---
_id: '2807'
abstract:
- lang: eng
text: 'We consider several basic problems of algebraic topology, with connections
to combinatorial and geometric questions, from the point of view of computational
complexity. The extension problem asks, given topological spaces X; Y , a subspace
A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X
→ Y . For computational purposes, we assume that X and Y are represented as finite
simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map.
In this generality the problem is undecidable, as follows from Novikov''s result
from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study
the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected;
informally, this means that Y has \no holes up to dimension k-1" (a basic
example of such a Y is the sphere Sk). We prove that, on the one hand, this problem
is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2,
we obtain an algorithm that solves the extension problem in polynomial time assuming
Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides
a classification of all extensions up to homotopy (continuous deformation). This
relies on results of our SODA 2012 paper, and the main new ingredient is a machinery
of objects with polynomial-time homology, which is a polynomial-time analog of
objects with effective homology developed earlier by Sergeraert et al. We also
consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected
Y . Their computability was established by Brown in 1957; we show that πk(Y )
can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick
proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where
Y is a cell complex with certain rather compact encoding. We strengthen his result
to #P-hardness for Y given as a simplicial complex. '
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: 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, Vokřínek L, Wagner U. Extending continuous maps:
Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of
Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683'
apa: 'Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013).
Extending continuous maps: Polynomiality and undecidability. In 45th Annual
ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United
States: ACM. https://doi.org/10.1145/2488608.2488683'
chicago: 'Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner.
“Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual
ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683.'
ieee: 'M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous
maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory
of computing, Palo Alto, CA, United States, 2013, pp. 595–604.'
ista: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous
maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of
computing. STOC: Symposium on the Theory of Computing, 595–604.'
mla: 'Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.”
45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604,
doi:10.1145/2488608.2488683.'
short: M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual
ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604.
conference:
end_date: 2013-06-04
location: Palo Alto, CA, United States
name: 'STOC: Symposium on the Theory of Computing'
start_date: 2013-06-01
date_created: 2018-12-11T11:59:42Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2021-01-12T06:59:51Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2488608.2488683
file:
- access_level: open_access
checksum: 06c2ce5c1135fbc1f71ca15eeb242dcf
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:14:29Z
date_updated: 2020-07-14T12:45:48Z
file_id: '5081'
file_name: IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf
file_size: 447945
relation: main_file
file_date_updated: 2020-07-14T12:45:48Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 595 - 604
publication: 45th Annual ACM Symposium on theory of computing
publication_status: published
publisher: ACM
publist_id: '4078'
pubrep_id: '533'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Extending continuous maps: Polynomiality and undecidability'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2812'
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 ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel
sets of scalar functions on 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.'
acknowledgement: Some of the authors were partially supported by the GIGA ANR grant
(contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827).
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. In: Proceedings of the 29th Annual Symposium on Computational
Geometry. ACM; 2013:117-125. doi:10.1145/2462356.2462373'
apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2013).
Homological reconstruction and simplification in R3. In Proceedings of the
29th annual symposium on Computational Geometry (pp. 117–125). Rio de Janeiro,
Brazil: ACM. https://doi.org/10.1145/2462356.2462373'
chicago: Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André
Lieutier. “Homological Reconstruction and Simplification in R3.” In Proceedings
of the 29th Annual Symposium on Computational Geometry, 117–25. ACM, 2013.
https://doi.org/10.1145/2462356.2462373.
ieee: D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological
reconstruction and simplification in R3,” in Proceedings of the 29th annual
symposium on Computational Geometry, Rio de Janeiro, Brazil, 2013, pp. 117–125.
ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction
and simplification in R3. Proceedings of the 29th annual symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, 117–125.'
mla: Attali, Dominique, et al. “Homological Reconstruction and Simplification in
R3.” Proceedings of the 29th Annual Symposium on Computational Geometry,
ACM, 2013, pp. 117–25, doi:10.1145/2462356.2462373.
short: D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings
of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125.
conference:
end_date: 2013-06-20
location: Rio de Janeiro, Brazil
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2013-06-17
date_created: 2018-12-11T11:59:44Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2026-06-18T17:57:27Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2462356.2462373
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://hal.archives-ouvertes.fr/hal-00833791/
month: '06'
oa: 1
oa_version: Submitted Version
page: 117 - 125
publication: Proceedings of the 29th annual symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4072'
quality_controlled: '1'
related_material:
record:
- id: '1805'
relation: later_version
status: public
scopus_import: 1
status: public
title: Homological reconstruction and simplification in R3
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2815'
abstract:
- lang: eng
text: The fact that a sum of isotropic Gaussian kernels can have more modes than
kernels is surprising. Extra (ghost) modes do not exist in ℝ1 and are generally
not well studied in higher dimensions. We study a configuration of n+1 Gaussian
kernels for which there are exactly n+2 modes. We show that all modes lie on a
finite set of lines, which we call axes, and study the restriction of the Gaussian
mixture to these axes in order to discover that there are an exponential number
of critical points in this configuration. Although the existence of ghost modes
remained unknown due to the difficulty of finding examples in ℝ2, we show that
the resilience of ghost modes grows like the square root of the dimension. In
addition, we exhibit finite configurations of isotropic Gaussian kernels with
superlinearly many modes.
acknowledgement: This research is partially supported by the National Science Foundation
(NSF) under Grant DBI-0820624, by the European Science Foundation under the Research
Networking Programme, and the Russian Government Project 11.G34.31.0053.
