---
_id: '6050'
abstract:
- lang: eng
text: 'We answer a question of David Hilbert: given two circles it is not possible
in general to construct their centers using only a straightedge. On the other
hand, we give infinitely many families of pairs of circles for which such construction
is possible. '
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Fedorov, Roman
last_name: Fedorov
citation:
ama: Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of
the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240
apa: Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge.
Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240
chicago: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.”
Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240.
ieee: A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings
of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.
ista: Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings
of the American Mathematical Society. 147, 91–102.
mla: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.”
Proceedings of the American Mathematical Society, vol. 147, AMS, 2019,
pp. 91–102, doi:10.1090/proc/14240.
short: A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society
147 (2019) 91–102.
date_created: 2019-02-24T22:59:19Z
date_published: 2019-01-01T00:00:00Z
date_updated: 2023-08-24T14:48:59Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/14240
external_id:
arxiv:
- '1709.02562'
isi:
- '000450363900008'
intvolume: ' 147'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1709.02562
month: '01'
oa: 1
oa_version: Preprint
page: 91-102
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: AMS
quality_controlled: '1'
scopus_import: '1'
status: public
title: Two circles and only a straightedge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 147
year: '2019'
...
---
_id: '6634'
abstract:
- lang: eng
text: In this paper we prove several new results around Gromov's waist theorem.
We give a simple proof of Vaaler's theorem on sections of the unit cube using
the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective
spaces, flat tori, convex bodies in Euclidean space; and establish waist-type
results in terms of the Hausdorff measure.
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alfredo
full_name: Hubard, Alfredo
last_name: Hubard
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different
spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490.
doi:10.12775/TMNA.2019.008
apa: Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for
the waists of different spaces. Topological Methods in Nonlinear Analysis.
Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008
chicago: Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds
for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis.
Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008.
ieee: A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists
of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53,
no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.
ista: Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists
of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.
mla: Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different
Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka
Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008.
short: A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis
53 (2019) 457–490.
date_created: 2019-07-14T21:59:19Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-08-29T06:32:48Z
day: '01'
department:
- _id: HeEd
doi: 10.12775/TMNA.2019.008
ec_funded: 1
external_id:
arxiv:
- '1612.06926'
isi:
- '000472541600004'
intvolume: ' 53'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.06926
month: '06'
oa: 1
oa_version: Preprint
page: 457-490
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Topological Methods in Nonlinear Analysis
publication_status: published
publisher: Akademicka Platforma Czasopism
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower and upper bounds for the waists of different spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2019'
...
---
_id: '6756'
abstract:
- lang: eng
text: "We study the topology generated by the temperature fluctuations of the cosmic
microwave background (CMB) radiation, as quantified by the number of components
and holes, formally given by the Betti numbers, in the growing excursion sets.
We compare CMB maps observed by the Planck satellite with a thousand simulated
maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations.
The comparison is multi-scale, being performed on a sequence of degraded maps
with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over
\U0001D54A2 is incomplete due to obfuscation effects by bright point sources and
other extended foreground objects like our own galaxy. To deal with such situations,
where analysis in the presence of “masks” is of importance, we introduce the concept
of relative homology. The parametric χ2-test shows differences between observations
and simulations, yielding p-values at percent to less than permil levels roughly
between 2 and 7°, with the difference in the number of components and holes peaking
at more than 3σ sporadically at these scales. The highest observed deviation between
the observations and simulations for b0 and b1 is approximately between 3σ and
4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler
characteristic at 3.66° in the literature, computed from independent measurements
of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave
Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler
characteristic is phenomenologically related to the strongly anomalous behaviour
of components and holes, or the zeroth and first Betti numbers, respectively.
Further, since these topological descriptors show consistent anomalous behaviour
over independent measurements of Planck and WMAP, instrumental and systematic
errors may be an unlikely source. These are also the scales at which the observed
maps exhibit low variance compared to the simulations, and approximately the range
of scales at which the power spectrum exhibits a dip with respect to the theoretical
model. Non-parametric tests show even stronger differences at almost all scales.
Crucially, Gaussian simulations based on power-spectrum matching the characteristics
of the observed dipped power spectrum are not able to resolve the anomaly. Understanding
the origin of the anomalies in the CMB, whether cosmological in nature or arising
due to late-time effects, is an extremely challenging task. Regardless, beyond
the trivial possibility that this may still be a manifestation of an extreme Gaussian
case, these observations, along with the super-horizon scales involved, may motivate
the study of primordial non-Gaussianity. Alternative scenarios worth exploring
may be models with non-trivial topology, including topological defect models."
article_number: A163
article_processing_charge: No
article_type: original
author:
- first_name: Pratyush
full_name: Pranav, Pratyush
last_name: Pranav
- first_name: Robert J.
full_name: Adler, Robert J.
last_name: Adler
- first_name: Thomas
full_name: Buchert, Thomas
last_name: Buchert
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Bernard J.T.
full_name: Jones, Bernard J.T.
last_name: Jones
- first_name: Armin
full_name: Schwartzman, Armin
last_name: Schwartzman
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
- first_name: Rien
full_name: Van De Weygaert, Rien
last_name: Van De Weygaert
citation:
ama: Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature
fluctuations in the cosmic microwave background. Astronomy and Astrophysics.
2019;627. doi:10.1051/0004-6361/201834916
apa: Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman,
A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations
in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences.
https://doi.org/10.1051/0004-6361/201834916
chicago: Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner,
Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert.
“Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.”
Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916.
ieee: P. Pranav et al., “Unexpected topology of the temperature fluctuations
in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627.
EDP Sciences, 2019.
ista: Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner
H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations
in the cosmic microwave background. Astronomy and Astrophysics. 627, A163.
mla: Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations
in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627,
A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916.
short: P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman,
H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).
date_created: 2019-08-04T21:59:18Z
date_published: 2019-07-17T00:00:00Z
date_updated: 2023-08-29T07:01:48Z
day: '17'
ddc:
- '520'
- '530'
department:
- _id: HeEd
doi: 10.1051/0004-6361/201834916
external_id:
arxiv:
- '1812.07678'
isi:
- '000475839300003'
file:
- access_level: open_access
checksum: 83b9209ed9eefbdcefd89019c5a97805
content_type: application/pdf
creator: dernst
date_created: 2019-08-05T08:08:59Z
date_updated: 2020-07-14T12:47:39Z
file_id: '6766'
file_name: 2019_AstronomyAstrophysics_Pranav.pdf
file_size: 14420451
relation: main_file
file_date_updated: 2020-07-14T12:47:39Z
has_accepted_license: '1'
intvolume: ' 627'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 265683E4-B435-11E9-9278-68D0E5697425
grant_number: M62909-18-1-2038
name: Toward Computational Information Topology
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Astronomy and Astrophysics
publication_identifier:
eissn:
- '14320746'
issn:
- '00046361'
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Unexpected topology of the temperature fluctuations in the cosmic microwave
background
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 627
year: '2019'
...
---
_id: '6793'
abstract:
- lang: eng
text: The Regge symmetry is a set of remarkable relations between two tetrahedra
whose edge lengths are related in a simple fashion. It was first discovered as
a consequence of an asymptotic formula in mathematical physics. Here, we give
a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic
geometry.
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Ivan
full_name: Izmestiev, Ivan
last_name: Izmestiev
citation:
ama: Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli
formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775.
doi:10.1112/blms.12276
apa: Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics,
and the Schläfli formula. Bulletin of the London Mathematical Society.
London Mathematical Society. https://doi.org/10.1112/blms.12276
chicago: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
and the Schläfli Formula.” Bulletin of the London Mathematical Society.
London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276.
ieee: A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the
Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51,
no. 5. London Mathematical Society, pp. 765–775, 2019.
ista: Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the
Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.
mla: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
and the Schläfli Formula.” Bulletin of the London Mathematical Society,
vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276.
short: A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51
(2019) 765–775.
date_created: 2019-08-11T21:59:23Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-08-29T07:08:34Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12276
ec_funded: 1
external_id:
arxiv:
- '1903.04929'
isi:
- '000478560200001'
intvolume: ' 51'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1903.04929
month: '10'
oa: 1
oa_version: Preprint
page: 765-775
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- '14692120'
issn:
- '00246093'
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Regge symmetry, confocal conics, and the Schläfli formula
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 51
year: '2019'
...
---
_id: '6828'
abstract:
- lang: eng
text: In this paper we construct a family of exact functors from the category of
Whittaker modules of the simple complex Lie algebra of type to the category of
finite-dimensional modules of the graded affine Hecke algebra of type . Using
results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors
map standard modules to standard modules (or zero) and simple modules to simple
modules (or zero). Moreover, we show that each simple module of the graded affine
Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker
category contains the BGG category as a full subcategory, our results generalize
results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between
finite-dimensional representations of and representations of the symmetric group
.
article_processing_charge: No
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
citation:
ama: Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra.
2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027
apa: Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal
of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027
chicago: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal
of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027.
ieee: A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra,
vol. 538. Elsevier, pp. 261–289, 2019.
ista: Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra.
538, 261–289.
mla: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of
Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.
short: A. Brown, Journal of Algebra 538 (2019) 261–289.
date_created: 2019-08-22T07:54:13Z
date_published: 2019-11-15T00:00:00Z
date_updated: 2023-08-29T07:11:47Z
day: '15'
department:
- _id: HeEd
doi: 10.1016/j.jalgebra.2019.07.027
external_id:
arxiv:
- '1805.04676'
isi:
- '000487176300011'
intvolume: ' 538'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1805.04676
month: '11'
oa: 1
oa_version: Preprint
page: 261-289
publication: Journal of Algebra
publication_identifier:
issn:
- 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Arakawa-Suzuki functors for Whittaker modules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 538
year: '2019'
...
---
_id: '7216'
abstract:
- lang: eng
text: 'We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system
to label a stream of noisy observations of transit vehicle trajectories with the
transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently
to large transit networks, our system first retrieves a small set of candidate
routes from a geometrically indexed data structure, then applies a fine-grained
scoring step to choose the best match. Given that real-time data remains unavailable
for the majority of the world’s transit agencies, these inferences can help feed
a real-time map of a transit system’s trips, infer transit trip delays in real
time, or measure and correct noisy transit tracking data. This system can run
on vehicle observations from a variety of sources that don’t attach route information
to vehicle observations, such as public imagery streams or user-contributed transit
vehicle sightings.We abstract away the specifics of the sensing system and demonstrate
the effectiveness of our system on a "semisynthetic" dataset of all New York City
buses, where we simulate sensed trajectories by starting with fully labeled vehicle
trajectories reported via the GTFS-Realtime protocol, removing the transit route
IDs, and perturbing locations with synthetic noise. Using just the geometric shapes
of the trajectories, we demonstrate that our system converges on the correct route
ID within a few minutes, even after a vehicle switches from serving one trip to
the next.'
article_number: '8917514'
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: James
full_name: Cook, James
last_name: Cook
- first_name: Alex
full_name: Fabrikant, Alex
last_name: Fabrikant
- first_name: Marco
full_name: Gruteser, Marco
last_name: Gruteser
citation:
ama: 'Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching
of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent
Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514'
apa: 'Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL:
Real-time matching of transit vehicle trajectories to transit routes at scale.
In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New
Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514'
chicago: 'Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL:
Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.”
In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019.
https://doi.org/10.1109/ITSC.2019.8917514.'
ieee: 'G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time
matching of transit vehicle trajectories to transit routes at scale,” in 2019
IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand,
2019.'
ista: 'Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching
of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent
Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference,
8917514.'
mla: 'Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle
Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation
Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514.'
short: G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent
Transportation Systems Conference, IEEE, 2019.
conference:
end_date: 2019-10-30
location: Auckland, New Zealand
name: 'ITSC: Intelligent Transportation Systems Conference'
start_date: 2019-10-27
date_created: 2019-12-29T23:00:47Z
date_published: 2019-11-28T00:00:00Z
date_updated: 2023-09-06T14:50:28Z
day: '28'
department:
- _id: HeEd
doi: 10.1109/ITSC.2019.8917514
external_id:
isi:
- '000521238102050'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
publication: 2019 IEEE Intelligent Transportation Systems Conference
publication_identifier:
isbn:
- '9781538670248'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'LiveTraVeL: Real-time matching of transit vehicle trajectories to transit
routes at scale'
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2019'
...
---
_id: '5678'
abstract:
- lang: eng
text: "The order-k Voronoi tessellation of a locally finite set \U0001D44B⊆ℝ\U0001D45B
decomposes ℝ\U0001D45B into convex domains whose points have the same k nearest
neighbors in X. Assuming X is a stationary Poisson point process, we give explicit
formulas for the expected number and total area of faces of a given dimension
per unit volume of space. We also develop a relaxed version of discrete Morse
theory and generalize by counting only faces, for which the k nearest points in
X are within a given distance threshold."
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
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete
and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2
apa: Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order
k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of
Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2.
ieee: H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete
and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.
ista: Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete
and Computational Geometry. 62(4), 865–878.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order
K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019,
pp. 865–878, doi:10.1007/s00454-018-0049-2.
short: H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019)
865–878.
date_created: 2018-12-16T22:59:20Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2023-09-07T12:07:12Z
day: '01'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s00454-018-0049-2
ec_funded: 1
external_id:
arxiv:
- '1709.09380'
isi:
- '000494042900008'
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oa: 1
oa_version: Published Version
page: 865–878
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call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
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call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
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publication: Discrete and Computational Geometry
publication_identifier:
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issn:
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publisher: Springer
quality_controlled: '1'
related_material:
record:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Poisson–Delaunay Mosaics of Order k
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name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 62
year: '2019'
...
---
_id: '6608'
abstract:
- lang: eng
text: We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner
and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete
application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha
complex, and we use the persistence diagram of the distance function to guide
the hole opening and closing operations. The dependences between the holes define
a partial order on the cells in K that characterizes what can and what cannot
be constructed using the operations. The relations in this partial order reveal
structural information about the underlying filtration of complexes beyond what
is expressed by the persistence diagram.
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: 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. Holes and dependences in an ordered complex. Computer
Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003
apa: Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered
complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003
chicago: Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in
an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003.
ieee: H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,”
Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019.
ista: Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex.
Computer Aided Geometric Design. 73, 1–15.
mla: Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an
Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019,
pp. 1–15, doi:10.1016/j.cagd.2019.06.003.
short: H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.
date_created: 2019-07-07T21:59:20Z
date_published: 2019-08-01T00:00:00Z
date_updated: 2023-09-07T13:15:29Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.cagd.2019.06.003
ec_funded: 1
external_id:
isi:
- '000485207800001'
file:
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checksum: 7c99be505dc7533257d42eb1830cef04
content_type: application/pdf
creator: kschuh
date_created: 2019-07-08T15:24:26Z
date_updated: 2020-07-14T12:47:34Z
file_id: '6624'
file_name: Elsevier_2019_Edelsbrunner.pdf
file_size: 2665013
relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
intvolume: ' 73'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '08'
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: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Computer Aided Geometric Design
publication_status: published
publisher: Elsevier
quality_controlled: '1'
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scopus_import: '1'
status: public
title: Holes and dependences in an ordered complex
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name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 73
year: '2019'
...
---
_id: '7950'
abstract:
- lang: eng
text: "The input to the token swapping problem is a graph with vertices v1, v2,
. . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The
goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number
of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token
swapping on a tree, also known as “sorting with a transposition tree,” is not
known to be in P nor NP-complete. We present some partial results:\r\n1. An
optimum swap sequence may need to perform a swap on a leaf vertex that has the
correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any
algorithm that fixes happy leaves—as all known approximation algorithms for the
problem do—has approximation factor at least 4/3. Furthermore, the two best-known
2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized
problem—weighted coloured token swapping—is NP-complete on trees, but solvable
in polynomial time on paths and stars. In this version, tokens and vertices
\ have colours, and colours have weights. The goal is to get every
token to a vertex of the same colour, and the cost of a swap is the sum of the
weights of the two tokens involved."
article_number: '1903.06981'
article_processing_charge: No
author:
- first_name: Ahmad
full_name: Biniaz, Ahmad
last_name: Biniaz
- first_name: Kshitij
full_name: Jain, Kshitij
last_name: Jain
- first_name: Anna
full_name: Lubiw, Anna
last_name: Lubiw
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tillmann
full_name: Miltzow, Tillmann
last_name: Miltzow
- first_name: Debajyoti
full_name: Mondal, Debajyoti
last_name: Mondal
- first_name: Anurag Murty
full_name: Naredla, Anurag Murty
last_name: Naredla
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Alexi
full_name: Turcotte, Alexi
last_name: Turcotte
citation:
ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv.
apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte,
A. (n.d.). Token swapping on trees. arXiv.
chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow,
Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token
Swapping on Trees.” ArXiv, n.d.
ieee: A. Biniaz et al., “Token swapping on trees,” arXiv. .
ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec
J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.
mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.
short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla,
J. Tkadlec, A. Turcotte, ArXiv (n.d.).
date_created: 2020-06-08T12:25:25Z
date_published: 2019-03-16T00:00:00Z
date_updated: 2024-01-04T12:42:08Z
day: '16'
department:
- _id: HeEd
- _id: UlWa
- _id: KrCh
external_id:
arxiv:
- '1903.06981'
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/1903.06981
month: '03'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '7944'
relation: dissertation_contains
status: public
- id: '12833'
relation: later_version
status: public
status: public
title: Token swapping on trees
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '188'
abstract:
- lang: eng
text: Smallest enclosing spheres of finite point sets are central to methods in
topological data analysis. Focusing on Bregman divergences to measure dissimilarity,
we prove bounds on the location of the center of a smallest enclosing sphere.
These bounds depend on the range of radii for which Bregman balls are convex.
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
alternative_title:
- Leibniz International Proceedings in Information, LIPIcs
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff
points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35'
apa: 'Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres
and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at
the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl
- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35'
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing
Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35.
ieee: 'H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and
Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational
Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.'
ista: 'Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff
points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz
International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.'
mla: Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points
in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.
short: H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2018, p. 35:1-35:13.
conference:
end_date: 2018-06-14
location: Budapest, Hungary
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2018-06-11
date_created: 2018-12-11T11:45:05Z
date_published: 2018-06-11T00:00:00Z
date_updated: 2021-01-12T06:53:48Z
day: '11'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2018.35
file:
- access_level: open_access
checksum: 7509403803b3ac1aee94bbc2ad293d21
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:31:31Z
date_updated: 2020-07-14T12:45:20Z
file_id: '5724'
file_name: 2018_LIPIcs_Edelsbrunner.pdf
file_size: 489080
relation: main_file
file_date_updated: 2020-07-14T12:45:20Z
has_accepted_license: '1'
intvolume: ' 99'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 35:1 - 35:13
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7733'
quality_controlled: '1'
scopus_import: 1
status: public
title: Smallest enclosing spheres and Chernoff points in Bregman geometry
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: 99
year: '2018'
...
---
_id: '201'
abstract:
- lang: eng
text: 'We describe arrangements of three-dimensional spheres from a geometrical
and topological point of view. Real data (fitting this setup) often consist of
soft spheres which show certain degree of deformation while strongly packing against
each other. In this context, we answer the following questions: If we model a
soft packing of spheres by hard spheres that are allowed to overlap, can we measure
the volume in the overlapped areas? Can we be more specific about the overlap
volume, i.e. quantify how much volume is there covered exactly twice, three times,
or k times? What would be a good optimization criteria that rule the arrangement
of soft spheres while making a good use of the available space? Fixing a particular
criterion, what would be the optimal sphere configuration? The first result of
this thesis are short formulas for the computation of volumes covered by at least
k of the balls. The formulas exploit information contained in the order-k Voronoi
diagrams and its closely related Level-k complex. The used complexes lead to a
natural generalization into poset diagrams, a theoretical formalism that contains
the order-k and degree-k diagrams as special cases. In parallel, we define different
criteria to determine what could be considered an optimal arrangement from a geometrical
point of view. Fixing a criterion, we find optimal soft packing configurations
in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools
from computational topology on real physical data, to show the potentials of higher-order
diagrams in the description of melting crystals. The results of the experiments
leaves us with an open window to apply the theories developed in this thesis in
real applications.'
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: Iglesias Ham M. Multiple covers with balls. 2018. doi:10.15479/AT:ISTA:th_1026
apa: Iglesias Ham, M. (2018). Multiple covers with balls. Institute of Science
and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1026
chicago: Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science
and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1026.
ieee: M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology
Austria, 2018.
ista: Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and
Technology Austria.
mla: Iglesias Ham, Mabel. Multiple Covers with Balls. Institute of Science
and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1026.
short: M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology
Austria, 2018.
date_created: 2018-12-11T11:45:10Z
date_published: 2018-06-11T00:00:00Z
date_updated: 2023-09-07T12:25:32Z
day: '11'
ddc:
- '514'
- '516'
degree_awarded: PhD
department:
- _id: HeEd
doi: 10.15479/AT:ISTA:th_1026
file:
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checksum: dd699303623e96d1478a6ae07210dd05
content_type: application/zip
creator: kschuh
date_created: 2019-02-05T07:43:31Z
date_updated: 2020-07-14T12:45:24Z
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file_name: IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip
file_size: 11827713
relation: source_file
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checksum: ba163849a190d2b41d66fef0e4983294
content_type: application/pdf
creator: kschuh
date_created: 2019-02-05T07:43:45Z
date_updated: 2020-07-14T12:45:24Z
file_id: '5919'
file_name: IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf
file_size: 4783846
relation: main_file
file_date_updated: 2020-07-14T12:45:24Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: '171'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '7712'
pubrep_id: '1026'
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: Multiple covers with balls
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '187'
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
from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. '
acknowledgement: This work is 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:
- LIPIcs
article_number: '34'
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
orcid: 0000-0002-8882-5116
citation:
ama: 'Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls.
In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.34'
apa: 'Edelsbrunner, H., & Osang, G. F. (2018). The multi-cover persistence of
Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry,
Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.34'
chicago: Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence
of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.34.
ieee: 'H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean
balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest,
Hungary, 2018, vol. 99.'
ista: 'Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean
balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.'
mla: Edelsbrunner, Herbert, and Georg F. Osang. The Multi-Cover Persistence of
Euclidean Balls. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2018, doi:10.4230/LIPIcs.SoCG.2018.34.
short: H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, 2018.
conference:
end_date: 2018-06-14
location: Budapest, Hungary
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2018-06-11
date_created: 2018-12-11T11:45:05Z
date_published: 2018-06-11T00:00:00Z
date_updated: 2023-09-07T13:29:00Z
day: '11'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2018.34
file:
- access_level: open_access
checksum: d8c0533ad0018eb4ed1077475eb8fc18
content_type: application/pdf
creator: dernst
date_created: 2018-12-18T09:27:22Z
date_updated: 2020-07-14T12:45:19Z
file_id: '5738'
file_name: 2018_LIPIcs_Edelsbrunner_Osang.pdf
file_size: 528018
relation: main_file
file_date_updated: 2020-07-14T12:45:19Z
has_accepted_license: '1'
intvolume: ' 99'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7732'
quality_controlled: '1'
related_material:
record:
- id: '9317'
relation: later_version
status: public
- id: '9056'
relation: dissertation_contains
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: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 99
year: '2018'
...
---
_id: '692'
abstract:
- lang: eng
text: We consider families of confocal conics and two pencils of Apollonian circles
having the same foci. We will show that these families of curves generate trivial
3-webs and find the exact formulas describing them.
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
citation:
ama: Akopyan A. 3-Webs generated by confocal conics and circles. Geometriae Dedicata.
2018;194(1):55-64. doi:10.1007/s10711-017-0265-6
apa: Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. Geometriae
Dedicata. Springer. https://doi.org/10.1007/s10711-017-0265-6
chicago: Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae
Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0265-6.
ieee: A. Akopyan, “3-Webs generated by confocal conics and circles,” Geometriae
Dedicata, vol. 194, no. 1. Springer, pp. 55–64, 2018.
ista: Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae
Dedicata. 194(1), 55–64.
mla: Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae
Dedicata, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:10.1007/s10711-017-0265-6.
short: A. Akopyan, Geometriae Dedicata 194 (2018) 55–64.
date_created: 2018-12-11T11:47:57Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-08T11:40:29Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s10711-017-0265-6
ec_funded: 1
external_id:
isi:
- '000431418800004'
file:
- access_level: open_access
checksum: 1febcfc1266486053a069e3425ea3713
content_type: application/pdf
creator: kschuh
date_created: 2020-01-03T11:35:08Z
date_updated: 2020-07-14T12:47:44Z
file_id: '7222'
file_name: 2018_Springer_Akopyan.pdf
file_size: 1140860
relation: main_file
file_date_updated: 2020-07-14T12:47:44Z
has_accepted_license: '1'
intvolume: ' 194'
isi: 1
issue: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 55 - 64
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Geometriae Dedicata
publication_status: published
publisher: Springer
publist_id: '7014'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 3-Webs generated by confocal conics and circles
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: 194
year: '2018'
...
