Carleton University,
2019, pp. 223–256, doi:10.20382/jocg.v10i1a9.
short: R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10
(2019) 223–256.
date_created: 2019-06-03T09:35:33Z
date_published: 2019-07-01T00:00:00Z
date_updated: 2021-01-12T08:07:50Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.20382/jocg.v10i1a9
ec_funded: 1
file:
- access_level: open_access
checksum: 57b4df2f16a74eb499734ec8ee240178
content_type: application/pdf
creator: mwintrae
date_created: 2019-06-03T09:30:01Z
date_updated: 2020-07-14T12:47:32Z
file_id: '6516'
file_name: mainJournalFinal.pdf
file_size: 2170882
relation: main_file
file_date_updated: 2020-07-14T12:47:32Z
has_accepted_license: '1'
intvolume: ' 10'
issue: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 223–256
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 'Journal of Computational Geometry '
publication_identifier:
issn:
- 1920-180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: 1
status: public
title: Simplices modelled on spaces of constant curvature
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: 10
year: '2019'
...
---
_id: '6628'
abstract:
- lang: eng
text: Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces
in Euclidean space by piecewise flat triangular meshes with a given number
of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this
Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and
d is the dimension of Euclidean space. Moreover the pro-portionality constant
can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In
this short note, we prove the extrinsic nature of this constant for manifolds
of sufficiently high codimension. We do so by constructing an family of isometric
embeddings of the flat torus in Euclidean space.
author:
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of
optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational
Geometry. ; 2019:275-279.'
apa: Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff
distance of optimal triangulations of manifolds. In The 31st Canadian Conference
in Computational Geometry (pp. 275–279). Edmonton, Canada.
chicago: Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff
Distance of Optimal Triangulations of Manifolds.” In The 31st Canadian Conference
in Computational Geometry, 275–79, 2019.
ieee: G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance
of optimal triangulations of manifolds,” in The 31st Canadian Conference in
Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.
ista: 'Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance
of optimal triangulations of manifolds. The 31st Canadian Conference in Computational
Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279.'
mla: Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff
Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference
in Computational Geometry, 2019, pp. 275–79.
short: G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational
Geometry, 2019, pp. 275–279.
conference:
end_date: 2019-08-10
location: Edmonton, Canada
name: 'CCCG: Canadian Conference in Computational Geometry'
start_date: 2019-08-08
date_created: 2019-07-12T08:34:57Z
date_published: 2019-08-01T00:00:00Z
date_updated: 2021-01-12T08:08:16Z
day: '01'
ddc:
- '004'
department:
- _id: HeEd
ec_funded: 1
file:
- access_level: open_access
checksum: ceabd152cfa55170d57763f9c6c60a53
content_type: application/pdf
creator: mwintrae
date_created: 2019-07-12T08:32:46Z
date_updated: 2020-07-14T12:47:34Z
file_id: '6629'
file_name: IntrinsicExtrinsicCCCG2019.pdf
file_size: 321176
relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Submitted Version
page: 275-279
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: The 31st Canadian Conference in Computational Geometry
publication_status: published
quality_controlled: '1'
scopus_import: 1
status: public
title: The extrinsic nature of the Hausdorff distance of optimal triangulations of
manifolds
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '6634'
abstract:
- lang: eng
text: In this paper we prove several new results around Gromov's waist theorem.
We give a simple proof of Vaaler's theorem on sections of the unit cube using
the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective
spaces, flat tori, convex bodies in Euclidean space; and establish waist-type
results in terms of the Hausdorff measure.
article_processing_charge: No
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: Alfredo
full_name: Hubard, Alfredo
last_name: Hubard
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different
spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490.
doi:10.12775/TMNA.2019.008
apa: Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for
the waists of different spaces. Topological Methods in Nonlinear Analysis.
Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008
chicago: Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds
for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis.
Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008.
ieee: A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists
of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53,
no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.
ista: Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists
of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.
mla: Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different
Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka
Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008.
short: A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis
53 (2019) 457–490.
date_created: 2019-07-14T21:59:19Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2025-04-15T06:50:28Z
day: '01'
department:
- _id: HeEd
doi: 10.12775/TMNA.2019.008
ec_funded: 1
external_id:
arxiv:
- '1612.06926'
isi:
- '000472541600004'
intvolume: ' 53'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.06926
month: '06'
oa: 1
oa_version: Preprint
page: 457-490
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Topological Methods in Nonlinear Analysis
publication_status: published
publisher: Akademicka Platforma Czasopism
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower and upper bounds for the waists of different spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2019'
...