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: Brittany Terese
full_name: Fasy, Brittany Terese
id: F65D502E-E68D-11E9-9252-C644099818F6
last_name: Fasy
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: 'Edelsbrunner H, Fasy BT, Rote G. Add isotropic Gaussian kernels at own risk:
More and more resilient modes in higher dimensions. Discrete & Computational
Geometry. 2013;49(4):797-822. doi:10.1007/s00454-013-9517-x'
apa: 'Edelsbrunner, H., Fasy, B. T., & Rote, G. (2013). Add isotropic Gaussian
kernels at own risk: More and more resilient modes in higher dimensions. Discrete
& Computational Geometry. Springer. https://doi.org/10.1007/s00454-013-9517-x'
chicago: 'Edelsbrunner, Herbert, Brittany Terese Fasy, and Günter Rote. “Add Isotropic
Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.”
Discrete & Computational Geometry. Springer, 2013. https://doi.org/10.1007/s00454-013-9517-x.'
ieee: 'H. Edelsbrunner, B. T. Fasy, and G. Rote, “Add isotropic Gaussian kernels
at own risk: More and more resilient modes in higher dimensions,” Discrete
& Computational Geometry, vol. 49, no. 4. Springer, pp. 797–822, 2013.'
ista: 'Edelsbrunner H, Fasy BT, Rote G. 2013. Add isotropic Gaussian kernels at
own risk: More and more resilient modes in higher dimensions. Discrete & Computational
Geometry. 49(4), 797–822.'
mla: 'Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk:
More and More Resilient Modes in Higher Dimensions.” Discrete & Computational
Geometry, vol. 49, no. 4, Springer, 2013, pp. 797–822, doi:10.1007/s00454-013-9517-x.'
short: H. Edelsbrunner, B.T. Fasy, G. Rote, Discrete & Computational Geometry
49 (2013) 797–822.
corr_author: '1'
date_created: 2018-12-11T11:59:44Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2026-06-18T18:35:33Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s00454-013-9517-x
external_id:
isi:
- '000320672400005'
intvolume: ' 49'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-013-9517-x
month: '06'
oa: 1
oa_version: Published Version
page: 797 - 822
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '3991'
quality_controlled: '1'
related_material:
record:
- id: '3134'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: 'Add isotropic Gaussian kernels at own risk: More and more resilient modes
in higher dimensions'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2013'
...
---
_id: '2822'
abstract:
- lang: eng
text: Identification of genes that control root system architecture in crop plants
requires innovations that enable high-throughput and accurate measurements of
root system architecture through time. We demonstrate the ability of a semiautomated
3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative
genetic basis of root system growth in a rice biparental mapping population, Bala
x Azucena. We phenotyped >1,400 3D root models and >57,000 2D images for
a suite of 25 traits that quantified the distribution, shape, extent of exploration,
and the intrinsic size of root networks at days 12, 14, and 16 of growth in a
gellan gum medium. From these data we identified 89 quantitative trait loci, some
of which correspond to those found previously in soil-grown plants, and provide
evidence for genetic tradeoffs in root growth allocations, such as between the
extent and thoroughness of exploration. We also developed a multivariate method
for generating and mapping central root architecture phenotypes and used it to
identify five major quantitative trait loci (r2 = 24-37%), two of which were not
identified by our univariate analysis. Our imaging and analytical platform provides
a means to identify genes with high potential for improving root traits and agronomic
qualities of crops.