---
_id: '58'
abstract:
- lang: eng
text: 'Inside a two-dimensional region (``cake""), there are m nonoverlapping
tiles of a certain kind (``toppings""). We want to expand the toppings
while keeping them nonoverlapping, and possibly add some blank pieces of the same
``certain kind,"" such that the entire cake is covered. How many blanks
must we add? We study this question in several cases: (1) The cake and toppings
are general polygons. (2) The cake and toppings are convex figures. (3) The cake
and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear
polygon and the toppings are axis-parallel rectangles. In all four cases, we provide
tight bounds on the number of blanks.'
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: Erel
full_name: Segal Halevi, Erel
last_name: Segal Halevi
citation:
ama: Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM
Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X
apa: Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements.
SIAM Journal on Discrete Mathematics. Society for Industrial and Applied
Mathematics . https://doi.org/10.1137/16M110407X
chicago: Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal
Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial
and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X.
ieee: A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,”
SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial
and Applied Mathematics , pp. 2242–2257, 2018.
ista: Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements.
SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.
mla: Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.”
SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial
and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X.
short: A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018)
2242–2257.
date_created: 2018-12-11T11:44:24Z
date_published: 2018-09-06T00:00:00Z
date_updated: 2023-09-11T12:48:39Z
day: '06'
department:
- _id: HeEd
doi: 10.1137/16M110407X
ec_funded: 1
external_id:
arxiv:
- '1604.00960'
isi:
- '000450810500036'
intvolume: ' 32'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1604.00960
month: '09'
oa: 1
oa_version: Preprint
page: 2242 - 2257
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: SIAM Journal on Discrete Mathematics
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7996'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting blanks in polygonal arrangements
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 32
year: '2018'
...
---
_id: '458'
abstract:
- lang: eng
text: We consider congruences of straight lines in a plane with the combinatorics
of the square grid, with all elementary quadrilaterals possessing an incircle.
It is shown that all the vertices of such nets (we call them incircular or IC-nets)
lie on confocal conics. Our main new results are on checkerboard IC-nets in the
plane. These are congruences of straight lines in the plane with the combinatorics
of the square grid, combinatorially colored as a checkerboard, such that all black
coordinate quadrilaterals possess inscribed circles. We show how this larger class
of IC-nets appears quite naturally in Laguerre geometry of oriented planes and
spheres and leads to new remarkable incidence theorems. Most of our results are
valid in hyperbolic and spherical geometries as well. We present also generalizations
in spaces of higher dimension, called checkerboard IS-nets. The construction of
these nets is based on a new 9 inspheres incidence theorem.
acknowledgement: DFG Collaborative Research Center TRR 109 “Discretization in Geometry
and Dynamics”; People Programme (Marie Curie Actions) of the European Union’s Seventh
Framework Programme (FP7/2007-2013) REA grant agreement n◦[291734]
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: Alexander
full_name: Bobenko, Alexander
last_name: Bobenko
citation:
ama: Akopyan A, Bobenko A. Incircular nets and confocal conics. Transactions
of the American Mathematical Society. 2018;370(4):2825-2854. doi:10.1090/tran/7292
apa: Akopyan, A., & Bobenko, A. (2018). Incircular nets and confocal conics.
Transactions of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/tran/7292
chicago: Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal
Conics.” Transactions of the American Mathematical Society. American Mathematical
Society, 2018. https://doi.org/10.1090/tran/7292.
ieee: A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” Transactions
of the American Mathematical Society, vol. 370, no. 4. American Mathematical
Society, pp. 2825–2854, 2018.
ista: Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions
of the American Mathematical Society. 370(4), 2825–2854.
mla: Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.”
Transactions of the American Mathematical Society, vol. 370, no. 4, American
Mathematical Society, 2018, pp. 2825–54, doi:10.1090/tran/7292.
short: A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society
370 (2018) 2825–2854.
date_created: 2018-12-11T11:46:35Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2023-09-11T14:19:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/tran/7292
ec_funded: 1
external_id:
isi:
- '000423197800019'
intvolume: ' 370'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1602.04637
month: '04'
oa: 1
oa_version: Preprint
page: 2825 - 2854
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '7363'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Incircular nets and confocal conics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 370
year: '2018'
...
---
_id: '106'
abstract:
- lang: eng
text: The goal of this article is to introduce the reader to the theory of intrinsic
geometry of convex surfaces. We illustrate the power of the tools by proving a
theorem on convex surfaces containing an arbitrarily long closed simple geodesic.
Let us remind ourselves that a curve in a surface is called geodesic if every
sufficiently short arc of the curve is length minimizing; if, in addition, it
has no self-intersections, we call it simple geodesic. A tetrahedron with equal
opposite edges is called isosceles. The axiomatic method of Alexandrov geometry
allows us to work with the metrics of convex surfaces directly, without approximating
it first by a smooth or polyhedral metric. Such approximations destroy the closed
geodesics on the surface; therefore it is difficult (if at all possible) to apply
approximations in the proof of our theorem. On the other hand, a proof in the
smooth or polyhedral case usually admits a translation into Alexandrov’s language;
such translation makes the result more general. In fact, our proof resembles a
translation of the proof given by Protasov. Note that the main theorem implies
in particular that a smooth convex surface does not have arbitrarily long simple
closed geodesics. However we do not know a proof of this corollary that is essentially
simpler than the one presented below.
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: Anton
full_name: Petrunin, Anton
last_name: Petrunin
citation:
ama: Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer.
2018;40(3):26-31. doi:10.1007/s00283-018-9795-5
apa: Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces.
Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5
chicago: Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.”
Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5.
ieee: A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical
Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.
ista: Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical
Intelligencer. 40(3), 26–31.
mla: Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.”
Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31,
doi:10.1007/s00283-018-9795-5.
short: A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.
date_created: 2018-12-11T11:44:40Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2023-09-13T08:49:16Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00283-018-9795-5
external_id:
arxiv:
- '1702.05172'
isi:
- '000444141200005'
intvolume: ' 40'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.05172
month: '09'
oa: 1
oa_version: Preprint
page: 26 - 31
publication: Mathematical Intelligencer
publication_status: published
publisher: Springer
publist_id: '7948'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Long geodesics on convex surfaces
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 40
year: '2018'
...
---
_id: '530'
abstract:
- lang: eng
text: Inclusion–exclusion is an effective method for computing the volume of a union
of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion
formulas for the subset of Rn covered by at least k balls in a finite set. We
implement two of the formulas in dimension n=3 and report on results obtained
with our software.
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: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: 'Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion.
Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014'
apa: 'Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls
I: Inclusion–exclusion. Computational Geometry: Theory and Applications.
Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014'
chicago: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications.
Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.'
ieee: 'H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,”
Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp.
119–133, 2018.'
ista: 'Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion.
Computational Geometry: Theory and Applications. 68, 119–133.'
mla: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications,
vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.'
short: 'H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications
68 (2018) 119–133.'
date_created: 2018-12-11T11:46:59Z
date_published: 2018-03-01T00:00:00Z
date_updated: 2023-09-13T08:59:00Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2017.06.014
ec_funded: 1
external_id:
isi:
- '000415778300010'
file:
- access_level: open_access
checksum: 1c8d58cd489a66cd3e2064c1141c8c5e
content_type: application/pdf
creator: dernst
date_created: 2019-02-12T06:47:52Z
date_updated: 2020-07-14T12:46:38Z
file_id: '5953'
file_name: 2018_Edelsbrunner.pdf
file_size: 708357
relation: main_file
file_date_updated: 2020-07-14T12:46:38Z
has_accepted_license: '1'
intvolume: ' 68'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Preprint
page: 119 - 133
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '7289'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multiple covers with balls I: Inclusion–exclusion'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 68
year: '2018'
...
---
_id: '193'
abstract:
- lang: eng
text: 'We show attacks on five data-independent memory-hard functions (iMHF) that
were submitted to the password hashing competition (PHC). Informally, an MHF is
a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly
lower hardware and/or energy cost than evaluating a single instance on a standard
single-core architecture. Data-independent means the memory access pattern of
the function is independent of the input; this makes iMHFs harder to construct
than data-dependent ones, but the latter can be attacked by various side-channel
attacks. Following [Alwen-Blocki''16], we capture the evaluation of an iMHF as
a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of
this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC.
Ideally, one would like the complexity of a DAG underlying an iMHF to be as close
to quadratic in the number of nodes of the graph as possible. Instead, we show
that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2,
TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show
that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have
exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial
property of each underlying DAG (called its depth-robustness. By establishing
upper bounds on this property we are then able to apply the general technique
of [Alwen-Block''16] for analyzing the hardware costs of an iMHF.'
acknowledgement: Leonid Reyzin was supported in part by IST Austria and by US NSF
grants 1012910, 1012798, and 1422965; this research was performed while he was visiting
IST Austria.
article_processing_charge: No
author:
- first_name: Joel F
full_name: Alwen, Joel F
id: 2A8DFA8C-F248-11E8-B48F-1D18A9856A87
last_name: Alwen
- first_name: Peter
full_name: Gazi, Peter
last_name: Gazi
- first_name: Chethan
full_name: Kamath Hosdurg, Chethan
id: 4BD3F30E-F248-11E8-B48F-1D18A9856A87
last_name: Kamath Hosdurg
- first_name: Karen
full_name: Klein, Karen
id: 3E83A2F8-F248-11E8-B48F-1D18A9856A87
last_name: Klein
- 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: Krzysztof Z
full_name: Pietrzak, Krzysztof Z
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
orcid: 0000-0002-9139-1654
- first_name: Lenoid
full_name: Reyzin, Lenoid
last_name: Reyzin
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
- first_name: Michal
full_name: Rybar, Michal
id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87
last_name: Rybar
citation:
ama: 'Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data
independent password hashing functions. In: Proceedings of the 2018 on Asia
Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534'
apa: 'Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak,
K. Z., … Rybar, M. (2018). On the memory hardness of data independent password
hashing functions. In Proceedings of the 2018 on Asia Conference on Computer
and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534'
chicago: Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F
Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar.
“On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings
of the 2018 on Asia Conference on Computer and Communication Security, 51–65.
ACM, 2018. https://doi.org/10.1145/3196494.3196534.
ieee: J. F. Alwen et al., “On the memory hardness of data independent password
hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer
and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.
ista: 'Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin
L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password
hashing functions. Proceedings of the 2018 on Asia Conference on Computer and
Communication Security. ASIACCS: Asia Conference on Computer and Communications
Security , 51–65.'
mla: Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password
Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer
and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.
short: J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak,
L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference
on Computer and Communication Security, ACM, 2018, pp. 51–65.
conference:
end_date: 2018-06-08
location: Incheon, Republic of Korea
name: 'ASIACCS: Asia Conference on Computer and Communications Security '
start_date: 2018-06-04
date_created: 2018-12-11T11:45:07Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-13T09:13:12Z
day: '01'
department:
- _id: KrPi
- _id: HeEd
- _id: VlKo
doi: 10.1145/3196494.3196534
ec_funded: 1
external_id:
isi:
- '000516620100005'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2016/783
month: '06'
oa: 1
oa_version: Submitted Version
page: 51 - 65
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
- _id: 258AA5B2-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '682815'
name: Teaching Old Crypto New Tricks
publication: Proceedings of the 2018 on Asia Conference on Computer and Communication
Security
publication_status: published
publisher: ACM
publist_id: '7723'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the memory hardness of data independent password hashing functions
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '312'
abstract:
- lang: eng
text: Motivated by biological questions, we study configurations of equal spheres
that neither pack nor cover. Placing their centers on a lattice, we define the
soft density of the configuration by penalizing multiple overlaps. Considering
the 1-parameter family of diagonally distorted 3-dimensional integer lattices,
we show that the soft density is maximized at the FCC lattice.
acknowledgement: This work was partially supported by the DFG Collaborative Research
Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35
of the Austrian Science Fund (FWF).
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: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft
sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201
apa: Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC
lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial
and Applied Mathematics . https://doi.org/10.1137/16M1097201
chicago: Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the
FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for
Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201.
ieee: H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice
for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society
for Industrial and Applied Mathematics , pp. 750–782, 2018.
ista: Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice
for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782.
mla: Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC
Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1,
Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201.
short: H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.
date_created: 2018-12-11T11:45:46Z
date_published: 2018-03-29T00:00:00Z
date_updated: 2023-09-13T09:34:38Z
day: '29'
department:
- _id: HeEd
doi: 10.1137/16M1097201
external_id:
isi:
- '000428958900038'
intvolume: ' 32'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf
month: '03'
oa: 1
oa_version: Submitted Version
page: 750 - 782
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: SIAM J Discrete Math
publication_identifier:
issn:
- '08954801'
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7553'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the optimality of the FCC lattice for soft sphere packing
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 32
year: '2018'
...
---
_id: '409'
abstract:
- lang: eng
text: We give a simple proof of T. Stehling's result [4], whereby in any normal
tiling of the plane with convex polygons with number of sides not less than six,
all tiles except a finite number are hexagons.
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
citation:
ama: Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus
Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005
apa: Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes
Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005
chicago: Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes
Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005.
ieee: A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes
Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.
ista: Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes
Rendus Mathematique. 356(4), 412–414.
mla: Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes
Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005.
short: A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.
date_created: 2018-12-11T11:46:19Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2023-09-13T09:34:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.crma.2018.03.005
external_id:
arxiv:
- '1805.01652'
isi:
- '000430402700009'
intvolume: ' 356'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1805.01652
month: '04'
oa: 1
oa_version: Preprint
page: 412-414
publication: Comptes Rendus Mathematique
publication_identifier:
issn:
- 1631073X
publication_status: published
publisher: Elsevier
publist_id: '7420'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the number of non-hexagons in a planar tiling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 356
year: '2018'
...
---
_id: '87'
abstract:
- lang: eng
text: Using the geodesic distance on the n-dimensional sphere, we study the expected
radius function of the Delaunay mosaic of a random set of points. Specifically,
we consider the partition of the mosaic into intervals of the radius function
and determine the expected number of intervals whose radii are less than or equal
to a given threshold. We find that the expectations are essentially the same as
for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the
points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to
the boundary complex of the convex hull in Rn+1, so we also get the expected number
of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in
Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric
to the standard n-simplex equipped with the Fisher information metric. It follows
that the latter space has similar stochastic properties as the n-dimensional Euclidean
space. Our results are therefore relevant in information geometry and in population
genetics.
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. Random inscribed polytopes have similar radius
functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238.
doi:10.1214/18-AAP1389
apa: Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have
similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes
Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied
Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389.
ieee: H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar
radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability,
vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.
ista: Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar
radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5),
3215–3238.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have
Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability,
vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.
short: H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.
date_created: 2018-12-11T11:44:33Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2023-09-15T12:10:35Z
day: '01'
department:
- _id: HeEd
doi: 10.1214/18-AAP1389
external_id:
arxiv:
- '1705.02870'
isi:
- '000442893500018'
intvolume: ' 28'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.02870
month: '10'
oa: 1
oa_version: Preprint
page: 3215 - 3238
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Annals of Applied Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7967'
quality_controlled: '1'
related_material:
record:
- id: '6287'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Random inscribed polytopes have similar radius functions as Poisson-Delaunay
mosaics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 28
year: '2018'
...
---
_id: '6355'
abstract:
- lang: eng
text: We prove that any cyclic quadrilateral can be inscribed in any closed convex
C1-curve. The smoothness condition is not required if the quadrilateral is a
rectangle.
article_number: e7
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: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
citation:
ama: Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed
convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7
apa: Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed
in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2018.7
chicago: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be
Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma.
Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.
ieee: A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in
any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge
University Press, 2018.
ista: Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in
any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.
mla: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed
in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6,
e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.
short: A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).
date_created: 2019-04-30T06:09:57Z
date_published: 2018-05-31T00:00:00Z
date_updated: 2023-09-19T14:50:12Z
day: '31'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
- _id: JaMa
doi: 10.1017/fms.2018.7
ec_funded: 1
external_id:
arxiv:
- '1712.10205'
isi:
- '000433915500001'
file:
- access_level: open_access
checksum: 5a71b24ba712a3eb2e46165a38fbc30a
content_type: application/pdf
creator: dernst
date_created: 2019-04-30T06:14:58Z
date_updated: 2020-07-14T12:47:28Z
file_id: '6356'
file_name: 2018_ForumMahtematics_Akopyan.pdf
file_size: 249246
relation: main_file
file_date_updated: 2020-07-14T12:47:28Z
has_accepted_license: '1'
intvolume: ' 6'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Forum of Mathematics, Sigma
publication_identifier:
issn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Any cyclic quadrilateral can be inscribed in any closed convex smooth curve
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: 6
year: '2018'
...
---
_id: '1064'
abstract:
- lang: eng
text: 'In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by
P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it
is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot
be separated into two subfamilies by a straight line disjoint from the disks.
In this note we show that essentially the same idea may work for different analogues
and generalizations of their result. In particular, we prove the following: Given
a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety
coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate
of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane
disjoint from the homothets.'
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: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Mikhail
full_name: Grigorev, Mikhail
last_name: Grigorev
citation:
ama: Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W.
Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009.
doi:10.1007/s00454-017-9883-x
apa: Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering
theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry.
Springer. https://doi.org/10.1007/s00454-017-9883-x
chicago: Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle
Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational
Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x.
ieee: A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem
by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry,
vol. 59, no. 4. Springer, pp. 1001–1009, 2018.
ista: Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by
A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009.
mla: Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and
R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer,
2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.
short: A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry
59 (2018) 1001–1009.
date_created: 2018-12-11T11:49:57Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-20T12:08:51Z
day: '01'
ddc:
- '516'
- '000'
department:
- _id: HeEd
doi: 10.1007/s00454-017-9883-x
ec_funded: 1
external_id:
isi:
- '000432205500011'
file:
- access_level: open_access
content_type: application/pdf
creator: dernst
date_created: 2019-01-18T09:27:36Z
date_updated: 2019-01-18T09:27:36Z
file_id: '5844'
file_name: 2018_DiscreteComp_Akopyan.pdf
file_size: 482518
relation: main_file
success: 1
file_date_updated: 2019-01-18T09:27:36Z
has_accepted_license: '1'
intvolume: ' 59'
isi: 1
issue: '4'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1001-1009
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer
publist_id: '6324'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the circle covering theorem by A.W. Goodman and R.E. Goodman
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: 59
year: '2018'
...
---
_id: '75'
abstract:
- lang: eng
text: We prove that any convex body in the plane can be partitioned into m convex
parts of equal areas and perimeters for any integer m≥2; this result was previously
known for prime powers m=pk. We also give a higher-dimensional generalization.
article_number: '1804.03057'
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: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number
of pieces. 2018. doi:10.48550/arXiv.1804.03057
apa: Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions
into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057
chicago: Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions
into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.
ieee: A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary
number of pieces.” arXiv, 2018.
ista: Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary
number of pieces. 1804.03057.
mla: Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of
Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.
short: A. Akopyan, S. Avvakumov, R. Karasev, (2018).
date_created: 2018-12-11T11:44:30Z
date_published: 2018-09-13T00:00:00Z
date_updated: 2023-12-18T10:51:02Z
day: '13'
department:
- _id: HeEd
- _id: JaMa
doi: 10.48550/arXiv.1804.03057
ec_funded: 1
external_id:
arxiv:
- '1804.03057'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.03057
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication_status: published
publisher: arXiv
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Convex fair partitions into arbitrary number of pieces
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '481'
abstract:
- lang: eng
text: We introduce planar matchings on directed pseudo-line arrangements, which
yield a planar set of pseudo-line segments such that only matching-partners are
adjacent. By translating the planar matching problem into a corresponding stable
roommates problem we show that such matchings always exist. Using our new framework,
we establish, for the first time, a complete, rigorous definition of weighted
straight skeletons, which are based on a so-called wavefront propagation process.
We present a generalized and unified approach to treat structural changes in the
wavefront that focuses on the restoration of weak planarity by finding planar
matchings.
acknowledgement: 'Supported by NSERC and the Ross and Muriel Cheriton Fellowship.
Research supported by Austrian Science Fund (FWF): P25816-N15.'
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons.
International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229.
doi:10.1142/S0218195916600050
apa: Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted
straight skeletons. International Journal of Computational Geometry and Applications.
World Scientific Publishing. https://doi.org/10.1142/S0218195916600050
chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for
Weighted Straight Skeletons.” International Journal of Computational Geometry
and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.
ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight
skeletons,” International Journal of Computational Geometry and Applications,
vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017.
ista: Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight
skeletons. International Journal of Computational Geometry and Applications. 26(3–4),
211–229.
mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.”
International Journal of Computational Geometry and Applications, vol.
26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.
short: T. Biedl, S. Huber, P. Palfrader, International Journal of Computational
Geometry and Applications 26 (2017) 211–229.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-04-13T00:00:00Z
date_updated: 2023-02-21T16:06:22Z
day: '13'
ddc:
- '004'
- '514'
- '516'
department:
- _id: HeEd
doi: 10.1142/S0218195916600050
file:
- access_level: open_access
checksum: f79e8558bfe4b368dfefeb8eec2e3a5e
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:34Z
date_updated: 2020-07-14T12:46:35Z
file_id: '4758'
file_name: IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf
file_size: 769296
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 26'
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 211 - 229
publication: International Journal of Computational Geometry and Applications
publication_status: published
publisher: World Scientific Publishing
publist_id: '7338'
pubrep_id: '949'
quality_controlled: '1'
related_material:
record:
- id: '10892'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Planar matchings for weighted straight skeletons
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: 26
year: '2017'
...
---
_id: '521'
abstract:
- lang: eng
text: Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y
induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful
in showing that the classical dimension raising theorems hold in large scale;
that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and
Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely
n-to-1 maps, which include the natural quotient maps via a finite group action,
and prove that they preserve the asymptotic dimension.
author:
- first_name: Kyle
full_name: Austin, Kyle
last_name: Austin
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
citation:
ama: Austin K, Virk Z. Higson compactification and dimension raising. Topology
and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005
apa: Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005
chicago: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.
ieee: K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology
and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.
ista: Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology
and its Applications. 215, 45–57.
mla: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.
short: K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.
date_created: 2018-12-11T11:46:56Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:01:21Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2016.10.005
intvolume: ' 215'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.03954v1
month: '01'
oa: 1
oa_version: Submitted Version
page: 45 - 57
publication: Topology and its Applications
publication_identifier:
issn:
- '01668641'
publication_status: published
publisher: Elsevier
publist_id: '7299'
quality_controlled: '1'
status: public
title: Higson compactification and dimension raising
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 215
year: '2017'
...
---
_id: '568'
abstract:
- lang: eng
text: 'We study robust properties of zero sets of continuous maps f: X → ℝn. Formally,
we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets
of all continuous maps g closer to f than r in the max-norm. All of these sets
are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined
by A and an element of a certain cohomotopy group which (by a recent result) is
computable whenever the dimension of X is at most 2n - 3. By considering all r
> 0 simultaneously, the pointed cohomotopy groups form a persistence module-a
structure leading to persistence diagrams as in the case of persistent homology
or well groups. Eventually, we get a descriptor of persistent robust properties
of zero sets that has better descriptive power (Theorem A) and better computability
status (Theorem B) than the established well diagrams. Moreover, if we endow every
point of each zero set with gradients of the perturbation, the robust description
of the zero sets by elements of cohomotopy groups is in some sense the best possible
(Theorem C).'
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications.
2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16
apa: Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology,
Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16
chicago: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology,
Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.
ieee: P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy
and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.
ista: Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and
Applications. 19(2), 313–342.
mla: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy
and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.
short: P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.
date_created: 2018-12-11T11:47:14Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:03:12Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.4310/HHA.2017.v19.n2.a16
ec_funded: 1
intvolume: ' 19'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1507.04310
month: '01'
oa: 1
oa_version: Submitted Version
page: 313 - 342
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 2590DB08-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '701309'
name: Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes
(H2020)
publication: Homology, Homotopy and Applications
publication_identifier:
issn:
- '15320073'
publication_status: published
publisher: International Press
publist_id: '7246'
quality_controlled: '1'
scopus_import: 1
status: public
title: Persistence of zero sets
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2017'
...
---
_id: '5803'
abstract:
- lang: eng
text: Different distance metrics produce Voronoi diagrams with different properties.
It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi
diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions.
In this paper, we first show that this metric produces a persistent VD on the
2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly
approximates the corresponding VD on the 2D real plane. Next, we show that on
a 3D digital plane D, the Euclidean metric spanning over its voxel set does not
guarantee a digital VD which is persistent with the real-space VD. As a solution,
we introduce a novel concept of functional-plane-convexity, which is ensured by
the Euclidean metric spanning over the pedal set of D. Necessary proofs and some
visual result have been provided to adjudge the merit and usefulness of the proposed
concept.
alternative_title:
- LNCS
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: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital
plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature;
2017:93-104. doi:10.1007/978-3-319-59108-7_8'
apa: 'Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi
diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256,
pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi
Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104.
Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.'
ieee: 'R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on
3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer
Nature, 2017, pp. 93–104.'
ista: 'Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on
3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.'
mla: Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram
on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer
Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.
short: R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature,
Cham, 2017, pp. 93–104.
conference:
end_date: 2017-06-21
location: Plovdiv, Bulgaria
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2017-06-19
date_created: 2019-01-08T20:42:56Z
date_published: 2017-05-17T00:00:00Z
date_updated: 2022-01-28T07:48:24Z
day: '17'
department:
- _id: HeEd
doi: 10.1007/978-3-319-59108-7_8
extern: '1'
intvolume: ' 10256'
language:
- iso: eng
month: '05'
oa_version: None
page: 93-104
place: Cham
publication: Combinatorial image analysis
publication_identifier:
isbn:
- 978-3-319-59107-0
- 978-3-319-59108-7
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Construction of persistent Voronoi diagram on 3D digital plane
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 10256
year: '2017'
...
---
_id: '688'
abstract:
- lang: eng
text: 'We show that the framework of topological data analysis can be extended from
metrics to general Bregman divergences, widening the scope of possible applications.
Examples are the Kullback - Leibler divergence, which is commonly used for comparing
text and images, and the Itakura - Saito divergence, popular for speech and sound.
In particular, we prove that appropriately generalized čech and Delaunay (alpha)
complexes capture the correct homotopy type, namely that of the corresponding
union of Bregman balls. Consequently, their filtrations give the correct persistence
diagram, namely the one generated by the uniformly growing Bregman balls. Moreover,
we show that unlike the metric setting, the filtration of Vietoris-Rips complexes
may fail to approximate the persistence diagram. We propose algorithms to compute
the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally
test their efficiency. Lastly, we explain their surprisingly good performance
by making a connection with discrete Morse theory. '
alternative_title:
- LIPIcs
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences.
In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916.
doi:10.4230/LIPIcs.SoCG.2017.39'
apa: 'Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with
Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational
Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2017.39'
chicago: Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with
Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39.
ieee: H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,”
presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia,
2017, vol. 77, pp. 391–3916.
ista: Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences.
Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.
mla: Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with
Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.
short: H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017, pp. 391–3916.
conference:
end_date: 2017-07-07
location: Brisbane, Australia
name: Symposium on Computational Geometry, SoCG
start_date: 2017-07-04
date_created: 2018-12-11T11:47:56Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2021-01-12T08:09:26Z
day: '01'
ddc:
- '514'
- '516'
department:
- _id: HeEd
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2017.39
file:
- access_level: open_access
checksum: 067ab0cb3f962bae6c3af6bf0094e0f3
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:03Z
date_updated: 2020-07-14T12:47:42Z
file_id: '4856'
file_name: IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf
file_size: 990546
relation: main_file
file_date_updated: 2020-07-14T12:47:42Z
has_accepted_license: '1'
intvolume: ' 77'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 391-3916
publication_identifier:
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7021'
pubrep_id: '895'
quality_controlled: '1'
scopus_import: 1
status: public
title: Topological data analysis with Bregman divergences
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 77
year: '2017'
...
---
_id: '707'
abstract:
- lang: eng
text: We answer a question of M. Gromov on the waist of the unit ball.
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. A tight estimate for the waist of the ball . Bulletin
of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062
apa: Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the
ball . Bulletin of the London Mathematical Society. Wiley-Blackwell. https://doi.org/10.1112/blms.12062
chicago: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of
the Ball .” Bulletin of the London Mathematical Society. Wiley-Blackwell,
2017. https://doi.org/10.1112/blms.12062.
ieee: A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,”
Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley-Blackwell,
pp. 690–693, 2017.
ista: Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin
of the London Mathematical Society. 49(4), 690–693.
mla: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the
Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley-Blackwell,
2017, pp. 690–93, doi:10.1112/blms.12062.
short: A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017)
690–693.
date_created: 2018-12-11T11:48:02Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2021-01-12T08:11:41Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12062
ec_funded: 1
intvolume: ' 49'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.06279
month: '08'
oa: 1
oa_version: Preprint
page: 690 - 693
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Bulletin of the London Mathematical Society
publication_identifier:
issn:
- '00246093'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6982'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'A tight estimate for the waist of the ball '
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2017'
...
---
_id: '718'
abstract:
- lang: eng
text: Mapping every simplex in the Delaunay mosaic of a discrete point set to the
radius of the smallest empty circumsphere gives a generalized discrete Morse function.
Choosing the points from a Poisson point process in ℝ n , we study the expected
number of simplices in the Delaunay mosaic as well as the expected number of critical
simplices and nonsingular intervals in the corresponding generalized discrete
gradient. Observing connections with other probabilistic models, we obtain precise
expressions for the expected numbers in low dimensions. In particular, we obtain
the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions
n ≤ 4.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
- first_name: Matthias
full_name: Reitzner, Matthias
last_name: Reitzner
citation:
ama: Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay
mosaics and their discrete Morse functions. Advances in Applied Probability.
2017;49(3):745-767. doi:10.1017/apr.2017.20
apa: Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes
of poisson Delaunay mosaics and their discrete Morse functions. Advances in
Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20
chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected
Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances
in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20.
ieee: H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson
Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability,
vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.
ista: Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay
mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3),
745–767.
mla: Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and
Their Discrete Morse Functions.” Advances in Applied Probability, vol.
49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.
short: H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability
49 (2017) 745–767.
date_created: 2018-12-11T11:48:07Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2023-09-07T12:07:12Z
day: '01'
department:
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doi: 10.1017/apr.2017.20
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external_id:
arxiv:
- '1607.05915'
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issue: '3'
language:
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url: https://arxiv.org/abs/1607.05915
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call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
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call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Advances in Applied Probability
publication_identifier:
issn:
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publisher: Cambridge University Press
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title: Expected sizes of poisson Delaunay mosaics and their discrete Morse functions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2017'
...
---
_id: '6287'
abstract:
- lang: eng
text: The main objects considered in the present work are simplicial and CW-complexes
with vertices forming a random point cloud. In particular, we consider a Poisson
point process in R^n and study Delaunay and Voronoi complexes of the first and
higher orders and weighted Delaunay complexes obtained as sections of Delaunay
complexes, as well as the Čech complex. Further, we examine theDelaunay complex
of a Poisson point process on the sphere S^n, as well as of a uniform point cloud,
which is equivalent to the convex hull, providing a connection to the theory of
random polytopes. Each of the complexes in question can be endowed with a radius
function, which maps its cells to the radii of appropriately chosen circumspheres,
called the radius of the cell. Applying and developing discrete Morse theory for
these functions, joining it together with probabilistic and sometimes analytic
machinery, and developing several integral geometric tools, we aim at getting
the distributions of circumradii of typical cells. For all considered complexes,
we are able to generalize and obtain up to constants the distribution of radii
of typical intervals of all types. In low dimensions the constants can be computed
explicitly, thus providing the explicit expressions for the expected numbers of
cells. In particular, it allows to find the expected density of simplices of every
dimension for a Poisson point process in R^4, whereas the result for R^3 was known
already in 1970's.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
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full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873
apa: Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute
of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873
chicago: Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute
of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.
ieee: A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of
Science and Technology Austria, 2017.
ista: Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute
of Science and Technology Austria.
mla: Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute
of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.
short: A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science
and Technology Austria, 2017.
date_created: 2019-04-09T15:04:32Z
date_published: 2017-10-27T00:00:00Z
date_updated: 2023-09-15T12:10:34Z
day: '27'
ddc:
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publisher: Institute of Science and Technology Austria
pubrep_id: '873'
related_material:
record:
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relation: part_of_dissertation
status: public
- id: '5678'
relation: part_of_dissertation
status: public
- id: '87'
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: 'Discrete Morse theory for random complexes '
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: '2017'
...
---
_id: '1433'
abstract:
- lang: eng
text: Phat is an open-source C. ++ library for the computation of persistent homology
by matrix reduction, targeted towards developers of software for topological data
analysis. We aim for a simple generic design that decouples algorithms from data
structures without sacrificing efficiency or user-friendliness. We provide numerous
different reduction strategies as well as data types to store and manipulate the
boundary matrix. We compare the different combinations through extensive experimental
evaluation and identify optimization techniques that work well in practical situations.
We also compare our software with various other publicly available libraries for
persistent homology.
article_processing_charge: No
article_type: original
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
last_name: Bauer
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Jan
full_name: Reininghaus, Jan
last_name: Reininghaus
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms
toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008
apa: Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent
homology algorithms toolbox. Journal of Symbolic Computation. Academic
Press. https://doi.org/10.1016/j.jsc.2016.03.008
chicago: Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat
- Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation.
Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.
ieee: U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology
algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic
Press, pp. 76–90, 2017.
ista: Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology
algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.
mla: Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal
of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.
short: U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation
78 (2017) 76–90.
date_created: 2018-12-11T11:51:59Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-09-20T09:42:40Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jsc.2016.03.008
ec_funded: 1
external_id:
isi:
- '000384396000005'
intvolume: ' 78'
isi: 1
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.1016/j.jsc.2016.03.008
month: '01'
oa: 1
oa_version: Published Version
page: 76 - 90
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Journal of Symbolic Computation
publication_identifier:
issn:
- ' 07477171'
publication_status: published
publisher: Academic Press
publist_id: '5765'
quality_controlled: '1'
related_material:
record:
- id: '10894'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Phat - Persistent homology algorithms toolbox
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 78
year: '2017'
...
---
_id: '1180'
abstract:
- lang: eng
text: In this article we define an algebraic vertex of a generalized polyhedron
and show that the set of algebraic vertices is the smallest set of points needed
to define the polyhedron. We prove that the indicator function of a generalized
polytope P is a linear combination of indicator functions of simplices whose vertices
are algebraic vertices of P. We also show that the indicator function of any generalized
polyhedron is a linear combination, with integer coefficients, of indicator functions
of cones with apices at algebraic vertices and line-cones. The concept of an algebraic
vertex is closely related to the Fourier–Laplace transform. We show that a point
v is an algebraic vertex of a generalized polyhedron P if and only if the tangent
cone of P, at v, has non-zero Fourier–Laplace transform.
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: Imre
full_name: Bárány, Imre
last_name: Bárány
- first_name: Sinai
full_name: Robins, Sinai
last_name: Robins
citation:
ama: Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026
apa: Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex
polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026
chicago: Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of
Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.
ieee: A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,”
Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.
ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 308, 627–644.
mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances
in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.
short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.
date_created: 2018-12-11T11:50:34Z
date_published: 2017-02-21T00:00:00Z
date_updated: 2023-09-20T11:21:27Z
day: '21'
department:
- _id: HeEd
doi: 10.1016/j.aim.2016.12.026
ec_funded: 1
external_id:
isi:
- '000409292900015'
intvolume: ' 308'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1508.07594
month: '02'
oa: 1
oa_version: Submitted Version
page: 627 - 644
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Advances in Mathematics
publication_identifier:
issn:
- '00018708'
publication_status: published
publisher: Academic Press
publist_id: '6173'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Algebraic vertices of non-convex polyhedra
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 308
year: '2017'
...
---
_id: '1173'
abstract:
- lang: eng
text: We introduce the Voronoi functional of a triangulation of a finite set of
points in the Euclidean plane and prove that among all geometric triangulations
of the point set, the Delaunay triangulation maximizes the functional. This result
neither extends to topological triangulations in the plane nor to geometric triangulations
in three and higher dimensions.
acknowledgement: This research is partially supported by the Russian Government under
the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by
ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by
NSF grants DMS-1101688, DMS-1400876.
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: Alexey
full_name: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
- 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, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is
maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910.
doi:10.1007/s00493-016-3308-y
apa: Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The
Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica.
Springer. https://doi.org/10.1007/s00493-016-3308-y
chicago: Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko.
“The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.”
Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y.
ieee: H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional
is maximized by the Delaunay triangulation in the plane,” Combinatorica,
vol. 37, no. 5. Springer, pp. 887–910, 2017.
ista: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional
is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5),
887–910.
mla: Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay
Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017,
pp. 887–910, doi:10.1007/s00493-016-3308-y.
short: H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017)
887–910.
date_created: 2018-12-11T11:50:32Z
date_published: 2017-10-01T00:00:00Z
date_updated: 2023-09-20T11:23:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00493-016-3308-y
ec_funded: 1
external_id:
isi:
- '000418056000005'
intvolume: ' 37'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1411.6337
month: '10'
oa: 1
oa_version: Submitted Version
page: 887 - 910
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Combinatorica
publication_identifier:
issn:
- '02099683'
publication_status: published
publisher: Springer
publist_id: '6182'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Voronoi functional is maximized by the Delaunay triangulation in the plane
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 37
year: '2017'
...
---
_id: '1072'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a radius parameter, we study the Čech,
Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized
discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel
sets of generalized discrete Morse functions, we prove that the four complexes
are simple-homotopy equivalent by a sequence of simplicial collapses, which are
explicitly described by a single discrete gradient field.
acknowledgement: This research has been supported by the EU project Toposys(FP7-ICT-318493-STREP),
by ESF under the ACAT Research Network Programme, by the Russian Government under
mega project 11.G34.31.0053, and by the DFG Collaborative Research Center SFB/TRR
109 “Discretization in Geometry and Dynamics”.
article_processing_charge: No
article_type: original
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. Transactions
of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991
apa: Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay
complexes. Transactions of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/tran/6991
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Complexes.” Transactions of the American Mathematical Society.
American Mathematical Society, 2017. https://doi.org/10.1090/tran/6991.
ieee: U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,”
Transactions of the American Mathematical Society, vol. 369, no. 5. American
Mathematical Society, pp. 3741–3762, 2017.
ista: Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes.
Transactions of the American Mathematical Society. 369(5), 3741–3762.
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Complexes.” Transactions of the American Mathematical Society, vol. 369,
no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991.
short: U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society
369 (2017) 3741–3762.
date_created: 2018-12-11T11:49:59Z
date_published: 2017-05-01T00:00:00Z
date_updated: 2023-09-20T12:05:56Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/tran/6991
ec_funded: 1
external_id:
arxiv:
- '1312.1231'
isi:
- '000398030400024'
intvolume: ' 369'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1312.1231
month: '05'
oa: 1
oa_version: Preprint
page: 3741 - 3762
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '6311'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Morse theory of Čech and delaunay complexes
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 369
year: '2017'
...
---
_id: '1065'
abstract:
- lang: eng
text: 'We consider the problem of reachability in pushdown graphs. We study the
problem for pushdown graphs with constant treewidth. Even for pushdown graphs
with treewidth 1, for the reachability problem we establish the following: (i)
the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem
would contradict the k-clique conjecture and imply faster combinatorial algorithms
for cliques in graphs.'
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- 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: Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information
Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003
apa: Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant
treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003
chicago: Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with
Constant Treewidth.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003.
ieee: K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,”
Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.
ista: Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth.
Information Processing Letters. 122, 25–29.
mla: Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant
Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp.
25–29, doi:10.1016/j.ipl.2017.02.003.
short: K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.
date_created: 2018-12-11T11:49:57Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-20T12:08:18Z
day: '01'
ddc:
- '000'
department:
- _id: KrCh
- _id: HeEd
doi: 10.1016/j.ipl.2017.02.003
ec_funded: 1
external_id:
isi:
- '000399506600005'
file:
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content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:17Z
date_updated: 2019-10-15T07:44:51Z
file_id: '4998'
file_name: IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf
file_size: 247657
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has_accepted_license: '1'
intvolume: ' 122'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 25 - 29
project:
- _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
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
publication: Information Processing Letters
publication_identifier:
issn:
- '00200190'
publication_status: published
publisher: Elsevier
publist_id: '6323'
pubrep_id: '991'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pushdown reachability with constant treewidth
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 122
year: '2017'
...
---
_id: '1022'
abstract:
- lang: eng
text: We introduce a multiscale topological description of the Megaparsec web-like
cosmic matter distribution. Betti numbers and topological persistence offer a
powerful means of describing the rich connectivity structure of the cosmic web
and of its multiscale arrangement of matter and galaxies. Emanating from algebraic
topology and Morse theory, Betti numbers and persistence diagrams represent an
extension and deepening of the cosmologically familiar topological genus measure
and the related geometric Minkowski functionals. In addition to a description
of the mathematical background, this study presents the computational procedure
for computing Betti numbers and persistence diagrams for density field filtrations.
The field may be computed starting from a discrete spatial distribution of galaxies
or simulation particles. The main emphasis of this study concerns an extensive
and systematic exploration of the imprint of different web-like morphologies and
different levels of multiscale clustering in the corresponding computed Betti
numbers and persistence diagrams. To this end, we use Voronoi clustering models
as templates for a rich variety of web-like configurations and the fractal-like
Soneira-Peebles models exemplify a range of multiscale configurations. We have
identified the clear imprint of cluster nodes, filaments, walls, and voids in
persistence diagrams, along with that of the nested hierarchy of structures in
multiscale point distributions. We conclude by outlining the potential of persistent
topology for understanding the connectivity structure of the cosmic web, in large
simulations of cosmic structure formation and in the challenging context of the
observed galaxy distribution in large galaxy surveys.
acknowledgement: Part of this work has been supported by the 7th Framework Programme
for Research of the European Commission, under FETOpen grant number 255827 (CGL
Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random
Systems via Algebraic Topology) number 320422.
article_processing_charge: No
author:
- first_name: Pratyush
full_name: Pranav, Pratyush
last_name: Pranav
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Rien
full_name: Van De Weygaert, Rien
last_name: Van De Weygaert
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Bernard
full_name: Jones, Bernard
last_name: Jones
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic
web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical
Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862
apa: Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M.,
Jones, B., & Wintraecken, M. (2017). The topology of the cosmic web in terms
of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society.
Oxford University Press. https://doi.org/10.1093/mnras/stw2862
chicago: Pranav, Pratyush, Herbert Edelsbrunner, Rien Van De Weygaert, Gert Vegter,
Michael Kerber, Bernard Jones, and Mathijs Wintraecken. “The Topology of the Cosmic
Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical
Society. Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862.
ieee: P. Pranav et al., “The topology of the cosmic web in terms of persistent
Betti numbers,” Monthly Notices of the Royal Astronomical Society, vol.
465, no. 4. Oxford University Press, pp. 4281–4310, 2017.
ista: Pranav P, Edelsbrunner H, Van De Weygaert R, Vegter G, Kerber M, Jones B,
Wintraecken M. 2017. The topology of the cosmic web in terms of persistent Betti
numbers. Monthly Notices of the Royal Astronomical Society. 465(4), 4281–4310.
mla: Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent
Betti Numbers.” Monthly Notices of the Royal Astronomical Society, vol.
465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:10.1093/mnras/stw2862.
short: P. Pranav, H. Edelsbrunner, R. Van De Weygaert, G. Vegter, M. Kerber, B.
Jones, M. Wintraecken, Monthly Notices of the Royal Astronomical Society 465 (2017)
4281–4310.
date_created: 2018-12-11T11:49:44Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-09-22T09:40:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/mnras/stw2862
external_id:
isi:
- '000395170200039'
intvolume: ' 465'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.04519
month: '01'
oa: 1
oa_version: Submitted Version
page: 4281 - 4310
publication: Monthly Notices of the Royal Astronomical Society
publication_identifier:
issn:
- '00358711'
publication_status: published
publisher: Oxford University Press
publist_id: '6373'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The topology of the cosmic web in terms of persistent Betti numbers
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 465
year: '2017'
...
---
_id: '737'
abstract:
- lang: eng
text: We generalize Brazas’ topology on the fundamental group to the whole universal
path space X˜ i.e., to the set of homotopy classes of all based paths. We develop
basic properties of the new notion and provide a complete comparison of the obtained
topology with the established topologies, in particular with the Lasso topology
and the CO topology, i.e., the topology that is induced by the compact-open topology.
It turns out that the new topology is the finest topology contained in the CO
topology, for which the action of the fundamental group on the universal path
space is a continuous group action.
article_processing_charge: No
author:
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Andreas
full_name: Zastrow, Andreas
last_name: Zastrow
citation:
ama: Virk Z, Zastrow A. A new topology on the universal path space. Topology
and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015
apa: Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2017.09.015
chicago: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path
Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015.
ieee: Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology
and its Applications, vol. 231. Elsevier, pp. 186–196, 2017.
ista: Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology
and its Applications. 231, 186–196.
mla: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.”
Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.
short: Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.
date_created: 2018-12-11T11:48:14Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:53:01Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2017.09.015
external_id:
isi:
- '000413889100012'
intvolume: ' 231'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 186 - 196
publication: Topology and its Applications
publication_identifier:
issn:
- '01668641'
publication_status: published
publisher: Elsevier
publist_id: '6930'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A new topology on the universal path space
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 231
year: '2017'
...
---
_id: '836'
abstract:
- lang: eng
text: Recent research has examined how to study the topological features of a continuous
self-map by means of the persistence of the eigenspaces, for given eigenvalues,
of the endomorphism induced in homology over a field. This raised the question
of how to select dynamically significant eigenvalues. The present paper aims to
answer this question, giving an algorithm that computes the persistence of eigenspaces
for every eigenvalue simultaneously, also expressing said eigenspaces as direct
sums of “finite” and “singular” subspaces.
alternative_title:
- PROMS
article_processing_charge: No
author:
- first_name: Marc
full_name: Ethier, Marc
last_name: Ethier
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: Marian
full_name: Mrozek, Marian
last_name: Mrozek
citation:
ama: 'Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the
Kronecker canonical form. In: Special Sessions in Applications of Computer
Algebra. Vol 198. Springer; 2017:119-136. doi:10.1007/978-3-319-56932-1_8'
apa: 'Ethier, M., Jablonski, G., & Mrozek, M. (2017). Finding eigenvalues of
self-maps with the Kronecker canonical form. In Special Sessions in Applications
of Computer Algebra (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. https://doi.org/10.1007/978-3-319-56932-1_8'
chicago: Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues
of Self-Maps with the Kronecker Canonical Form.” In Special Sessions in Applications
of Computer Algebra, 198:119–36. Springer, 2017. https://doi.org/10.1007/978-3-319-56932-1_8.
ieee: M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps
with the Kronecker canonical form,” in Special Sessions in Applications of
Computer Algebra, Kalamata, Greece, 2017, vol. 198, pp. 119–136.
ista: 'Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with
the Kronecker canonical form. Special Sessions in Applications of Computer Algebra.
ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.'
mla: Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical
Form.” Special Sessions in Applications of Computer Algebra, vol. 198,
Springer, 2017, pp. 119–36, doi:10.1007/978-3-319-56932-1_8.
short: M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications
of Computer Algebra, Springer, 2017, pp. 119–136.
conference:
end_date: 2015-07-23
location: Kalamata, Greece
name: 'ACA: Applications of Computer Algebra'
start_date: 2015-07-20
date_created: 2018-12-11T11:48:46Z
date_published: 2017-07-27T00:00:00Z
date_updated: 2023-09-26T15:50:52Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-56932-1_8
ec_funded: 1
external_id:
isi:
- '000434088200008'
intvolume: ' 198'
isi: 1
language:
- iso: eng
month: '07'
oa_version: None
page: 119 - 136
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Special Sessions in Applications of Computer Algebra
publication_identifier:
isbn:
- 978-331956930-7
publication_status: published
publisher: Springer
publist_id: '6812'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finding eigenvalues of self-maps with the Kronecker canonical form
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 198
year: '2017'
...
---
_id: '833'
abstract:
- lang: eng
text: We present an efficient algorithm to compute Euler characteristic curves of
gray scale images of arbitrary dimension. In various applications the Euler characteristic
curve is used as a descriptor of an image. Our algorithm is the first streaming
algorithm for Euler characteristic curves. The usage of streaming removes the
necessity to store the entire image in RAM. Experiments show that our implementation
handles terabyte scale images on commodity hardware. Due to lock-free parallelism,
it scales well with the number of processor cores. Additionally, we put the concept
of the Euler characteristic curve in the wider context of computational topology.
In particular, we explain the connection with persistence diagrams.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of
multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer;
2017:397-409. doi:10.1007/978-3-319-64689-3_32'
apa: 'Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic
curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger
(Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of
Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32'
chicago: Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic
Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden,
and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32.
ieee: 'T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves
of multidimensional images,” presented at the CAIP: Computer Analysis of Images
and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.'
ista: 'Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves
of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS,
vol. 10424, 397–409.'
mla: Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic
Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol.
