---
_id: '7791'
abstract:
- lang: eng
text: Extending a result of Milena Radnovic and Serge Tabachnikov, we establish
conditionsfor two different non-symmetric norms to define the same billiard reflection
law.
acknowledgement: AA was supported by European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818
Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4
and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169.
Open access funding provided by Institute of Science and Technology (IST Austria).
The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful
discussions.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. When different norms lead to same billiard trajectories?
European Journal of Mathematics. 2022;8(4):1309-1312. doi:10.1007/s40879-020-00405-0
apa: Akopyan, A., & Karasev, R. (2022). When different norms lead to same billiard
trajectories? European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00405-0
chicago: Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same
Billiard Trajectories?” European Journal of Mathematics. Springer Nature,
2022. https://doi.org/10.1007/s40879-020-00405-0.
ieee: A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,”
European Journal of Mathematics, vol. 8, no. 4. Springer Nature, pp. 1309–1312,
2022.
ista: Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories?
European Journal of Mathematics. 8(4), 1309–1312.
mla: Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard
Trajectories?” European Journal of Mathematics, vol. 8, no. 4, Springer
Nature, 2022, pp. 1309–12, doi:10.1007/s40879-020-00405-0.
short: A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.
date_created: 2020-05-03T22:00:48Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2024-02-22T15:58:42Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s40879-020-00405-0
ec_funded: 1
external_id:
arxiv:
- '1912.12685'
file:
- access_level: open_access
checksum: f53e71fd03744075adcd0b8fc1b8423d
content_type: application/pdf
creator: dernst
date_created: 2020-05-04T10:33:42Z
date_updated: 2020-07-14T12:48:03Z
file_id: '7796'
file_name: 2020_EuropMathematics_Akopyan.pdf
file_size: 263926
relation: main_file
file_date_updated: 2020-07-14T12:48:03Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1309 - 1312
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: When different norms lead to same billiard trajectories?
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2022'
...
---
_id: '11660'
abstract:
- lang: eng
text: 'We characterize critical points of 1-dimensional maps paired in persistent
homology geometrically and this way get elementary proofs of theorems about the
symmetry of persistence diagrams and the variation of such maps. In particular,
we identify branching points and endpoints of networks as the sole source of asymmetry
and relate the cycle basis in persistent homology with a version of the stable
marriage problem. Our analysis provides the foundations of fast algorithms for
maintaining collections of interrelated sorted lists together with their persistence
diagrams. '
acknowledgement: 'This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. '
alternative_title:
- LIPIcs
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to
the persistence of 1D maps. I: Geometric characterization of critical point pairs.
LIPIcs.'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization
of critical point pairs. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik.'
chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “A Window to the Persistence of 1D Maps. I: Geometric Characterization
of Critical Point Pairs.” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, n.d.'
ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “A
window to the persistence of 1D maps. I: Geometric characterization of critical
point pairs,” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.'
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window
to the persistence of 1D maps. I: Geometric characterization of critical point
pairs. LIPIcs.'
mla: 'Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric
Characterization of Critical Point Pairs.” LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik.'
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs
(n.d.).
date_created: 2022-07-27T09:31:15Z
date_published: 2022-07-25T00:00:00Z
date_updated: 2024-03-20T09:36:56Z
day: '25'
ddc:
- '510'
department:
- _id: GradSch
- _id: HeEd
ec_funded: 1
file:
- access_level: open_access
checksum: 95903f9d1649e8e437a967b6f2f64730
content_type: application/pdf
creator: scultrer
date_created: 2022-07-27T09:30:30Z
date_updated: 2022-07-27T09:30:30Z
file_id: '11661'
file_name: window 1.pdf
file_size: 564836
relation: main_file
file_date_updated: 2022-07-27T09:30:30Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Submitted Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: LIPIcs
publication_status: submitted
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
status: public
title: 'A window to the persistence of 1D maps. I: Geometric characterization of critical
point pairs'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '11658'
abstract:
- lang: eng
text: The depth of a cell in an arrangement of n (non-vertical) great-spheres in
Sd is the number of great-spheres that pass above the cell. We prove Euler-type
relations, which imply extensions of the classic Dehn–Sommerville relations for
convex polytopes to sublevel sets of the depth function, and we use the relations
to extend the expressions for the number of faces of neighborly polytopes to the
number of cells of levels in neighborly arrangements.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements:
Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings
on Mathematics.'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications.
Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz
Zentrum für Informatik.'
chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations
with Applications.” Leibniz International Proceedings on Mathematics. Schloss
Dagstuhl - Leibniz Zentrum für Informatik, n.d.'
ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth
in arrangements: Dehn–Sommerville–Euler relations with applications,” Leibniz
International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum
für Informatik.'
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in
arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International
Proceedings on Mathematics.'
mla: 'Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations
with Applications.” Leibniz International Proceedings on Mathematics, Schloss
Dagstuhl - Leibniz Zentrum für Informatik.'
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz
International Proceedings on Mathematics (n.d.).
date_created: 2022-07-27T09:27:34Z
date_published: 2022-07-27T00:00:00Z
date_updated: 2024-03-20T09:36:56Z
day: '27'
ddc:
- '510'
department:
- _id: GradSch
- _id: HeEd
ec_funded: 1
file:
- access_level: open_access
checksum: b2f511e8b1cae5f1892b0cdec341acac
content_type: application/pdf
creator: scultrer
date_created: 2022-07-27T09:25:53Z
date_updated: 2022-07-27T09:25:53Z
file_id: '11659'
file_name: D-S-E.pdf
file_size: 639266
relation: main_file
file_date_updated: 2022-07-27T09:25:53Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Submitted Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Leibniz International Proceedings on Mathematics
publication_status: submitted
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
status: public
title: 'Depth in arrangements: Dehn–Sommerville–Euler relations with applications'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '15090'
abstract:
- lang: eng
text: Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce
the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents
how points of different colors mingle. Our main results are bounds on the size
of the chromatic Delaunay mosaic, in which we assume that d and s are constants.
For example, if A is finite with n=#A, and the coloring is random, then the chromatic
Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets
and Poisson point processes in Rd, the expected number of cells within a closed
ball is only a constant times the number of points in this ball. Furthermore,
in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics
of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.
article_number: '2212.03121'
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Ondrej
full_name: Draganov, Ondrej
id: 2B23F01E-F248-11E8-B48F-1D18A9856A87
last_name: Draganov
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M.
On the size of chromatic Delaunay mosaics. arXiv.
apa: Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &
Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. arXiv.
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert
Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.”
ArXiv, n.d.
ieee: R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M.
Saghafian, “On the size of chromatic Delaunay mosaics,” arXiv. .
ista: Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M.
On the size of chromatic Delaunay mosaics. arXiv, 2212.03121.
mla: Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” ArXiv,
2212.03121.
short: R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian,
ArXiv (n.d.).
date_created: 2024-03-08T09:54:20Z
date_published: 2022-12-06T00:00:00Z
date_updated: 2024-03-20T09:36:56Z
day: '06'
department:
- _id: HeEd
ec_funded: 1
external_id:
arxiv:
- '2212.03121'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2212.03121
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '15094'
relation: dissertation_contains
status: public
status: public
title: On the size of chromatic Delaunay mosaics
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2022'
...
---
_id: '10208'
abstract:
- lang: eng
text: It is practical to collect a huge amount of movement data and environmental
context information along with the health signals of individuals because there
is the emergence of new generations of positioning and tracking technologies and
rapid advancements of health sensors. The study of the relations between these
datasets and their sequence similarity analysis is of interest to many applications
such as health monitoring and recommender systems. However, entering all movement
parameters and health signals can lead to the complexity of the problem and an
increase in its computational load. In this situation, dimension reduction techniques
can be used to avoid consideration of simultaneous dependent parameters in the
process of similarity measurement of the trajectories. The present study provides
a framework, named CaDRAW, to use spatial–temporal data and movement parameters
along with independent context information in the process of measuring the similarity
of trajectories. In this regard, the omission of dependent movement characteristic
signals is conducted by using an unsupervised feature selection dimension reduction
technique. To evaluate the effectiveness of the proposed framework, it was applied
to a real contextualized movement and related health signal datasets of individuals.
The results indicated the capability of the proposed framework in measuring the
similarity and in decreasing the characteristic signals in such a way that the
similarity results -before and after reduction of dependent characteristic signals-
have small differences. The mean differences between the obtained results before
and after reducing the dimension were 0.029 and 0.023 for the round path, respectively.
acknowledgement: The third author acknowledges the funding received from the Wittgenstein
Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.
article_processing_charge: No
article_type: original
author:
- first_name: Samira
full_name: Goudarzi, Samira
last_name: Goudarzi
- first_name: Mohammad
full_name: Sharif, Mohammad
last_name: Sharif
- first_name: Farid
full_name: Karimipour, Farid
id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425
last_name: Karimipour
orcid: 0000-0001-6746-4174
citation:
ama: Goudarzi S, Sharif M, Karimipour F. A context-aware dimension reduction framework
for trajectory and health signal analyses. Journal of Ambient Intelligence
and Humanized Computing. 2022;13:2621–2635. doi:10.1007/s12652-021-03569-z
apa: Goudarzi, S., Sharif, M., & Karimipour, F. (2022). A context-aware dimension
reduction framework for trajectory and health signal analyses. Journal of Ambient
Intelligence and Humanized Computing. Springer Nature. https://doi.org/10.1007/s12652-021-03569-z
chicago: Goudarzi, Samira, Mohammad Sharif, and Farid Karimipour. “A Context-Aware
Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal
of Ambient Intelligence and Humanized Computing. Springer Nature, 2022. https://doi.org/10.1007/s12652-021-03569-z.
ieee: S. Goudarzi, M. Sharif, and F. Karimipour, “A context-aware dimension reduction
framework for trajectory and health signal analyses,” Journal of Ambient Intelligence
and Humanized Computing, vol. 13. Springer Nature, pp. 2621–2635, 2022.
ista: Goudarzi S, Sharif M, Karimipour F. 2022. A context-aware dimension reduction
framework for trajectory and health signal analyses. Journal of Ambient Intelligence
and Humanized Computing. 13, 2621–2635.
mla: Goudarzi, Samira, et al. “A Context-Aware Dimension Reduction Framework for
Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and
Humanized Computing, vol. 13, Springer Nature, 2022, pp. 2621–2635, doi:10.1007/s12652-021-03569-z.
short: S. Goudarzi, M. Sharif, F. Karimipour, Journal of Ambient Intelligence and
Humanized Computing 13 (2022) 2621–2635.
date_created: 2021-11-02T09:28:55Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2023-08-02T13:31:48Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s12652-021-03569-z
external_id:
isi:
- '000712198000001'
file:
- access_level: open_access
checksum: 0a8961416a9bb2be5a1cebda65468bcf
content_type: application/pdf
creator: fkarimip
date_created: 2021-11-12T19:38:05Z
date_updated: 2022-12-20T23:30:08Z
embargo: 2022-11-12
file_id: '10279'
file_name: A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence
2021 (Preprint version).pdf
file_size: 1634958
relation: main_file
file_date_updated: 2022-12-20T23:30:08Z
has_accepted_license: '1'
intvolume: ' 13'
isi: 1
keyword:
- general computer science
language:
- iso: eng
month: '05'
oa: 1
oa_version: Submitted Version
page: 2621–2635
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Journal of Ambient Intelligence and Humanized Computing
publication_identifier:
eissn:
- 1868-5145
issn:
- 1868-5137
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A context-aware dimension reduction framework for trajectory and health signal
analyses
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 13
year: '2022'
...
---
_id: '10071'
alternative_title:
- Early Career
article_processing_charge: No
article_type: letter_note
author:
- first_name: Henry
full_name: Adams, Henry
last_name: Adams
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Sarah
full_name: Percival, Sarah
last_name: Percival
- first_name: Lori
full_name: Ziegelmeier, Lori
last_name: Ziegelmeier
citation:
ama: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon.
Notices of the American Mathematical Society. 2021;68(9):1511-1514. doi:10.1090/noti2349
apa: Adams, H., Kourimska, H., Heiss, T., Percival, S., & Ziegelmeier, L. (2021).
How to tutorial-a-thon. Notices of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/noti2349
chicago: Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier.
“How to Tutorial-a-Thon.” Notices of the American Mathematical Society.
American Mathematical Society, 2021. https://doi.org/10.1090/noti2349.
ieee: H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to
tutorial-a-thon,” Notices of the American Mathematical Society, vol. 68,
no. 9. American Mathematical Society, pp. 1511–1514, 2021.
ista: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon.
Notices of the American Mathematical Society. 68(9), 1511–1514.
mla: Adams, Henry, et al. “How to Tutorial-a-Thon.” Notices of the American Mathematical
Society, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14,
doi:10.1090/noti2349.
short: H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of
the American Mathematical Society 68 (2021) 1511–1514.
date_created: 2021-10-03T22:01:22Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2021-12-03T07:31:26Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/noti2349
intvolume: ' 68'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ams.org/notices/
month: '10'
oa: 1
oa_version: Published Version
page: 1511-1514
publication: Notices of the American Mathematical Society
publication_identifier:
eissn:
- 1088-9477
issn:
- 0002-9920
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: How to tutorial-a-thon
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 68
year: '2021'
...