article_processing_charge: No
author:
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Anjali
full_name: Iyer Pascuzzi, Anjali
last_name: Iyer Pascuzzi
- first_name: Jill
full_name: Anderson, Jill
last_name: Anderson
- first_name: Cheng
full_name: Lee, Cheng
last_name: Lee
- first_name: Paul
full_name: Zurek, Paul
last_name: Zurek
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
orcid: 0000-0003-2012-9947
- first_name: Ying
full_name: Zheng, Ying
last_name: Zheng
- first_name: Alexander
full_name: Bucksch, Alexander
last_name: Bucksch
- first_name: Yuriy
full_name: Mileyko, Yuriy
last_name: Mileyko
- first_name: Taras
full_name: Galkovskyi, Taras
last_name: Galkovskyi
- first_name: Brad
full_name: Moore, Brad
last_name: Moore
- first_name: John
full_name: Harer, John
last_name: Harer
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Thomas
full_name: Mitchell Olds, Thomas
last_name: Mitchell Olds
- first_name: Joshua
full_name: Weitz, Joshua
last_name: Weitz
- first_name: Philip
full_name: Benfey, Philip
last_name: Benfey
citation:
ama: Topp C, Iyer Pascuzzi A, Anderson J, et al. 3D phenotyping and quantitative
trait locus mapping identify core regions of the rice genome controlling root
architecture. PNAS. 2013;110(18):E1695-E1704. doi:10.1073/pnas.1304354110
apa: Topp, C., Iyer Pascuzzi, A., Anderson, J., Lee, C., Zurek, P., Symonova, O.,
… Benfey, P. (2013). 3D phenotyping and quantitative trait locus mapping identify
core regions of the rice genome controlling root architecture. PNAS. National
Academy of Sciences. https://doi.org/10.1073/pnas.1304354110
chicago: Topp, Christopher, Anjali Iyer Pascuzzi, Jill Anderson, Cheng Lee, Paul
Zurek, Olga Symonova, Ying Zheng, et al. “3D Phenotyping and Quantitative Trait
Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.”
PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1304354110.
ieee: C. Topp et al., “3D phenotyping and quantitative trait locus mapping
identify core regions of the rice genome controlling root architecture,” PNAS,
vol. 110, no. 18. National Academy of Sciences, pp. E1695–E1704, 2013.
ista: Topp C, Iyer Pascuzzi A, Anderson J, Lee C, Zurek P, Symonova O, Zheng Y,
Bucksch A, Mileyko Y, Galkovskyi T, Moore B, Harer J, Edelsbrunner H, Mitchell
Olds T, Weitz J, Benfey P. 2013. 3D phenotyping and quantitative trait locus mapping
identify core regions of the rice genome controlling root architecture. PNAS.
110(18), E1695–E1704.
mla: Topp, Christopher, et al. “3D Phenotyping and Quantitative Trait Locus Mapping
Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS,
vol. 110, no. 18, National Academy of Sciences, 2013, pp. E1695–704, doi:10.1073/pnas.1304354110.
short: C. Topp, A. Iyer Pascuzzi, J. Anderson, C. Lee, P. Zurek, O. Symonova, Y.
Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. Moore, J. Harer, H. Edelsbrunner,
T. Mitchell Olds, J. Weitz, P. Benfey, PNAS 110 (2013) E1695–E1704.
date_created: 2018-12-11T11:59:47Z
date_published: 2013-04-30T00:00:00Z
date_updated: 2025-09-29T13:57:21Z
day: '30'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1073/pnas.1304354110
external_id:
isi:
- '000318682300008'
pmid:
- '25673779'
intvolume: ' 110'
isi: 1
issue: '18'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/
month: '04'
oa: 1
oa_version: Submitted Version
page: E1695 - E1704
pmid: 1
publication: PNAS
publication_status: published
publisher: National Academy of Sciences
publist_id: '3979'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 3D phenotyping and quantitative trait locus mapping identify core regions of
the rice genome controlling root architecture
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 110
year: '2013'
...
---
_id: '2843'
abstract:
- lang: eng
text: 'Mathematical objects can be measured unambiguously, but not so objects from
our physical world. Even the total length of tubelike shapes has its difficulties.
We introduce a combination of geometric, probabilistic, and topological methods
to design a stable length estimate for tube-like shapes; that is: one that is
insensitive to small shape changes.'
alternative_title:
- LNCS
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. Stable length estimates of tube-like shapes.
In: 17th IAPR International Conference on Discrete Geometry for Computer Imagery.
Vol 7749. Springer; 2013:XV-XIX. doi:10.1007/978-3-642-37067-0'
apa: 'Edelsbrunner, H., & Pausinger, F. (2013). Stable length estimates of tube-like
shapes. In 17th IAPR International Conference on Discrete Geometry for Computer
Imagery (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. https://doi.org/10.1007/978-3-642-37067-0'
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates
of Tube-like Shapes.” In 17th IAPR International Conference on Discrete Geometry
for Computer Imagery, 7749:XV–XIX. Springer, 2013. https://doi.org/10.1007/978-3-642-37067-0.
ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,”
in 17th IAPR International Conference on Discrete Geometry for Computer Imagery,
Seville, Spain, 2013, vol. 7749, pp. XV–XIX.
ista: 'Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes.
17th IAPR International Conference on Discrete Geometry for Computer Imagery.
DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.'