10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32.
short: T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer,
2017, pp. 397–409.
conference:
end_date: 2017-08-24
location: Ystad, Sweden
name: 'CAIP: Computer Analysis of Images and Patterns'
start_date: 2017-08-22
date_created: 2018-12-11T11:48:45Z
date_published: 2017-07-28T00:00:00Z
date_updated: 2023-09-26T16:10:03Z
day: '28'
department:
- _id: HeEd
doi: 10.1007/978-3-319-64689-3_32
editor:
- first_name: Michael
full_name: Felsberg, Michael
last_name: Felsberg
- first_name: Anders
full_name: Heyden, Anders
last_name: Heyden
- first_name: Norbert
full_name: Krüger, Norbert
last_name: Krüger
external_id:
isi:
- '000432085900032'
intvolume: ' 10424'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.02045
month: '07'
oa: 1
oa_version: Submitted Version
page: 397 - 409
publication_identifier:
issn:
- '03029743'
publication_status: published
publisher: Springer
publist_id: '6815'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Streaming algorithm for Euler characteristic curves of multidimensional images
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 10424
year: '2017'
...
---
_id: '84'
abstract:
- lang: eng
text: The advent of high-throughput technologies and the concurrent advances in
information sciences have led to a data revolution in biology. This revolution
is most significant in molecular biology, with an increase in the number and scale
of the “omics” projects over the last decade. Genomics projects, for example,
have produced impressive advances in our knowledge of the information concealed
into genomes, from the many genes that encode for the proteins that are responsible
for most if not all cellular functions, to the noncoding regions that are now
known to provide regulatory functions. Proteomics initiatives help to decipher
the role of post-translation modifications on the protein structures and provide
maps of protein-protein interactions, while functional genomics is the field that
attempts to make use of the data produced by these projects to understand protein
functions. The biggest challenge today is to assimilate the wealth of information
provided by these initiatives into a conceptual framework that will help us decipher
life. For example, the current views of the relationship between protein structure
and function remain fragmented. We know of their sequences, more and more about
their structures, we have information on their biological activities, but we have
difficulties connecting this dotted line into an informed whole. We lack the experimental
and computational tools for directly studying protein structure, function, and
dynamics at the molecular and supra-molecular levels. In this chapter, we review
some of the current developments in building the computational tools that are
needed, focusing on the role that geometry and topology play in these efforts.
One of our goals is to raise the general awareness about the importance of geometric
methods in elucidating the mysterious foundations of our very existence. Another
goal is the broadening of what we consider a geometric algorithm. There is plenty
of valuable no-man’s-land between combinatorial and numerical algorithms, and
it seems opportune to explore this land with a computational-geometric frame of
mind.
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: Patrice
full_name: Koehl, Patrice
last_name: Koehl
citation:
ama: 'Edelsbrunner H, Koehl P. Computational topology for structural molecular biology.
In: Toth C, O’Rourke J, Goodman J, eds. Handbook of Discrete and Computational
Geometry, Third Edition. Handbook of Discrete and Computational Geometry.
Taylor & Francis; 2017:1709-1735. doi:10.1201/9781315119601'
apa: Edelsbrunner, H., & Koehl, P. (2017). Computational topology for structural
molecular biology. In C. Toth, J. O’Rourke, & J. Goodman (Eds.), Handbook
of Discrete and Computational Geometry, Third Edition (pp. 1709–1735). Taylor
& Francis. https://doi.org/10.1201/9781315119601
chicago: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural
Molecular Biology.” In Handbook of Discrete and Computational Geometry, Third
Edition, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35.
Handbook of Discrete and Computational Geometry. Taylor & Francis, 2017. https://doi.org/10.1201/9781315119601.
ieee: H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular
biology,” in Handbook of Discrete and Computational Geometry, Third Edition,
C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor & Francis, 2017, pp. 1709–1735.
ista: 'Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular
biology. In: Handbook of Discrete and Computational Geometry, Third Edition. ,
1709–1735.'
mla: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural
Molecular Biology.” Handbook of Discrete and Computational Geometry, Third
Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35,
doi:10.1201/9781315119601.
short: H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.),
Handbook of Discrete and Computational Geometry, Third Edition, Taylor & Francis,
2017, pp. 1709–1735.
date_created: 2018-12-11T11:44:32Z
date_published: 2017-11-09T00:00:00Z
date_updated: 2023-10-16T11:15:22Z
day: '09'
department:
- _id: HeEd
doi: 10.1201/9781315119601
editor:
- first_name: Csaba
full_name: Toth, Csaba
last_name: Toth
- first_name: Joseph
full_name: O'Rourke, Joseph
last_name: O'Rourke
- first_name: Jacob
full_name: Goodman, Jacob
last_name: Goodman
language:
- iso: eng
month: '11'
oa_version: None
page: 1709 - 1735
publication: Handbook of Discrete and Computational Geometry, Third Edition
publication_identifier:
eisbn:
- '9781498711425'
publication_status: published
publisher: Taylor & Francis
publist_id: '7970'
quality_controlled: '1'
scopus_import: '1'
series_title: Handbook of Discrete and Computational Geometry
status: public
title: Computational topology for structural molecular biology
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2017'
...
---
_id: '909'
abstract:
- lang: eng
text: We study the lengths of curves passing through a fixed number of points on
the boundary of a convex shape in the plane. We show that, for any convex shape
K, there exist four points on the boundary of K such that the length of any curve
passing through these points is at least half of the perimeter of K. It is also
shown that the same statement does not remain valid with the additional constraint
that the points are extreme points of K. Moreover, the factor ½ cannot
be achieved with any fixed number of extreme points. We conclude the paper with
a few other inequalities related to the perimeter of a convex shape.
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: Vladislav
full_name: Vysotsky, Vladislav
last_name: Vysotsky
citation:
ama: Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points
of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596.
doi:10.4169/amer.math.monthly.124.7.588
apa: Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through
boundary points of a planar convex shape. The American Mathematical Monthly.
Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588
chicago: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing
through Boundary Points of a Planar Convex Shape.” The American Mathematical
Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588.
ieee: A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary
points of a planar convex shape,” The American Mathematical Monthly, vol.
124, no. 7. Mathematical Association of America, pp. 588–596, 2017.
ista: Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary
points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.
mla: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing
through Boundary Points of a Planar Convex Shape.” The American Mathematical
Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96,
doi:10.4169/amer.math.monthly.124.7.588.
short: A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.
date_created: 2018-12-11T11:49:09Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-10-17T11:24:57Z
day: '01'
department:
- _id: HeEd
doi: 10.4169/amer.math.monthly.124.7.588
ec_funded: 1
external_id:
arxiv:
- '1605.07997'
isi:
- '000413947300002'
intvolume: ' 124'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.07997
month: '01'
oa: 1
oa_version: Submitted Version
page: 588 - 596
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: The American Mathematical Monthly
publication_identifier:
issn:
- '00029890'
publication_status: published
publisher: Mathematical Association of America
publist_id: '6534'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the lengths of curves passing through boundary points of a planar convex
shape
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 124
year: '2017'
...
---
_id: '1149'
abstract:
- lang: eng
text: 'We study the usefulness of two most prominent publicly available rigorous
ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other
based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable
of handling entire sets of initial conditions and provide tight rigorous outer
enclosures of the images under a time-T map. We conduct extensive benchmark computations
using the well-known Lorenz system, and compare the computation time against the
final accuracy achieved. We also discuss the effect of a few technical parameters,
such as the order of the numerical integration method, the value of T, and the
phase space resolution. We conclude that COSY may provide more precise results
due to its ability of avoiding the variable dependency problem. However, the overall
cost of computations conducted using CAPD is typically lower, especially when
intervals of parameters are involved. Moreover, access to COSY is limited (registration
required) and the rigorous ODE integrators are not publicly available, while CAPD
is an open source free software project. Therefore, we recommend the latter integrator
for this kind of computations. Nevertheless, proper choice of the various integration
parameters turns out to be of even greater importance than the choice of the integrator
itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved.'
acknowledgement: "MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9,
and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially
supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry
of Education, Science, Technology, Culture and Sports, Japan. KM was supported by
NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR
and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part
of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch conducted
by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER)
through COMPETE – Programa Operacional Factores de Competitividade (POFC) and from
the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT)
in the framework of the research project FCOMP-01-0124-FEDER-010645 (Ref. FCT PTDC/MAT/098871/2008);
from the People Programme (Marie Curie Actions) of the European Union's Seventh
Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from
the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department
of Mathematics of Kyoto University for making their server available for conducting
the computations described in the paper, and to the reviewers for helpful comments
that contributed towards increasing the quality of the paper."
author:
- first_name: Tomoyuki
full_name: Miyaji, Tomoyuki
last_name: Miyaji
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
- first_name: Marcio
full_name: Gameiro, Marcio
last_name: Gameiro
- first_name: Hiroshi
full_name: Kokubu, Hiroshi
last_name: Kokubu
- first_name: Konstantin
full_name: Mischaikow, Konstantin
last_name: Mischaikow
citation:
ama: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous
ODE integrators for multi scale set oriented computations. Applied Numerical
Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005
apa: Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016).
A study of rigorous ODE integrators for multi scale set oriented computations.
Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005
chicago: Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and
Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set
Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016.
https://doi.org/10.1016/j.apnum.2016.04.005.
ieee: T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study
of rigorous ODE integrators for multi scale set oriented computations,” Applied
Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016.
ista: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of
rigorous ODE integrators for multi scale set oriented computations. Applied Numerical
Mathematics. 107, 34–47.
mla: Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale
Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier,
2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005.
short: T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical
Mathematics 107 (2016) 34–47.
date_created: 2018-12-11T11:50:25Z
date_published: 2016-09-01T00:00:00Z
date_updated: 2021-01-12T06:48:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.apnum.2016.04.005
ec_funded: 1
intvolume: ' 107'
language:
- iso: eng
month: '09'
oa_version: None
page: 34 - 47
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Applied Numerical Mathematics
publication_status: published
publisher: Elsevier
publist_id: '6209'
quality_controlled: '1'
scopus_import: 1
status: public
title: A study of rigorous ODE integrators for multi scale set oriented computations
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 107
year: '2016'
...
---
_id: '1216'
abstract:
- lang: eng
text: 'A framework fo r extracting features in 2D transient flows, based on the
acceleration field to ensure Galilean invariance is proposed in this paper. The
minima of the acceleration magnitude (a superset of acceleration zeros) are extracted
and discriminated into vortices and saddle points, based on the spectral properties
of the velocity Jacobian. The extraction of topological features is performed
with purely combinatorial algorithms from discrete computational topology. The
feature points are prioritized with persistence, as a physically meaningful importance
measure. These feature points are tracked in time with a robust algorithm for
tracking features. Thus, a space-time hierarchy of the minima is built and vortex
merging events are detected. We apply the acceleration feature extraction strategy
to three two-dimensional shear flows: (1) an incompressible periodic cylinder
wake, (2) an incompressible planar mixing layer and (3) a weakly compressible
planar jet. The vortex-like acceleration feature points are shown to be well aligned
with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure
field and minima of λ2.'
acknowledgement: "The authors acknowledge funding of the German Re-\r\nsearch Foundation
\ (DFG) via the Collaborative Re-\r\nsearch Center (SFB 557) \\Control of
\ Complex Turbu-\r\nlent Shear Flows\" and the Emmy Noether Program.\r\nFurther
\ funding was provided by the Zuse Institute\r\nBerlin (ZIB), the DFG-CNRS
\ research group \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence
'Closed-loop control of turbulent shear ows\r\nusing reduced-order models' (TUCOROM)
of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean Social
\ Fund (ESF App. No. 100098251). We\r\nthank the Ambrosys Ltd. Society
\ for Complex Sys-\r\ntems Management and the Bernd R. Noack Cybernet-\r\nics
\ Foundation for additional support. A part of this\r\nwork was performed
using HPC resources from GENCI-[CCRT/CINES/IDRIS] supported by the Grant 2011-\r\n[x2011020912"
author:
- first_name: Jens
full_name: Kasten, Jens
last_name: Kasten
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Hans
full_name: Hege, Hans
last_name: Hege
- first_name: Bernd
full_name: Noack, Bernd
last_name: Noack
- first_name: Guillaume
full_name: Daviller, Guillaume
last_name: Daviller
- first_name: Marek
full_name: Morzyński, Marek
last_name: Morzyński
citation:
ama: Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady
shear flows. Archives of Mechanics. 2016;68(1):55-80.
apa: Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., &
Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. Archives
of Mechanics. Polish Academy of Sciences Publishing House.
chicago: Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume
Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear
Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House,
2016.
ieee: J. Kasten et al., “Acceleration feature points of unsteady shear flows,”
Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing
House, pp. 55–80, 2016.
ista: Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M.
2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics.
68(1), 55–80.
mla: Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.”
Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing
House, 2016, pp. 55–80.
short: J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński,
Archives of Mechanics 68 (2016) 55–80.
date_created: 2018-12-11T11:50:46Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:09Z
day: '01'
department:
- _id: HeEd
intvolume: ' 68'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf
month: '01'
oa: 1
oa_version: Published Version
page: 55 - 80
publication: Archives of Mechanics
publication_status: published
publisher: Polish Academy of Sciences Publishing House
publist_id: '6118'
quality_controlled: '1'
scopus_import: 1
status: public
title: Acceleration feature points of unsteady shear flows
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2016'
...
---
_id: '1222'
abstract:
- lang: eng
text: We consider packings of congruent circles on a square flat torus, i.e., periodic
(w.r.t. a square lattice) planar circle packings, with the maximal circle radius.
This problem is interesting due to a practical reason—the problem of “super resolution
of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly,
for the case N=7 there are three different optimal arrangements. Our proof is
based on a computer enumeration of toroidal irreducible contact graphs.
acknowledgement: We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy
for some useful comments and remarks, and especially Thom Sulanke for modifying
surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant
DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported
by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg
State University) under RF Government Grant 11.G34.31.0026.
author:
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
citation:
ama: Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat
torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6
apa: Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles
on a square flat torus. Discrete & Computational Geometry. Springer.
https://doi.org/10.1007/s00454-015-9742-6
chicago: Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles
on a Square Flat Torus.” Discrete & Computational Geometry. Springer,
2016. https://doi.org/10.1007/s00454-015-9742-6.
ieee: O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square
flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer,
pp. 1–20, 2016.
ista: Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square
flat torus. Discrete & Computational Geometry. 55(1), 1–20.
mla: Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on
a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no.
1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.
short: O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20.
date_created: 2018-12-11T11:50:48Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:11Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-015-9742-6
intvolume: ' 55'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1212.0649
month: '01'
oa: 1
oa_version: Preprint
page: 1 - 20
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '6111'
quality_controlled: '1'
scopus_import: 1
status: public
title: Optimal packings of congruent circles on a square flat torus
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2016'
...
---
_id: '1237'
abstract:
- lang: eng
text: 'Bitmap images of arbitrary dimension may be formally perceived as unions
of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology
and homology groups are well known topological invariants of such sets. Cohomological
operations, such as the cup product, provide higher-order algebraic topological
invariants, especially important for digital images of dimension higher than 3.
If such an operation is determined at the level of simplicial chains [see e.g.
González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively
computable. However, decomposing a cubical complex into a simplicial one deleteriously
affects the efficiency of such an approach. In order to avoid this overhead, a
direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015,
253-275] for the cup product in cohomology, and implemented in the ChainCon software
package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for
the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series,
1947, 290-320] directly at the level of cubical chains, and we prove the correctness
of this formula. An implementation of this formula is programmed in C++ within
the ChainCon software framework. We provide a few examples and discuss the effectiveness
of this approach. One specific application follows from the fact that Steenrod
squares yield tests for the topological extension problem: Can a given map A →
Sd to a sphere Sd be extended to a given super-complex X of A? In particular,
the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value
r > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the
extension problem.'
acknowledgement: The research conducted by both authors has received funding from
the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework
Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and
no. 622033 (for P. P.).
alternative_title:
- LNCS
author:
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: 'Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667.
Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13'
apa: 'Krcál, M., & Pilarczyk, P. (2016). Computation of cubical Steenrod squares
(Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image
Context, Marseille, France: Springer. https://doi.org/10.1007/978-3-319-39441-1_13'
chicago: Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,”
9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13.
ieee: 'M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented
at the CTIC: Computational Topology in Image Context, Marseille, France, 2016,
vol. 9667, pp. 140–151.'
ista: 'Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC:
Computational Topology in Image Context, LNCS, vol. 9667, 140–151.'
mla: Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares.
Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.
short: M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.
conference:
end_date: 2016-06-17
location: Marseille, France
name: 'CTIC: Computational Topology in Image Context'
start_date: 2016-06-15
date_created: 2018-12-11T11:50:52Z
date_published: 2016-06-02T00:00:00Z
date_updated: 2021-01-12T06:49:18Z
day: '02'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_13
ec_funded: 1
intvolume: ' 9667'
language:
- iso: eng
month: '06'
oa_version: None
page: 140 - 151
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication_status: published
publisher: Springer
publist_id: '6096'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computation of cubical Steenrod squares
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 9667
year: '2016'
...
---
_id: '1252'
abstract:
- lang: eng
text: We study the homomorphism induced in homology by a closed correspondence between
topological spaces, using projections from the graph of the correspondence to
its domain and codomain. We provide assumptions under which the homomorphism induced
by an outer approximation of a continuous map coincides with the homomorphism
induced in homology by the map. In contrast to more classical results we do not
require that the projection to the domain have acyclic preimages. Moreover, we
show that it is possible to retrieve correct homological information from a correspondence
even if some data is missing or perturbed. Finally, we describe an application
to combinatorial maps that are either outer approximations of continuous maps
or reconstructions of such maps from a finite set of data points.
acknowledgement: "The authors gratefully acknowledge the support of the Lorenz Center
which\r\nprovided an opportunity for us to discuss in depth the work of this paper.
Research leading to these results has received funding from Fundo Europeu de Desenvolvimento
Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade
(POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia
e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie
Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013)
under REA grant agreement no. 622033 (supporting PP). The work of the first and
third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019,
1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second
author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029),
Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan."
article_processing_charge: No
article_type: original
author:
- first_name: Shaun
full_name: Harker, Shaun
last_name: Harker
- first_name: Hiroshi
full_name: Kokubu, Hiroshi
last_name: Kokubu
- first_name: Konstantin
full_name: Mischaikow, Konstantin
last_name: Mischaikow
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from
a correspondence. Proceedings of the American Mathematical Society. 2016;144(4):1787-1801.
doi:10.1090/proc/12812
apa: Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing
a map on homology from a correspondence. Proceedings of the American Mathematical
Society. American Mathematical Society. https://doi.org/10.1090/proc/12812
chicago: Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk.
“Inducing a Map on Homology from a Correspondence.” Proceedings of the American
Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12812.
ieee: S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on
homology from a correspondence,” Proceedings of the American Mathematical Society,
vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.
ista: Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology
from a correspondence. Proceedings of the American Mathematical Society. 144(4),
1787–1801.
mla: Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” Proceedings
of the American Mathematical Society, vol. 144, no. 4, American Mathematical
Society, 2016, pp. 1787–801, doi:10.1090/proc/12812.
short: S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American
Mathematical Society 144 (2016) 1787–1801.
date_created: 2018-12-11T11:50:57Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2022-05-24T09:35:58Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/12812
ec_funded: 1
external_id:
arxiv:
- '1411.7563'
intvolume: ' 144'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1411.7563
month: '04'
oa: 1
oa_version: Preprint
page: 1787 - 1801
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Proceedings of the American Mathematical Society
publication_identifier:
issn:
- 1088-6826
publication_status: published
publisher: American Mathematical Society
publist_id: '6075'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inducing a map on homology from a correspondence
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...
---
_id: '1254'
abstract:
- lang: eng
text: We use rigorous numerical techniques to compute a lower bound for the exponent
of expansivity outside a neighborhood of the critical point for thousands of intervals
of parameter values in the quadratic family. We first compute a radius of the
critical neighborhood outside which the map is uniformly expanding. This radius
is taken as small as possible, yet large enough for our numerical procedure to
succeed in proving that the expansivity exponent outside this neighborhood is
positive. Then, for each of the intervals, we compute a lower bound for this expansivity
exponent, valid for all the parameters in that interval. We illustrate and study
the distribution of the radii and the expansivity exponents. The results of our
computations are mathematically rigorous. The source code of the software and
the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/.
acknowledgement: "AG and PP were partially supported by Abdus Salam International
Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS,
and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento
Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade
(POFC) and from the Portuguese national funds through Fundação para a Ciência e
a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions)
of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant
agreement no. 622033. The authors gratefully acknowledge the Department of\r\nMathematics
\ of Kyoto University for providing access\r\nto their server for conducting
\ computations for this\r\nproject."
author:
- first_name: Ali
full_name: Golmakani, Ali
last_name: Golmakani
- first_name: Stefano
full_name: Luzzatto, Stefano
last_name: Luzzatto
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical
neighborhood in the quadratic family. Experimental Mathematics. 2016;25(2):116-124.
doi:10.1080/10586458.2015.1048011
apa: Golmakani, A., Luzzatto, S., & Pilarczyk, P. (2016). Uniform expansivity
outside a critical neighborhood in the quadratic family. Experimental Mathematics.
Taylor and Francis. https://doi.org/10.1080/10586458.2015.1048011
chicago: Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity
Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics.
Taylor and Francis, 2016. https://doi.org/10.1080/10586458.2015.1048011.
ieee: A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside
a critical neighborhood in the quadratic family,” Experimental Mathematics,
vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016.
ista: Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a
critical neighborhood in the quadratic family. Experimental Mathematics. 25(2),
116–124.
mla: Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood
in the Quadratic Family.” Experimental Mathematics, vol. 25, no. 2, Taylor
and Francis, 2016, pp. 116–24, doi:10.1080/10586458.2015.1048011.
short: A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016)
116–124.
date_created: 2018-12-11T11:50:58Z
date_published: 2016-04-02T00:00:00Z
date_updated: 2021-01-12T06:49:25Z
day: '02'
department:
- _id: HeEd
doi: 10.1080/10586458.2015.1048011
ec_funded: 1
intvolume: ' 25'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1504.00116
month: '04'
oa: 1
oa_version: Preprint
page: 116 - 124
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Experimental Mathematics
publication_status: published
publisher: Taylor and Francis
publist_id: '6071'
quality_controlled: '1'
scopus_import: 1
status: public
title: Uniform expansivity outside a critical neighborhood in the quadratic family
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2016'
...
---
_id: '1272'
abstract:
- lang: eng
text: We study different means to extend offsetting based on skeletal structures
beyond the well-known constant-radius and mitered offsets supported by Voronoi
diagrams and straight skeletons, for which the orthogonal distance of offset elements
to their respective input elements is constant and uniform over all input elements.
Our main contribution is a new geometric structure, called variable-radius Voronoi
diagram, which supports the computation of variable-radius offsets, i.e., offsets
whose distance to the input is allowed to vary along the input. We discuss properties
of this structure and sketch a prototype implementation that supports the computation
of variable-radius offsets based on this new variant of Voronoi diagrams.
acknowledgement: 'This work was supported by Austrian Science Fund (FWF): P25816-N15.'
author:
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using
skeletons. Computer-Aided Design and Applications. 2016;13(5):712-721.
doi:10.1080/16864360.2016.1150718
apa: Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of
planar structures using skeletons. Computer-Aided Design and Applications.
Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718
chicago: Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting
of Planar Structures Using Skeletons.” Computer-Aided Design and Applications.
Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718.
ieee: M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures
using skeletons,” Computer-Aided Design and Applications, vol. 13, no.
5. Taylor and Francis, pp. 712–721, 2016.
ista: Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures
using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.
mla: Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.”
Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis,
2016, pp. 712–21, doi:10.1080/16864360.2016.1150718.
short: M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13
(2016) 712–721.
date_created: 2018-12-11T11:51:04Z
date_published: 2016-09-02T00:00:00Z
date_updated: 2021-01-12T06:49:32Z
day: '02'
ddc:
- '004'
- '516'
department:
- _id: HeEd
doi: 10.1080/16864360.2016.1150718
file:
- access_level: open_access
checksum: c746f3a48edb62b588d92ea5d0fd2c0e
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:20Z
date_updated: 2020-07-14T12:44:42Z
file_id: '5206'
file_name: IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf
file_size: 1678369
relation: main_file
file_date_updated: 2020-07-14T12:44:42Z
has_accepted_license: '1'
intvolume: ' 13'
issue: '5'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 712 - 721
publication: Computer-Aided Design and Applications
publication_status: published
publisher: Taylor and Francis
publist_id: '6048'
pubrep_id: '694'
quality_controlled: '1'
scopus_import: 1
status: public
title: Generalized offsetting of planar structures using skeletons
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 13
year: '2016'
...
---
_id: '1295'
abstract:
- lang: eng
text: Voronoi diagrams and Delaunay triangulations have been extensively used to
represent and compute geometric features of point configurations. We introduce
a generalization to poset diagrams and poset complexes, which contain order-k
and degree-k Voronoi diagrams and their duals as special cases. Extending a result
of Aurenhammer from 1990, we show how to construct poset diagrams as weighted
Voronoi diagrams of average balls.
acknowledgement: This work is partially supported by the Toposys project FP7-ICT-318493-STREP,
and by ESF under the ACAT Research Network Programme.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: 'Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages.
Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030'
apa: 'Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls
II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier.
https://doi.org/10.1016/j.endm.2016.09.030'
chicago: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier,
2016. https://doi.org/10.1016/j.endm.2016.09.030.'
ieee: 'H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted
averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier,
pp. 169–174, 2016.'
ista: 'Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted
averages. Electronic Notes in Discrete Mathematics. 54, 169–174.'
mla: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol.
54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030.'
short: H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics
54 (2016) 169–174.
date_created: 2018-12-11T11:51:12Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2021-01-12T06:49:41Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.endm.2016.09.030
ec_funded: 1
intvolume: ' 54'
language:
- iso: eng
month: '10'
oa_version: None
page: 169 - 174
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Electronic Notes in Discrete Mathematics
publication_status: published
publisher: Elsevier
publist_id: '5976'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Multiple covers with balls II: Weighted averages'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 54
year: '2016'
...
---
_id: '1292'
abstract:
- lang: eng
text: We give explicit formulas and algorithms for the computation of the Thurston–Bennequin
invariant of a nullhomologous Legendrian knot on a page of a contact open book
and on Heegaard surfaces in convex position. Furthermore, we extend the results
to rationally nullhomologous knots in arbitrary 3-manifolds.
acknowledgement: "The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful
discussions and advice and Christian Evers for helpful remarks on a draft version."
author:
- first_name: Sebastian
full_name: Durst, Sebastian
last_name: Durst
- first_name: Marc
full_name: Kegel, Marc
last_name: Kegel
- first_name: Mirko D
full_name: Klukas, Mirko D
id: 34927512-F248-11E8-B48F-1D18A9856A87
last_name: Klukas
citation:
ama: Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in
open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4
apa: Durst, S., Kegel, M., & Klukas, M. D. (2016). Computing the Thurston–Bennequin
invariant in open books. Acta Mathematica Hungarica. Springer. https://doi.org/10.1007/s10474-016-0648-4
chicago: Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin
Invariant in Open Books.” Acta Mathematica Hungarica. Springer, 2016. https://doi.org/10.1007/s10474-016-0648-4.
ieee: S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant
in open books,” Acta Mathematica Hungarica, vol. 150, no. 2. Springer,
pp. 441–455, 2016.
ista: Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant
in open books. Acta Mathematica Hungarica. 150(2), 441–455.
mla: Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open
Books.” Acta Mathematica Hungarica, vol. 150, no. 2, Springer, 2016, pp.
441–55, doi:10.1007/s10474-016-0648-4.
short: S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455.
date_created: 2018-12-11T11:51:11Z
date_published: 2016-12-01T00:00:00Z
date_updated: 2021-01-12T06:49:40Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10474-016-0648-4
intvolume: ' 150'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.00794
month: '12'
oa: 1
oa_version: Preprint
page: 441 - 455
publication: Acta Mathematica Hungarica
publication_status: published
publisher: Springer
publist_id: '6023'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computing the Thurston–Bennequin invariant in open books
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 150
year: '2016'
...
---
_id: '1330'
abstract:
- lang: eng
text: In this paper we investigate the existence of closed billiard trajectories
in not necessarily smooth convex bodies. In particular, we show that if a body
K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K
is acute (in a certain sense), then there is a closed billiard trajectory in K.
acknowledgement: Supported by People Programme (Marie Curie Actions) of the European
Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734].
Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a
ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part
by the Moebius Contest Foundation for Young Scientists, and in part by the Simons
Foundation.
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
citation:
ama: Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel
Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z
apa: Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute
angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z
chicago: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with
Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z.
ieee: A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,”
Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845,
2016.
ista: Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles.
Israel Journal of Mathematics. 216(2), 833–845.
mla: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute
Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016,
pp. 833–45, doi:10.1007/s11856-016-1429-z.
short: A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.
date_created: 2018-12-11T11:51:24Z
date_published: 2016-10-15T00:00:00Z
date_updated: 2021-01-12T06:49:56Z
day: '15'
department:
- _id: HeEd
doi: 10.1007/s11856-016-1429-z
ec_funded: 1
intvolume: ' 216'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1506.06014
month: '10'
oa: 1
oa_version: Preprint
page: 833 - 845
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Israel Journal of Mathematics
publication_status: published
publisher: Springer
publist_id: '5938'
quality_controlled: '1'
scopus_import: 1
status: public
title: Billiards in convex bodies with acute angles
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 216
year: '2016'
...
---
_id: '1360'
abstract:
- lang: eng
text: 'We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard
trajectories in convex bodies, when the length is measured with a (possibly asymmetric)
norm. We prove a lower bound for the length of the shortest closed billiard trajectory,
related to the non-symmetric Mahler problem. With this technique we are able to
give short and elementary proofs to some known results. '
acknowledgement: The first and third authors were supported by the Dynasty Foundation.
The first, second and third authors were supported by the Russian Foundation for
Basic Re- search grant 15-31-20403 (mol a ved).
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: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
- first_name: Anastasia
full_name: Sharipova, Anastasia
last_name: Sharipova
citation:
ama: Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed
billiard trajectories in asymmetric normed spaces. Proceedings of the American
Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062
apa: Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary
approach to closed billiard trajectories in asymmetric normed spaces. Proceedings
of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062
chicago: Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova.
“Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.”
Proceedings of the American Mathematical Society. American Mathematical
Society, 2016. https://doi.org/10.1090/proc/13062.
ieee: A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach
to closed billiard trajectories in asymmetric normed spaces,” Proceedings of
the American Mathematical Society, vol. 144, no. 10. American Mathematical
Society, pp. 4501–4513, 2016.
ista: Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach
to closed billiard trajectories in asymmetric normed spaces. Proceedings of the
American Mathematical Society. 144(10), 4501–4513.
mla: Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories
in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society,
vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062.
short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American
Mathematical Society 144 (2016) 4501–4513.
date_created: 2018-12-11T11:51:34Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2021-01-12T06:50:09Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/13062
ec_funded: 1
intvolume: ' 144'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1401.0442
month: '10'
oa: 1
oa_version: Preprint
page: 4501 - 4513
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '5885'
quality_controlled: '1'
scopus_import: 1
status: public
title: Elementary approach to closed billiard trajectories in asymmetric normed spaces
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...
---
_id: '1408'
abstract:
- lang: eng
text: 'The concept of well group in a special but important case captures homological
properties of the zero set of a continuous map (Formula presented.) on a compact
space K that are invariant with respect to perturbations of f. The perturbations
are arbitrary continuous maps within (Formula presented.) distance r from f for
a given (Formula presented.). The main drawback of the approach is that the computability
of well groups was shown only when (Formula presented.) or (Formula presented.).
Our contribution to the theory of well groups is twofold: on the one hand we improve
on the computability issue, but on the other hand we present a range of examples
where the well groups are incomplete invariants, that is, fail to capture certain
important robust properties of the zero set. For the first part, we identify a
computable subgroup of the well group that is obtained by cap product with the
pullback of the orientation of (Formula presented.) by f. In other words, well
groups can be algorithmically approximated from below. When f is smooth and (Formula
presented.), our approximation of the (Formula presented.)th well group is exact.
For the second part, we find examples of maps (Formula presented.) with all well
groups isomorphic but whose perturbations have different zero sets. We discuss
on a possible replacement of the well groups of vector valued maps by an invariant
of a better descriptive power and computability status.'
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). '
article_processing_charge: Yes (via OA deal)
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. On computability and triviality of well groups. Discrete
& Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2
apa: Franek, P., & Krcál, M. (2016). On computability and triviality of well
groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2
chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well
Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.
ieee: P. Franek and M. Krcál, “On computability and triviality of well groups,”
Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164,
2016.
ista: Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete
& Computational Geometry. 56(1), 126–164.
mla: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.”
Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016,
pp. 126–64, doi:10.1007/s00454-016-9794-2.
short: P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.
date_created: 2018-12-11T11:51:51Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2023-02-23T10:02:11Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-016-9794-2
ec_funded: 1
file:
- access_level: open_access
checksum: e0da023abf6b72abd8c6a8c76740d53c
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:55Z
date_updated: 2020-07-14T12:44:53Z
file_id: '4846'
file_name: IST-2016-614-v1+1_s00454-016-9794-2.pdf
file_size: 905303
relation: main_file
file_date_updated: 2020-07-14T12:44:53Z
has_accepted_license: '1'
intvolume: ' 56'
issue: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 126 - 164
project:
- _id: 25F8B9BC-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M01980
name: Robust invariants of Nonlinear Systems
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5799'
pubrep_id: '614'
quality_controlled: '1'
related_material:
record:
- id: '1510'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: On computability and triviality of well groups
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: 56
year: '2016'
...
---
_id: '1289'
abstract:
- lang: eng
text: 'Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI)
magnifying endoscopic (ME) images of the stomach, we combine methods from image
processing, topology, geometry, and machine learning to classify patterns into
three classes: oval, tubular and irregular. Training the algorithm on a small
number of images of each type, we achieve a high rate of correct classifications.
The analysis of the learning algorithm reveals that a handful of geometric and
topological features are responsible for the overwhelming majority of decisions.'
article_processing_charge: No
author:
- first_name: Olga
full_name: Dunaeva, Olga
last_name: Dunaeva
- 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: Lukyanov, Anton
last_name: Lukyanov
- first_name: Michael
full_name: Machin, Michael
last_name: Machin
- first_name: Daria
full_name: Malkova, Daria
last_name: Malkova
- first_name: Roman
full_name: Kuvaev, Roman
last_name: Kuvaev
- first_name: Sergey
full_name: Kashin, Sergey
last_name: Kashin
citation:
ama: Dunaeva O, Edelsbrunner H, Lukyanov A, et al. The classification of endoscopy
images with persistent homology. Pattern Recognition Letters. 2016;83(1):13-22.
doi:10.1016/j.patrec.2015.12.012
apa: Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., Malkova, D., Kuvaev,
R., & Kashin, S. (2016). The classification of endoscopy images with persistent
homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2015.12.012
chicago: Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria
Malkova, Roman Kuvaev, and Sergey Kashin. “The Classification of Endoscopy Images
with Persistent Homology.” Pattern Recognition Letters. Elsevier, 2016.
https://doi.org/10.1016/j.patrec.2015.12.012.
ieee: O. Dunaeva et al., “The classification of endoscopy images with persistent
homology,” Pattern Recognition Letters, vol. 83, no. 1. Elsevier, pp. 13–22,
2016.
ista: Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin
S. 2016. The classification of endoscopy images with persistent homology. Pattern
Recognition Letters. 83(1), 13–22.
mla: Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent
Homology.” Pattern Recognition Letters, vol. 83, no. 1, Elsevier, 2016,
pp. 13–22, doi:10.1016/j.patrec.2015.12.012.
short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev,
S. Kashin, Pattern Recognition Letters 83 (2016) 13–22.
date_created: 2018-12-11T11:51:10Z
date_published: 2016-11-01T00:00:00Z
date_updated: 2023-02-23T10:04:40Z
day: '01'
ddc:
- '004'
- '514'
department:
- _id: HeEd
doi: 10.1016/j.patrec.2015.12.012
file:
- access_level: open_access
checksum: 33458bbb8c32a339e1adeca6d5a1112d
content_type: application/pdf
creator: dernst
date_created: 2019-04-17T07:55:51Z
date_updated: 2020-07-14T12:44:42Z
file_id: '6334'
file_name: 2016-Edelsbrunner_The_classification.pdf
file_size: 1921113
relation: main_file
file_date_updated: 2020-07-14T12:44:42Z
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intvolume: ' 83'
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Submitted Version
page: 13 - 22
publication: Pattern Recognition Letters
publication_status: published
publisher: Elsevier
publist_id: '6027'
pubrep_id: '975'
quality_controlled: '1'
related_material:
record:
- id: '1568'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: The classification of endoscopy images with persistent homology
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 83
year: '2016'
...
---
_id: '1617'
abstract:
- lang: eng
text: 'We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d
is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of
equal measure and placing a random point inside each of the N=md cubes. We prove
that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d,
where the upper bound with an unspecified constant Cd was proven earlier by Beck.
Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality
and a suitably taylored Bernstein inequality; we have reasons to believe that
the upper bound has the sharp scaling in N. Additional heuristics suggest that
jittered sampling should be able to improve known bounds on the inverse of the
star-discrepancy in the regime N≳dd. We also prove a partition principle showing
that every partition of [0,1]d combined with a jittered sampling construction
gives rise to a set whose expected squared L2-discrepancy is smaller than that
of purely random points.'
acknowledgement: We are grateful to the referee whose suggestions greatly improved
the quality and clarity of the exposition.
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
- first_name: Stefan
full_name: Steinerberger, Stefan
last_name: Steinerberger
citation:
ama: Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal
of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003
apa: Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered
sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003
chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003.
ieee: F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,”
Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016.
ista: Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling.
Journal of Complexity. 33, 199–216.
mla: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216,
doi:10.1016/j.jco.2015.11.003.
short: F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.
date_created: 2018-12-11T11:53:03Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2021-01-12T06:52:02Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.11.003
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1510.00251
month: '04'
oa: 1
oa_version: Submitted Version
page: 199 - 216
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5549'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the discrepancy of jittered sampling
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2016'
...
---
_id: '5806'
abstract:
- lang: eng
text: Although the concept of functional plane for naive plane is studied and reported
in the literature in great detail, no similar study is yet found for naive sphere.
This article exposes the first study in this line, opening up further prospects
of analyzing the topological properties of sphere in the discrete space. We show
that each quadraginta octant Q of a naive sphere forms a bijection with its projected
pixel set on a unique coordinate plane, which thereby serves as the functional
plane of Q, and hence gives rise to merely mono-jumps during back projection.
The other two coordinate planes serve as para-functional and dia-functional planes
for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds
neither of the two. Owing to this, the quadraginta octants form symmetry groups
and subgroups with equivalent jump conditions. We also show a potential application
in generating a special class of discrete 3D circles based on back projection
and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry,
uniqueness, and bounded distance from the underlying real sphere and real plane.
alternative_title:
- LNCS
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: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere
with application to circle drawing. In: Discrete Geometry for Computer Imagery.
Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20'
apa: 'Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants
of naive sphere with application to circle drawing. In Discrete Geometry for
Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta
Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry
for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.'
ieee: R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive
sphere with application to circle drawing,” in Discrete Geometry for Computer
Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267.
ista: 'Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive
sphere with application to circle drawing. Discrete Geometry for Computer Imagery.
DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS,
vol. 9647, 256–267.'
mla: Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants
of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for
Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.
short: R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer
Nature, Cham, 2016, pp. 256–267.
conference:
end_date: 2016-04-20
location: Nantes, France
name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
start_date: 2016-04-18
date_created: 2019-01-08T20:44:37Z
date_published: 2016-04-09T00:00:00Z
date_updated: 2022-01-28T08:10:11Z
day: '09'
department:
- _id: HeEd
doi: 10.1007/978-3-319-32360-2_20
extern: '1'
intvolume: ' 9647'
language:
- iso: eng
month: '04'
oa_version: None
page: 256-267
place: Cham
publication: Discrete Geometry for Computer Imagery
publication_identifier:
eisbn:
- 978-3-319-32360-2
isbn:
- 978-3-319-32359-6
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On functionality of quadraginta octants of naive sphere with application to
circle drawing
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9647
year: '2016'
...
---
_id: '5805'
abstract:
- lang: eng
text: Discretization of sphere in the integer space follows a particular discretization
scheme, which, in principle, conforms to some topological model. This eventually
gives rise to interesting topological properties of a discrete spherical surface,
which need to be investigated for its analytical characterization. This paper
presents some novel results on the local topological properties of the naive model
of discrete sphere. They follow from the bijection of each quadraginta octant
of naive sphere with its projection map called f -map on the corresponding functional
plane and from the characterization of certain jumps in the f-map. As an application,
we have shown how these properties can be used in designing an efficient reconstruction
algorithm for a naive spherical surface from an input voxel set when it is sparse
or noisy.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Nabhasmita
full_name: Sen, Nabhasmita
last_name: Sen
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Sen N, Biswas R, Bhowmick P. On some local topological properties of naive
discrete sphere. In: Computational Topology in Image Context. Vol 9667.
Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23'
apa: 'Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological
properties of naive discrete sphere. In Computational Topology in Image Context
(Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23'
chicago: 'Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological
Properties of Naive Discrete Sphere.” In Computational Topology in Image Context,
9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.'
ieee: 'N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties
of naive discrete sphere,” in Computational Topology in Image Context,
vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.'
ista: 'Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of
naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol.
9667, 253–264.'
mla: Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete
Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature,
2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23.
short: N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context,
Springer Nature, Cham, 2016, pp. 253–264.
conference:
end_date: 2016-06-17
location: Marseille, France
name: 'CTIC: Computational Topology in Image Context'
start_date: 2016-06-15
date_created: 2019-01-08T20:44:24Z
date_published: 2016-06-02T00:00:00Z
date_updated: 2022-01-28T08:01:22Z
day: '02'
department:
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_23
extern: '1'
intvolume: ' 9667'
language:
- iso: eng
month: '06'
oa_version: None
page: 253-264
place: Cham
publication: Computational Topology in Image Context
publication_identifier:
eisbn:
- 978-3-319-39441-1
eissn:
- 1611-3349
isbn:
- 978-3-319-39440-4
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On some local topological properties of naive discrete sphere
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9667
year: '2016'
...
---
_id: '5809'
abstract:
- lang: eng
text: A discrete spherical circle is a topologically well-connected 3D circle in
the integer space, which belongs to a discrete sphere as well as a discrete plane.
It is one of the most important 3D geometric primitives, but has not possibly
yet been studied up to its merit. This paper is a maiden exposition of some of
its elementary properties, which indicates a sense of its profound theoretical
prospects in the framework of digital geometry. We have shown how different types
of discretization can lead to forbidden and admissible classes, when one attempts
to define the discretization of a spherical circle in terms of intersection between
a discrete sphere and a discrete plane. Several fundamental theoretical results
have been presented, the algorithm for construction of discrete spherical circles
has been discussed, and some test results have been furnished to demonstrate its
practicality and usefulness.
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: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
- first_name: Valentin E.
full_name: Brimkov, Valentin E.
last_name: Brimkov
citation:
ama: 'Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete
spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer
Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7'
apa: 'Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity
and smoothness of discrete spherical circles. In Combinatorial image analysis
(Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7'
chicago: 'Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity
and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis,
9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.'
ieee: 'R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness
of discrete spherical circles,” in Combinatorial image analysis, vol. 9448,
Cham: Springer Nature, 2016, pp. 86–100.'
ista: 'Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness
of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.'
mla: Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical
Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016,
pp. 86–100, doi:10.1007/978-3-319-26145-4_7.
short: R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis,
Springer Nature, Cham, 2016, pp. 86–100.
conference:
end_date: 2015-11-27
location: Kolkata, India
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2015-11-24
date_created: 2019-01-08T20:45:19Z
date_published: 2016-01-06T00:00:00Z
date_updated: 2022-01-28T08:13:03Z
day: '06'
department:
- _id: HeEd
doi: 10.1007/978-3-319-26145-4_7
extern: '1'
intvolume: ' 9448'
language:
- iso: eng
month: '01'
oa_version: None
page: 86-100
place: Cham
publication: Combinatorial image analysis
publication_identifier:
eisbn:
- 978-3-319-26145-4
eissn:
- 1611-3349
isbn:
- 978-3-319-26144-7
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On the connectivity and smoothness of discrete spherical circles
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9448
year: '2016'
...
---
_id: '1662'
abstract:
- lang: eng
text: We introduce a modification of the classic notion of intrinsic volume using
persistence moments of height functions. Evaluating the modified first intrinsic
volume on digital approximations of a compact body with smoothly embedded boundary
in Rn, we prove convergence to the first intrinsic volume of the body as the resolution
of the approximation improves. We have weaker results for the other modified intrinsic
volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional
unit ball.
acknowledgement: "This research is partially supported by the Toposys project FP7-ICT-318493-STREP,
and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne
Marie Svane for her comments on an early version of this paper. The second author
wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for
enlightening discussions and their kind hospitality during a visit of their department
in 2014."
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic
volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004
apa: Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence
of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016.
https://doi.org/10.1016/j.aim.2015.10.004.
ieee: H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic
volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703,
2016.
ista: Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic
volume. Advances in Mathematics. 287, 674–703.
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press,
2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004.
short: H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.
date_created: 2018-12-11T11:53:20Z
date_published: 2016-01-10T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '10'
ddc:
- '004'
department:
- _id: HeEd
doi: 10.1016/j.aim.2015.10.004
ec_funded: 1
file:
- access_level: open_access
checksum: f8869ec110c35c852ef6a37425374af7
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:10Z
date_updated: 2020-07-14T12:45:10Z
file_id: '4928'
file_name: IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf
file_size: 248985
relation: main_file
file_date_updated: 2020-07-14T12:45:10Z
has_accepted_license: '1'
intvolume: ' 287'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 674 - 703
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '5488'
pubrep_id: '774'
quality_controlled: '1'
related_material:
record:
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Approximation and convergence of the intrinsic volume
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 287
year: '2016'
...
---
_id: '1424'
abstract:
- lang: eng
text: We consider the problem of statistical computations with persistence diagrams,
a summary representation of topological features in data. These diagrams encode
persistent homology, a widely used invariant in topological data analysis. While
several avenues towards a statistical treatment of the diagrams have been explored
recently, we follow an alternative route that is motivated by the success of methods
based on the embedding of probability measures into reproducing kernel Hilbert
spaces. In fact, a positive definite kernel on persistence diagrams has recently
been proposed, connecting persistent homology to popular kernel-based learning
techniques such as support vector machines. However, important properties of that
kernel enabling a principled use in the context of probability measure embeddings
remain to be explored. Our contribution is to close this gap by proving universality
of a variant of the original kernel, and to demonstrate its effective use in twosample
hypothesis testing on synthetic as well as real-world data.
acknowledgement: This work was partially supported by the Austrian Science FUnd, project
no. KLI 00012.
alternative_title:
- Advances in Neural Information Processing Systems
author:
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Marc
full_name: Niethammer, Marc
last_name: Niethammer
- first_name: Weili
full_name: Lin, Weili
last_name: Lin
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
citation:
ama: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data
analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems;
2015:3070-3078.'
apa: 'Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical
topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented
at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information
Processing Systems.'
chicago: Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer.
“Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural
Information Processing Systems, 2015.
ieee: 'R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological
data analysis-A kernel perspective,” presented at the NIPS: Neural Information
Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.'
ista: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological
data analysis-A kernel perspective. NIPS: Neural Information Processing Systems,
Advances in Neural Information Processing Systems, vol. 28, 3070–3078.'
mla: Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective.
Vol. 28, Neural Information Processing Systems, 2015, pp. 3070–78.
short: R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information
Processing Systems, 2015, pp. 3070–3078.
conference:
end_date: 2015-12-12
location: Montreal, Canada
name: 'NIPS: Neural Information Processing Systems'
start_date: 2015-12-07
date_created: 2018-12-11T11:51:56Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2021-01-12T06:50:38Z
day: '01'
department:
- _id: HeEd
intvolume: ' 28'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective
month: '12'
oa: 1
oa_version: Submitted Version
page: 3070 - 3078
publication_status: published
publisher: Neural Information Processing Systems
publist_id: '5782'
quality_controlled: '1'
status: public
title: Statistical topological data analysis-A kernel perspective
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2015'
...
---
_id: '1483'
abstract:
- lang: eng
text: Topological data analysis offers a rich source of valuable information to
study vision problems. Yet, so far we lack a theoretically sound connection to
popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In
this work, we establish such a connection by designing a multi-scale kernel for
persistence diagrams, a stable summary representation of topological features
in data. We show that this kernel is positive definite and prove its stability
with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets
for 3D shape classification/retrieval and texture recognition show considerable
performance gains of the proposed method compared to an alternative approach that
is based on the recently introduced persistence landscapes.
author:
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
citation:
ama: 'Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for
topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106'
apa: 'Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale
kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR:
Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106'
chicago: Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable
Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106.
ieee: 'J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel
for topological machine learning,” presented at the CVPR: Computer Vision and
Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.'
ista: 'Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel
for topological machine learning. CVPR: Computer Vision and Pattern Recognition,
4741–4748.'
mla: Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine
Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106.
short: J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.
conference:
end_date: 2015-06-12
location: Boston, MA, USA
name: 'CVPR: Computer Vision and Pattern Recognition'
start_date: 2015-06-07
date_created: 2018-12-11T11:52:17Z
date_published: 2015-10-14T00:00:00Z
date_updated: 2021-01-12T06:51:03Z
day: '14'
department:
- _id: HeEd
doi: 10.1109/CVPR.2015.7299106
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1412.6821
month: '10'
oa: 1
oa_version: Preprint
page: 4741 - 4748
publication_identifier:
eisbn:
- '978-1-4673-6964-0 '
publication_status: published
publisher: IEEE
publist_id: '5709'
scopus_import: 1
status: public
title: A stable multi-scale kernel for topological machine learning
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '1495'
abstract:
- lang: eng
text: 'Motivated by biological questions, we study configurations of equal-sized
disks in the Euclidean plane that neither pack nor cover. Measuring the quality
by the probability that a random point lies in exactly one disk, we show that
the regular hexagonal grid gives the maximum among lattice configurations. '
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
- first_name: Vitaliy
full_name: Kurlin, Vitaliy
last_name: Kurlin
citation:
ama: 'Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: Proceedings
of the 27th Canadian Conference on Computational Geometry. Vol 2015-August.