---
_id: '10367'
abstract:
- lang: eng
text: How information is created, shared and consumed has changed rapidly in recent
decades, in part thanks to new social platforms and technologies on the web. With
ever-larger amounts of unstructured and limited labels, organizing and reconciling
information from different sources and modalities is a central challenge in machine
learning. This cutting-edge tutorial aims to introduce the multimodal entailment
task, which can be useful for detecting semantic alignments when a single modality
alone does not suffice for a whole content understanding. Starting with a brief
overview of natural language processing, computer vision, structured data and
neural graph learning, we lay the foundations for the multimodal sections to follow.
We then discuss recent multimodal learning literature covering visual, audio and
language streams, and explore case studies focusing on tasks which require fine-grained
understanding of visual and linguistic semantics question answering, veracity
and hatred classification. Finally, we introduce a new dataset for recognizing
multimodal entailment, exploring it in a hands-on collaborative section. Overall,
this tutorial gives an overview of multimodal learning, introduces a multimodal
entailment dataset, and encourages future research in the topic.
acknowledgement: "We would like to thank Abby Schantz, Abe Ittycheriah, Aliaksei Severyn,
Allan Heydon, Aly\r\nGrealish, Andrey Vlasov, Arkaitz Zubiaga, Ashwin Kakarla, Chen
Sun, Clayton Williams, Cong\r\nYu, Cordelia Schmid, Da-Cheng Juan, Dan Finnie, Dani
Valevski, Daniel Rocha, David Price, David Sklar, Devi Krishna, Elena Kochkina,
Enrique Alfonseca, Franc¸oise Beaufays, Isabelle Augenstein, Jialu Liu, John Cantwell,
John Palowitch, Jordan Boyd-Graber, Lei Shi, Luis Valente, Maria Voitovich, Mehmet
Aktuna, Mogan Brown, Mor Naaman, Natalia P, Nidhi Hebbar, Pete Aykroyd, Rahul Sukthankar,
Richa Dixit, Steve Pucci, Tania Bedrax-Weiss, Tobias Kaufmann, Tom Boulos, Tu Tsao,
Vladimir Chtchetkine, Yair Kurzion, Yifan Xu and Zach Hynes."
article_processing_charge: No
author:
- first_name: Cesar
full_name: Ilharco, Cesar
last_name: Ilharco
- first_name: Afsaneh
full_name: Shirazi, Afsaneh
last_name: Shirazi
- first_name: Arjun
full_name: Gopalan, Arjun
last_name: Gopalan
- first_name: Arsha
full_name: Nagrani, Arsha
last_name: Nagrani
- first_name: Blaž
full_name: Bratanič, Blaž
last_name: Bratanič
- first_name: Chris
full_name: Bregler, Chris
last_name: Bregler
- first_name: Christina
full_name: Liu, Christina
last_name: Liu
- first_name: Felipe
full_name: Ferreira, Felipe
last_name: Ferreira
- first_name: Gabriek
full_name: Barcik, Gabriek
last_name: Barcik
- first_name: Gabriel
full_name: Ilharco, Gabriel
last_name: Ilharco
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
- first_name: Jannis
full_name: Bulian, Jannis
last_name: Bulian
- first_name: Jared
full_name: Frank, Jared
last_name: Frank
- first_name: Lucas
full_name: Smaira, Lucas
last_name: Smaira
- first_name: Qin
full_name: Cao, Qin
last_name: Cao
- first_name: Ricardo
full_name: Marino, Ricardo
last_name: Marino
- first_name: Roma
full_name: Patel, Roma
last_name: Patel
- first_name: Thomas
full_name: Leung, Thomas
last_name: Leung
- first_name: Vaiva
full_name: Imbrasaite, Vaiva
last_name: Imbrasaite
citation:
ama: 'Ilharco C, Shirazi A, Gopalan A, et al. Recognizing multimodal entailment.
In: 59th Annual Meeting of the Association for Computational Linguistics and
the 11th International Joint Conference on Natural Language Processing, Tutorial
Abstracts. Association for Computational Linguistics; 2021:29-30. doi:10.18653/v1/2021.acl-tutorials.6'
apa: 'Ilharco, C., Shirazi, A., Gopalan, A., Nagrani, A., Bratanič, B., Bregler,
C., … Imbrasaite, V. (2021). Recognizing multimodal entailment. In 59th Annual
Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts (pp. 29–30).
Bangkok, Thailand: Association for Computational Linguistics. https://doi.org/10.18653/v1/2021.acl-tutorials.6'
chicago: Ilharco, Cesar, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaž Bratanič,
Chris Bregler, Christina Liu, et al. “Recognizing Multimodal Entailment.” In 59th
Annual Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts, 29–30.
Association for Computational Linguistics, 2021. https://doi.org/10.18653/v1/2021.acl-tutorials.6.
ieee: C. Ilharco et al., “Recognizing multimodal entailment,” in 59th
Annual Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts, Bangkok,
Thailand, 2021, pp. 29–30.
ista: 'Ilharco C, Shirazi A, Gopalan A, Nagrani A, Bratanič B, Bregler C, Liu C,
Ferreira F, Barcik G, Ilharco G, Osang GF, Bulian J, Frank J, Smaira L, Cao Q,
Marino R, Patel R, Leung T, Imbrasaite V. 2021. Recognizing multimodal entailment.
59th Annual Meeting of the Association for Computational Linguistics and the 11th
International Joint Conference on Natural Language Processing, Tutorial Abstracts.
ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference
on Natural Language Processing, 29–30.'
mla: Ilharco, Cesar, et al. “Recognizing Multimodal Entailment.” 59th Annual
Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts, Association
for Computational Linguistics, 2021, pp. 29–30, doi:10.18653/v1/2021.acl-tutorials.6.
short: C. Ilharco, A. Shirazi, A. Gopalan, A. Nagrani, B. Bratanič, C. Bregler,
C. Liu, F. Ferreira, G. Barcik, G. Ilharco, G.F. Osang, J. Bulian, J. Frank, L.
Smaira, Q. Cao, R. Marino, R. Patel, T. Leung, V. Imbrasaite, in:, 59th Annual
Meeting of the Association for Computational Linguistics and the 11th International
Joint Conference on Natural Language Processing, Tutorial Abstracts, Association
for Computational Linguistics, 2021, pp. 29–30.
conference:
end_date: 2021-08-06
location: Bangkok, Thailand
name: 'ACL: Association for Computational Linguistics ; IJCNLP: International Joint
Conference on Natural Language Processing'
start_date: 2021-08-01
date_created: 2021-11-28T23:01:30Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2022-01-26T14:26:36Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.18653/v1/2021.acl-tutorials.6
file:
- access_level: open_access
checksum: b14052a025a6ecf675bdfe51db98c0d7
content_type: application/pdf
creator: cchlebak
date_created: 2021-11-29T08:41:00Z
date_updated: 2021-11-29T08:41:00Z
file_id: '10368'
file_name: 2021_ACL_Ilharco.pdf
file_size: 1227703
relation: main_file
success: 1
file_date_updated: 2021-11-29T08:41:00Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://aclanthology.org/2021.acl-tutorials.6/
month: '08'
oa: 1
oa_version: Published Version
page: 29-30
publication: 59th Annual Meeting of the Association for Computational Linguistics
and the 11th International Joint Conference on Natural Language Processing, Tutorial
Abstracts
publication_identifier:
isbn:
- 9-781-9540-8557-2
publication_status: published
publisher: Association for Computational Linguistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Recognizing multimodal entailment
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '10608'
abstract:
- lang: eng
text: We consider infinite-dimensional properties in coarse geometry for hyperspaces
consisting of finite subsets of metric spaces with the Hausdorff metric. We see
that several infinite-dimensional properties are preserved by taking the hyperspace
of subsets with at most n points. On the other hand, we prove that, if a metric
space contains a sequence of long intervals coarsely, then its hyperspace of finite
subsets is not coarsely embeddable into any uniformly convex Banach space. As
a corollary, the hyperspace of finite subsets of the real line is not coarsely
embeddable into any uniformly convex Banach space. It is also shown that every
(not necessarily bounded geometry) metric space with straight finite decomposition
complexity has metric sparsification property.
acknowledgement: We would like to thank the referees for their careful reading and
the comments that improved our work. The third named author would like to thank
the Division of Mathematics, Physics and Earth Sciences of the Graduate School of
Science and Engineering of Ehime University and the second named author for hosting
his visit in June 2018. Open access funding provided by Institute of Science and
Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Thomas
full_name: Weighill, Thomas
last_name: Weighill
- first_name: Takamitsu
full_name: Yamauchi, Takamitsu
last_name: Yamauchi
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
citation:
ama: Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics. 2021. doi:10.1007/s40879-021-00515-3
apa: Weighill, T., Yamauchi, T., & Zava, N. (2021). Coarse infinite-dimensionality
of hyperspaces of finite subsets. European Journal of Mathematics. Springer
Nature. https://doi.org/10.1007/s40879-021-00515-3
chicago: Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality
of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer
Nature, 2021. https://doi.org/10.1007/s40879-021-00515-3.
ieee: T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of
hyperspaces of finite subsets,” European Journal of Mathematics. Springer
Nature, 2021.
ista: Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics.
mla: Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of
Finite Subsets.” European Journal of Mathematics, Springer Nature, 2021,
doi:10.1007/s40879-021-00515-3.
short: T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).
date_created: 2022-01-09T23:01:27Z
date_published: 2021-12-30T00:00:00Z
date_updated: 2022-01-10T08:36:55Z
day: '30'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s40879-021-00515-3
file:
- access_level: open_access
checksum: c435dcfa1ad3aadc5cdd7366bc7f4e98
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-10T08:33:22Z
date_updated: 2022-01-10T08:33:22Z
file_id: '10610'
file_name: 2021_EuJournalMath_Weighill.pdf
file_size: 384908
relation: main_file
success: 1
file_date_updated: 2022-01-10T08:33:22Z
has_accepted_license: '1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coarse infinite-dimensionality of hyperspaces of finite subsets
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '9296'
abstract:
- lang: eng
text: ' matching is compatible to two or more labeled point sets of size n with
labels {1,…,n} if its straight-line drawing on each of these point sets is
crossing-free. We study the maximum number of edges in a matching compatible to
two or more labeled point sets in general position in the plane. We show that
for any two labeled convex sets of n points there exists a compatible matching
with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct
compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use
probabilistic arguments to show that for any ℓ given sets of n points there
exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges.
Finally, we show that Θ(logn) copies of any set of n points are necessary and
sufficient for the existence of a labeling such that any compatible matching consists
only of a single edge.'
acknowledgement: 'A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411.
Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative
DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported
by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by
ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23
(RiSE).'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Irene
full_name: Parada, Irene
last_name: Parada
- first_name: Daniel
full_name: Perz, Daniel
last_name: Perz
- first_name: Alexander
full_name: Pilz, Alexander
last_name: Pilz
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: 'Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings.
In: 15th International Conference on Algorithms and Computation. Vol 12635.
Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18'
apa: 'Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D.,
Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International
Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon,
Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18'
chicago: Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada,
Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible
Matchings.” In 15th International Conference on Algorithms and Computation,
12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.
ieee: O. Aichholzer et al., “On compatible matchings,” in 15th International
Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635,
pp. 221–233.
ista: 'Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec
J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference
on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol.
12635, 221–233.'
mla: Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International
Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021,
pp. 221–33, doi:10.1007/978-3-030-68211-8_18.
short: O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz,
J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and
Computation, Springer Nature, 2021, pp. 221–233.
conference:
end_date: 2021-03-02
location: Yangon, Myanmar
name: 'WALCOM: Algorithms and Computation'
start_date: 2021-02-28
date_created: 2021-03-28T22:01:41Z
date_published: 2021-02-16T00:00:00Z
date_updated: 2023-02-21T16:33:44Z
day: '16'
department:
- _id: UlWa
- _id: HeEd
- _id: KrCh
doi: 10.1007/978-3-030-68211-8_18
ec_funded: 1
external_id:
arxiv:
- '2101.03928'
intvolume: ' 12635'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2101.03928
month: '02'
oa: 1
oa_version: Preprint
page: 221-233
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
publication: 15th International Conference on Algorithms and Computation
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030682101'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11938'
relation: later_version
status: public
scopus_import: '1'
status: public
title: On compatible matchings
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 12635
year: '2021'
...
---
_id: '9465'
abstract:
- lang: eng
text: "Given a locally finite set \U0001D44B⊆ℝ\U0001D451 and an integer \U0001D458≥0,
we consider the function \U0001D430\U0001D458:Del\U0001D458(\U0001D44B)→ℝ on the
dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion
of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf
Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett
114:76–83, 2014). While this function is not necessarily generalized discrete
Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete
Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that
its increments can be meaningfully classified into critical and non-critical steps.