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like
Shapes.” 17th IAPR International Conference on Discrete Geometry for Computer
Imagery, vol. 7749, Springer, 2013, pp. XV–XIX, doi:10.1007/978-3-642-37067-0.
short: H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on
Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX.
conference:
end_date: 2013-03-22
location: Seville, Spain
name: 'DGCI: Discrete Geometry for Computer Imagery'
start_date: 2013-03-20
date_created: 2018-12-11T11:59:53Z
date_published: 2013-02-21T00:00:00Z
date_updated: 2026-04-16T10:09:03Z
day: '21'
department:
- _id: HeEd
doi: 10.1007/978-3-642-37067-0
intvolume: ' 7749'
language:
- iso: eng
month: '02'
oa_version: None
page: XV - XIX
publication: 17th IAPR International Conference on Discrete Geometry for Computer
Imagery
publication_status: published
publisher: Springer
publist_id: '3952'
quality_controlled: '1'
related_material:
record:
- id: '2255'
relation: later_version
status: public
scopus_import: 1
status: public
title: Stable length estimates of tube-like shapes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7749
year: '2013'
...
---
_id: '2887'
abstract:
- lang: eng
text: 'Root system growth and development is highly plastic and is influenced by
the surrounding environment. Roots frequently grow in heterogeneous environments
that include interactions from neighboring plants and physical impediments in
the rhizosphere. To investigate how planting density and physical objects affect
root system growth, we grew rice in a transparent gel system in close proximity
with another plant or a physical object. Root systems were imaged and reconstructed
in three dimensions. Root-root interaction strength was calculated using quantitative
metrics that characterize the extent towhich the reconstructed root systems overlap
each other. Surprisingly, we found the overlap of root systems of the same genotype
was significantly higher than that of root systems of different genotypes. Root
systems of the same genotype tended to grow toward each other but those of different
genotypes appeared to avoid each other. Shoot separation experiments excluded
the possibility of aerial interactions, suggesting root communication. Staggered
plantings indicated that interactions likely occur at root tips in close proximity.
Recognition of obstacles also occurred through root tips, but through physical
contact in a size-dependent manner. These results indicate that root systems use
two different forms of communication to recognize objects and alter root architecture:
root-root recognition, possibly mediated through root exudates, and root-object
recognition mediated by physical contact at the root tips. This finding suggests
that root tips act as local sensors that integrate rhizosphere information into
global root architectural changes.'
article_processing_charge: No
article_type: original
author:
- first_name: Suqin
full_name: Fang, Suqin
last_name: Fang
- first_name: Randy
full_name: Clark, Randy
last_name: Clark
- first_name: Ying
full_name: Zheng, Ying
last_name: Zheng
- first_name: Anjali
full_name: Iyer Pascuzzi, Anjali
last_name: Iyer Pascuzzi
- first_name: Joshua
full_name: Weitz, Joshua
last_name: Weitz
- first_name: Leon
full_name: Kochian, Leon
last_name: Kochian
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Hong
full_name: Liao, Hong
last_name: Liao
- first_name: Philip
full_name: Benfey, Philip
last_name: Benfey
citation:
ama: Fang S, Clark R, Zheng Y, et al. Genotypic recognition and spatial responses
by rice roots. PNAS. 2013;110(7):2670-2675. doi:10.1073/pnas.1222821110
apa: Fang, S., Clark, R., Zheng, Y., Iyer Pascuzzi, A., Weitz, J., Kochian, L.,
… Benfey, P. (2013). Genotypic recognition and spatial responses by rice roots.
PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1222821110
chicago: Fang, Suqin, Randy Clark, Ying Zheng, Anjali Iyer Pascuzzi, Joshua Weitz,
Leon Kochian, Herbert Edelsbrunner, Hong Liao, and Philip Benfey. “Genotypic Recognition
and Spatial Responses by Rice Roots.” PNAS. National Academy of Sciences,
2013. https://doi.org/10.1073/pnas.1222821110.
ieee: S. Fang et al., “Genotypic recognition and spatial responses by rice
roots,” PNAS, vol. 110, no. 7. National Academy of Sciences, pp. 2670–2675,
2013.
ista: Fang S, Clark R, Zheng Y, Iyer Pascuzzi A, Weitz J, Kochian L, Edelsbrunner
H, Liao H, Benfey P. 2013. Genotypic recognition and spatial responses by rice
roots. PNAS. 110(7), 2670–2675.
mla: Fang, Suqin, et al. “Genotypic Recognition and Spatial Responses by Rice Roots.”
PNAS, vol. 110, no. 7, National Academy of Sciences, 2013, pp. 2670–75,
doi:10.1073/pnas.1222821110.
short: S. Fang, R. Clark, Y. Zheng, A. Iyer Pascuzzi, J. Weitz, L. Kochian, H. Edelsbrunner,
H. Liao, P. Benfey, PNAS 110 (2013) 2670–2675.
date_created: 2018-12-11T12:00:09Z
date_published: 2013-02-12T00:00:00Z
date_updated: 2026-06-18T18:36:41Z
day: '12'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1073/pnas.1222821110
external_id:
isi:
- '000315812800060'
pmid:
- '23362379'
intvolume: ' 110'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/
month: '02'
oa: 1
oa_version: Published Version
page: 2670 - 2675
pmid: 1
publication: PNAS
publication_status: published
publisher: National Academy of Sciences
publist_id: '3872'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Genotypic recognition and spatial responses by rice roots
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 110
year: '2013'
...