Queen’s University; 2015:128-135.'
apa: 'Edelsbrunner, H., Iglesias Ham, M., & Kurlin, V. (2015). Relaxed disk
packing. In Proceedings of the 27th Canadian Conference on Computational Geometry
(Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University.'
chicago: Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed
Disk Packing.” In Proceedings of the 27th Canadian Conference on Computational
Geometry, 2015–August:128–35. Queen’s University, 2015.
ieee: H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in
Proceedings of the 27th Canadian Conference on Computational Geometry,
Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.
ista: 'Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings
of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference
on Computational Geometry vol. 2015–August, 128–135.'
mla: Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” Proceedings of the
27th Canadian Conference on Computational Geometry, vol. 2015–August, Queen’s
University, 2015, pp. 128–35.
short: H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th
Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.
conference:
end_date: 2015-08-12
location: Ontario, Canada
name: 'CCCG: Canadian Conference on Computational Geometry'
start_date: 2015-08-10
date_created: 2018-12-11T11:52:21Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2021-01-12T06:51:09Z
day: '01'
department:
- _id: HeEd
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1505.03402
month: '08'
oa: 1
oa_version: Submitted Version
page: 128-135
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the 27th Canadian Conference on Computational Geometry
publication_status: published
publisher: Queen's University
publist_id: '5684'
quality_controlled: '1'
scopus_import: 1
status: public
title: Relaxed disk packing
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 2015-August
year: '2015'
...
---
_id: '1510'
abstract:
- lang: eng
text: 'The concept of well group in a special but important case captures homological
properties of the zero set of a continuous map f from K to R^n on a compact space
K that are invariant with respect to perturbations of f. The perturbations are
arbitrary continuous maps within L_infty distance r from f for a given r >
0. The main drawback of the approach is that the computability of well groups
was shown only when dim K = n or n = 1. Our contribution to the theory of well
groups is twofold: on the one hand we improve on the computability issue, but
on the other hand we present a range of examples where the well groups are incomplete
invariants, that is, fail to capture certain important robust properties of the
zero set. For the first part, we identify a computable subgroup of the well group
that is obtained by cap product with the pullback of the orientation of R^n by
f. In other words, well groups can be algorithmically approximated from below.
When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well
group is exact. For the second part, we find examples of maps f, f'' from K to
R^n with all well groups isomorphic but whose perturbations have different zero
sets. We discuss on a possible replacement of the well groups of vector valued
maps by an invariant of a better descriptive power and computability status. '
alternative_title:
- LIPIcs
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: 'Franek P, Krcál M. On computability and triviality of well groups. In: Vol
34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:10.4230/LIPIcs.SOCG.2015.842'
apa: 'Franek, P., & Krcál, M. (2015). On computability and triviality of well
groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational
Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SOCG.2015.842'
chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well
Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. https://doi.org/10.4230/LIPIcs.SOCG.2015.842.
ieee: 'P. Franek and M. Krcál, “On computability and triviality of well groups,”
presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands,
2015, vol. 34, pp. 842–856.'
ista: 'Franek P, Krcál M. 2015. On computability and triviality of well groups.
SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.'
mla: Franek, Peter, and Marek Krcál. On Computability and Triviality of Well
Groups. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015,
pp. 842–56, doi:10.4230/LIPIcs.SOCG.2015.842.
short: P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2015, pp. 842–856.
conference:
end_date: 2015-06-25
location: Eindhoven, Netherlands
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2015-06-22
date_created: 2018-12-11T11:52:26Z
date_published: 2015-06-11T00:00:00Z
date_updated: 2023-02-21T17:02:57Z
day: '11'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.4230/LIPIcs.SOCG.2015.842
ec_funded: 1
file:
- access_level: open_access
checksum: 49eb5021caafaabe5356c65b9c5f8c9c
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:19Z
date_updated: 2020-07-14T12:44:59Z
file_id: '5001'
file_name: IST-2016-503-v1+1_32.pdf
file_size: 623563
relation: main_file
file_date_updated: 2020-07-14T12:44:59Z
has_accepted_license: '1'
intvolume: ' 34'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 842 - 856
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '5667'
pubrep_id: '503'
quality_controlled: '1'
related_material:
record:
- id: '1408'
relation: later_version
status: public
scopus_import: 1
status: public
title: On computability and triviality of well groups
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: 34
year: '2015'
...
---
_id: '1531'
abstract:
- lang: eng
text: The Heat Kernel Signature (HKS) is a scalar quantity which is derived from
the heat kernel of a given shape. Due to its robustness, isometry invariance,
and multiscale nature, it has been successfully applied in many geometric applications.
From a more general point of view, the HKS can be considered as a descriptor of
the metric of a Riemannian manifold. Given a symmetric positive definite tensor
field we may interpret it as the metric of some Riemannian manifold and thereby
apply the HKS to visualize and analyze the given tensor data. In this paper, we
propose a generalization of this approach that enables the treatment of indefinite
tensor fields, like the stress tensor, by interpreting them as a generator of
a positive definite tensor field. To investigate the usefulness of this approach
we consider the stress tensor from the two-point-load model example and from a
mechanical work piece.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Valentin
full_name: Zobel, Valentin
last_name: Zobel
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
citation:
ama: 'Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor
fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40.
1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13'
apa: Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite
2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz
(Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued
Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13
chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric
Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data, edited by
Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13.
ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D
tensor fields using The Heat Kernel Signature,” in Visualization and Processing
of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz
and T. Schultz, Eds. Springer, 2015, pp. 257–267.
ista: 'Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D
tensor fields using The Heat Kernel Signature. In: Visualization and Processing
of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization,
vol. 40, 257–267.'
mla: Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields
Using The Heat Kernel Signature.” Visualization and Processing of Higher Order
Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz,
1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13.
short: V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer,
2015, pp. 257–267.
date_created: 2018-12-11T11:52:33Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2022-06-10T09:50:14Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-319-15090-1_13
edition: '1'
editor:
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Thomas
full_name: Schultz, Thomas
last_name: Schultz
intvolume: ' 40'
language:
- iso: eng
month: '01'
oa_version: None
page: 257 - 267
publication: Visualization and Processing of Higher Order Descriptors for Multi-Valued
Data
publication_identifier:
isbn:
- 978-3-319-15089-5
publication_status: published
publisher: Springer
publist_id: '5640'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 40
year: '2015'
...
---
_id: '1555'
abstract:
- lang: eng
text: We show that incorporating spatial dispersal of individuals into a simple
vaccination epidemic model may give rise to a model that exhibits rich dynamical
behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as
a basis, we describe the spread of an infectious disease in a population split
into two regions. In each subpopulation, both forward and backward bifurcations
can occur. This implies that for disconnected regions the two-patch system may
admit several steady states. We consider traveling between the regions and investigate
the impact of spatial dispersal of individuals on the model dynamics. We establish
conditions for the existence of multiple nontrivial steady states in the system,
and we study the structure of the equilibria. The mathematical analysis reveals
an unusually rich dynamical behavior, not normally found in the simple epidemic
models. In addition to the disease-free equilibrium, eight endemic equilibria
emerge from backward transcritical and saddle-node bifurcation points, forming
an interesting bifurcation diagram. Stability of steady states, their bifurcations,
and the global dynamics are investigated with analytical tools, numerical simulations,
and rigorous set-oriented numerical computations.
acknowledgement: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg,
Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported
by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework
Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de
Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de
Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia
e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559
in the framework of the EPIDELAY project.
article_processing_charge: No
article_type: original
author:
- first_name: Diána
full_name: Knipl, Diána
last_name: Knipl
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
- first_name: Gergely
full_name: Röst, Gergely
last_name: Röst
citation:
ama: Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination
model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017.
doi:10.1137/140993934
apa: Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure
in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems.
Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934
chicago: Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure
in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems.
Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934.
ieee: D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two
patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol.
14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.
ista: Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch
vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017.
mla: Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination
Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society
for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934.
short: D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems
14 (2015) 980–1017.
date_created: 2018-12-11T11:52:42Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2021-01-12T06:51:34Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1137/140993934
ec_funded: 1
intvolume: ' 14'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://discovery.ucl.ac.uk/1473750/1/99393.pdf
month: '01'
oa: 1
oa_version: Published Version
page: 980 - 1017
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
eissn:
- 1536-0040
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '5616'
quality_controlled: '1'
scopus_import: 1
status: public
title: Rich bifurcation structure in a two patch vaccination model
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2015'
...
---
_id: '1568'
abstract:
- lang: eng
text: Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI)
magnifying endoscopy (ME) images of the stomach, we combine methods from image
processing, computational topology, and machine learning to classify patterns
into normal, tubular, vessel. Training the algorithm on a small number of images
of each type, we achieve a high rate of correct classifications. The analysis
of the learning algorithm reveals that a handful of geometric and topological
features are responsible for the overwhelming majority of decisions.
acknowledgement: This research is supported by the project No. 477 of P.G. Demidov
Yaroslavl State University within State Assignment for Research.
author:
- first_name: Olga
full_name: Dunaeva, Olga
last_name: Dunaeva
- 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: Lukyanov, Anton
last_name: Lukyanov
- first_name: Michael
full_name: Machin, Michael
last_name: Machin
- first_name: Daria
full_name: Malkova, Daria
last_name: Malkova
citation:
ama: 'Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification
of endoscopy images with persistent homology. In: Proceedings - 16th International
Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE;
2015:7034731. doi:10.1109/SYNASC.2014.81'
apa: 'Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D.
(2015). The classification of endoscopy images with persistent homology. In Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81'
chicago: Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and
Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.”
In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms
for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81.
ieee: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The
classification of endoscopy images with persistent homology,” in Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing, Timisoara, Romania, 2015, p. 7034731.
ista: 'Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification
of endoscopy images with persistent homology. Proceedings - 16th International
Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC:
Symbolic and Numeric Algorithms for Scientific Computing, 7034731.'
mla: Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent
Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric
Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81.
short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing, IEEE, 2015, p. 7034731.
conference:
end_date: 2014-09-25
location: Timisoara, Romania
name: 'SYNASC: Symbolic and Numeric Algorithms for Scientific Computing'
start_date: 2014-09-22
date_created: 2018-12-11T11:52:46Z
date_published: 2015-02-05T00:00:00Z
date_updated: 2023-02-21T16:57:29Z
day: '05'
department:
- _id: HeEd
doi: 10.1109/SYNASC.2014.81
language:
- iso: eng
month: '02'
oa_version: None
page: '7034731'
publication: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms
for Scientific Computing
publication_status: published
publisher: IEEE
publist_id: '5603'
quality_controlled: '1'
related_material:
record:
- id: '1289'
relation: later_version
status: public
scopus_import: 1
status: public
title: The classification of endoscopy images with persistent homology
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '1567'
abstract:
- lang: eng
text: My personal journey to the fascinating world of geometric forms started more
than 30 years ago with the invention of alpha shapes in the plane. It took about
10 years before we generalized the concept to higher dimensions, we produced working
software with a graphics interface for the three-dimensional case. At the same
time, we added homology to the computations. Needless to say that this foreshadowed
the inception of persistent homology, because it suggested the study of filtrations
to capture the scale of a shape or data set. Importantly, this method has fast
algorithms. The arguably most useful result on persistent homology is the stability
of its diagrams under perturbations.
alternative_title:
- LNCS
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
citation:
ama: 'Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International
Symposium. Vol 9411. Springer Nature; 2015.'
apa: 'Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd
International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer
Nature.'
chicago: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In
23rd International Symposium, Vol. 9411. Springer Nature, 2015.
ieee: H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd
International Symposium, Los Angeles, CA, United States, 2015, vol. 9411.
ista: 'Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International
Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.'
mla: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd
International Symposium, vol. 9411, Springer Nature, 2015.
short: H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015.
conference:
end_date: 2015-09-26
location: Los Angeles, CA, United States
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2015-09-24
date_created: 2018-12-11T11:52:46Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2022-01-28T08:25:00Z
day: '01'
department:
- _id: HeEd
intvolume: ' 9411'
language:
- iso: eng
month: '01'
oa_version: None
publication: 23rd International Symposium
publication_status: published
publisher: Springer Nature
publist_id: '5604'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Shape, homology, persistence, and stability
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9411
year: '2015'
...
---
_id: '1563'
abstract:
- lang: eng
text: For a given self-map $f$ of $M$, a closed smooth connected and simply-connected
manifold of dimension $m\geq 4$, we provide an algorithm for estimating the values
of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic
points in the smooth homotopy class of $f$. Our results are based on the combinatorial
scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed
Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm
programmed in C++ is publicly available at {\tt http://www.pawelpilarczyk.com/combtop/}.
author:
- first_name: Grzegorz
full_name: Graff, Grzegorz
last_name: Graff
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number
of periodic points for smooth self-maps of simply-connected manifolds. Topological
Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014
apa: Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating
the minimal number of periodic points for smooth self-maps of simply-connected
manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder
Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014
chicago: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating
the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected
Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder
Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014.
ieee: G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal
number of periodic points for smooth self-maps of simply-connected manifolds,”
Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder
Center for Nonlinear Studies, pp. 273–286, 2015.
ista: Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal
number of periodic points for smooth self-maps of simply-connected manifolds.
Topological Methods in Nonlinear Analysis. 45(1), 273–286.
mla: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating
the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected
Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1,
Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014.
short: G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015)
273–286.
date_created: 2018-12-11T11:52:44Z
date_published: 2015-03-01T00:00:00Z
date_updated: 2021-01-12T06:51:37Z
day: '01'
department:
- _id: HeEd
doi: 10.12775/TMNA.2015.014
intvolume: ' 45'
issue: '1'
language:
- iso: eng
month: '03'
oa_version: None
page: 273 - 286
publication: Topological Methods in Nonlinear Analysis
publication_status: published
publisher: Juliusz Schauder Center for Nonlinear Studies
publist_id: '5608'
quality_controlled: '1'
scopus_import: 1
status: public
title: An algorithmic approach to estimating the minimal number of periodic points
for smooth self-maps of simply-connected manifolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2015'
...
---
_id: '1578'
abstract:
- lang: eng
text: We prove that the dual of the digital Voronoi diagram constructed by flooding
the plane from the data points gives a geometrically and topologically correct
dual triangulation. This provides the proof of correctness for recently developed
GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional
Delaunay triangulations.
acknowledgement: "The research of the second author is partially supported by NSF
under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n"
author:
- first_name: Thanhtung
full_name: Cao, Thanhtung
last_name: Cao
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Tiowseng
full_name: Tan, Tiowseng
last_name: Tan
citation:
ama: Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital
Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001
apa: Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically
correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001
chicago: Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations
from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry.
Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001.
ieee: T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct
digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier,
pp. 507–519, 2015.
ista: Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct
digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.
mla: Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi
Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp.
507–19, doi:10.1016/j.comgeo.2015.04.001.
short: T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.
date_created: 2018-12-11T11:52:49Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2021-01-12T06:51:43Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.04.001
intvolume: ' 48'
issue: '7'
language:
- iso: eng
month: '08'
oa_version: None
page: 507 - 519
publication: Computational Geometry
publication_status: published
publisher: Elsevier
publist_id: '5593'
quality_controlled: '1'
scopus_import: 1
status: public
title: Triangulations from topologically correct digital Voronoi diagrams
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2015'
...
---
_id: '1584'
abstract:
- lang: eng
text: We investigate weighted straight skeletons from a geometric, graph-theoretical,
and combinatorial point of view. We start with a thorough definition and shed
light on some ambiguity issues in the procedural definition. We investigate the
geometry, combinatorics, and topology of faces and the roof model, and we discuss
in which cases a weighted straight skeleton is connected. Finally, we show that
the weighted straight skeleton of even a simple polygon may be non-planar and
may contain cycles, and we discuss under which restrictions on the weights and/or
the input polygon the weighted straight skeleton still behaves similar to its
unweighted counterpart. In particular, we obtain a non-procedural description
and a linear-time construction algorithm for the straight skeleton of strictly
convex polygons with arbitrary weights.
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Dominik
full_name: Kaaser, Dominik
last_name: Kaaser
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight
skeletons in the plane. Computational Geometry: Theory and Applications.
2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004'
apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint
of: Weighted straight skeletons in the plane. Computational Geometry: Theory
and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004'
chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry:
Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.'
ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted
straight skeletons in the plane,” Computational Geometry: Theory and Applications,
vol. 48, no. 5. Elsevier, pp. 429–442, 2015.'
ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted
straight skeletons in the plane. Computational Geometry: Theory and Applications.
48(5), 429–442.'
mla: 'Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.”
Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier,
2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.'
short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry:
Theory and Applications 48 (2015) 429–442.'
date_created: 2018-12-11T11:52:51Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2023-02-23T10:05:22Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.01.004
file:
- access_level: open_access
checksum: 5b33719a86f7f4c8e5dc62c1b6893f49
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:17:36Z
date_updated: 2020-07-14T12:45:03Z
file_id: '5292'
file_name: IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf
file_size: 508379
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has_accepted_license: '1'
intvolume: ' 48'
issue: '5'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 429 - 442
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5587'
pubrep_id: '475'
quality_controlled: '1'
related_material:
record:
- id: '1582'
relation: other
status: public
scopus_import: 1
status: public
title: 'Reprint of: Weighted straight skeletons in the plane'
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: 48
year: '2015'
...
---
_id: '1582'
abstract:
- lang: eng
text: We investigate weighted straight skeletons from a geometric, graph-theoretical,
and combinatorial point of view. We start with a thorough definition and shed
light on some ambiguity issues in the procedural definition. We investigate the
geometry, combinatorics, and topology of faces and the roof model, and we discuss
in which cases a weighted straight skeleton is connected. Finally, we show that
the weighted straight skeleton of even a simple polygon may be non-planar and
may contain cycles, and we discuss under which restrictions on the weights and/or
the input polygon the weighted straight skeleton still behaves similar to its
unweighted counterpart. In particular, we obtain a non-procedural description
and a linear-time construction algorithm for the straight skeleton of strictly
convex polygons with arbitrary weights.
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Dominik
full_name: Kaaser, Dominik
last_name: Kaaser
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons
in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133.
doi:10.1016/j.comgeo.2014.08.006'
apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted
straight skeletons in the plane. Computational Geometry: Theory and Applications.
Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006'
chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory
and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.'
ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight
skeletons in the plane,” Computational Geometry: Theory and Applications,
vol. 48, no. 2. Elsevier, pp. 120–133, 2015.'
ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight
skeletons in the plane. Computational Geometry: Theory and Applications. 48(2),
120–133.'
mla: 'Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational
Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33,
doi:10.1016/j.comgeo.2014.08.006.'
short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry:
Theory and Applications 48 (2015) 120–133.'
date_created: 2018-12-11T11:52:51Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2023-02-23T10:05:27Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.006
file:
- access_level: open_access
checksum: c1ef67f6ec925e12f73a96b8fe285ab4
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file_size: 505987
relation: main_file
file_date_updated: 2020-07-14T12:45:02Z
has_accepted_license: '1'
intvolume: ' 48'
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 120 - 133
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5589'
pubrep_id: '474'
quality_controlled: '1'
related_material:
record:
- id: '1584'
relation: other
status: public
scopus_import: 1
status: public
title: Weighted straight skeletons in the plane
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: 48
year: '2015'
...
---
_id: '1583'
abstract:
- lang: eng
text: We study the characteristics of straight skeletons of monotone polygonal chains
and use them to devise an algorithm for computing positively weighted straight
skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space,
where n denotes the number of vertices of the polygon.
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Dominik
full_name: Kaaser, Dominik
last_name: Kaaser
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing
positively weighted straight skeletons of monotone polygons. Information Processing
Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021
apa: Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple
algorithm for computing positively weighted straight skeletons of monotone polygons.
Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021
chicago: Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone
Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021.
ieee: T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm
for computing positively weighted straight skeletons of monotone polygons,” Information
Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015.
ista: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm
for computing positively weighted straight skeletons of monotone polygons. Information
Processing Letters. 115(2), 243–247.
mla: Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted
Straight Skeletons of Monotone Polygons.” Information Processing Letters,
vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021.
short: T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing
Letters 115 (2015) 243–247.
date_created: 2018-12-11T11:52:51Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2021-01-12T06:51:45Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.ipl.2014.09.021
file:
- access_level: open_access
checksum: 2779a648610c9b5c86d0b51a62816d23
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:18:45Z
date_updated: 2020-07-14T12:45:03Z
file_id: '5367'
file_name: IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf
file_size: 270137
relation: main_file
file_date_updated: 2020-07-14T12:45:03Z
has_accepted_license: '1'
intvolume: ' 115'
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 243 - 247
publication: Information Processing Letters
publication_status: published
publisher: Elsevier
publist_id: '5588'
pubrep_id: '473'
quality_controlled: '1'
scopus_import: 1
status: public
title: A simple algorithm for computing positively weighted straight skeletons of
monotone polygons
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: 115
year: '2015'
...
---
_id: '1590'
abstract:
- lang: eng
text: 'The straight skeleton of a polygon is the geometric graph obtained by tracing
the vertices during a mitered offsetting process. It is known that the straight
skeleton of a simple polygon is a tree, and one can naturally derive directions
on the edges of the tree from the propagation of the shrinking process. In this
paper, we ask the reverse question: Given a tree with directed edges, can it be
the straight skeleton of a polygon? And if so, can we find a suitable simple polygon?
We answer these questions for all directed trees where the order of edges around
each node is fixed.'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Thomas
full_name: Hackl, Thomas
last_name: Hackl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: 'Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight
skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer
Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28'
apa: 'Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P.,
& Vogtenhuber, B. (2015). Representing directed trees as straight skeletons.
In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los
Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28'
chicago: Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber,
Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight
Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer
Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28.
ieee: O. Aichholzer et al., “Representing directed trees as straight skeletons,”
in Graph Drawing and Network Visualization, vol. 9411, Springer Nature,
2015, pp. 335–347.
ista: 'Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber
B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and
Network Visualization. LNCS, vol. 9411, 335–347.'
mla: Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.”
Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015,
pp. 335–47, doi:10.1007/978-3-319-27261-0_28.
short: O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber,
in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.
conference:
end_date: 2015-09-26
location: Los Angeles, CA, United States
name: 'GD: International Symposium on Graph Drawing'
start_date: 2015-09-24
date_created: 2018-12-11T11:52:54Z
date_published: 2015-11-27T00:00:00Z
date_updated: 2022-01-28T09:10:37Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-27261-0_28
intvolume: ' 9411'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1508.01076
month: '11'
oa: 1
oa_version: Preprint
page: 335 - 347
publication: Graph Drawing and Network Visualization
publication_identifier:
eisbn:
- 978-3-319-27261-0
isbn:
- 978-3-319-27260-3
publication_status: published
publisher: Springer Nature
publist_id: '5581'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Representing directed trees as straight skeletons
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9411
year: '2015'
...
---
_id: '1682'
abstract:
- lang: eng
text: 'We study the problem of robust satisfiability of systems of nonlinear equations,
namely, whether for a given continuous function f:K→ ℝn on a finite simplicial
complex K and α > 0, it holds that each function g: K → ℝn such that ||g -
f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps
into a sphere, we particularly show that this problem is decidable in polynomial
time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension
of previous computational applications of topological degree and related concepts
in numerical and interval analysis. Via a reverse reduction, we prove that the
problem is undecidable when dim K > 2n - 2, where the threshold comes from
the stable range in homotopy theory. For the lucidity of our exposition, we focus
on the setting when f is simplexwise linear. Such functions can approximate general
continuous functions, and thus we get approximation schemes and undecidability
of the robust satisfiability in other possible settings.'
article_number: '26'
author:
- first_name: Peter
full_name: Franek, Peter
last_name: Franek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. Robust satisfiability of systems of equations. Journal
of the ACM. 2015;62(4). doi:10.1145/2751524
apa: Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations.
Journal of the ACM. ACM. https://doi.org/10.1145/2751524
chicago: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.”
Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524.
ieee: P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal
of the ACM, vol. 62, no. 4. ACM, 2015.
ista: Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal
of the ACM. 62(4), 26.
mla: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.”
