---
_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
article_processing_charge: No
author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
orcid: 0000-0003-2012-9947
- 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).
corr_author: '1'
date_created: 2018-12-11T11:54:02Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2025-09-23T08:30:43Z
day: '01'
ddc:
- '000'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1371/journal.pone.0127657
external_id:
isi:
- '000356630900069'
file:
- access_level: open_access
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
relation: main_file
file_date_updated: 2020-07-14T12:45:16Z
has_accepted_license: '1'
intvolume: ' 10'
isi: 1
issue: '6'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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:
record:
- id: '9737'
relation: research_data
status: public
scopus_import: '1'
status: public
title: 'DynamicRoots: A software platform for the reconstruction and analysis of growing
plant roots'
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 10
year: '2015'
...
---
OA_place: publisher
OA_type: free access
_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.'
article_processing_charge: No
article_type: original
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.'
corr_author: '1'
date_created: 2018-12-11T11:54:06Z
date_published: 2015-06-03T00:00:00Z
date_updated: 2025-09-23T09:18:30Z
day: '03'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.010
ec_funded: 1
external_id:
isi:
- '000357353200006'
intvolume: ' 48'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.comgeo.2014.08.010
month: '06'
oa: 1
oa_version: Published Version
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 48
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
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: 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.
corr_author: '1'
date_created: 2018-12-11T11:54:14Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2025-09-23T09:23:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10955-015-1238-5
ec_funded: 1
external_id:
arxiv:
- '1406.5313'
isi:
- '000356579000009'
intvolume: ' 160'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 160
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.
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: 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: 2025-09-23T14:08:54Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s10208-014-9223-y
ec_funded: 1
external_id:
isi:
- '000360862900004'
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'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 15
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. "
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
- 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.
corr_author: '1'
date_created: 2018-12-11T11:54:49Z
date_published: 2015-03-06T00:00:00Z
date_updated: 2025-09-23T09:44:12Z
day: '06'
department:
- _id: HeEd
doi: 10.1016/j.physleta.2014.12.010
external_id:
isi:
- '000349586000006'
intvolume: ' 379'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 379
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.
article_processing_charge: No
arxiv: 1
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: 2025-06-11T06:37:43Z
day: '14'
department:
- _id: HeEd
doi: 10.1109/CVPR.2015.7299106
external_id:
arxiv:
- '1412.6821'
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. '
article_processing_charge: No
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: 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: 2025-06-11T06:38:01Z
day: '01'
department:
- _id: HeEd
ec_funded: 1
external_id:
arxiv:
- '1505.03402'
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: 2DF688A6-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
orcid: 0000-0001-8878-8397
- 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: 2025-09-18T14:30:52Z
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: 2025-09-23T10:37:17Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1137/140993934
ec_funded: 1
external_id:
isi:
- '000357310400015'
intvolume: ' 14'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14
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: '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: '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.
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
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: 2025-09-23T13:44:17Z
day: '05'
department:
- _id: HeEd
doi: 10.1109/SYNASC.2014.81
external_id:
isi:
- '000366596600074'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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"
article_processing_charge: No
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: 2025-09-29T10:58:50Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.04.001
external_id:
isi:
- '000355887700001'
intvolume: ' 48'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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.
article_processing_charge: No
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: 2025-09-29T11:06:26Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.006
external_id:
isi:
- '000345056700007'
file:
- access_level: open_access
checksum: c1ef67f6ec925e12f73a96b8fe285ab4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:28Z
date_updated: 2020-07-14T12:45:02Z
file_id: '5215'
file_name: IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf
file_size: 505987
relation: main_file
file_date_updated: 2020-07-14T12:45:02Z
has_accepted_license: '1'
intvolume: ' 48'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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.
article_processing_charge: No
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: 2025-09-22T14:35:14Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.ipl.2014.09.021
external_id:
isi:
- '000346225300034'
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
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intvolume: ' 115'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 115
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.
article_processing_charge: No
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: 2025-09-29T11:06:25Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.01.004
external_id:
isi:
- '000351967400008'
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
relation: main_file
file_date_updated: 2020-07-14T12:45:03Z
has_accepted_license: '1'
intvolume: ' 48'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 48
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
arxiv: 1
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: Graph Drawing and Network Visualization'
start_date: 2015-09-24
date_created: 2018-12-11T11:52:54Z
date_published: 2015-11-27T00:00:00Z
date_updated: 2025-09-23T10:35:07Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-27261-0_28
external_id:
arxiv:
- '1508.01076'
isi:
- '000373628600028'
intvolume: ' 9411'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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'
article_processing_charge: No
arxiv: 1
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).
corr_author: '1'
date_created: 2018-12-11T11:53:27Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2025-09-23T10:38:46Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2751524
external_id:
arxiv:
- '1402.0858'
isi:
- '000361200500001'
intvolume: ' 62'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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 → ∞.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: 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: 2025-09-23T09:35:36Z
day: '14'
department:
- _id: HeEd
doi: 10.1137/140993843
ec_funded: 1
external_id:
arxiv:
- '1410.3736'
isi:
- '000360691500009'
intvolume: ' 47'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 47
year: '2015'
...