---
_id: '2906'
abstract:
- lang: eng
text: "Motivated by an application in cell biology, we describe an extension of
the kinetic data structures framework from Delaunay triangulations to fixed-radius
alpha complexes. Our algorithm is implemented\r\nusing CGAL, following the exact
geometric computation paradigm. We report on several\r\ntechniques to accelerate
the computation that turn our implementation applicable to the underlying biological\r\nproblem."
alternative_title:
- ALENEX
article_processing_charge: No
author:
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Kerber M, Edelsbrunner H. 3D kinetic alpha complexes and their implementation.
In: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments.
Society for Industrial and Applied Mathematics; 2013:70-77. doi:10.1137/1.9781611972931.6'
apa: 'Kerber, M., & Edelsbrunner, H. (2013). 3D kinetic alpha complexes and
their implementation. In 2013 Proceedings of the 15th Workshop on Algorithm
Engineering and Experiments (pp. 70–77). New Orleans, LA, United States: Society
for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611972931.6'
chicago: Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes
and Their Implementation.” In 2013 Proceedings of the 15th Workshop on Algorithm
Engineering and Experiments, 70–77. Society for Industrial and Applied Mathematics,
2013. https://doi.org/10.1137/1.9781611972931.6.
ieee: M. Kerber and H. Edelsbrunner, “3D kinetic alpha complexes and their implementation,”
in 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments,
New Orleans, LA, United States, 2013, pp. 70–77.
ista: 'Kerber M, Edelsbrunner H. 2013. 3D kinetic alpha complexes and their implementation.
2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments.
ALENEX: Algorithm Engineering and Experiments, ALENEX, , 70–77.'
mla: Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and
Their Implementation.” 2013 Proceedings of the 15th Workshop on Algorithm Engineering
and Experiments, Society for Industrial and Applied Mathematics, 2013, pp.
70–77, doi:10.1137/1.9781611972931.6.
short: M. Kerber, H. Edelsbrunner, in:, 2013 Proceedings of the 15th Workshop on
Algorithm Engineering and Experiments, Society for Industrial and Applied Mathematics,
2013, pp. 70–77.
conference:
end_date: 2013-01-07
location: New Orleans, LA, United States
name: 'ALENEX: Algorithm Engineering and Experiments'
start_date: 2013-01-07
corr_author: '1'
date_created: 2018-12-11T12:00:16Z
date_published: 2013-01-01T00:00:00Z
date_updated: 2025-06-03T11:47:11Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1137/1.9781611972931.6
file:
- access_level: open_access
checksum: a15a3ba22df9445731507f3e06c9fcee
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:57Z
date_updated: 2020-07-14T12:45:52Z
file_id: '4720'
file_name: IST-2016-547-v1+1_2013-P-08-MedusaII.pdf
file_size: 403013
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: 70 - 77
publication: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments
publication_status: published
publisher: Society for Industrial and Applied Mathematics
publist_id: '3841'
pubrep_id: '547'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 3D kinetic alpha complexes and their implementation
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2939'
abstract:
- lang: eng
text: In this paper, we present the first output-sensitive algorithm to compute
the persistence diagram of a filtered simplicial complex. For any Γ > 0, it
returns only those homology classes with persistence at least Γ. Instead of the
classical reduction via column operations, our algorithm performs rank computations
on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0, 1), the
running time is O (C (1 - δ) Γ R d (n) log n), where C (1 - δ) Γ is the number
of homology classes with persistence at least (1 - δ) Γ, n is the total number
of simplices in the complex, d its dimension, and R d (n) is the complexity of
computing the rank of an n × n matrix with O (d n) nonzero entries. Depending
on the choice of the rank algorithm, this yields a deterministic O (C (1 - δ)
Γ n 2.376) algorithm, an O (C (1 - δ) Γ n 2.28) Las-Vegas algorithm, or an O (C
(1 - δ) Γ n 2 + ε{lunate}) Monte-Carlo algorithm for an arbitrary ε{lunate} >
0. The space complexity of the Monte-Carlo version is bounded by O (d n) = O (n
log n).
acknowledgement: The authors thank Herbert Edelsbrunner for many helpful discussions
and suggestions. Moreover, they are grateful for the careful reviews that helped
to improve the quality of the paper.
article_processing_charge: No
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
citation:
ama: 'Chen C, Kerber M. An output sensitive algorithm for persistent homology. Computational
Geometry: Theory and Applications. 2013;46(4):435-447. doi:10.1016/j.comgeo.2012.02.010'
apa: 'Chen, C., & Kerber, M. (2013). An output sensitive algorithm for persistent
homology. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2012.02.010'
chicago: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent
Homology.” Computational Geometry: Theory and Applications. Elsevier, 2013.
https://doi.org/10.1016/j.comgeo.2012.02.010.'
ieee: 'C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,”
Computational Geometry: Theory and Applications, vol. 46, no. 4. Elsevier,
pp. 435–447, 2013.'
ista: 'Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology.