This result extends to the case of weighted points and sheds light on k-fold covers
with balls in Euclidean space."
article_number: '15'
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: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
citation:
ama: Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order
k. Journal of Geometry. 2021;112(1). doi:10.1007/s00022-021-00577-4
apa: Edelsbrunner, H., Nikitenko, A., & Osang, G. F. (2021). A step in the Delaunay
mosaic of order k. Journal of Geometry. Springer Nature. https://doi.org/10.1007/s00022-021-00577-4
chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. “A Step in the
Delaunay Mosaic of Order K.” Journal of Geometry. Springer Nature, 2021.
https://doi.org/10.1007/s00022-021-00577-4.
ieee: H. Edelsbrunner, A. Nikitenko, and G. F. Osang, “A step in the Delaunay mosaic
of order k,” Journal of Geometry, vol. 112, no. 1. Springer Nature, 2021.
ista: Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic
of order k. Journal of Geometry. 112(1), 15.
mla: Edelsbrunner, Herbert, et al. “A Step in the Delaunay Mosaic of Order K.” Journal
of Geometry, vol. 112, no. 1, 15, Springer Nature, 2021, doi:10.1007/s00022-021-00577-4.
short: H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021).
date_created: 2021-06-06T22:01:29Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2022-05-12T11:41:45Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00022-021-00577-4
file:
- access_level: open_access
checksum: e52a832f1def52a2b23d21bcc09e646f
content_type: application/pdf
creator: kschuh
date_created: 2021-06-11T13:16:26Z
date_updated: 2021-06-11T13:16:26Z
file_id: '9544'
file_name: 2021_Geometry_Edelsbrunner.pdf
file_size: 694706
relation: main_file
success: 1
file_date_updated: 2021-06-11T13:16:26Z
has_accepted_license: '1'
intvolume: ' 112'
issue: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Journal of Geometry
publication_identifier:
eissn:
- '14208997'
issn:
- '00472468'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A step in the Delaunay mosaic of order k
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: 112
year: '2021'
...
---
_id: '9345'
abstract:
- lang: eng
text: Modeling a crystal as a periodic point set, we present a fingerprint consisting
of density functionsthat facilitates the efficient search for new materials and
material properties. We prove invarianceunder isometries, continuity, and completeness
in the generic case, which are necessary featuresfor the reliable comparison of
crystals. The proof of continuity integrates methods from discretegeometry and
lattice theory, while the proof of generic completeness combines techniques fromgeometry
with analysis. The fingerprint has a fast algorithm based on Brillouin zones and
relatedinclusion-exclusion formulae. We have implemented the algorithm and describe
its application tocrystal structure prediction.
acknowledgement: The authors thank Janos Pach for insightful discussions on the topic
of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned
in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.
alternative_title:
- LIPIcs
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: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Vitaliy
full_name: ' Kurlin , Vitaliy'
last_name: ' Kurlin '
- first_name: Philip
full_name: Smith, Philip
last_name: Smith
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint
of a periodic point set. In: 37th International Symposium on Computational
Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik;
2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32'
apa: 'Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M.
(2021). The density fingerprint of a periodic point set. In 37th International
Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16).
Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32'
chicago: Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and
Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th
International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32.
ieee: H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The
density fingerprint of a periodic point set,” in 37th International Symposium
on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16.
ista: 'Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density
fingerprint of a periodic point set. 37th International Symposium on Computational
Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol.
189, 32:1-32:16.'
mla: Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point
Set.” 37th International Symposium on Computational Geometry (SoCG 2021),
vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16,
doi:10.4230/LIPIcs.SoCG.2021.32.
short: H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th
International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.
conference:
end_date: 2021-06-11
location: Virtual
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-04-22T08:09:58Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-02-23T13:55:40Z
day: '02'
ddc:
- '004'
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.32
ec_funded: 1
file:
- access_level: open_access
checksum: 1787baef1523d6d93753b90d0c109a6d
content_type: application/pdf
creator: mwintrae
date_created: 2021-04-22T08:08:14Z
date_updated: 2021-04-22T08:08:14Z
file_id: '9346'
file_name: df_socg_final_version.pdf
file_size: 3117435
relation: main_file
success: 1
file_date_updated: 2021-04-22T08:08:14Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 32:1-32:16
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 25C5A090-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00312
name: The Wittgenstein Prize
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 37th International Symposium on Computational Geometry (SoCG 2021)
publication_identifier:
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
status: public
title: The density fingerprint of a periodic point set
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: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9604'
abstract:
- lang: eng
text: Generalizing Lee’s inductive argument for counting the cells of higher order
Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse
theoretic quantities for piecewise constant functions on planar arrangements.
Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number
of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for
1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s
first k-1 sublevel sets. We get similar expressions for the vertices, edges, and
polygons of the order-k Voronoi tessellation.
alternative_title:
- LIPIcs
article_number: '16'
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells
of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz
International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with
morse theory. In Leibniz International Proceedings in Informatics (Vol.
189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16'
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3
with Morse Theory.” In Leibniz International Proceedings in Informatics,
Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting
cells of order-k voronoi tessellations in ℝ3 with morse theory,” in
Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting
cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz
International Proceedings in Informatics. SoCG: International Symposium on Computational
Geometry, LIPIcs, vol. 189, 16.'
mla: Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in
ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics,
vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:,
Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2021.
conference:
end_date: 2021-06-11
location: Online
name: 'SoCG: International Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-06-27T22:01:48Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-02-23T14:02:28Z
day: '02'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.16
ec_funded: 1
file:
- access_level: open_access
checksum: 22b11a719018b22ecba2471b51f2eb40
content_type: application/pdf
creator: asandaue
date_created: 2021-06-28T13:11:39Z
date_updated: 2021-06-28T13:11:39Z
file_id: '9611'
file_name: 2021_LIPIcs_Biswas.pdf
file_size: 727817
relation: main_file
success: 1
file_date_updated: 2021-06-28T13:11:39Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- '9783959771849'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting cells of order-k voronoi tessellations in ℝ3 with morse
theory
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: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9824'
abstract:
- lang: eng
text: We define a new compact coordinate system in which each integer triplet addresses
a voxel in the BCC grid, and we investigate some of its properties. We propose
a characterization of 3D discrete analytical planes with their topological features
(in the Cartesian and in the new coordinate system) such as the interrelation
between the thickness of the plane and the separability constraint we aim to obtain.
acknowledgement: 'This work has been partially supported by the Ministry of Education,
Science and Technological Development of the Republic of Serbia through the project
no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from
the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and
the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’,
Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Lidija
full_name: Čomić, Lidija
last_name: Čomić
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- 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, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic
grid - coordinate system and discrete analytical plane definition. In: Discrete
Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163.
doi:10.1007/978-3-030-76657-3_10'
apa: 'Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021).
Body centered cubic grid - coordinate system and discrete analytical plane definition.
In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163).
Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10'
chicago: Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and
Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical
Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63.
Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.
ieee: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered
cubic grid - coordinate system and discrete analytical plane definition,” in Discrete
Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp.
152–163.
ista: 'Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered
cubic grid - coordinate system and discrete analytical plane definition. Discrete
Geometry and Mathematical Morphology. DGMM: International Conference on Discrete
Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163.'
mla: Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete
Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology,
vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.
short: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete
Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.
conference:
end_date: 2021-05-27
location: Uppsala, Sweden
name: 'DGMM: International Conference on Discrete Geometry and Mathematical Morphology'
start_date: 2021-05-24
date_created: 2021-08-08T22:01:29Z
date_published: 2021-05-16T00:00:00Z
date_updated: 2022-05-31T06:58:21Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/978-3-030-76657-3_10
ec_funded: 1
intvolume: ' 12708'
language:
- iso: eng
month: '05'
oa_version: None
page: 152-163
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: Discrete Geometry and Mathematical Morphology
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030766566'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Body centered cubic grid - coordinate system and discrete analytical plane
definition
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12708
year: '2021'
...
---
_id: '8317'
abstract:
- lang: eng
text: When can a polyomino piece of paper be folded into a unit cube? Prior work
studied tree-like polyominoes, but polyominoes with holes remain an intriguing
open problem. We present sufficient conditions for a polyomino with one or several
holes to fold into a cube, and conditions under which cube folding is impossible.
In particular, we show that all but five special “basic” holes guarantee foldability.
acknowledgement: This research was performed in part at the 33rd Bellairs Winter Workshop
on Computational Geometry. We thank all other participants for a fruitful atmosphere.
H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially
funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.
article_number: '101700'
article_processing_charge: No
article_type: original
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Hugo A.
full_name: Akitaya, Hugo A.
last_name: Akitaya
- first_name: Kenneth C.
full_name: Cheung, Kenneth C.
last_name: Cheung
- first_name: Erik D.
full_name: Demaine, Erik D.
last_name: Demaine
- first_name: Martin L.
full_name: Demaine, Martin L.
last_name: Demaine
- first_name: Sándor P.
full_name: Fekete, Sándor P.
last_name: Fekete
- first_name: Linda
full_name: Kleist, Linda
last_name: Kleist
- first_name: Irina
full_name: Kostitsyna, Irina
last_name: Kostitsyna
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Klara
full_name: Mundilova, Klara
last_name: Mundilova
- first_name: Christiane
full_name: Schmidt, Christiane
last_name: Schmidt
citation:
ama: 'Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes
into a cube. Computational Geometry: Theory and Applications. 2021;93.
doi:10.1016/j.comgeo.2020.101700'
apa: 'Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M.
L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a
cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700'
chicago: 'Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine,
Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes
with Holes into a Cube.” Computational Geometry: Theory and Applications.
Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700.'
ieee: 'O. Aichholzer et al., “Folding polyominoes with holes into a cube,”
Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.'
ista: 'Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist
L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding
polyominoes with holes into a cube. Computational Geometry: Theory and Applications.
93, 101700.'
mla: 'Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational
Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.'
short: 'O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P.
Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt,
Computational Geometry: Theory and Applications 93 (2021).'
date_created: 2020-08-30T22:01:09Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-08-04T10:57:42Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2020.101700
external_id:
arxiv:
- '1910.09917'
isi:
- '000579185100004'
intvolume: ' 93'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.09917v3
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: 'Computational Geometry: Theory and Applications'
publication_identifier:
issn:
- '09257721'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '6989'
relation: shorter_version
status: public
scopus_import: '1'
status: public
title: Folding polyominoes with holes into a cube
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 93
year: '2021'
...
---
_id: '8773'
abstract:
- lang: eng
text: Let g be a complex semisimple Lie algebra. We give a classification of contravariant
forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We
prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose
dimension is given by the cardinality of the Weyl group of g. We also describe
a procedure for parabolically inducing contravariant forms. As a corollary, we
deduce the existence of the Shapovalov form on a Verma module, and provide a formula
for the dimension of the space of contravariant forms on the degenerate Whittaker
modules M(χ,η) introduced by McDowell.
acknowledgement: "We would like to thank Peter Trapa for useful discussions, and Dragan
Milicic and Arun Ram for valuable feedback on the structure of the paper. The first
author acknowledges the support of the European Unions Horizon 2020 research and
innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411.
The second author is\r\nsupported by the National Science Foundation Award No. 1803059."
article_processing_charge: No
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Anna
full_name: Romanov, Anna
last_name: Romanov
citation:
ama: Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings
of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205
apa: Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules.
Proceedings of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/proc/15205
chicago: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.”
Proceedings of the American Mathematical Society. American Mathematical
Society, 2021. https://doi.org/10.1090/proc/15205.
ieee: A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings
of the American Mathematical Society, vol. 149, no. 1. American Mathematical
Society, pp. 37–52, 2021.
ista: Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings
of the American Mathematical Society. 149(1), 37–52.
mla: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.”
Proceedings of the American Mathematical Society, vol. 149, no. 1, American
Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.
short: A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149
(2021) 37–52.
date_created: 2020-11-19T10:17:40Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T11:11:47Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/15205
ec_funded: 1
external_id:
arxiv:
- '1910.08286'
isi:
- '000600416300004'
intvolume: ' 149'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.08286
month: '01'
oa: 1
oa_version: Preprint
page: 37-52
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: Contravariant forms on Whittaker modules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 149
year: '2021'
...
---
_id: '9253'
abstract:
- lang: eng
text: In March 2020, the Austrian government introduced a widespread lock-down in
response to the COVID-19 pandemic. Based on subjective impressions and anecdotal
evidence, Austrian public and private life came to a sudden halt. Here we assess
the effect of the lock-down quantitatively for all regions in Austria and present
an analysis of daily changes of human mobility throughout Austria using near-real-time
anonymized mobile phone data. We describe an efficient data aggregation pipeline
and analyze the mobility by quantifying mobile-phone traffic at specific point
of interests (POIs), analyzing individual trajectories and investigating the cluster
structure of the origin-destination graph. We found a reduction of commuters at
Viennese metro stations of over 80% and the number of devices with a radius of
gyration of less than 500 m almost doubled. The results of studying crowd-movement
behavior highlight considerable changes in the structure of mobility networks,
revealed by a higher modularity and an increase from 12 to 20 detected communities.