---
_id: '6648'
abstract:
- lang: eng
text: "Various kinds of data are routinely represented as discrete probability distributions.
Examples include text documents summarized by histograms of word occurrences and
images represented as histograms of oriented gradients. Viewing a discrete probability
distribution as a point in the standard simplex of the appropriate dimension,
we can understand collections of such objects in geometric and topological terms.
Importantly, instead of using the standard Euclidean distance, we look into dissimilarity
measures with information-theoretic justification, and we develop the theory\r\nneeded
for applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable the usage of existing computational topology software
in this context."
alternative_title:
- LIPIcs
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
space. In: 35th International Symposium on Computational Geometry. Vol
129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31'
apa: 'Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis
in information space. In 35th International Symposium on Computational Geometry
(Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31'
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
Analysis in Information Space.” In 35th International Symposium on Computational
Geometry, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2019. https://doi.org/10.4230/LIPICS.SOCG.2019.31.
ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
space,” in 35th International Symposium on Computational Geometry, Portland,
OR, United States, 2019, vol. 129, p. 31:1-31:14.
ista: 'Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information
space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium
on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.'
mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
35th International Symposium on Computational Geometry, vol. 129, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:10.4230/LIPICS.SOCG.2019.31.
short: H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on
Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019,
p. 31:1-31:14.
conference:
end_date: 2019-06-21
location: Portland, OR, United States
name: 'SoCG 2019: Symposium on Computational Geometry'
start_date: 2019-06-18
corr_author: '1'
date_created: 2019-07-17T10:36:09Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2024-10-09T20:58:55Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPICS.SOCG.2019.31
external_id:
arxiv:
- '1903.08510'
file:
- access_level: open_access
checksum: 8ec8720730d4c789bf7b06540f1c29f4
content_type: application/pdf
creator: dernst
date_created: 2019-07-24T06:40:01Z
date_updated: 2020-07-14T12:47:35Z
file_id: '6666'
file_name: 2019_LIPICS_Edelsbrunner.pdf
file_size: 1355179
relation: main_file
file_date_updated: 2020-07-14T12:47:35Z
has_accepted_license: '1'
intvolume: ' 129'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 31:1-31:14
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: 35th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959771047'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: 1
status: public
title: Topological data analysis in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/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: 129
year: '2019'
...
---
_id: '6671'
abstract:
- lang: eng
text: 'In this paper we discuss three results. The first two concern general sets
of positive reach: we first characterize the reach of a closed set by means of
a bound on the metric distortion between the distance measured in the ambient
Euclidean space and the shortest path distance measured in the set. Secondly,
we prove that the intersection of a ball with radius less than the reach with
the set is geodesically convex, meaning that the shortest path between any two
points in the intersection lies itself in the intersection. For our third result
we focus on manifolds with positive reach and give a bound on the angle between
tangent spaces at two different points in terms of the reach and the distance
between the two points.'
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: 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: Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic
convexity and the variation of tangent spaces. Journal of Applied and Computational
Topology. 2019;3(1-2):29–58. doi:10.1007/s41468-019-00029-8
apa: Boissonnat, J.-D., Lieutier, A., & Wintraecken, M. (2019). The reach, metric
distortion, geodesic convexity and the variation of tangent spaces. Journal
of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-019-00029-8
chicago: Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The
Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.”
Journal of Applied and Computational Topology. Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8.
ieee: J.-D. Boissonnat, A. Lieutier, and M. Wintraecken, “The reach, metric distortion,
geodesic convexity and the variation of tangent spaces,” Journal of Applied
and Computational Topology, vol. 3, no. 1–2. Springer Nature, pp. 29–58, 2019.
ista: Boissonnat J-D, Lieutier A, Wintraecken M. 2019. The reach, metric distortion,
geodesic convexity and the variation of tangent spaces. Journal of Applied and
Computational Topology. 3(1–2), 29–58.
mla: Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity
and the Variation of Tangent Spaces.” Journal of Applied and Computational
Topology, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:10.1007/s41468-019-00029-8.
short: J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational
Topology 3 (2019) 29–58.
corr_author: '1'
date_created: 2019-07-24T08:37:29Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2025-04-14T07:44:06Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s41468-019-00029-8
ec_funded: 1
file:
- access_level: open_access
checksum: a5b244db9f751221409cf09c97ee0935
content_type: application/pdf
creator: dernst
date_created: 2019-07-31T08:09:56Z
date_updated: 2020-07-14T12:47:36Z
file_id: '6741'
file_name: 2019_JournAppliedComputTopol_Boissonnat.pdf
file_size: 2215157
relation: main_file
file_date_updated: 2020-07-14T12:47:36Z
has_accepted_license: '1'
intvolume: ' 3'
issue: 1-2
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 29–58
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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, metric distortion, geodesic convexity and the variation of tangent
spaces
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: 3
year: '2019'
...