Computational Geometry: Theory and Applications. 46(4), 435–447.'
mla: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent
Homology.” Computational Geometry: Theory and Applications, vol. 46, no.
4, Elsevier, 2013, pp. 435–47, doi:10.1016/j.comgeo.2012.02.010.'
short: 'C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013)
435–447.'
corr_author: '1'
date_created: 2018-12-11T12:00:27Z
date_published: 2013-05-01T00:00:00Z
date_updated: 2025-09-29T13:26:21Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2012.02.010
external_id:
isi:
- '000314437000004'
intvolume: ' 46'
isi: 1
issue: '4'
language:
- iso: eng
month: '05'
oa_version: None
page: 435 - 447
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '3796'
quality_controlled: '1'
related_material:
record:
- id: '3367'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: An output sensitive algorithm for persistent homology
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 46
year: '2013'
...
---
_id: '2901'
abstract:
- lang: eng
text: ' We introduce the M-modes problem for graphical models: predicting the M
label configurations of highest probability that are at the same time local maxima
of the probability landscape. M-modes have multiple possible applications: because
they are intrinsically diverse, they provide a principled alternative to non-maximum
suppression techniques for structured prediction, they can act as codebook vectors
for quantizing the configuration space, or they can form component centers for
mixture model approximation. We present two algorithms for solving the M-modes
problem. The first algorithm solves the problem in polynomial time when the underlying
graphical model is a simple chain. The second algorithm solves the problem for
junction chains. In synthetic and real dataset, we demonstrate how M-modes can
improve the performance of prediction. We also use the generated modes as a tool
to understand the topography of the probability distribution of configurations,
for example with relation to the training set size and amount of noise in the
data. '
alternative_title:
- PMLR
article_processing_charge: No
author:
- first_name: Chao
full_name: Chen, Chao
id: 3E92416E-F248-11E8-B48F-1D18A9856A87
last_name: Chen
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Zhu
full_name: Yan, Zhu
last_name: Yan
- first_name: Dimitris
full_name: Metaxas, Dimitris
last_name: Metaxas
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. Computing the M most probable
modes of a graphical model. In: Proceedings of the 16th International Conference
on Artificial Intelligence and Statistics. Vol 31. Journal of Machine Learning
Research; 2013:161-169.'
apa: 'Chen, C., Kolmogorov, V., Yan, Z., Metaxas, D., & Lampert, C. (2013).
Computing the M most probable modes of a graphical model. In Proceedings of
the 16th International Conference on Artificial Intelligence and Statistics
(Vol. 31, pp. 161–169). Scottsdale, AZ, United States: Journal of Machine Learning
Research.'
chicago: Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph
Lampert. “Computing the M Most Probable Modes of a Graphical Model.” In Proceedings
of the 16th International Conference on Artificial Intelligence and Statistics,
31:161–69. Journal of Machine Learning Research, 2013.
ieee: C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, and C. Lampert, “Computing the
M most probable modes of a graphical model,” in Proceedings of the 16th International
Conference on Artificial Intelligence and Statistics, Scottsdale, AZ, United
States, 2013, vol. 31, pp. 161–169.
ista: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. 2013. Computing the M
most probable modes of a graphical model. Proceedings of the 16th International
Conference on Artificial Intelligence and Statistics. AISTATS: Conference on Uncertainty
in Artificial Intelligence, PMLR, vol. 31, 161–169.'
mla: Chen, Chao, et al. “Computing the M Most Probable Modes of a Graphical Model.”
Proceedings of the 16th International Conference on Artificial Intelligence
and Statistics, vol. 31, Journal of Machine Learning Research, 2013, pp. 161–69.
short: C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, Proceedings
of the 16th International Conference on Artificial Intelligence and Statistics,
Journal of Machine Learning Research, 2013, pp. 161–169.
conference:
end_date: 2013-05-01
location: Scottsdale, AZ, United States
name: 'AISTATS: Conference on Uncertainty in Artificial Intelligence'
start_date: 2013-04-29
das_tickbox: '1'
date_created: 2018-12-11T12:00:14Z
date_published: 2013-01-01T00:00:00Z
date_updated: 2026-07-06T13:43:58Z
day: '01'
department:
- _id: HeEd
- _id: VlKo
- _id: ChLa
intvolume: ' 31'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://jmlr.org/proceedings/papers/v31/chen13a.html
month: '01'
oa: 1
oa_version: None
page: 161 - 169
publication: Proceedings of the 16th International Conference on Artificial Intelligence
and Statistics
publication_status: published
publisher: Journal of Machine Learning Research
publist_id: '3846'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing the M most probable modes of a graphical model
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2013'
...