We demonstrate the relevance of mobility data for epidemiological studies by showing
a significant correlation of the outflow from the town of Ischgl (an early COVID-19
hotspot) and the reported COVID-19 cases with an 8-day time lag. This research
indicates that mobile phone usage data permits the moment-by-moment quantification
of mobility behavior for a whole country. We emphasize the need to improve the
availability of such data in anonymized form to empower rapid response to combat
COVID-19 and future pandemics.
article_processing_charge: No
author:
- first_name: Georg
full_name: Heiler, Georg
last_name: Heiler
- first_name: Tobias
full_name: Reisch, Tobias
last_name: Reisch
- first_name: Jan
full_name: Hurt, Jan
last_name: Hurt
- first_name: Mohammad
full_name: Forghani, Mohammad
last_name: Forghani
- first_name: Aida
full_name: Omani, Aida
last_name: Omani
- first_name: Allan
full_name: Hanbury, Allan
last_name: Hanbury
- first_name: Farid
full_name: Karimipour, Farid
id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425
last_name: Karimipour
orcid: 0000-0001-6746-4174
citation:
ama: 'Heiler G, Reisch T, Hurt J, et al. Country-wide mobility changes observed
using mobile phone data during COVID-19 pandemic. In: 2020 IEEE International
Conference on Big Data. IEEE; 2021:3123-3132. doi:10.1109/bigdata50022.2020.9378374'
apa: 'Heiler, G., Reisch, T., Hurt, J., Forghani, M., Omani, A., Hanbury, A., &
Karimipour, F. (2021). Country-wide mobility changes observed using mobile phone
data during COVID-19 pandemic. In 2020 IEEE International Conference on Big
Data (pp. 3123–3132). Atlanta, GA, United States: IEEE. https://doi.org/10.1109/bigdata50022.2020.9378374'
chicago: Heiler, Georg, Tobias Reisch, Jan Hurt, Mohammad Forghani, Aida Omani,
Allan Hanbury, and Farid Karimipour. “Country-Wide Mobility Changes Observed Using
Mobile Phone Data during COVID-19 Pandemic.” In 2020 IEEE International Conference
on Big Data, 3123–32. IEEE, 2021. https://doi.org/10.1109/bigdata50022.2020.9378374.
ieee: G. Heiler et al., “Country-wide mobility changes observed using mobile
phone data during COVID-19 pandemic,” in 2020 IEEE International Conference
on Big Data, Atlanta, GA, United States, 2021, pp. 3123–3132.
ista: 'Heiler G, Reisch T, Hurt J, Forghani M, Omani A, Hanbury A, Karimipour F.
2021. Country-wide mobility changes observed using mobile phone data during COVID-19
pandemic. 2020 IEEE International Conference on Big Data. Big Data: International
Conference on Big Data, 3123–3132.'
mla: Heiler, Georg, et al. “Country-Wide Mobility Changes Observed Using Mobile
Phone Data during COVID-19 Pandemic.” 2020 IEEE International Conference on
Big Data, IEEE, 2021, pp. 3123–32, doi:10.1109/bigdata50022.2020.9378374.
short: G. Heiler, T. Reisch, J. Hurt, M. Forghani, A. Omani, A. Hanbury, F. Karimipour,
in:, 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–3132.
conference:
end_date: 2020-12-13
location: Atlanta, GA, United States
name: 'Big Data: International Conference on Big Data'
start_date: 2020-12-10
date_created: 2021-03-21T11:34:07Z
date_published: 2021-03-19T00:00:00Z
date_updated: 2023-08-07T14:00:13Z
day: '19'
department:
- _id: HeEd
doi: 10.1109/bigdata50022.2020.9378374
external_id:
arxiv:
- '2008.10064'
isi:
- '000662554703032'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2008.10064
month: '03'
oa: 1
oa_version: Preprint
page: 3123-3132
publication: 2020 IEEE International Conference on Big Data
publication_identifier:
isbn:
- '9781728162515'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Country-wide mobility changes observed using mobile phone data during COVID-19
pandemic
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '9317'
abstract:
- lang: eng
text: Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r
consists of all points in Rd that have k or more points of X within distance r.
We consider two filtrations—one in scale obtained by fixing k and increasing r,
and the other in depth obtained by fixing r and decreasing k—and we compute the
persistence diagrams of both. While standard methods suffice for the filtration
in scale, we need novel geometric and topological concepts for the filtration
in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal
integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module
of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.
acknowledgement: "This 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), and by the DFG Collaborative Research Center
TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35
of the Austrian Science Fund (FWF)\r\nOpen Access funding provided by the Institute
of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
citation:
ama: Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. Discrete
and Computational Geometry. 2021;65:1296–1313. doi:10.1007/s00454-021-00281-9
apa: Edelsbrunner, H., & Osang, G. F. (2021). The multi-cover persistence of
Euclidean balls. Discrete and Computational Geometry. Springer Nature.
https://doi.org/10.1007/s00454-021-00281-9
chicago: Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence
of Euclidean Balls.” Discrete and Computational Geometry. Springer Nature,
2021. https://doi.org/10.1007/s00454-021-00281-9.
ieee: H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean
balls,” Discrete and Computational Geometry, vol. 65. Springer Nature,
pp. 1296–1313, 2021.
ista: Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls.
Discrete and Computational Geometry. 65, 1296–1313.
mla: Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of
Euclidean Balls.” Discrete and Computational Geometry, vol. 65, Springer
Nature, 2021, pp. 1296–1313, doi:10.1007/s00454-021-00281-9.
short: H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021)
1296–1313.
date_created: 2021-04-11T22:01:15Z
date_published: 2021-03-31T00:00:00Z
date_updated: 2023-08-07T14:35:44Z
day: '31'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s00454-021-00281-9
ec_funded: 1
external_id:
isi:
- '000635460400001'
file:
- access_level: open_access
checksum: 59b4e1e827e494209bcb4aae22e1d347
content_type: application/pdf
creator: cchlebak
date_created: 2021-12-01T10:56:53Z
date_updated: 2021-12-01T10:56:53Z
file_id: '10394'
file_name: 2021_DisCompGeo_Edelsbrunner_Osang.pdf
file_size: 677704
relation: main_file
success: 1
file_date_updated: 2021-12-01T10:56:53Z
has_accepted_license: '1'
intvolume: ' 65'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 1296–1313
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: 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: '187'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The multi-cover persistence of Euclidean balls
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 65
year: '2021'
...
---
_id: '9602'
abstract:
- lang: eng
text: "An ordered graph is a graph with a linear ordering on its vertex set. We
prove that for every positive integer k, there exists a constant ck > 0 such that
any ordered graph G on n vertices with the property that neither G nor its complement
contains an induced monotone path of size k, has either a clique or an independent
set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and
Thomassé, who proved the analogous result for unordered graphs.\r\nA key idea
of the above paper was to show that any unordered graph on n vertices that does
not contain an induced path of size k, and whose maximum degree is at most c(k)n
for some small c(k) > 0, contains two disjoint linear size subsets with no edge
between them. This approach fails for ordered graphs, because the analogous statement
is false for k ≥ 3, by a construction of Fox. We provide some further examples
showing that this statement also fails for ordered graphs avoiding other ordered
trees."
acknowledgement: We would like to thank the anonymous referees for their useful comments
and suggestions. János Pach is partially supported by Austrian Science Fund (FWF)
grant Z 342-N31 and by ERC Advanced grant “GeoScape.” István Tomon is partially
supported by Swiss National Science Foundation grant no. 200021_196965, and thanks
the support of MIPT Moscow. Both authors are partially supported by The Russian
Government in the framework of MegaGrant no. 075-15-2019-1926.
article_processing_charge: No
article_type: original
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: István
full_name: Tomon, István
last_name: Tomon
citation:
ama: Pach J, Tomon I. Erdős-Hajnal-type results for monotone paths. Journal of
Combinatorial Theory Series B. 2021;151:21-37. doi:10.1016/j.jctb.2021.05.004
apa: Pach, J., & Tomon, I. (2021). Erdős-Hajnal-type results for monotone paths.
Journal of Combinatorial Theory. Series B. Elsevier. https://doi.org/10.1016/j.jctb.2021.05.004
chicago: Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone
Paths.” Journal of Combinatorial Theory. Series B. Elsevier, 2021. https://doi.org/10.1016/j.jctb.2021.05.004.
ieee: J. Pach and I. Tomon, “Erdős-Hajnal-type results for monotone paths,” Journal
of Combinatorial Theory. Series B, vol. 151. Elsevier, pp. 21–37, 2021.
ista: Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal
of Combinatorial Theory. Series B. 151, 21–37.
mla: Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.”
Journal of Combinatorial Theory. Series B, vol. 151, Elsevier, 2021, pp.
21–37, doi:10.1016/j.jctb.2021.05.004.
short: J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.
date_created: 2021-06-27T22:01:47Z
date_published: 2021-06-09T00:00:00Z
date_updated: 2023-08-10T13:38:00Z
day: '09'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1016/j.jctb.2021.05.004
external_id:
isi:
- '000702280800002'
file:
- access_level: open_access
checksum: 15fbc9064cd9d1c777ac0043b78c8f12
content_type: application/pdf
creator: asandaue
date_created: 2021-06-28T13:33:23Z
date_updated: 2021-06-28T13:33:23Z
file_id: '9612'
file_name: 2021_JournalOfCombinatorialTheory_Pach.pdf
file_size: 418168
relation: main_file
success: 1
file_date_updated: 2021-06-28T13:33:23Z
has_accepted_license: '1'
intvolume: ' 151'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 21-37
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Journal of Combinatorial Theory. Series B
publication_identifier:
issn:
- 0095-8956
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Erdős-Hajnal-type results for monotone paths
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 151
year: '2021'
...
---
_id: '9821'
abstract:
- lang: eng
text: Heart rate variability (hrv) is a physiological phenomenon of the variation
in the length of the time interval between consecutive heartbeats. In many cases
it could be an indicator of the development of pathological states. The classical
approach to the analysis of hrv includes time domain methods and frequency domain
methods. However, attempts are still being made to define new and more effective
hrv assessment tools. Persistent homology is a novel data analysis tool developed
in the recent decades that is rooted at algebraic topology. The Topological Data
Analysis (TDA) approach focuses on examining the shape of the data in terms of
connectedness and holes, and has recently proved to be very effective in various
fields of research. In this paper we propose the use of persistent homology to
the hrv analysis. We recall selected topological descriptors used in the literature
and we introduce some new topological descriptors that reflect the specificity
of hrv, and we discuss their relation to the standard hrv measures. In particular,
we show that this novel approach provides a collection of indices that might be
at least as useful as the classical parameters in differentiating between series
of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering
from a stroke episode.
acknowledgement: We express our gratitude to the anonymous referees who provided constructive
comments that helped us improve the quality of the paper.
article_number: e0253851
article_processing_charge: Yes
article_type: original
author:
- first_name: Grzegorz
full_name: Graff, Grzegorz
last_name: Graff
- first_name: Beata
full_name: Graff, Beata
last_name: Graff
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: Dariusz
full_name: Gąsecki, Dariusz
last_name: Gąsecki
- first_name: Krzysztof
full_name: Narkiewicz, Krzysztof
last_name: Narkiewicz
citation:
ama: Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. Persistent
homology as a new method of the assessment of heart rate variability. PLoS
ONE. 2021;16(7). doi:10.1371/journal.pone.0253851
apa: Graff, G., Graff, B., Pilarczyk, P., Jablonski, G., Gąsecki, D., & Narkiewicz,
K. (2021). Persistent homology as a new method of the assessment of heart rate
variability. PLoS ONE. Public Library of Science. https://doi.org/10.1371/journal.pone.0253851
chicago: Graff, Grzegorz, Beata Graff, Pawel Pilarczyk, Grzegorz Jablonski, Dariusz
Gąsecki, and Krzysztof Narkiewicz. “Persistent Homology as a New Method of the
Assessment of Heart Rate Variability.” PLoS ONE. Public Library of Science,
2021. https://doi.org/10.1371/journal.pone.0253851.
ieee: G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, and K. Narkiewicz,
“Persistent homology as a new method of the assessment of heart rate variability,”
PLoS ONE, vol. 16, no. 7. Public Library of Science, 2021.
ista: Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. 2021.
Persistent homology as a new method of the assessment of heart rate variability.