Journal of the ACM, vol. 62, no. 4, 26, ACM, 2015, doi:10.1145/2751524.
short: P. Franek, M. Krcál, Journal of the ACM 62 (2015).
date_created: 2018-12-11T11:53:27Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2021-01-12T06:52:30Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2751524
intvolume: ' 62'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1402.0858
month: '08'
oa: 1
oa_version: Preprint
publication: Journal of the ACM
publication_status: published
publisher: ACM
publist_id: '5466'
quality_controlled: '1'
scopus_import: 1
status: public
title: Robust satisfiability of systems of equations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 62
year: '2015'
...
---
_id: '1710'
abstract:
- lang: eng
text: 'We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by
a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles
incident on the hollow. It is assumed that u satisfies the so-called single impact
condition (SIC): each incident particle is elastically reflected by graph(u) and
goes away without hitting the graph of u anymore. We solve the problem: find the
function u minimizing the force of resistance created by the flow. We show that
the graph of the minimizer is formed by two arcs of parabolas symmetric to each
other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals
1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This
result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014),
pp. 2730-2742] stating in particular that the minimal resistance of a hollow in
higher dimensions equals 0.5. We additionally consider a similar problem of minimal
resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1
is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x =
(x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow
is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides
with 0.6435 when d = 1) and converges to 0.5 as d → ∞.'
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
full_name: Plakhov, Alexander
last_name: Plakhov
citation:
ama: Akopyan A, Plakhov A. Minimal resistance of curves under the single impact
assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769.
doi:10.1137/140993843
apa: Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the
single impact assumption. Society for Industrial and Applied Mathematics.
SIAM. https://doi.org/10.1137/140993843
chicago: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves
under the Single Impact Assumption.” Society for Industrial and Applied Mathematics.
SIAM, 2015. https://doi.org/10.1137/140993843.
ieee: A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single
impact assumption,” Society for Industrial and Applied Mathematics, vol.
47, no. 4. SIAM, pp. 2754–2769, 2015.
ista: Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single
impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769.
mla: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under
the Single Impact Assumption.” Society for Industrial and Applied Mathematics,
vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843.
short: A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47
(2015) 2754–2769.
date_created: 2018-12-11T11:53:36Z
date_published: 2015-07-14T00:00:00Z
date_updated: 2021-01-12T06:52:41Z
day: '14'
department:
- _id: HeEd
doi: 10.1137/140993843
ec_funded: 1
intvolume: ' 47'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1410.3736
month: '07'
oa: 1
oa_version: Preprint
page: 2754 - 2769
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Society for Industrial and Applied Mathematics
publication_status: published
publisher: SIAM
publist_id: '5423'
quality_controlled: '1'
scopus_import: 1
status: public
title: Minimal resistance of curves under the single impact assumption
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 47
year: '2015'
...
---
_id: '1828'
abstract:
- lang: eng
text: We construct a non-linear Markov process connected with a biological model
of a bacterial genome recombination. The description of invariant measures of
this process gives us the solution of one problem in elementary probability theory.
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: Sergey
full_name: Pirogov, Sergey
last_name: Pirogov
- first_name: Aleksandr
full_name: Rybko, Aleksandr
last_name: Rybko
citation:
ama: Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination
process. Journal of Statistical Physics. 2015;160(1):163-167. doi:10.1007/s10955-015-1238-5
apa: Akopyan, A., Pirogov, S., & Rybko, A. (2015). Invariant measures of genetic
recombination process. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-015-1238-5
chicago: Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures
of Genetic Recombination Process.” Journal of Statistical Physics. Springer,
2015. https://doi.org/10.1007/s10955-015-1238-5.
ieee: A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination
process,” Journal of Statistical Physics, vol. 160, no. 1. Springer, pp.
163–167, 2015.
ista: Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination
process. Journal of Statistical Physics. 160(1), 163–167.
mla: Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.”
Journal of Statistical Physics, vol. 160, no. 1, Springer, 2015, pp. 163–67,
doi:10.1007/s10955-015-1238-5.
short: A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015)
163–167.
date_created: 2018-12-11T11:54:14Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2021-01-12T06:53:28Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10955-015-1238-5
ec_funded: 1
intvolume: ' 160'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: arxiv.org/abs/1406.5313
month: '07'
oa: 1
oa_version: Preprint
page: 163 - 167
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '5276'
quality_controlled: '1'
scopus_import: 1
status: public
title: Invariant measures of genetic recombination process
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 160
year: '2015'
...
---
_id: '1938'
abstract:
- lang: eng
text: 'We numerically investigate the distribution of extrema of ''chaotic'' Laplacian
eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a)
we count extrema on grid graphs with a small number of randomly added edges and
show the behavior to coincide with the 1957 prediction of Longuet-Higgins for
the continuous case and (b) we compute the regularity of their spatial distribution
using discrepancy, which is a classical measure from the theory of Monte Carlo
integration. The first part suggests that grid graphs with randomly added edges
should behave like two-dimensional surfaces with ergodic geodesic flow; in the
second part we show that the extrema are more regularly distributed in space than
the grid Z2.'
acknowledgement: "F.P. was supported by the Graduate School of IST Austria. S.S. was
partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and
Michael Kerber for sharing their implementation of the persistence algorithm. "
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
- first_name: Stefan
full_name: Steinerberger, Stefan
last_name: Steinerberger
citation:
ama: Pausinger F, Steinerberger S. On the distribution of local extrema in quantum
chaos. Physics Letters, Section A. 2015;379(6):535-541. doi:10.1016/j.physleta.2014.12.010
apa: Pausinger, F., & Steinerberger, S. (2015). On the distribution of local
extrema in quantum chaos. Physics Letters, Section A. Elsevier. https://doi.org/10.1016/j.physleta.2014.12.010
chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local
Extrema in Quantum Chaos.” Physics Letters, Section A. Elsevier, 2015.
https://doi.org/10.1016/j.physleta.2014.12.010.
ieee: F. Pausinger and S. Steinerberger, “On the distribution of local extrema in
quantum chaos,” Physics Letters, Section A, vol. 379, no. 6. Elsevier,
pp. 535–541, 2015.
ista: Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in
quantum chaos. Physics Letters, Section A. 379(6), 535–541.
mla: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local
Extrema in Quantum Chaos.” Physics Letters, Section A, vol. 379, no. 6,
Elsevier, 2015, pp. 535–41, doi:10.1016/j.physleta.2014.12.010.
short: F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.
date_created: 2018-12-11T11:54:49Z
date_published: 2015-03-06T00:00:00Z
date_updated: 2021-01-12T06:54:12Z
day: '06'
department:
- _id: HeEd
doi: 10.1016/j.physleta.2014.12.010
intvolume: ' 379'
issue: '6'
language:
- iso: eng
month: '03'
oa_version: None
page: 535 - 541
publication: Physics Letters, Section A
publication_status: published
publisher: Elsevier
publist_id: '5152'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the distribution of local extrema in quantum chaos
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 379
year: '2015'
...
---
_id: '2035'
abstract:
- lang: eng
text: "Considering a continuous self-map and the induced endomorphism on homology,
we study the eigenvalues and eigenspaces of the latter. Taking a filtration of
representations, we define the persistence of the eigenspaces, effectively introducing
a hierarchical organization of the map. The algorithm that computes this information
for a finite sample is proved to be stable, and to give the correct answer for
a sufficiently dense sample. Results computed with an implementation of the algorithm
provide evidence of its practical utility.\r\n"
acknowledgement: This research is partially supported by the Toposys project FP7-ICT-318493-STREP,
by ESF under the ACAT Research Network Programme, by the Russian Government under
mega project 11.G34.31.0053, and by the Polish National Science Center under Grant
No. N201 419639.
author:
- 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: Marian
full_name: Mrozek, Marian
last_name: Mrozek
citation:
ama: Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map.
Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y
apa: Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology
of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y
chicago: Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent
Homology of a Self-Map.” Foundations of Computational Mathematics. Springer,
2015. https://doi.org/10.1007/s10208-014-9223-y.
ieee: H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of
a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5.
Springer, pp. 1213–1244, 2015.
ista: Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a
self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.
mla: Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations
of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44,
doi:10.1007/s10208-014-9223-y.
short: H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics
15 (2015) 1213–1244.
date_created: 2018-12-11T11:55:20Z
date_published: 2015-10-01T00:00:00Z
date_updated: 2021-01-12T06:54:53Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s10208-014-9223-y
ec_funded: 1
file:
- access_level: open_access
checksum: 3566f3a8b0c1bc550e62914a88c584ff
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:10Z
date_updated: 2020-07-14T12:45:26Z
file_id: '4670'
file_name: IST-2016-486-v1+1_s10208-014-9223-y.pdf
file_size: 1317546
relation: main_file
file_date_updated: 2020-07-14T12:45:26Z
has_accepted_license: '1'
intvolume: ' 15'
issue: '5'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1213 - 1244
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Foundations of Computational Mathematics
publication_status: published
publisher: Springer
publist_id: '5022'
pubrep_id: '486'
quality_controlled: '1'
scopus_import: 1
status: public
title: The persistent homology of a self-map
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: 15
year: '2015'
...
---
_id: '1805'
abstract:
- lang: eng
text: 'We consider the problem of deciding whether the persistent homology group
of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex
X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded
in double-struck R3. As a consequence, we show that it is NP-hard to simplify
level and sublevel sets of scalar functions on double-struck S3 within a given
tolerance constraint. This problem has relevance to the visualization of medical
images by isosurfaces. We also show an implication to the theory of well groups
of scalar functions: not every well group can be realized by some level set, and
deciding whether a well group can be realized is NP-hard.'
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Olivier
full_name: Devillers, Olivier
last_name: Devillers
- first_name: Marc
full_name: Glisse, Marc
last_name: Glisse
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
citation:
ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction
and simplification in R3. Computational Geometry: Theory and Applications.
2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010'
apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015).
Homological reconstruction and simplification in R3. Computational Geometry:
Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010'
chicago: 'Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André
Lieutier. “Homological Reconstruction and Simplification in R3.” Computational
Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.'
ieee: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological
reconstruction and simplification in R3,” Computational Geometry: Theory and
Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.'
ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction
and simplification in R3. Computational Geometry: Theory and Applications. 48(8),
606–621.'
mla: 'Attali, Dominique, et al. “Homological Reconstruction and Simplification in
R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier,
2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010.'
short: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational
Geometry: Theory and Applications 48 (2015) 606–621.'
date_created: 2018-12-11T11:54:06Z
date_published: 2015-06-03T00:00:00Z
date_updated: 2023-02-23T10:59:19Z
day: '03'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.010
ec_funded: 1
intvolume: ' 48'
issue: '8'
language:
- iso: eng
month: '06'
oa_version: None
page: 606 - 621
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5305'
quality_controlled: '1'
related_material:
record:
- id: '2812'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Homological reconstruction and simplification in R3
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2015'
...
---
_id: '1793'
abstract:
- lang: eng
text: We present a software platform for reconstructing and analyzing the growth
of a plant root system from a time-series of 3D voxelized shapes. It aligns the
shapes with each other, constructs a geometric graph representation together with
the function that records the time of growth, and organizes the branches into
a hierarchy that reflects the order of creation. The software includes the automatic
computation of structural and dynamic traits for each root in the system enabling
the quantification of growth on fine-scale. These are important advances in plant
phenotyping with applications to the study of genetic and environmental influences
on growth.
article_number: e0127657
author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for
the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6).
doi:10.1371/journal.pone.0127657'
apa: 'Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software
platform for the reconstruction and analysis of growing plant roots. PLoS One.
Public Library of Science. https://doi.org/10.1371/journal.pone.0127657'
chicago: 'Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots:
A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.”
PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.'
ieee: 'O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform
for the reconstruction and analysis of growing plant roots,” PLoS One,
vol. 10, no. 6. Public Library of Science, 2015.'
ista: 'Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform
for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.'
mla: 'Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction
and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657,
Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.'
short: O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).
date_created: 2018-12-11T11:54:02Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2023-02-23T14:06:33Z
day: '01'
ddc:
- '000'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1371/journal.pone.0127657
file:
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checksum: d20f26461ca575276ad3ed9ce4bfc787
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:30Z
date_updated: 2020-07-14T12:45:16Z
file_id: '5150'
file_name: IST-2016-454-v1+1_journal.pone.0127657.pdf
file_size: 1850825
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intvolume: ' 10'
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month: '06'
oa: 1
oa_version: Published Version
publication: PLoS One
publication_status: published
publisher: Public Library of Science
publist_id: '5318'
pubrep_id: '454'
quality_controlled: '1'
related_material:
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status: public
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title: 'DynamicRoots: A software platform for the reconstruction and analysis of growing
plant roots'
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volume: 10
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author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for
the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001
apa: Symonova, O., Topp, C., & Edelsbrunner, H. (2015). Root traits computed
by DynamicRoots for the maize root shown in fig 2. Public Library of Science.
https://doi.org/10.1371/journal.pone.0127657.s001
chicago: Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits
Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of
Science, 2015. https://doi.org/10.1371/journal.pone.0127657.s001.
ieee: O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots
for the maize root shown in fig 2.” Public Library of Science, 2015.
ista: Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots
for the maize root shown in fig 2, Public Library of Science, 10.1371/journal.pone.0127657.s001.
mla: Symonova, Olga, et al. Root Traits Computed by DynamicRoots for the Maize
Root Shown in Fig 2. Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.s001.
short: O. Symonova, C. Topp, H. Edelsbrunner, (2015).
date_created: 2021-07-28T06:20:13Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2023-02-23T10:14:42Z
day: '01'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1371/journal.pone.0127657.s001
month: '06'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '1793'
relation: used_in_publication
status: public
status: public
title: Root traits computed by DynamicRoots for the maize root shown in fig 2
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2015'
...
---
_id: '1792'
abstract:
- lang: eng
text: Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop
a new concept of variation of multivariate functions on a compact Hausdorff space
with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka
theorem that holds for this notion of variation and discrepancy with respect to
D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions,
such as extreme or isotropic discrepancy. For extreme discrepancy, our result
coincides with the usual Koksma-Hlawka theorem. We show that the space of functions
of bounded D-variation contains important discontinuous functions and is closed
under natural algebraic operations. Finally, we illustrate the results on concrete
integration problems from integral geometry and stereology.
acknowledgement: F.P. is supported by the Graduate School of IST Austria, A.M.S is
supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by
a grant from the Villum Foundation.
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
- first_name: Anne
full_name: Svane, Anne
last_name: Svane
citation:
ama: Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems.
Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002
apa: Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general
discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002
chicago: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General
Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002.
ieee: F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy
systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797,
2015.
ista: Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy
systems. Journal of Complexity. 31(6), 773–797.
mla: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General
Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press,
2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002.
short: F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.
date_created: 2018-12-11T11:54:02Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.06.002
intvolume: ' 31'
issue: '6'
language:
- iso: eng
month: '12'
oa_version: None
page: 773 - 797
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5320'
quality_controlled: '1'
related_material:
record:
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: A Koksma-Hlawka inequality for general discrepancy systems
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2015'
...
---
_id: '1399'
abstract:
- lang: eng
text: This thesis is concerned with the computation and approximation of intrinsic
volumes. Given a smooth body M and a certain digital approximation of it, we develop
algorithms to approximate various intrinsic volumes of M using only measurements
taken from its digital approximations. The crucial idea behind our novel algorithms
is to link the recent theory of persistent homology to the theory of intrinsic
volumes via the Crofton formula from integral geometry and, in particular, via
Euler characteristic computations. Our main contributions are a multigrid convergent
digital algorithm to compute the first intrinsic volume of a solid body in R^n
as well as an appropriate integration pipeline to approximate integral-geometric
integrals defined over the Grassmannian manifold.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Pausinger F. On the approximation of intrinsic volumes. 2015.
apa: Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute
of Science and Technology Austria.
chicago: Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute
of Science and Technology Austria, 2015.
ieee: F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science
and Technology Austria, 2015.
ista: Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of
Science and Technology Austria.
mla: Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute
of Science and Technology Austria, 2015.
short: F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science
and Technology Austria, 2015.
date_created: 2018-12-11T11:51:48Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
degree_awarded: PhD
department:
- _id: HeEd
language:
- iso: eng
month: '06'
oa_version: None
page: '144'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '5808'
related_material:
record:
- id: '1662'
relation: part_of_dissertation
status: public
- id: '1792'
relation: part_of_dissertation
status: public
- id: '2255'
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: On the approximation of intrinsic volumes
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2015'
...
---
_id: '10893'
abstract:
- lang: eng
text: Saddle periodic orbits are an essential and stable part of the topological
skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm
to robustly extract these features. In this chapter, we present a novel technique
to extract saddle periodic orbits. Exploiting the analytic properties of such
an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent
(FTLE) that indicates its presence. Using persistent homology, we can then extract
the robust cycles of this field. These cycles thereby represent the saddle periodic
orbits of the given vector field. We discuss the different existing FTLE approximation
schemes regarding their applicability to this specific problem and propose an
adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate
our method using simple analytic vector field data.
acknowledgement: First, we thank the reviewers of this paper for their ideas and critical
comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions.
This research is supported by the European Commission under the TOPOSYS project
FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the
European Science Foundation under the ACAT Research Network Program.
article_processing_charge: No
author:
- first_name: Jens
full_name: Kasten, Jens
last_name: Kasten
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Wieland
full_name: Reich, Wieland
last_name: Reich
- first_name: Gerik
full_name: Scheuermann, Gerik
last_name: Scheuermann
citation:
ama: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of
saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological
Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization.
Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4'
apa: 'Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward
the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci,
& R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization
III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4'
chicago: 'Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward
the Extraction of Saddle Periodic Orbits.” In Topological Methods in Data Analysis
and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014.
https://doi.org/10.1007/978-3-319-04099-8_4.'
ieee: 'J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction
of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization
III , vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham:
Springer, 2014, pp. 55–69.'
ista: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction
of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization
III . vol. 1, 55–69.'
mla: Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological
Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer
et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4.
short: J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I.
Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and
Visualization III , Springer, Cham, 2014, pp. 55–69.
date_created: 2022-03-21T07:11:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2022-06-21T12:01:47Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_4
ec_funded: 1
editor:
- first_name: Peer-Timo
full_name: Bremer, Peer-Timo
last_name: Bremer
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Valerio
full_name: Pascucci, Valerio
last_name: Pascucci
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
intvolume: ' 1'
language:
- iso: eng
month: '03'
oa_version: None
page: 55-69
place: Cham
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Topological Methods in Data Analysis and Visualization III '
publication_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Toward the extraction of saddle periodic orbits
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2014'
...
---
_id: '1816'
abstract:
- lang: eng
text: Watermarking techniques for vector graphics dislocate vertices in order to
embed imperceptible, yet detectable, statistical features into the input data.
The embedding process may result in a change of the topology of the input data,
e.g., by introducing self-intersections, which is undesirable or even disastrous
for many applications. In this paper we present a watermarking framework for two-dimensional
vector graphics that employs conventional watermarking techniques but still provides
the guarantee that the topology of the input data is preserved. The geometric
part of this framework computes so-called maximum perturbation regions (MPR) of
vertices. We propose two efficient algorithms to compute MPRs based on Voronoi
diagrams and constrained triangulations. Furthermore, we present two algorithms
to conditionally correct the watermarked data in order to increase the watermark
embedding capacity and still guarantee topological correctness. While we focus
on the watermarking of input formed by straight-line segments, one of our approaches
can also be extended to circular arcs. We conclude the paper by demonstrating
and analyzing the applicability of our framework in conjunction with two well-known
watermarking techniques.
acknowledgement: 'Work by Martin Held and Stefan Huber was supported by Austrian Science
Fund (FWF): L367-N15 and P25816-N15.'
author:
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Peter
full_name: Meerwald, Peter
last_name: Meerwald
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
citation:
ama: Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector
graphics. International Journal of Computational Geometry and Applications.
2014;24(1):61-86. doi:10.1142/S0218195914500034
apa: Huber, S., Held, M., Meerwald, P., & Kwitt, R. (2014). Topology-preserving
watermarking of vector graphics. International Journal of Computational Geometry
and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195914500034
chicago: Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving
Watermarking of Vector Graphics.” International Journal of Computational Geometry
and Applications. World Scientific Publishing, 2014. https://doi.org/10.1142/S0218195914500034.
ieee: S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking
of vector graphics,” International Journal of Computational Geometry and Applications,
vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.
ista: Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking
of vector graphics. International Journal of Computational Geometry and Applications.
24(1), 61–86.
mla: Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.”
International Journal of Computational Geometry and Applications, vol.
24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:10.1142/S0218195914500034.
short: S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational
Geometry and Applications 24 (2014) 61–86.
date_created: 2018-12-11T11:54:10Z
date_published: 2014-03-16T00:00:00Z
date_updated: 2021-01-12T06:53:23Z
day: '16'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1142/S0218195914500034
file:
- access_level: open_access
checksum: be45c133ab4d43351260e21beaa8f4b1
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:43Z
date_updated: 2020-07-14T12:45:17Z
file_id: '4704'
file_name: IST-2016-443-v1+1_S0218195914500034.pdf
file_size: 991734
relation: main_file
file_date_updated: 2020-07-14T12:45:17Z
has_accepted_license: '1'
intvolume: ' 24'
issue: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 61 - 86
publication: International Journal of Computational Geometry and Applications
publication_status: published
publisher: World Scientific Publishing
publist_id: '5290'
pubrep_id: '443'
quality_controlled: '1'
scopus_import: 1
status: public
title: Topology-preserving watermarking of vector graphics
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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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2014'
...
---
_id: '1842'
abstract:
- lang: eng
text: We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2
outerplanar triangulations in both convex and general cases. We also prove that
the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by
O(n3) and O(n10), in the convex and general case, respectively. We then apply
similar methods to prove an (Formula presented.) upper bound on the Ramsey number
of a path with n ordered vertices.
acknowledgement: Marek Krčál was supported by the ERC Advanced Grant No. 267165.
author:
- first_name: Josef
full_name: Cibulka, Josef
last_name: Cibulka
- first_name: Pu
full_name: Gao, Pu
last_name: Gao
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Tomáš
full_name: Valla, Tomáš
last_name: Valla
- first_name: Pavel
full_name: Valtr, Pavel
last_name: Valtr
citation:
ama: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number
of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79.
doi:10.1007/s00454-014-9646-x
apa: Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the
geometric ramsey number of outerplanar graphs. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x
chicago: Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On
the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational
Geometry. Springer, 2014. https://doi.org/10.1007/s00454-014-9646-x.
ieee: J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey
number of outerplanar graphs,” Discrete & Computational Geometry, vol.
53, no. 1. Springer, pp. 64–79, 2014.
ista: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey
number of outerplanar graphs. Discrete & Computational Geometry. 53(1), 64–79.
mla: Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.”
Discrete & Computational Geometry, vol. 53, no. 1, Springer, 2014,
pp. 64–79, doi:10.1007/s00454-014-9646-x.
short: J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational
Geometry 53 (2014) 64–79.
date_created: 2018-12-11T11:54:18Z
date_published: 2014-11-14T00:00:00Z
date_updated: 2021-01-12T06:53:33Z
day: '14'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-014-9646-x
intvolume: ' 53'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.7004
month: '11'
oa: 1
oa_version: Submitted Version
page: 64 - 79
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5260'
scopus_import: 1
status: public
title: On the geometric ramsey number of outerplanar graphs
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 53
year: '2014'
...
---
_id: '1876'
abstract:
- lang: eng
text: We study densities of functionals over uniformly bounded triangulations of
a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay
triangulation if this is the case for finite sets.
article_processing_charge: No
article_type: original
author:
- first_name: Nikolai
full_name: Dolbilin, Nikolai
last_name: Dolbilin
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Alexey
full_name: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
citation:
ama: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations
of delaunay sets. Moscow Mathematical Journal. 2014;14(3):491-504. doi:10.17323/1609-4514-2014-14-3-491-504
apa: Dolbilin, N., Edelsbrunner, H., Glazyrin, A., & Musin, O. (2014). Functionals
on triangulations of delaunay sets. Moscow Mathematical Journal. Independent
University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-3-491-504
chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin.
“Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal.
Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-3-491-504.
ieee: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations
of delaunay sets,” Moscow Mathematical Journal, vol. 14, no. 3. Independent
University of Moscow, pp. 491–504, 2014.
ista: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations
of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.
mla: Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.”
Moscow Mathematical Journal, vol. 14, no. 3, Independent University of
Moscow, 2014, pp. 491–504, doi:10.17323/1609-4514-2014-14-3-491-504.
short: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical
Journal 14 (2014) 491–504.
date_created: 2018-12-11T11:54:29Z
date_published: 2014-07-01T00:00:00Z
date_updated: 2022-03-03T11:47:09Z
day: '01'
department:
- _id: HeEd
doi: 10.17323/1609-4514-2014-14-3-491-504
external_id:
arxiv:
- '1211.7053'
intvolume: ' 14'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1211.7053
month: '07'
oa: 1
oa_version: Submitted Version
page: 491 - 504
publication: Moscow Mathematical Journal
publication_identifier:
issn:
- '16093321'
publication_status: published
publisher: Independent University of Moscow
publist_id: '5220'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functionals on triangulations of delaunay sets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2014'
...