---
_id: '2859'
abstract:
- lang: eng
text: Given a continuous function f:X-R on a topological space, we consider the
preimages of intervals and their homology groups and show how to read the ranks
of these groups from the extended persistence diagram of f. In addition, we quantify
the robustness of the homology classes under perturbations of f using well groups,
and we show how to read the ranks of these groups from the same extended persistence
diagram. The special case X=R3 has ramifications in the fields of medical imaging
and scientific visualization.
article_processing_charge: No
arxiv: 1
author:
- first_name: Paul
full_name: Bendich, Paul
id: 43F6EC54-F248-11E8-B48F-1D18A9856A87
last_name: Bendich
- 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: Morozov, Dmitriy
last_name: Morozov
- first_name: Amit
full_name: Patel, Amit
id: 34A254A0-F248-11E8-B48F-1D18A9856A87
last_name: Patel
citation:
ama: Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level
and interlevel sets. Homology, Homotopy and Applications. 2013;15(1):51-72.
doi:10.4310/HHA.2013.v15.n1.a3
apa: Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2013). Homology
and robustness of level and interlevel sets. Homology, Homotopy and Applications.
International Press of Boston. https://doi.org/10.4310/HHA.2013.v15.n1.a3
chicago: Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “Homology
and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications.
International Press of Boston, 2013. https://doi.org/10.4310/HHA.2013.v15.n1.a3.
ieee: P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness
of level and interlevel sets,” Homology, Homotopy and Applications, vol.
15, no. 1. International Press of Boston, pp. 51–72, 2013.
ista: Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness
of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72.
mla: Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.”
Homology, Homotopy and Applications, vol. 15, no. 1, International Press
of Boston, 2013, pp. 51–72, doi:10.4310/HHA.2013.v15.n1.a3.
short: P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and
Applications 15 (2013) 51–72.
das_tickbox: '1'
date_created: 2018-12-11T11:59:58Z
date_published: 2013-05-01T00:00:00Z
date_updated: 2026-07-06T13:38:59Z
day: '01'
department:
- _id: HeEd
doi: 10.4310/HHA.2013.v15.n1.a3
external_id:
arxiv:
- '1102.3389'
isi:
- '000322423600003'
intvolume: ' 15'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1102.3389v1
month: '05'
oa: 1
oa_version: Preprint
page: 51 - 72
publication: Homology, Homotopy and Applications
publication_status: published
publisher: International Press of Boston
publist_id: '3930'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homology and robustness of level and interlevel sets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2013'
...
---
_id: '2849'
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: Nataliya
full_name: Strelkova, Nataliya
last_name: Strelkova
citation:
ama: Edelsbrunner H, Strelkova N. On the configuration space of Steiner minimal
trees. Russian Mathematical Surveys. 2012;67(6):1167-1168. doi:10.1070/RM2012v067n06ABEH004820
apa: Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space of
Steiner minimal trees. Russian Mathematical Surveys. IOP Publishing. https://doi.org/10.1070/RM2012v067n06ABEH004820
chicago: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space
of Steiner Minimal Trees.” Russian Mathematical Surveys. IOP Publishing,
2012. https://doi.org/10.1070/RM2012v067n06ABEH004820.
ieee: H. Edelsbrunner and N. Strelkova, “On the configuration space of Steiner minimal
trees,” Russian Mathematical Surveys, vol. 67, no. 6. IOP Publishing, pp.
1167–1168, 2012.
ista: Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal
trees. Russian Mathematical Surveys. 67(6), 1167–1168.
mla: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space
of Steiner Minimal Trees.” Russian Mathematical Surveys, vol. 67, no. 6,
IOP Publishing, 2012, pp. 1167–68, doi:10.1070/RM2012v067n06ABEH004820.
short: H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168.
date_created: 2018-12-11T11:59:55Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2025-09-30T08:19:37Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1070/RM2012v067n06ABEH004820
external_id:
isi:
- '000315950100005'
file:
- access_level: open_access
checksum: 44ee8d173487e8ed41a51136816bbeb4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:14:26Z
date_updated: 2020-07-14T12:45:51Z
file_id: '5078'
file_name: IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf
file_size: 392021
relation: main_file
file_date_updated: 2020-07-14T12:45:51Z
has_accepted_license: '1'
intvolume: ' 67'
isi: 1
issue: '6'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Submitted Version
page: 1167 - 1168
publication: Russian Mathematical Surveys
publication_status: published
publisher: IOP Publishing
publist_id: '3943'
pubrep_id: '546'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the configuration space of Steiner minimal trees
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 67
year: '2012'
...