PLoS ONE. 16(7), e0253851.
mla: Graff, Grzegorz, et al. “Persistent Homology as a New Method of the Assessment
of Heart Rate Variability.” PLoS ONE, vol. 16, no. 7, e0253851, Public
Library of Science, 2021, doi:10.1371/journal.pone.0253851.
short: G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz,
PLoS ONE 16 (2021).
date_created: 2021-08-08T22:01:28Z
date_published: 2021-07-01T00:00:00Z
date_updated: 2023-08-10T14:21:42Z
day: '01'
ddc:
- '006'
department:
- _id: HeEd
doi: 10.1371/journal.pone.0253851
external_id:
isi:
- '000678124900050'
pmid:
- '34292957'
file:
- access_level: open_access
checksum: 0277aa155d5db1febd2cb384768bba5f
content_type: application/pdf
creator: asandaue
date_created: 2021-08-09T09:25:41Z
date_updated: 2021-08-09T09:25:41Z
file_id: '9832'
file_name: 2021_PLoSONE_Graff.pdf
file_size: 2706919
relation: main_file
success: 1
file_date_updated: 2021-08-09T09:25:41Z
has_accepted_license: '1'
intvolume: ' 16'
isi: 1
issue: '7'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
pmid: 1
publication: PLoS ONE
publication_identifier:
eissn:
- '19326203'
publication_status: published
publisher: Public Library of Science
quality_controlled: '1'
scopus_import: '1'
status: public
title: Persistent homology as a new method of the assessment of heart rate variability
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 16
year: '2021'
...
---
_id: '10222'
abstract:
- lang: eng
text: Consider a random set of points on the unit sphere in ℝd, which can be either
uniformly sampled or a Poisson point process. Its convex hull is a random inscribed
polytope, whose boundary approximates the sphere. We focus on the case d = 3,
for which there are elementary proofs and fascinating formulas for metric properties.
In particular, we study the fraction of acute facets, the expected intrinsic volumes,
the total edge length, and the distance to a fixed point. Finally we generalize
the results to the ellipsoid with homeoid density.
acknowledgement: "This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.\r\nWe
are grateful to Dmitry Zaporozhets and Christoph Thäle for valuable comments and
for directing us to relevant references. We also thank to Anton Mellit for a useful
discussion on Bessel functions."
article_processing_charge: Yes (via OA deal)
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
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed
in the 2-sphere. Experimental Mathematics. 2021:1-15. doi:10.1080/10586458.2021.1980459
apa: Akopyan, A., Edelsbrunner, H., & Nikitenko, A. (2021). The beauty of random
polytopes inscribed in the 2-sphere. Experimental Mathematics. Taylor and
Francis. https://doi.org/10.1080/10586458.2021.1980459
chicago: Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty
of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics.
Taylor and Francis, 2021. https://doi.org/10.1080/10586458.2021.1980459.
ieee: A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes
inscribed in the 2-sphere,” Experimental Mathematics. Taylor and Francis,
pp. 1–15, 2021.
ista: Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes
inscribed in the 2-sphere. Experimental Mathematics., 1–15.
mla: Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.”
Experimental Mathematics, Taylor and Francis, 2021, pp. 1–15, doi:10.1080/10586458.2021.1980459.
short: A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021)
1–15.
date_created: 2021-11-07T23:01:25Z
date_published: 2021-10-25T00:00:00Z
date_updated: 2023-08-14T11:57:07Z
day: '25'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1080/10586458.2021.1980459
ec_funded: 1
external_id:
arxiv:
- '2007.07783'
isi:
- '000710893500001'
file:
- access_level: open_access
checksum: 3514382e3a1eb87fa6c61ad622874415
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T11:55:10Z
date_updated: 2023-08-14T11:55:10Z
file_id: '14053'
file_name: 2023_ExperimentalMath_Akopyan.pdf
file_size: 1966019
relation: main_file
success: 1
file_date_updated: 2023-08-14T11:55:10Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1-15
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: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Experimental Mathematics
publication_identifier:
eissn:
- 1944-950X
issn:
- 1058-6458
publication_status: published
publisher: Taylor and Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: The beauty of random polytopes inscribed in the 2-sphere
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '8940'
abstract:
- lang: eng
text: We quantise Whitney’s construction to prove the existence of a triangulation
for any C^2 manifold, so that we get an algorithm with explicit bounds. We also
give a new elementary proof, which is completely geometric.
acknowledgement: This work has been funded by the European Research Council under
the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations
of Geometric Understanding in Higher Dimensions). The third author also received
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding
provided by the Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: 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 J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds:
An elementary and quantified version of Whitney’s method. Discrete & Computational
Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8'
apa: 'Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating
submanifolds: An elementary and quantified version of Whitney’s method. Discrete
& Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8'
chicago: 'Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken.
“Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s
Method.” Discrete & Computational Geometry. Springer Nature, 2021.
https://doi.org/10.1007/s00454-020-00250-8.'
ieee: 'J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds:
An elementary and quantified version of Whitney’s method,” Discrete & Computational
Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.'
ista: 'Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds:
An elementary and quantified version of Whitney’s method. Discrete & Computational
Geometry. 66(1), 386–434.'
mla: 'Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary
and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry,
vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.'
short: J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational
Geometry 66 (2021) 386–434.
date_created: 2020-12-12T11:07:02Z
date_published: 2021-07-01T00:00:00Z
date_updated: 2023-09-05T15:02:40Z
day: '01'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00250-8
ec_funded: 1
external_id:
isi:
- '000597770300001'
file:
- access_level: open_access
checksum: c848986091e56699dc12de85adb1e39c
content_type: application/pdf
creator: kschuh
date_created: 2021-08-06T09:52:29Z
date_updated: 2021-08-06T09:52:29Z
file_id: '9795'
file_name: 2021_DescreteCompGeopmetry_Boissonnat.pdf
file_size: 983307
relation: main_file
success: 1
file_date_updated: 2021-08-06T09:52:29Z
has_accepted_license: '1'
intvolume: ' 66'
isi: 1
issue: '1'
keyword:
- Theoretical Computer Science
- Computational Theory and Mathematics
- Geometry and Topology
- Discrete Mathematics and Combinatorics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 386-434
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: 'Triangulating submanifolds: An elementary and quantified version of Whitney’s
method'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 66
year: '2021'
...
---
_id: '9111'
abstract:
- lang: eng
text: 'We study the probabilistic convergence between the mapper graph and the Reeb
graph of a topological space X equipped with a continuous function f:X→R. We first
give a categorification of the mapper graph and the Reeb graph by interpreting
them in terms of cosheaves and stratified covers of the real line R. We then introduce
a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium
on point-based graphics, 2007), referred to as the enhanced mapper graph, and
demonstrate that such a construction approximates the Reeb graph of (X,f) when
it is applied to points randomly sampled from a probability density function concentrated
on (X,f). Our techniques are based on the interleaving distance of constructible
cosheaves and topological estimation via kernel density estimates. Following Munch
and Wang (In: 32nd international symposium on computational geometry, volume 51
of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany,
pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible
R-space (with a fixed open cover), approximates the Reeb graph of the same space.
We then construct an isomorphism between the mapper of (X,f) to the mapper of
a super-level set of a probability density function concentrated on (X,f). Finally,
building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b),
we show that, with high probability, we can recover the mapper of the super-level
set given a sufficiently large sample. Our work is the first to consider the mapper
construction using the theory of cosheaves in a probabilistic setting. It is part
of an ongoing effort to combine sheaf theory, probability, and statistics, to
support topological data analysis with random data.'
acknowledgement: "AB was supported in part by the European Union’s Horizon 2020 research
and innovation\r\nprogramme under the Marie Sklodowska-Curie GrantAgreement No.
754411 and NSF IIS-1513616. OB was supported in part by the Israel Science Foundation,
Grant 1965/19. BW was supported in part by NSF IIS-1513616 and DBI-1661375. EM was
supported in part by NSF CMMI-1800466, DMS-1800446, and CCF-1907591.We would like
to thank the Institute for Mathematics and its Applications for hosting a workshop
titled Bridging Statistics and Sheaves in May 2018, where this work was conceived.\r\nOpen
Access funding provided by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Omer
full_name: Bobrowski, Omer
last_name: Bobrowski
- first_name: Elizabeth
full_name: Munch, Elizabeth
last_name: Munch
- first_name: Bei
full_name: Wang, Bei
last_name: Wang
citation:
ama: Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability
of random mapper graphs. Journal of Applied and Computational Topology.
2021;5(1):99-140. doi:10.1007/s41468-020-00063-x
apa: Brown, A., Bobrowski, O., Munch, E., & Wang, B. (2021). Probabilistic convergence
and stability of random mapper graphs. Journal of Applied and Computational
Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00063-x
chicago: Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic
Convergence and Stability of Random Mapper Graphs.” Journal of Applied and
Computational Topology. Springer Nature, 2021. https://doi.org/10.1007/s41468-020-00063-x.
ieee: A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence
and stability of random mapper graphs,” Journal of Applied and Computational
Topology, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021.
ista: Brown A, Bobrowski O, Munch E, Wang B. 2021. Probabilistic convergence and
stability of random mapper graphs. Journal of Applied and Computational Topology.
5(1), 99–140.
mla: Brown, Adam, et al. “Probabilistic Convergence and Stability of Random Mapper
Graphs.” Journal of Applied and Computational Topology, vol. 5, no. 1,
Springer Nature, 2021, pp. 99–140, doi:10.1007/s41468-020-00063-x.
short: A. Brown, O. Bobrowski, E. Munch, B. Wang, Journal of Applied and Computational
Topology 5 (2021) 99–140.
date_created: 2021-02-11T14:41:02Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-09-05T15:37:56Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s41468-020-00063-x
ec_funded: 1
external_id:
arxiv:
- '1909.03488'
file:
- access_level: open_access
checksum: 3f02e9d47c428484733da0f588a3c069
content_type: application/pdf
creator: dernst
date_created: 2021-02-11T14:43:59Z
date_updated: 2021-02-11T14:43:59Z
file_id: '9112'
file_name: 2020_JourApplCompTopology_Brown.pdf
file_size: 2090265
relation: main_file
success: 1
file_date_updated: 2021-02-11T14:43:59Z
has_accepted_license: '1'
intvolume: ' 5'
issue: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 99-140
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Probabilistic convergence and stability of random mapper graphs
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 5
year: '2021'
...
---
_id: '9056'
abstract:
- lang: eng
text: "In this thesis we study persistence of multi-covers of Euclidean balls and
the geometric structures underlying their computation, in particular Delaunay
mosaics and Voronoi tessellations. The k-fold cover for some discrete input point
set consists of the space where at least k balls of radius r around the input
points overlap. Persistence is a notion that captures, in some sense, the topology
of the shape underlying the input. While persistence is usually computed for the
union of balls, the k-fold cover is of interest as it captures local density,\r\nand
thus might approximate the shape of the input better if the input data is noisy.
To compute persistence of these k-fold covers, we need a discretization that is
provided by higher-order Delaunay mosaics. We present and implement a simple and
efficient algorithm for the computation of higher-order Delaunay mosaics, and
use it to give experimental results for their combinatorial properties. The algorithm
makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order
Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the
tiling, we also obtain higher-order α-shapes as slices. These allow us to compute
persistence of the multi-covers for varying radius r; the computation for varying
k is less straight-foward and involves the rhomboid tiling directly. We apply
our algorithms to experimental sphere packings to shed light on their structural
properties. Finally, inspired by periodic structures in packings and materials,
we propose and implement an algorithm for periodic Delaunay triangulations to
be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss
the implications on persistence for periodic data sets."
alternative_title:
- ISTA Thesis
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
citation:
ama: Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056
apa: Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute
of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056
chicago: Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute
of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056.
ieee: G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of
Science and Technology Austria, Klosterneuburg, 2021.
ista: 'Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg:
Institute of Science and Technology Austria.'
mla: Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute
of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.
short: G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science
and Technology Austria, 2021.
date_created: 2021-02-02T14:11:06Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-07T13:29:01Z
day: '01'
ddc:
- '006'
- '514'
- '516'
degree_awarded: PhD
department:
- _id: HeEd
- _id: GradSch
doi: 10.15479/AT:ISTA:9056
file:
- access_level: closed
checksum: bcf27986147cab0533b6abadd74e7629
content_type: application/zip
creator: patrickd
date_created: 2021-02-02T14:09:25Z
date_updated: 2021-02-03T10:37:28Z
file_id: '9063'
file_name: thesis_source.zip
file_size: 13446994
relation: source_file
- access_level: open_access
checksum: 9cc8af266579a464385bbe2aff6af606
content_type: application/pdf
creator: patrickd
date_created: 2021-02-02T14:09:18Z
date_updated: 2021-02-02T14:09:18Z
file_id: '9064'
file_name: thesis_pdfA2b.pdf
file_size: 5210329
relation: main_file
success: 1
file_date_updated: 2021-02-03T10:37:28Z
has_accepted_license: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '134'
place: Klosterneuburg
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '187'
relation: part_of_dissertation
status: public
- id: '8703'
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: Multi-cover persistence and Delaunay mosaics
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '10204'
abstract:
- lang: eng
text: Two common representations of close packings of identical spheres consisting
of hexagonal layers, called Barlow stackings, appear abundantly in minerals and
metals. These motifs, however, occupy an identical portion of space and bear identical
first-order topological signatures as measured by persistent homology. Here we
present a novel method based on k-fold covers that unambiguously distinguishes
between these patterns. Moreover, our approach provides topological evidence that
the FCC motif is the more stable of the two in the context of evolving experimental
sphere packings during the transition from disordered to an ordered state. We
conclude that our approach can be generalised to distinguish between various Barlow
stackings manifested in minerals and metals.
acknowledgement: MS acknowledges the support by Australian Research Council funding
through the ARC Training Centre for M3D Innovation (IC180100008). MS thanks M. Hanifpour
and N. Francois for their input and valuable discussions. This project has received
funding from the European Research Council (ERC) under the European Union's Horizon
2020 research and innovation programme, grant no. 788183 and from the Wittgenstein
Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.
article_processing_charge: No
article_type: original
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: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mohammad
full_name: Saadatfar, Mohammad
last_name: Saadatfar
citation:
ama: Osang GF, Edelsbrunner H, Saadatfar M. Topological signatures and stability
of hexagonal close packing and Barlow stackings. Soft Matter. 2021;17(40):9107-9115.
doi:10.1039/d1sm00774b
apa: Osang, G. F., Edelsbrunner, H., & Saadatfar, M. (2021). Topological signatures
and stability of hexagonal close packing and Barlow stackings. Soft Matter.