---
_id: '1929'
abstract:
- lang: eng
text: We propose an algorithm for the generalization of cartographic objects that
can be used to represent maps on different scales.
acknowledgement: We would like to offer our special thanks to students of the Department
of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev
for participation in developing the program and assistance in preparation of test
data. This work was supported by grant 11.G34.31.0053 from the government of the
Russian Federation.
article_processing_charge: No
article_type: original
author:
- first_name: V V
full_name: Alexeev, V V
last_name: Alexeev
- first_name: V G
full_name: Bogaevskaya, V G
last_name: Bogaevskaya
- first_name: M M
full_name: Preobrazhenskaya, M M
last_name: Preobrazhenskaya
- first_name: A Y
full_name: Ukhalov, A Y
last_name: Ukhalov
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Olga
full_name: Yakimova, Olga
last_name: Yakimova
citation:
ama: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H,
Yakimova O. An algorithm for cartographic generalization that preserves global
topology. Journal of Mathematical Sciences. 2014;203(6):754-760. doi:10.1007/s10958-014-2165-8
apa: Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y.,
Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization
that preserves global topology. Journal of Mathematical Sciences. Springer.
https://doi.org/10.1007/s10958-014-2165-8
chicago: Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert
Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization
That Preserves Global Topology.” Journal of Mathematical Sciences. Springer,
2014. https://doi.org/10.1007/s10958-014-2165-8.
ieee: V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H.
Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that
preserves global topology,” Journal of Mathematical Sciences, vol. 203,
no. 6. Springer, pp. 754–760, 2014.
ista: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner
H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves
global topology. Journal of Mathematical Sciences. 203(6), 754–760.
mla: Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves
Global Topology.” Journal of Mathematical Sciences, vol. 203, no. 6, Springer,
2014, pp. 754–60, doi:10.1007/s10958-014-2165-8.
short: V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner,
O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.
date_created: 2018-12-11T11:54:46Z
date_published: 2014-11-16T00:00:00Z
date_updated: 2022-05-24T10:39:06Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/s10958-014-2165-8
intvolume: ' 203'
issue: '6'
language:
- iso: eng
month: '11'
oa_version: None
page: 754 - 760
publication: Journal of Mathematical Sciences
publication_identifier:
eissn:
- 1573-8795
issn:
- 1072-3374
publication_status: published
publisher: Springer
publist_id: '5165'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An algorithm for cartographic generalization that preserves global topology
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 203
year: '2014'
...
---
_id: '1930'
abstract:
- lang: eng
text: (Figure Presented) Data acquisition, numerical inaccuracies, and sampling
often introduce noise in measurements and simulations. Removing this noise is
often necessary for efficient analysis and visualization of this data, yet many
denoising techniques change the minima and maxima of a scalar field. For example,
the extrema can appear or disappear, spatially move, and change their value. This
can lead to wrong interpretations of the data, e.g., when the maximum temperature
over an area is falsely reported being a few degrees cooler because the denoising
method is unaware of these features. Recently, a topological denoising technique
based on a global energy optimization was proposed, which allows the topology-controlled
denoising of 2D scalar fields. While this method preserves the minima and maxima,
it is constrained by the size of the data. We extend this work to large 2D data
and medium-sized 3D data by introducing a novel domain decomposition approach.
It allows processing small patches of the domain independently while still avoiding
the introduction of new critical points. Furthermore, we propose an iterative
refinement of the solution, which decreases the optimization energy compared to
the previous approach and therefore gives smoother results that are closer to
the input. We illustrate our technique on synthetic and real-world 2D and 3D data
sets that highlight potential applications.
acknowledgement: RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship;
MPC-VCC
author:
- first_name: David
full_name: Günther, David
last_name: Günther
- first_name: Alec
full_name: Jacobson, Alec
last_name: Jacobson
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hans
full_name: Seidel, Hans
last_name: Seidel
- first_name: Olga
full_name: Sorkine Hornung, Olga
last_name: Sorkine Hornung
- first_name: Tino
full_name: Weinkauf, Tino
last_name: Weinkauf
citation:
ama: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf
T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields.
IEEE Transactions on Visualization and Computer Graphics. 2014;20(12):2585-2594.
doi:10.1109/TVCG.2014.2346432
apa: Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O.,
& Weinkauf, T. (2014). Fast and memory-efficient topological denoising of
2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics.
IEEE. https://doi.org/10.1109/TVCG.2014.2346432
chicago: Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine
Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of
2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics.
IEEE, 2014. https://doi.org/10.1109/TVCG.2014.2346432.
ieee: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and
T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar
fields,” IEEE Transactions on Visualization and Computer Graphics, vol.
20, no. 12. IEEE, pp. 2585–2594, 2014.
ista: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf
T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields.
IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.
mla: Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of
2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics,
vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:10.1109/TVCG.2014.2346432.
short: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T.
Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.
date_created: 2018-12-11T11:54:46Z
date_published: 2014-12-31T00:00:00Z
date_updated: 2021-01-12T06:54:09Z
day: '31'
department:
- _id: HeEd
doi: 10.1109/TVCG.2014.2346432
intvolume: ' 20'
issue: '12'
language:
- iso: eng
month: '12'
oa_version: None
page: 2585 - 2594
publication: IEEE Transactions on Visualization and Computer Graphics
publication_status: published
publisher: IEEE
publist_id: '5164'
quality_controlled: '1'
scopus_import: 1
status: public
title: Fast and memory-efficient topological denoising of 2D and 3D scalar fields
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 20
year: '2014'
...
---
_id: '2043'
abstract:
- lang: eng
text: Persistent homology is a popular and powerful tool for capturing topological
features of data. Advances in algorithms for computing persistent homology have
reduced the computation time drastically – as long as the algorithm does not exhaust
the available memory. Following up on a recently presented parallel method for
persistence computation on shared memory systems [1], we demonstrate that a simple
adaption of the standard reduction algorithm leads to a variant for distributed
systems. Our algorithmic design ensures that the data is distributed over the
nodes without redundancy; this permits the computation of much larger instances
than on a single machine. Moreover, we observe that the parallelism at least compensates
for the overhead caused by communication between nodes, and often even speeds
up the computation compared to sequential and even parallel shared memory algorithms.
In our experiments, we were able to compute the persistent homology of filtrations
with more than a billion (109) elements within seconds on a cluster with 32 nodes
using less than 6GB of memory per node.
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
citation:
ama: 'Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology.
In: McGeoch C, Meyer U, eds. Proceedings of the Workshop on Algorithm Engineering
and Experiments. Society of Industrial and Applied Mathematics; 2014:31-38.
doi:10.1137/1.9781611973198.4'
apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Distributed computation
of persistent homology. In C. McGeoch & U. Meyer (Eds.), Proceedings of
the Workshop on Algorithm Engineering and Experiments (pp. 31–38). Portland,
USA: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973198.4'
chicago: Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation
of Persistent Homology.” In Proceedings of the Workshop on Algorithm Engineering
and Experiments, edited by Catherine McGeoch and Ulrich Meyer, 31–38. Society
of Industrial and Applied Mathematics, 2014. https://doi.org/10.1137/1.9781611973198.4.
ieee: U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent
homology,” in Proceedings of the Workshop on Algorithm Engineering and Experiments,
Portland, USA, 2014, pp. 31–38.
ista: 'Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent
homology. Proceedings of the Workshop on Algorithm Engineering and Experiments.
ALENEX: Algorithm Engineering and Experiments, 31–38.'
mla: Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” Proceedings
of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch
and Ulrich Meyer, Society of Industrial and Applied Mathematics, 2014, pp. 31–38,
doi:10.1137/1.9781611973198.4.
short: U. Bauer, M. Kerber, J. Reininghaus, in:, C. McGeoch, U. Meyer (Eds.), Proceedings
of the Workshop on Algorithm Engineering and Experiments, Society of Industrial
and Applied Mathematics, 2014, pp. 31–38.
conference:
end_date: 2014-01-05
location: Portland, USA
name: 'ALENEX: Algorithm Engineering and Experiments'
start_date: 2014-01-05
date_created: 2018-12-11T11:55:23Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:54:56Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973198.4
ec_funded: 1
editor:
- first_name: Catherine
full_name: ' McGeoch, Catherine'
last_name: ' McGeoch'
- first_name: Ulrich
full_name: Meyer, Ulrich
last_name: Meyer
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.0710
month: '01'
oa: 1
oa_version: Submitted Version
page: 31 - 38
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Workshop on Algorithm Engineering and Experiments
publication_status: published
publisher: Society of Industrial and Applied Mathematics
publist_id: '5008'
quality_controlled: '1'
scopus_import: 1
status: public
title: Distributed computation of persistent homology
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2044'
abstract:
- lang: eng
text: We present a parallel algorithm for computing the persistent homology of a
filtered chain complex. Our approach differs from the commonly used reduction
algorithm by first computing persistence pairs within local chunks, then simplifying
the unpaired columns, and finally applying standard reduction on the simplified
matrix. The approach generalizes a technique by Günther et al., which uses discrete
Morse Theory to compute persistence; we derive the same worst-case complexity
bound in a more general context. The algorithm employs several practical optimization
techniques, which are of independent interest. Our sequential implementation of
the algorithm is competitive with state-of-the-art methods, and we further improve
the performance through parallel computation.
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
citation:
ama: 'Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent
Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological
Methods in Data Analysis and Visualization III. Mathematics and Visualization.
Springer; 2014:103-117. doi:10.1007/978-3-319-04099-8_7'
apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Clear and Compress: Computing
Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, & R.
Peikert (Eds.), Topological Methods in Data Analysis and Visualization III
(pp. 103–117). Springer. https://doi.org/10.1007/978-3-319-04099-8_7'
chicago: 'Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress:
Computing Persistent Homology in Chunks.” In Topological Methods in Data Analysis
and Visualization III, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_7.'
ieee: 'U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent
Homology in Chunks,” in Topological Methods in Data Analysis and Visualization
III, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014,
pp. 103–117.'
ista: 'Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent
Homology in Chunks. In: Topological Methods in Data Analysis and Visualization
III. , 103–117.'
mla: 'Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in
Chunks.” Topological Methods in Data Analysis and Visualization III, edited
by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:10.1007/978-3-319-04099-8_7.'
short: U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci,
R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III,
Springer, 2014, pp. 103–117.
date_created: 2018-12-11T11:55:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2021-01-12T06:54:56Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_7
ec_funded: 1
editor:
- first_name: Peer-Timo
full_name: Bremer, Peer-Timo
last_name: Bremer
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Valerio
full_name: Pascucci, Valerio
last_name: Pascucci
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1303.0477
month: '03'
oa: 1
oa_version: Submitted Version
page: 103 - 117
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Topological Methods in Data Analysis and Visualization III
publication_status: published
publisher: Springer
publist_id: '5007'
quality_controlled: '1'
scopus_import: 1
series_title: Mathematics and Visualization
status: public
title: 'Clear and Compress: Computing Persistent Homology in Chunks'
type: book_chapter
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2153'
abstract:
- lang: eng
text: 'We define a simple, explicit map sending a morphism f : M → N of pointwise
finite dimensional persistence modules to a matching between the barcodes of M
and N. Our main result is that, in a precise sense, the quality of this matching
is tightly controlled by the lengths of the longest intervals in the barcodes
of ker f and coker f . As an immediate corollary, we obtain a new proof of the
algebraic stability theorem for persistence barcodes [5, 9], a fundamental result
in the theory of persistent homology. In contrast to previous proofs, ours shows
explicitly how a δ-interleaving morphism between two persistence modules induces
a δ-matching between the barcodes of the two modules. Our main result also specializes
to a structure theorem for submodules and quotients of persistence modules. Copyright
is held by the owner/author(s).'
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Lesnick, Michael
last_name: Lesnick
citation:
ama: 'Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability
of persistence. In: Proceedings of the Annual Symposium on Computational Geometry.
ACM; 2014:355-364. doi:10.1145/2582112.2582168'
apa: 'Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the
algebraic stability of persistence. In Proceedings of the Annual Symposium
on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168'
chicago: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and
the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium
on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168.
ieee: U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic
stability of persistence,” in Proceedings of the Annual Symposium on Computational
Geometry, Kyoto, Japan, 2014, pp. 355–364.
ista: 'Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic
stability of persistence. Proceedings of the Annual Symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, 355–364.'
mla: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the
Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on
Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168.
short: U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 355–364.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582168
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1311.3681
month: '06'
oa: 1
oa_version: Submitted Version
page: 355 - 364
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4853'
quality_controlled: '1'
scopus_import: 1
status: public
title: Induced matchings of barcodes and the algebraic stability of persistence
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2156'
abstract:
- lang: eng
text: We propose a metric for Reeb graphs, called the functional distortion distance.
Under this distance, the Reeb graph is stable against small changes of input functions.
At the same time, it remains discriminative at differentiating input functions.
In particular, the main result is that the functional distortion distance between
two Reeb graphs is bounded from below by the bottleneck distance between both
the ordinary and extended persistence diagrams for appropriate dimensions. As
an application of our results, we analyze a natural simplification scheme for
Reeb graphs, and show that persistent features in Reeb graph remains persistent
under simplification. Understanding the stability of important features of the
Reeb graph under simplification is an interesting problem on its own right, and
critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).
acknowledgement: National Science Foundation under grants CCF-1319406, CCF-1116258.
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Xiaoyin
full_name: Ge, Xiaoyin
last_name: Ge
- first_name: Yusu
full_name: Wang, Yusu
last_name: Wang
citation:
ama: 'Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings
of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169'
apa: 'Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb
graphs. In Proceedings of the Annual Symposium on Computational Geometry
(pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169'
chicago: Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb
Graphs.” In Proceedings of the Annual Symposium on Computational Geometry,
464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169.
ieee: U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in
Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan,
2014, pp. 464–473.
ista: 'Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings
of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, 464–473.'
mla: Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings
of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73,
doi:10.1145/2582112.2582169.
short: U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 464–473.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:02Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:39Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582169
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1307.2839
month: '06'
oa: 1
oa_version: Submitted Version
page: 464 - 473
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4850'
quality_controlled: '1'
scopus_import: 1
status: public
title: Measuring distance between Reeb graphs
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2155'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a positive radius, we study the Čech,
Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete
Morse theory. We prove that the latter three complexes are simple-homotopy equivalent.
Our results have applications in topological data analysis and in the reconstruction
of shapes from sampled data. Copyright is held by the owner/author(s).
acknowledgement: This research is partially supported by ESF under the ACAT Research
Network Programme, and by the Russian Government under mega project 11.G34.31.0053
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations.
In: Proceedings of the Annual Symposium on Computational Geometry. ACM;
2014:484-490. doi:10.1145/2582112.2582167'
apa: 'Bauer, U., & Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay
filtrations. In Proceedings of the Annual Symposium on Computational Geometry
(pp. 484–490). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582167'
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Filtrations.” In Proceedings of the Annual Symposium on Computational
Geometry, 484–90. ACM, 2014. https://doi.org/10.1145/2582112.2582167.
ieee: U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,”
in Proceedings of the Annual Symposium on Computational Geometry, Kyoto,
Japan, 2014, pp. 484–490.
ista: 'Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations.
Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium
on Computational Geometry, 484–490.'
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Filtrations.” Proceedings of the Annual Symposium on Computational Geometry,
ACM, 2014, pp. 484–90, doi:10.1145/2582112.2582167.
short: U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 484–490.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582167
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1312.1231
month: '06'
oa: 1
oa_version: Submitted Version
page: 484 - 490
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4851'
quality_controlled: '1'
scopus_import: 1
status: public
title: The morse theory of Čech and Delaunay filtrations
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2177'
abstract:
- lang: eng
text: We give evidence for the difficulty of computing Betti numbers of simplicial
complexes over a finite field. We do this by reducing the rank computation for
sparse matrices with to non-zero entries to computing Betti numbers of simplicial
complexes consisting of at most a constant times to simplices. Together with the
known reduction in the other direction, this implies that the two problems have
the same computational complexity.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Salman
full_name: Parsa, Salman
id: 4BDBD4F2-F248-11E8-B48F-1D18A9856A87
last_name: Parsa
citation:
ama: 'Edelsbrunner H, Parsa S. On the computational complexity of betti numbers
reductions from matrix rank. In: Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11'
apa: 'Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity
of betti numbers reductions from matrix rank. In Proceedings of the Annual
ACM-SIAM Symposium on Discrete Algorithms (pp. 152–160). Portland, USA: SIAM.
https://doi.org/10.1137/1.9781611973402.11'
chicago: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity
of Betti Numbers Reductions from Matrix Rank.” In Proceedings of the Annual
ACM-SIAM Symposium on Discrete Algorithms, 152–60. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.11.
ieee: H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers
reductions from matrix rank,” in Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, Portland, USA, 2014, pp. 152–160.
ista: 'Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers
reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete
Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.'
mla: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of
Betti Numbers Reductions from Matrix Rank.” Proceedings of the Annual ACM-SIAM
Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–60, doi:10.1137/1.9781611973402.11.
short: H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, SIAM, 2014, pp. 152–160.
conference:
end_date: 2014-01-07
location: Portland, USA
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2014-01-05
date_created: 2018-12-11T11:56:09Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:55:48Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973402.11
language:
- iso: eng
month: '01'
oa_version: None
page: 152 - 160
publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
publication_status: published
publisher: SIAM
publist_id: '4805'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the computational complexity of betti numbers reductions from matrix rank
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2184'
abstract:
- lang: eng
text: 'Given topological spaces X,Y, a fundamental problem of algebraic topology
is understanding the structure of all continuous maps X→ Y. We consider a computational
version, where X,Y are given as finite simplicial complexes, and the goal is to
compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem
in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected;
in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical
tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and
simplicial sets) with algorithmic tools from effective algebraic topology (locally
effective simplicial sets and objects with effective homology). In contrast, [X,Y]
is known to be uncomputable for general X,Y, since for X = S1 it includes a well
known undecidable problem: testing triviality of the fundamental group of Y. In
follow-up papers, the algorithm is shown to run in polynomial time for d fixed,
and extended to other problems, such as the extension problem, where we are given
a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or
computing the Z2-index-everything in the stable range. Outside the stable range,
the extension problem is undecidable.'
acknowledgement: The research by M. K. was supported by project GAUK 49209. The research
by M. K. was also supported by project 1M0545 by the Ministry of Education of the
Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague
(project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss
National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).
article_number: '17 '
author:
- first_name: Martin
full_name: Čadek, Martin
last_name: Čadek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Francis
full_name: Sergeraert, Francis
last_name: Sergeraert
- first_name: Lukáš
full_name: Vokřínek, Lukáš
last_name: Vokřínek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing
all maps into a sphere. Journal of the ACM. 2014;61(3). doi:10.1145/2597629
apa: Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner,
U. (2014). Computing all maps into a sphere. Journal of the ACM. ACM. https://doi.org/10.1145/2597629
chicago: Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek,
and Uli Wagner. “Computing All Maps into a Sphere.” Journal of the ACM.
ACM, 2014. https://doi.org/10.1145/2597629.
ieee: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner,
“Computing all maps into a sphere,” Journal of the ACM, vol. 61, no. 3.
ACM, 2014.
ista: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing
all maps into a sphere. Journal of the ACM. 61(3), 17.
mla: Čadek, Martin, et al. “Computing All Maps into a Sphere.” Journal of the
ACM, vol. 61, no. 3, 17, ACM, 2014, doi:10.1145/2597629.
short: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal
of the ACM 61 (2014).
date_created: 2018-12-11T11:56:12Z
date_published: 2014-05-01T00:00:00Z
date_updated: 2021-01-12T06:55:50Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2597629
intvolume: ' 61'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1105.6257
month: '05'
oa: 1
oa_version: Preprint
publication: Journal of the ACM
publication_status: published
publisher: ACM
publist_id: '4797'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computing all maps into a sphere
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 61
year: '2014'
...
---
_id: '2905'
abstract:
- lang: eng
text: "Persistent homology is a recent grandchild of homology that has found use
in\r\nscience and engineering as well as in mathematics. This paper surveys the
method as well\r\nas the applications, neglecting completeness in favor of highlighting
ideas and directions."
acknowledgement: This research is partially supported by NSF under grant DBI-0820624,
by ESF under the Research Networking Programme, and by the Russian Government Project
11.G34.31.0053.
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: Dmitriy
full_name: Morozovy, Dmitriy
last_name: Morozovy
citation:
ama: 'Edelsbrunner H, Morozovy D. Persistent homology: Theory and practice. In:
European Mathematical Society Publishing House; 2014:31-50. doi:10.4171/120-1/3'
apa: 'Edelsbrunner, H., & Morozovy, D. (2014). Persistent homology: Theory and
practice (pp. 31–50). Presented at the ECM: European Congress of Mathematics,
Kraków, Poland: European Mathematical Society Publishing House. https://doi.org/10.4171/120-1/3'
chicago: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory
and Practice,” 31–50. European Mathematical Society Publishing House, 2014. https://doi.org/10.4171/120-1/3.'
ieee: 'H. Edelsbrunner and D. Morozovy, “Persistent homology: Theory and practice,”
presented at the ECM: European Congress of Mathematics, Kraków, Poland, 2014,
pp. 31–50.'
ista: 'Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice.
ECM: European Congress of Mathematics, 31–50.'
mla: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. Persistent Homology: Theory
and Practice. European Mathematical Society Publishing House, 2014, pp. 31–50,
doi:10.4171/120-1/3.'
short: H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing
House, 2014, pp. 31–50.
conference:
end_date: 2012-07-07
location: Kraków, Poland
name: 'ECM: European Congress of Mathematics'
start_date: 2012-07-02
date_created: 2018-12-11T12:00:16Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T07:00:36Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4171/120-1/3
file:
- access_level: open_access
checksum: 1d4a046f1af945c407c5c4d411d4c5e4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:43Z
date_updated: 2020-07-14T12:45:52Z
file_id: '5232'
file_name: IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf
file_size: 435320
relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Submitted Version
page: 31 - 50
publication_status: published
publisher: European Mathematical Society Publishing House
publist_id: '3842'
pubrep_id: '544'
quality_controlled: '1'
status: public
title: 'Persistent homology: Theory and practice'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '10892'
abstract:
- lang: eng
text: "In this paper, we introduce planar matchings on directed pseudo-line arrangements,
which yield a planar set of pseudo-line segments such that only matching-partners
are adjacent. By translating the planar matching problem into a corresponding
stable roommates problem we show that such matchings always exist.\r\nUsing our
new framework, we establish, for the first time, a complete, rigorous definition
of weighted straight skeletons, which are based on a so-called wavefront propagation
process. We present a generalized and unified approach to treat structural changes
in the wavefront that focuses on the restoration of weak planarity by finding
planar matchings."
acknowledgement: 'T. Biedl was supported by NSERC and the Ross and Muriel Cheriton
Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: 'Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons.
In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature;
2014:117-127. doi:10.1007/978-3-319-13075-0_10'
apa: 'Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted
straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889,
pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10'
chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for
Weighted Straight Skeletons.” In 25th International Symposium, ISAAC 2014,
8889:117–27. Springer Nature, 2014. https://doi.org/10.1007/978-3-319-13075-0_10.
ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight
skeletons,” in 25th International Symposium, ISAAC 2014, Jeonju, Korea,
2014, vol. 8889, pp. 117–127.
ista: 'Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight
skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium
on Algorithms and Computation, LNCS, vol. 8889, 117–127.'
mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.”
25th International Symposium, ISAAC 2014, vol. 8889, Springer Nature, 2014,
pp. 117–27, doi:10.1007/978-3-319-13075-0_10.
short: T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC
2014, Springer Nature, 2014, pp. 117–127.
conference:
end_date: 2014-12-17
location: Jeonju, Korea
name: 'ISAAC: International Symposium on Algorithms and Computation'
start_date: 2014-12-15
date_created: 2022-03-21T07:09:03Z
date_published: 2014-11-08T00:00:00Z
date_updated: 2023-02-23T12:20:55Z
day: '08'
department:
- _id: HeEd
doi: 10.1007/978-3-319-13075-0_10
intvolume: ' 8889'
language:
- iso: eng
month: '11'
oa_version: None
page: 117-127
publication: 25th International Symposium, ISAAC 2014
publication_identifier:
eisbn:
- '9783319130750'
eissn:
- 1611-3349
isbn:
- '9783319130743'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '481'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Planar matchings for weighted straight skeletons
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8889
year: '2014'
...