---
OA_place: publisher
OA_type: hybrid
_id: '6756'
abstract:
- lang: eng
text: "We study the topology generated by the temperature fluctuations of the cosmic
microwave background (CMB) radiation, as quantified by the number of components
and holes, formally given by the Betti numbers, in the growing excursion sets.
We compare CMB maps observed by the Planck satellite with a thousand simulated
maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations.
The comparison is multi-scale, being performed on a sequence of degraded maps
with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over
\U0001D54A2 is incomplete due to obfuscation effects by bright point sources and
other extended foreground objects like our own galaxy. To deal with such situations,
where analysis in the presence of “masks” is of importance, we introduce the concept
of relative homology. The parametric χ2-test shows differences between observations
and simulations, yielding p-values at percent to less than permil levels roughly
between 2 and 7°, with the difference in the number of components and holes peaking
at more than 3σ sporadically at these scales. The highest observed deviation between
the observations and simulations for b0 and b1 is approximately between 3σ and
4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler
characteristic at 3.66° in the literature, computed from independent measurements
of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave
Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler
characteristic is phenomenologically related to the strongly anomalous behaviour
of components and holes, or the zeroth and first Betti numbers, respectively.
Further, since these topological descriptors show consistent anomalous behaviour
over independent measurements of Planck and WMAP, instrumental and systematic
errors may be an unlikely source. These are also the scales at which the observed
maps exhibit low variance compared to the simulations, and approximately the range
of scales at which the power spectrum exhibits a dip with respect to the theoretical
model. Non-parametric tests show even stronger differences at almost all scales.
Crucially, Gaussian simulations based on power-spectrum matching the characteristics
of the observed dipped power spectrum are not able to resolve the anomaly. Understanding
the origin of the anomalies in the CMB, whether cosmological in nature or arising
due to late-time effects, is an extremely challenging task. Regardless, beyond
the trivial possibility that this may still be a manifestation of an extreme Gaussian
case, these observations, along with the super-horizon scales involved, may motivate
the study of primordial non-Gaussianity. Alternative scenarios worth exploring
may be models with non-trivial topology, including topological defect models."
acknowledgement: 'PP is grateful to Julian Borill from the Planck consortium for providing
the data, and for the illuminating discussions and inputs. PP also thanks Hans Kristen
Eriksen, Anne Ducout, and Francois R. Bouchet for significantly helpful discussions
at various stages. The authors collectively thank the anonymous referee for the
invaluable comments and suggestions that have added significant value to the contents
of the manuscript. PP and RA acknowledge the support of ERC advanced grant Understanding
Random Systems through Algebraic Topology (URSAT) (no: 320422, PI: RA). This work
is also part of a project that has received funding for PP and TB from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement ERC advanced grant 740021– Advances in Research on THeories
of the dark UniverSe (ARTHUS), PI: TB). HE and HW acknowledge the support by the
Office of Naval Research, through grant N62909-18-1-2038, and by the DFG Collaborative
Research Center TRR 109, “Discretization in Geometry and Dynamics”, through grant
I02979-N35 of the Austrian Science Fund (FWF). PP acknowledges the support and use
of resources at the NERSC computing center.'
article_number: A163
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Pratyush
full_name: Pranav, Pratyush
last_name: Pranav
- first_name: Robert J.
full_name: Adler, Robert J.
last_name: Adler
- first_name: Thomas
full_name: Buchert, Thomas
last_name: Buchert
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Bernard J.T.
full_name: Jones, Bernard J.T.
last_name: Jones
- first_name: Armin
full_name: Schwartzman, Armin
last_name: Schwartzman
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
- first_name: Rien
full_name: Van De Weygaert, Rien
last_name: Van De Weygaert
citation:
ama: Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature
fluctuations in the cosmic microwave background. Astronomy and Astrophysics.
2019;627. doi:10.1051/0004-6361/201834916
apa: Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman,
A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations
in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences.
https://doi.org/10.1051/0004-6361/201834916
chicago: Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner,
Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert.
“Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.”
Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916.
ieee: P. Pranav et al., “Unexpected topology of the temperature fluctuations
in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627.
EDP Sciences, 2019.
ista: Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner
H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations
in the cosmic microwave background. Astronomy and Astrophysics. 627, A163.
mla: Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations
in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627,
A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916.
short: P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman,
H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).
date_created: 2019-08-04T21:59:18Z
date_published: 2019-07-17T00:00:00Z
date_updated: 2025-05-20T08:01:55Z
day: '17'
ddc:
- '520'
- '530'
department:
- _id: HeEd
doi: 10.1051/0004-6361/201834916
external_id:
arxiv:
- '1812.07678'
isi:
- '000475839300003'
file:
- access_level: open_access
checksum: 83b9209ed9eefbdcefd89019c5a97805
content_type: application/pdf
creator: dernst
date_created: 2019-08-05T08:08:59Z
date_updated: 2020-07-14T12:47:39Z
file_id: '6766'
file_name: 2019_AstronomyAstrophysics_Pranav.pdf
file_size: 14420451
relation: main_file
file_date_updated: 2020-07-14T12:47:39Z
has_accepted_license: '1'
intvolume: ' 627'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 265683E4-B435-11E9-9278-68D0E5697425
grant_number: M62909-18-1-2038
name: Toward Computational Information Topology
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Astronomy and Astrophysics
publication_identifier:
eissn:
- 1432-0746
issn:
- 0004-6361
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Unexpected topology of the temperature fluctuations in the cosmic microwave
background
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: 627
year: '2019'
...
---
_id: '6793'
abstract:
- lang: eng
text: The Regge symmetry is a set of remarkable relations between two tetrahedra
whose edge lengths are related in a simple fashion. It was first discovered as
a consequence of an asymptotic formula in mathematical physics. Here, we give
a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic
geometry.
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: Ivan
full_name: Izmestiev, Ivan
last_name: Izmestiev
citation:
ama: Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli
formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775.
doi:10.1112/blms.12276
apa: Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics,
and the Schläfli formula. Bulletin of the London Mathematical Society.
London Mathematical Society. https://doi.org/10.1112/blms.12276
chicago: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
and the Schläfli Formula.” Bulletin of the London Mathematical Society.
London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276.
ieee: A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the
Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51,
no. 5. London Mathematical Society, pp. 765–775, 2019.
ista: Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the
Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.
mla: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
and the Schläfli Formula.” Bulletin of the London Mathematical Society,
vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276.
short: A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51
(2019) 765–775.
date_created: 2019-08-11T21:59:23Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2025-07-10T11:53:52Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12276
ec_funded: 1
external_id:
arxiv:
- '1903.04929'
isi:
- '000478560200001'
intvolume: ' 51'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1903.04929
month: '10'
oa: 1
oa_version: Preprint
page: 765-775
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- 1469-2120
issn:
- 0024-6093
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Regge symmetry, confocal conics, and the Schläfli formula
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2019'
...
---
_id: '6828'
abstract:
- lang: eng
text: In this paper we construct a family of exact functors from the category of
Whittaker modules of the simple complex Lie algebra of type to the category of
finite-dimensional modules of the graded affine Hecke algebra of type . Using
results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors
map standard modules to standard modules (or zero) and simple modules to simple
modules (or zero). Moreover, we show that each simple module of the graded affine
Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker
category contains the BGG category as a full subcategory, our results generalize
results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between
finite-dimensional representations of and representations of the symmetric group
.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
citation:
ama: Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra.
2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027
apa: Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal
of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027
chicago: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal
of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027.
ieee: A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra,
vol. 538. Elsevier, pp. 261–289, 2019.
ista: Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra.
538, 261–289.
mla: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of
Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.
short: A. Brown, Journal of Algebra 538 (2019) 261–289.
date_created: 2019-08-22T07:54:13Z
date_published: 2019-11-15T00:00:00Z
date_updated: 2023-08-29T07:11:47Z
day: '15'
department:
- _id: HeEd
doi: 10.1016/j.jalgebra.2019.07.027
external_id:
arxiv:
- '1805.04676'
isi:
- '000487176300011'
intvolume: ' 538'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1805.04676
month: '11'
oa: 1
oa_version: Preprint
page: 261-289
publication: Journal of Algebra
publication_identifier:
issn:
- 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Arakawa-Suzuki functors for Whittaker modules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 538
year: '2019'
...