Royal Society of Chemistry . https://doi.org/10.1039/d1sm00774b
chicago: Osang, Georg F, Herbert Edelsbrunner, and Mohammad Saadatfar. “Topological
Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft
Matter. Royal Society of Chemistry , 2021. https://doi.org/10.1039/d1sm00774b.
ieee: G. F. Osang, H. Edelsbrunner, and M. Saadatfar, “Topological signatures and
stability of hexagonal close packing and Barlow stackings,” Soft Matter,
vol. 17, no. 40. Royal Society of Chemistry , pp. 9107–9115, 2021.
ista: Osang GF, Edelsbrunner H, Saadatfar M. 2021. Topological signatures and stability
of hexagonal close packing and Barlow stackings. Soft Matter. 17(40), 9107–9115.
mla: Osang, Georg F., et al. “Topological Signatures and Stability of Hexagonal
Close Packing and Barlow Stackings.” Soft Matter, vol. 17, no. 40, Royal
Society of Chemistry , 2021, pp. 9107–15, doi:10.1039/d1sm00774b.
short: G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.
date_created: 2021-10-31T23:01:30Z
date_published: 2021-10-20T00:00:00Z
date_updated: 2023-10-03T09:24:27Z
day: '20'
ddc:
- '540'
department:
- _id: HeEd
doi: 10.1039/d1sm00774b
ec_funded: 1
external_id:
isi:
- '000700090000001'
pmid:
- '34569592'
file:
- access_level: open_access
checksum: b4da0c420530295e61b153960f6cb350
content_type: application/pdf
creator: dernst
date_created: 2023-10-03T09:21:42Z
date_updated: 2023-10-03T09:21:42Z
file_id: '14385'
file_name: 2021_SoftMatter_acceptedversion_Osang.pdf
file_size: 4678788
relation: main_file
success: 1
file_date_updated: 2023-10-03T09:21:42Z
has_accepted_license: '1'
intvolume: ' 17'
isi: 1
issue: '40'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Submitted Version
page: 9107-9115
pmid: 1
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
publication: Soft Matter
publication_identifier:
eissn:
- 1744-6848
issn:
- 1744-683X
publication_status: published
publisher: 'Royal Society of Chemistry '
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological signatures and stability of hexagonal close packing and Barlow
stackings
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 17
year: '2021'
...
---
_id: '9605'
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: The authors want to thank the reviewers for many helpful comments
and suggestions.
alternative_title:
- LIPIcs
article_number: '27'
article_processing_charge: No
author:
- first_name: René
full_name: Corbet, René
last_name: Corbet
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- 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.
In: Leibniz International Proceedings in Informatics. Vol 189. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.27'
apa: 'Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2021). Computing
the multicover bifiltration. In Leibniz International Proceedings in Informatics
(Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.27'
chicago: Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing
the Multicover Bifiltration.” In Leibniz International Proceedings in Informatics,
Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.27.
ieee: R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover
bifiltration,” in Leibniz International Proceedings in Informatics, Online,
2021, vol. 189.
ista: 'Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration.
Leibniz International Proceedings in Informatics. SoCG: International Symposium
on Computational Geometry, LIPIcs, vol. 189, 27.'
mla: Corbet, René, et al. “Computing the Multicover Bifiltration.” Leibniz International
Proceedings in Informatics, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.27.
short: R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International
Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2021.
conference:
end_date: 2021-06-11
location: Online
name: 'SoCG: International Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-06-27T22:01:49Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-10-04T12:03:39Z
day: '02'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.27
external_id:
arxiv:
- '2103.07823'
file:
- access_level: open_access
checksum: 0de217501e7ba8b267d58deed0d51761
content_type: application/pdf
creator: cziletti
date_created: 2021-06-28T12:40:47Z
date_updated: 2021-06-28T12:40:47Z
file_id: '9610'
file_name: 2021_LIPIcs_Corbet.pdf
file_size: '1367983'
relation: main_file
success: 1
file_date_updated: 2021-06-28T12:40:47Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- '9783959771849'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
link:
- relation: extended_version
url: https://arxiv.org/abs/2103.07823
record:
- id: '12709'
relation: later_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: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9441'
abstract:
- lang: eng
text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension
and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate
multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension
of the manifold. A natural way to approximate a smooth isomanifold M is to consider
its Piecewise-Linear (PL) approximation M̂ based on a triangulation \U0001D4AF
of the ambient space ℝ^d. 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 (d^{2.5}), M̂
is O(D²)-close and isotopic to M, 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 M̂ 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: We thank Dominique Attali, Guilherme de Fonseca, Arijit Ghosh, Vincent
Pilaud and Aurélien Alvarez for their comments and suggestions. We also acknowledge
the reviewers.
alternative_title:
- LIPIcs
article_processing_charge: No
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 J-D, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in
time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In: 37th
International Symposium on Computational Geometry (SoCG 2021). Vol 189. Leibniz
International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2021:17:1-17:16. doi:10.4230/LIPIcs.SoCG.2021.17'
apa: 'Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Tracing
isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations.
In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol.
189, p. 17:1-17:16). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für
Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.17'
chicago: 'Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken.
“Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn
Triangulations.” In 37th International Symposium on Computational Geometry
(SoCG 2021), 189:17:1-17:16. Leibniz International Proceedings in Informatics
(LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.17.'
ieee: J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds
in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations,”
in 37th International Symposium on Computational Geometry (SoCG 2021),
Virtual, 2021, vol. 189, p. 17:1-17:16.
ista: 'Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Tracing isomanifolds
in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. 37th
International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium
on Computational GeometryLeibniz International Proceedings in Informatics (LIPIcs),
LIPIcs, vol. 189, 17:1-17:16.'
mla: Boissonnat, Jean-Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial
in d Using Coxeter-Freudenthal-Kuhn Triangulations.” 37th International Symposium
on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2021, p. 17:1-17:16, doi:10.4230/LIPIcs.SoCG.2021.17.
short: J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, in:, 37th International
Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, Dagstuhl, Germany, 2021, p. 17:1-17:16.
conference:
end_date: 2021-06-11
location: Virtual
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-06-02T10:10:55Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-10-10T07:34:34Z
day: '02'
ddc:
- '005'
- '516'
- '514'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.17
ec_funded: 1
file:
- access_level: open_access
checksum: c322aa48d5d35a35877896cc565705b6
content_type: application/pdf
creator: mwintrae
date_created: 2021-06-02T10:22:33Z
date_updated: 2021-06-02T10:22:33Z
file_id: '9442'
file_name: LIPIcs-SoCG-2021-17.pdf
file_size: 1972902
relation: main_file
success: 1
file_date_updated: 2021-06-02T10:22:33Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 17:1-17:16
place: Dagstuhl, Germany
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 37th International Symposium on Computational Geometry (SoCG 2021)
publication_identifier:
isbn:
- 978-3-95977-184-9
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '12960'
relation: later_version
status: public
series_title: Leibniz International Proceedings in Informatics (LIPIcs)
status: public
title: Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn
triangulations
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: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '8338'
abstract:
- lang: eng
text: Canonical parametrisations of classical confocal coordinate systems are introduced
and exploited to construct non-planar analogues of incircular (IC) nets on individual
quadrics and systems of confocal quadrics. Intimate connections with classical
deformations of quadrics that are isometric along asymptotic lines and circular
cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces
of Blaschke type generated by asymptotic and characteristic lines that are diagonally
related to lines of curvature is proved theoretically and established constructively.
Appropriate samplings (grids) of these webs lead to three-dimensional extensions
of non-planar IC nets. Three-dimensional octahedral grids composed of planes and
spatially extending (checkerboard) IC-nets are shown to arise in connection with
systems of confocal quadrics in Minkowski space. In this context, the Laguerre
geometric notion of conical octahedral grids of planes is introduced. The latter
generalise the octahedral grids derived from systems of confocal quadrics in Minkowski
space. An explicit construction of conical octahedral grids is presented. The
results are accompanied by various illustrations which are based on the explicit
formulae provided by the theory.
acknowledgement: This research was supported by the DFG Collaborative Research Center
TRR 109 “Discretization in Geometry and Dynamics”. W.K.S. was also supported by
the Australian Research Council (DP1401000851). A.V.A. was also supported by the
European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (Grant Agreement No. 78818 Alpha).
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: Alexander I.
full_name: Bobenko, Alexander I.
last_name: Bobenko
- first_name: Wolfgang K.
full_name: Schief, Wolfgang K.
last_name: Schief
- first_name: Jan
full_name: Techter, Jan
last_name: Techter
citation:
ama: Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal)
quadrics and 3-dimensional webs. Discrete and Computational Geometry. 2021;66:938-976.
doi:10.1007/s00454-020-00240-w
apa: Akopyan, A., Bobenko, A. I., Schief, W. K., & Techter, J. (2021). On mutually
diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational
Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00240-w
chicago: Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter.
“On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete
and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00240-w.
ieee: A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal
nets on (confocal) quadrics and 3-dimensional webs,” Discrete and Computational
Geometry, vol. 66. Springer Nature, pp. 938–976, 2021.
ista: Akopyan A, Bobenko AI, Schief WK, Techter J. 2021. On mutually diagonal nets
on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry.
66, 938–976.
mla: Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics
and 3-Dimensional Webs.” Discrete and Computational Geometry, vol. 66,
Springer Nature, 2021, pp. 938–76, doi:10.1007/s00454-020-00240-w.
short: A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational
Geometry 66 (2021) 938–976.
date_created: 2020-09-06T22:01:13Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2024-03-07T14:51:11Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00240-w
ec_funded: 1
external_id:
arxiv:
- '1908.00856'
isi:
- '000564488500002'
intvolume: ' 66'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1908.00856
month: '10'
oa: 1
oa_version: Preprint
page: 938-976
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
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: On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 66
year: '2021'
...
---
_id: '8248'
abstract:
- lang: eng
text: 'We consider the following setting: suppose that we are given a manifold M
in Rd with positive reach. Moreover assume that we have an embedded simplical
complex A without boundary, whose vertex set lies on the manifold, is sufficiently
dense and such that all simplices in A have sufficient quality. We prove that
if, locally, interiors of the projection of the simplices onto the tangent space
do not intersect, then A is a triangulation of the manifold, that is, they are
homeomorphic.'
acknowledgement: "Open access funding provided by the Institute of Science and Technology
(IST Austria). Arijit Ghosh is supported by the Ramanujan Fellowship (No. SB/S2/RJN-064/2015),
India.\r\nThis work has been funded by the European Research Council under the European
Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric
Understanding in Higher Dimensions). The third author is supported by Ramanujan
Fellowship (No. SB/S2/RJN-064/2015), India. The fifth author also received funding
from the European Union’s Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie Grant Agreement No. 754411."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- first_name: Ramsay
full_name: Dyer, Ramsay
last_name: Dyer
- first_name: Arijit
full_name: Ghosh, Arijit
last_name: Ghosh
- first_name: Andre
full_name: Lieutier, Andre
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, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions
for triangulating submanifolds of Euclidean space. Discrete and Computational
Geometry. 2021;66:666-686. doi:10.1007/s00454-020-00233-9
apa: Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., & Wintraecken, M.
(2021). Local conditions for triangulating submanifolds of Euclidean space. Discrete
and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00233-9
chicago: Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and
Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean
Space.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00233-9.
ieee: J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local
conditions for triangulating submanifolds of Euclidean space,” Discrete and
Computational Geometry, vol. 66. Springer Nature, pp. 666–686, 2021.
ista: Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. 2021. Local conditions
for triangulating submanifolds of Euclidean space. Discrete and Computational
Geometry. 66, 666–686.
mla: Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds
of Euclidean Space.” Discrete and Computational Geometry, vol. 66, Springer
Nature, 2021, pp. 666–86, doi:10.1007/s00454-020-00233-9.
short: J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete
and Computational Geometry 66 (2021) 666–686.
date_created: 2020-08-11T07:11:51Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2024-03-07T14:54:59Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00233-9
ec_funded: 1
external_id:
isi:
- '000558119300001'
has_accepted_license: '1'
intvolume: ' 66'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-020-00233-9
month: '09'
oa: 1
oa_version: Published Version
page: 666-686
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Local conditions for triangulating submanifolds of Euclidean 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: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 66
year: '2021'
...
---
_id: '7905'
abstract:
- lang: eng
text: We investigate a sheaf-theoretic interpretation of stratification learning
from geometric and topological perspectives. Our main result is the construction
of stratification learning algorithms framed in terms of a sheaf on a partially
ordered set with the Alexandroff topology. We prove that the resulting decomposition
is the unique minimal stratification for which the strata are homogeneous and
the given sheaf is constructible. In particular, when we choose to work with the
local homology sheaf, our algorithm gives an alternative to the local homology
transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM
Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the
cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2),
195–222, 2020). Additionally, we give examples of stratifications based on the
geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018),
illustrating how the sheaf-theoretic approach can be used to study stratifications
from both topological and geometric perspectives. This approach also points toward
future applications of sheaf theory in the study of topological data analysis
by illustrating the utility of the language of sheaf theory in generalizing existing
algorithms.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). This work was partially supported by NSF IIS-1513616 and NSF ABI-1661375.
The authors would like to thank the anonymous referees for their insightful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Bei
full_name: Wang, Bei
last_name: Wang
citation:
ama: Brown A, Wang B. Sheaf-theoretic stratification learning from geometric and
topological perspectives. Discrete and Computational Geometry. 2021;65:1166-1198.
doi:10.1007/s00454-020-00206-y
apa: Brown, A., & Wang, B. (2021). Sheaf-theoretic stratification learning from
geometric and topological perspectives. Discrete and Computational Geometry.
Springer Nature. https://doi.org/10.1007/s00454-020-00206-y
chicago: Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from
Geometric and Topological Perspectives.” Discrete and Computational Geometry.
Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00206-y.
ieee: A. Brown and B. Wang, “Sheaf-theoretic stratification learning from geometric
and topological perspectives,” Discrete and Computational Geometry, vol.
65. Springer Nature, pp. 1166–1198, 2021.
ista: Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric
and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198.
mla: Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric
and Topological Perspectives.” Discrete and Computational Geometry, vol.
65, Springer Nature, 2021, pp. 1166–98, doi:10.1007/s00454-020-00206-y.
short: A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.
date_created: 2020-05-30T10:26:04Z
date_published: 2021-06-01T00:00:00Z
date_updated: 2024-03-07T15:01:58Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00206-y
external_id:
arxiv:
- '1712.07734'
isi:
- '000536324700001'
file:
- access_level: open_access
checksum: 487a84ea5841b75f04f66d7ebd71b67e
content_type: application/pdf
creator: dernst
date_created: 2020-11-25T09:06:41Z
date_updated: 2020-11-25T09:06:41Z
file_id: '8803'
file_name: 2020_DiscreteCompGeometry_Brown.pdf
file_size: 1013730
relation: main_file
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intvolume: ' 65'
isi: 1
language:
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oa: 1
oa_version: Published Version
page: 1166-1198
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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: Sheaf-theoretic stratification learning from geometric and topological perspectives
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: 65
year: '2021'
...
---
_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.
date_created: 2020-03-05T13:30:18Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2021-01-12T08:14:13Z
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
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: 14
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
- first_name: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
- 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: 2021-01-12T08:17:06Z
day: '22'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/978-3-030-43408-3_8
ec_funded: 1
file:
- access_level: open_access
checksum: 7b5e0de10675d787a2ddb2091370b8d8
content_type: application/pdf
creator: dernst
date_created: 2020-10-08T08:56:14Z
date_updated: 2020-10-08T08:56:14Z
file_id: '8628'
file_name: 2020-B-01-PoissonExperimentalSurvey.pdf
file_size: 2207071
relation: main_file
success: 1
file_date_updated: 2020-10-08T08:56:14Z
has_accepted_license: '1'
intvolume: ' 15'
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: 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:
- '21978549'
isbn:
- '9783030434076'
issn:
- '21932808'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Radius functions on Poisson–Delaunay mosaics and related complexes experimentally
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
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.
date_created: 2021-03-16T08:55:19Z
date_published: 2020-11-17T00:00:00Z
date_updated: 2021-03-22T09:01:50Z
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
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: 2021-04-06T11:32:32Z
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: The Wittgenstein Prize
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: '9630'
abstract:
- lang: eng
text: Various kinds of data are routinely represented as discrete probability distributions.
Examples include text documents summarized by histograms of word occurrences and
images represented as histograms of oriented gradients. Viewing a discrete probability
distribution as a point in the standard simplex of the appropriate dimension,
we can understand collections of such objects in geometric and topological terms. Importantly,
instead of using the standard Euclidean distance, we look into dissimilarity measures
with information-theoretic justification, and we develop the theory needed for
applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable the usage of existing computational topology software
in this context.
acknowledgement: This research is partially supported by the Office of Naval Research,
through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
the Austrian Science Fund (FWF).
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
space. 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.
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2021-08-11T12:26:34Z
day: '14'
ddc:
- '510'
- '000'
department:
- _id: HeEd
doi: 10.20382/jocg.v11i2a7
file:
- access_level: open_access
checksum: f02d0b2b3838e7891a6c417fc34ffdcd
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intvolume: ' 11'
issue: '2'
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month: '12'
oa: 1
oa_version: Published Version
page: 162-182
project:
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
publication: Journal of Computational Geometry
publication_identifier:
eissn:
- 1920180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological data analysis in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 11
year: '2020'
...
---
_id: '8538'
abstract:
- lang: eng
text: We prove some recent experimental observations of Dan Reznik concerning periodic
billiard orbits in ellipses. For example, the sum of cosines of the angles of
a periodic billiard polygon remains constant in the 1-parameter family of such
polygons (that exist due to the Poncelet porism). In our proofs, we use geometric
and complex analytic methods.
acknowledgement: " This paper would not be written if not for Dan Reznik’s curiosity
and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller
for interesting discussions. It is a pleasure to thank the Mathematical Institute
of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy
for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality.
AA was supported by European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported
by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR
191."
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Richard
full_name: Schwartz, Richard
last_name: Schwartz
- first_name: Serge
full_name: Tabachnikov, Serge
last_name: Tabachnikov
citation:
ama: Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. European
Journal of Mathematics. 2020. doi:10.1007/s40879-020-00426-9
apa: Akopyan, A., Schwartz, R., & Tabachnikov, S. (2020). Billiards in ellipses
revisited. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00426-9
chicago: Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in
Ellipses Revisited.” European Journal of Mathematics. Springer Nature,
2020. https://doi.org/10.1007/s40879-020-00426-9.
ieee: A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,”
European Journal of Mathematics. Springer Nature, 2020.
ista: Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited.
European Journal of Mathematics.
mla: Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal
of Mathematics, Springer Nature, 2020, doi:10.1007/s40879-020-00426-9.
short: A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics
(2020).
date_created: 2020-09-20T22:01:38Z
date_published: 2020-09-09T00:00:00Z
date_updated: 2021-12-02T15:10:17Z
day: '09'
department:
- _id: HeEd
doi: 10.1007/s40879-020-00426-9
ec_funded: 1
external_id:
arxiv:
- '2001.02934'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2001.02934
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Billiards in ellipses revisited
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2020'
...
---
_id: '7952'
abstract:
- lang: eng
text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension
and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued
smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate
an isomanifold is to consider its Piecewise-Linear (PL) approximation based on
a triangulation \U0001D4AF of the ambient space ℝ^d. In this paper, we give conditions
under which the PL-approximation of an isomanifold is topologically equivalent
to the isomanifold. The conditions are easy to satisfy in the sense that they
can always be met by taking a sufficiently fine triangulation \U0001D4AF. This
contrasts with previous results on the triangulation of manifolds where, in arbitrary
dimensions, delicate perturbations are needed to guarantee topological correctness,
which leads to strong limitations in practice. We further give a bound on the
Fréchet distance between the original isomanifold and its PL-approximation. Finally
we show analogous results for the PL-approximation of an isomanifold with boundary. "
alternative_title:
- LIPIcs
article_number: 20:1-20:18
article_processing_charge: No
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations
of isomanifolds. In: 36th International Symposium on Computational Geometry.
Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.20'
apa: 'Boissonnat, J.-D., & Wintraecken, M. (2020). The topological correctness
of PL-approximations of isomanifolds. In 36th International Symposium on Computational
Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.20'
chicago: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
of PL-Approximations of Isomanifolds.” In 36th International Symposium on Computational
Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
https://doi.org/10.4230/LIPIcs.SoCG.2020.20.
ieee: J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations
of isomanifolds,” in 36th International Symposium on Computational Geometry,
Zürich, Switzerland, 2020, vol. 164.
ista: 'Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations
of isomanifolds. 36th International Symposium on Computational Geometry. SoCG:
Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18.'
mla: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
of PL-Approximations of Isomanifolds.” 36th International Symposium on Computational
Geometry, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2020, doi:10.4230/LIPIcs.SoCG.2020.20.
short: J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
conference:
end_date: 2020-06-26
location: Zürich, Switzerland
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2020-06-22
date_created: 2020-06-09T07:24:11Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-02T06:49:16Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2020.20
ec_funded: 1
file:
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creator: dernst
date_created: 2020-06-17T10:13:34Z
date_updated: 2020-07-14T12:48:06Z
file_id: '7969'
file_name: 2020_LIPIcsSoCG_Boissonnat.pdf
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file_date_updated: 2020-07-14T12:48:06Z
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intvolume: ' 164'
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month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 36th International Symposium on Computational Geometry
publication_identifier:
isbn:
- 978-3-95977-143-6
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
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relation: later_version
status: public
scopus_import: '1'
status: public
title: The topological correctness of PL-approximations of isomanifolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 164
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
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: 2023-08-17T13:48:31Z
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:
- '16179692'
isbn:
- '9783030360191'
issn:
- '00758434'
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
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
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: 2023-08-18T06:45:48Z
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:
- '10957219'
issn:
- 0040585X
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weighted Poisson–Delaunay mosaics
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2020'
...
---
_id: '7666'
abstract:
- lang: eng
text: Generalizing the decomposition of a connected planar graph into a tree and
a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition
of a smooth vector field. Specifically, we show that for every polyhedral complex,
K, and every dimension, p, there is a partition of the set of p-cells into a maximal
p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the
p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition
is unique, and it can be computed by a matrix reduction algorithm that also constructs
canonical bases of cycle and boundary groups.
acknowledgement: This project has received funding from the European Research Council
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: 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: Katharina
full_name: Ölsböck, Katharina
id: 4D4AA390-F248-11E8-B48F-1D18A9856A87
last_name: Ölsböck
orcid: 0000-0002-4672-8297
citation:
ama: Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex.
Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x
apa: Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an
ordered complex. Discrete and Computational Geometry. Springer Nature.
https://doi.org/10.1007/s00454-020-00188-x
chicago: Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases
of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature,
2020. https://doi.org/10.1007/s00454-020-00188-x.
ieee: H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,”
Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775,
2020.
ista: Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex.
Discrete and Computational Geometry. 64, 759–775.
mla: Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of
an Ordered Complex.” Discrete and Computational Geometry, vol. 64, Springer
Nature, 2020, pp. 759–75, doi:10.1007/s00454-020-00188-x.
short: H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020)
759–775.
date_created: 2020-04-19T22:00:56Z
date_published: 2020-03-20T00:00:00Z
date_updated: 2023-08-21T06:13:48Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00188-x
ec_funded: 1
external_id:
isi:
- '000520918800001'
file:
- access_level: open_access
checksum: f8cc96e497f00c38340b5dafe0cb91d7
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T13:22:21Z
date_updated: 2020-11-20T13:22:21Z
file_id: '8786'
file_name: 2020_DiscreteCompGeo_Edelsbrunner.pdf
file_size: 701673
relation: main_file
success: 1
file_date_updated: 2020-11-20T13:22:21Z
has_accepted_license: '1'
intvolume: ' 64'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 759-775
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _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: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tri-partitions and bases of an ordered complex
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2020'
...
---
_id: '7962'
abstract:
- lang: eng
text: 'A string graph is the intersection graph of a family of continuous arcs in
the plane. The intersection graph of a family of plane convex sets is a string
graph, but not all string graphs can be obtained in this way. We prove the following
structure theorem conjectured by Janson and Uzzell: The vertex set of almost all
string graphs on n vertices can be partitioned into five cliques such that some
pair of them is not connected by any edge (n→∞). We also show that every graph
with the above property is an intersection graph of plane convex sets. As a corollary,
we obtain that almost all string graphs on n vertices are intersection graphs
of plane convex sets.'
article_processing_charge: No
article_type: original
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Bruce
full_name: Reed, Bruce
last_name: Reed
- first_name: Yelena
full_name: Yuditsky, Yelena
last_name: Yuditsky
citation:
ama: Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs
of plane convex sets. Discrete and Computational Geometry. 2020;63(4):888-917.
doi:10.1007/s00454-020-00213-z
apa: Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are
intersection graphs of plane convex sets. Discrete and Computational Geometry.
Springer Nature. https://doi.org/10.1007/s00454-020-00213-z
chicago: Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs
Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry.
Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z.
ieee: J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection
graphs of plane convex sets,” Discrete and Computational Geometry, vol.
63, no. 4. Springer Nature, pp. 888–917, 2020.
ista: Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection
graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917.
mla: Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane
Convex Sets.” Discrete and Computational Geometry, vol. 63, no. 4, Springer
Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z.
short: J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020)
888–917.
date_created: 2020-06-14T22:00:51Z
date_published: 2020-06-05T00:00:00Z
date_updated: 2023-08-21T08:49:18Z
day: '05'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00213-z
external_id:
arxiv:
- '1803.06710'
isi:
- '000538229000001'
intvolume: ' 63'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1803.06710
month: '06'
oa: 1
oa_version: Preprint
page: 888-917
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Almost all string graphs are intersection graphs of plane convex sets
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2020'
...
---
_id: '8323'
article_processing_charge: No
article_type: letter_note
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
citation:
ama: Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry.
2020;64:571-574. doi:10.1007/s00454-020-00237-5
apa: Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational
Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5
chicago: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational
Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5.
ieee: J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry,
vol. 64. Springer Nature, pp. 571–574, 2020.
ista: Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry.
64, 571–574.
mla: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry,
vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5.
short: J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.
date_created: 2020-08-30T22:01:12Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2023-08-22T09:05:04Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00237-5
external_id:
isi:
- '000561483500001'
intvolume: ' 64'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-020-00237-5
month: '10'
oa: 1
oa_version: None
page: 571-574
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer Nature
scopus_import: '1'
status: public
title: A farewell to Ricky Pollack
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2020'
...
---
_id: '8580'
abstract:
- lang: eng
text: We evaluate the usefulness of persistent homology in the analysis of heart
rate variability. In our approach we extract several topological descriptors characterising
datasets of RR-intervals, which are later used in classical machine learning algorithms.
By this method we are able to differentiate the group of patients with the history
of transient ischemic attack and the group of hypertensive patients.
article_number: '9158054'
article_processing_charge: No
author:
- first_name: Grzegorz
full_name: Graff, Grzegorz
last_name: Graff
- first_name: Beata
full_name: Graff, Beata
last_name: Graff
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: Krzysztof
full_name: Narkiewicz, Krzysztof
last_name: Narkiewicz
citation:
ama: 'Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent
homology in the analysis of heart rate variability. In: 11th Conference of
the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054'
apa: 'Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application
of persistent homology in the analysis of heart rate variability. In 11th Conference
of the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054'
chicago: 'Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz.
“The Application of Persistent Homology in the Analysis of Heart Rate Variability.”
In 11th Conference of the European Study Group on Cardiovascular Oscillations:
Computation and Modelling in Physiology: New Challenges and Opportunities, .
IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054.'
ieee: 'G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of
persistent homology in the analysis of heart rate variability,” in 11th Conference
of the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.'
ista: 'Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent
homology in the analysis of heart rate variability. 11th Conference of the European
Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology:
New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular
Oscillations, 9158054.'
mla: 'Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis
of Heart Rate Variability.” 11th Conference of the European Study Group on
Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges
and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.'
short: 'G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of
the European Study Group on Cardiovascular Oscillations: Computation and Modelling
in Physiology: New Challenges and Opportunities, , IEEE, 2020.'
conference:
end_date: 2020-07-15
location: Pisa, Italy
name: 'ESGCO: European Study Group on Cardiovascular Oscillations'
start_date: 2020-07-15
date_created: 2020-09-28T08:59:27Z
date_published: 2020-08-01T00:00:00Z
date_updated: 2023-08-22T09:33:34Z
day: '01'
department:
- _id: HeEd
doi: 10.1109/ESGCO49734.2020.9158054
external_id:
isi:
- '000621172600045'
isi: 1
language:
- iso: eng
month: '08'
oa_version: None
publication: '11th Conference of the European Study Group on Cardiovascular Oscillations:
Computation and Modelling in Physiology: New Challenges and Opportunities, '
publication_identifier:
isbn:
- '9781728157511'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: The application of persistent homology in the analysis of heart rate variability
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2020'
...
---
_id: '10867'
abstract:
- lang: eng
text: In this paper we find a tight estimate for Gromov’s waist of the balls in
spaces of constant curvature, deduce the estimates for the balls in Riemannian
manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar
result for normed spaces.
acknowledgement: ' Supported by the Russian Foundation for Basic Research grant 18-01-00036.'
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: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International
Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037
apa: Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical
spaces. International Mathematics Research Notices. Oxford University Press.
https://doi.org/10.1093/imrn/rny037
chicago: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and
Spherical Spaces.” International Mathematics Research Notices. Oxford University
Press, 2020. https://doi.org/10.1093/imrn/rny037.
ieee: A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,”
International Mathematics Research Notices, vol. 2020, no. 3. Oxford University
Press, pp. 669–697, 2020.
ista: Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces.
International Mathematics Research Notices. 2020(3), 669–697.
mla: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical
Spaces.” International Mathematics Research Notices, vol. 2020, no. 3,
Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.
short: A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020)
669–697.
date_created: 2022-03-18T11:39:30Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2023-08-24T14:19:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/imrn/rny037
external_id:
arxiv:
- '1702.07513'
isi:
- '000522852700002'
intvolume: ' 2020'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.07513
month: '02'
oa: 1
oa_version: Preprint
page: 669-697
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Waist of balls in hyperbolic and spherical spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2020
year: '2020'
...
---
_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.
date_created: 2020-02-06T14:56:53Z
date_published: 2020-02-10T00:00:00Z
date_updated: 2023-09-07T13:15:30Z
day: '10'
ddc:
- '514'
degree_awarded: PhD
department:
- _id: HeEd
- _id: GradSch
doi: 10.15479/AT:ISTA:7460
file:
- access_level: open_access
checksum: 1df9f8c530b443c0e63a3f2e4fde412e
content_type: application/pdf
creator: koelsboe
date_created: 2020-02-06T14:43:54Z
date_updated: 2020-07-14T12:47:58Z
file_id: '7461'
file_name: thesis_ist-final_noack.pdf
file_size: 76195184
relation: main_file
- access_level: closed
checksum: 7a52383c812b0be64d3826546509e5a4
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
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2020'
...
---
_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.
date_created: 2020-06-08T00:49:46Z
date_published: 2020-06-09T00:00:00Z
date_updated: 2023-09-07T13:17:37Z
day: '09'
ddc:
- '516'
- '514'
degree_awarded: PhD
department:
- _id: HeEd
- _id: UlWa
doi: 10.15479/AT:ISTA:7944
file:
- access_level: open_access
checksum: df688bc5a82b50baee0b99d25fc7b7f0
content_type: application/pdf
creator: zmasarov
date_created: 2020-06-08T00:34:00Z
date_updated: 2020-07-14T12:48:05Z
file_id: '7945'
file_name: THESIS_Zuzka_Masarova.pdf
file_size: 13661779
relation: main_file
- access_level: closed
checksum: 45341a35b8f5529c74010b7af43ac188
content_type: application/zip
creator: zmasarov
date_created: 2020-06-08T00:35:30Z
date_updated: 2020-07-14T12:48:05Z
file_id: '7946'
file_name: THESIS_Zuzka_Masarova_SOURCE_FILES.zip
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
name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC
BY-SA 4.0)
short: CC BY-SA (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
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: Annual 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: Annual European Symposium on Algorithms'
start_date: 2020-09-07
date_created: 2020-10-25T23:01:18Z
date_published: 2020-08-26T00:00:00Z
date_updated: 2023-09-07T13:29:00Z
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publication: 28th Annual European Symposium on Algorithms
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publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
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status: public
title: Generalizing CGAL periodic Delaunay triangulations
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...
---
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abstract:
- lang: eng
text: Fejes Tóth [3] studied approximations of smooth surfaces in three-space by
piecewise flat triangular meshes with a given number of vertices on the surface
that are optimal with respect to Hausdorff distance. He proves that this Hausdorff
distance decreases inversely proportional with the number of vertices of the approximating
mesh if the surface is convex. He also claims that this Hausdorff distance is
inversely proportional to the square of the number of vertices for a specific
non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by
two congruent circles. We refute this claim, and show that the asymptotic behavior
of the Hausdorff distance is linear, that is the same as for convex surfaces.
acknowledgement: "The authors are greatly indebted to Dror Atariah, Günther Rote and
John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel
Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion.
This work has been supported in part by the European Union’s Seventh Framework Programme
for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL
Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic
Foundations of Geometry Understanding in Higher Dimensions), the European Union’s
Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie
grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31."
article_processing_charge: No
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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. Refutation of a claim made by Fejes Tóth on the accuracy
of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199.
doi:10.1556/012.2020.57.2.1454
apa: Vegter, G., & Wintraecken, M. (2020). Refutation of a claim made by Fejes
Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica.
Akadémiai Kiadó. https://doi.org/10.1556/012.2020.57.2.1454
chicago: Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes
Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum
Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454.
ieee: G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on
the accuracy of surface meshes,” Studia Scientiarum Mathematicarum Hungarica,
vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.
ista: Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on
the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2),
193–199.
mla: Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes
Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum
Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454.
short: G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57
(2020) 193–199.
date_created: 2020-07-24T07:09:18Z
date_published: 2020-07-24T00:00:00Z
date_updated: 2023-10-10T13:05:27Z
day: '24'
ddc:
- '510'
department:
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doi: 10.1556/012.2020.57.2.1454
ec_funded: 1
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isi:
- '000570978400005'
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issue: '2'
language:
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month: '07'
oa: 1
oa_version: Published Version
page: 193-199
project:
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call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Studia Scientiarum Mathematicarum Hungarica
publication_identifier:
eissn:
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issn:
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publication_status: published
publisher: Akadémiai Kiadó
quality_controlled: '1'
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title: Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes
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type: journal_article
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...
---
_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.
date_created: 2021-02-17T15:13:01Z
date_published: 2020-06-20T00:00:00Z
date_updated: 2023-10-17T12:34:51Z
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
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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
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year: '2020'
...
---
_id: '9156'
abstract:
- lang: eng
text: The morphometric approach [11, 14] writes the solvation free energy 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 Gaussian curvature. Together with the derivatives of the weighted
volume in [7], the weighted area in [4], and the weighted mean curvature in [1],
this yields the derivative of the morphometric expression of solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics
simulations. 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 Gaussian curvature derivative of a
space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88.
doi:10.1515/cmb-2020-0101
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature
derivative of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0101
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative
of a space-filling diagram,” Computational and Mathematical Biophysics,
vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 74–88.
date_created: 2021-02-17T15:12:44Z
date_published: 2020-07-21T00:00:00Z
date_updated: 2023-10-17T12:35:10Z
day: '21'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0101
ec_funded: 1
external_id:
arxiv:
- '1908.06777'
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oa_version: Published Version
page: 74-88
project:
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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 Gaussian 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: '15064'
abstract:
- lang: eng
text: We call a continuous self-map that reveals itself through a discrete set of
point-value pairs a sampled dynamical system. Capturing the available information
with chain maps on Delaunay complexes, we use persistent homology to quantify
the evidence of recurrent behavior. We establish a sampling theorem to recover
the eigenspaces of the endomorphism on homology induced by the self-map. Using
a combinatorial gradient flow arising from the discrete Morse theory for Čech
and Delaunay complexes, we construct a chain map to transform the problem from
the natural but expensive Čech complexes to the computationally efficient Delaunay
triangulations. The fast chain map algorithm has applications beyond dynamical
systems.
acknowledgement: This research has been supported by the DFG Collaborative Research
Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant
No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant
No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding
provided by Projekt DEAL.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: U.
full_name: Bauer, U.
last_name: Bauer
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: M.
full_name: Mrozek, M.
last_name: Mrozek
citation:
ama: Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow
and homology inference for self-maps. Journal of Applied and Computational
Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8
apa: Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay
gradient flow and homology inference for self-maps. Journal of Applied and
Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8
chicago: Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay
Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and
Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8.
ieee: U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient
flow and homology inference for self-maps,” Journal of Applied and Computational
Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.
ista: Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient
flow and homology inference for self-maps. Journal of Applied and Computational
Topology. 4(4), 455–480.
mla: Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.”
Journal of Applied and Computational Topology, vol. 4, no. 4, Springer
Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8.
short: U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and
Computational Topology 4 (2020) 455–480.
date_created: 2024-03-04T10:47:49Z
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- '500'
department:
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doi: 10.1007/s41468-020-00058-8
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checksum: eed1168b6e66cd55272c19bb7fca8a1c
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creator: dernst
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date_updated: 2024-03-04T10:52:42Z
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has_accepted_license: '1'
intvolume: ' 4'
issue: '4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 455-480
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: Čech-Delaunay gradient flow and homology inference for self-maps
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...