---
_id: '2902'
abstract:
- lang: eng
text: 'We present an algorithm for simplifying linear cartographic objects and results
obtained with a computer program implementing this algorithm. '
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: Oleg
full_name: Musin, Oleg
last_name: Musin
- first_name: Alexey
full_name: Ukhalov, Alexey
last_name: Ukhalov
- first_name: Olga
full_name: Yakimova, Olga
last_name: Yakimova
- first_name: Vladislav
full_name: Alexeev, Vladislav
last_name: Alexeev
- first_name: Victoriya
full_name: Bogaevskaya, Victoriya
last_name: Bogaevskaya
- first_name: Andrey
full_name: Gorohov, Andrey
last_name: Gorohov
- first_name: Margarita
full_name: Preobrazhenskaya, Margarita
last_name: Preobrazhenskaya
citation:
ama: Edelsbrunner H, Musin O, Ukhalov A, et al. Fractal and computational geometry
for generalizing cartographic objects. Modeling and Analysis of Information
Systems. 2012;19(6):152-160.
apa: Edelsbrunner, H., Musin, O., Ukhalov, A., Yakimova, O., Alexeev, V., Bogaevskaya,
V., … Preobrazhenskaya, M. (2012). Fractal and computational geometry for generalizing
cartographic objects. Modeling and Analysis of Information Systems. Russian
Academy of Sciences.
chicago: Edelsbrunner, Herbert, Oleg Musin, Alexey Ukhalov, Olga Yakimova, Vladislav
Alexeev, Victoriya Bogaevskaya, Andrey Gorohov, and Margarita Preobrazhenskaya.
“Fractal and computational geometry for generalizing cartographic objects.” Modeling
and Analysis of Information Systems. Russian Academy of Sciences, 2012.
ieee: H. Edelsbrunner et al., “Fractal and computational geometry for generalizing
cartographic objects,” Modeling and Analysis of Information Systems, vol.
19, no. 6. Russian Academy of Sciences, pp. 152–160, 2012.
ista: Edelsbrunner H, Musin O, Ukhalov A, Yakimova O, Alexeev V, Bogaevskaya V,
Gorohov A, Preobrazhenskaya M. 2012. Fractal and computational geometry for generalizing
cartographic objects. Modeling and Analysis of Information Systems. 19(6), 152–160.
mla: Edelsbrunner, Herbert, et al. “Fractal and computational geometry for generalizing
cartographic objects.” Modeling and Analysis of Information Systems, vol.
19, no. 6, Russian Academy of Sciences, 2012, pp. 152–60.
short: H. Edelsbrunner, O. Musin, A. Ukhalov, O. Yakimova, V. Alexeev, V. Bogaevskaya,
A. Gorohov, M. Preobrazhenskaya, Modeling and Analysis of Information Systems
19 (2012) 152–160.
date_created: 2018-12-11T12:00:15Z
date_published: 2012-12-01T00:00:00Z
date_updated: 2026-06-18T18:37:14Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
intvolume: ' 19'
issue: '6'
language:
- iso: rus
main_file_link:
- open_access: '1'
url: http://mi.mathnet.ru/eng/mais280
month: '12'
oa: 1
oa_version: Published Version
page: 152 - 160
publication: Modeling and Analysis of Information Systems
publication_status: published
publisher: Russian Academy of Sciences
publist_id: '3845'
quality_controlled: '1'
status: public
title: Fractal and computational geometry for generalizing cartographic objects
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2012'
...
---
_id: '2903'
abstract:
- lang: eng
text: In order to enjoy a digital version of the Jordan Curve Theorem, it is common
to use the closed topology for the foreground and the open topology for the background
of a 2-dimensional binary image. In this paper, we introduce a single topology
that enjoys this theorem for all thresholds decomposing a real-valued image into
foreground and background. This topology is easy to construct and it generalizes
to n-dimensional images.
author:
- 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: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
orcid: 0000-0003-2012-9947
citation:
ama: 'Edelsbrunner H, Symonova O. The adaptive topology of a digital image. In:
IEEE; 2012:41-48. doi:10.1109/ISVD.2012.11'
apa: 'Edelsbrunner, H., & Symonova, O. (2012). The adaptive topology of a digital
image (pp. 41–48). Presented at the ISVD: International Symposium on Voronoi Diagrams
in Science and Engineering, New Brunswick, NJ, USA : IEEE. https://doi.org/10.1109/ISVD.2012.11'
chicago: Edelsbrunner, Herbert, and Olga Symonova. “The Adaptive Topology of a Digital
Image,” 41–48. IEEE, 2012. https://doi.org/10.1109/ISVD.2012.11.
ieee: 'H. Edelsbrunner and O. Symonova, “The adaptive topology of a digital image,”
presented at the ISVD: International Symposium on Voronoi Diagrams in Science
and Engineering, New Brunswick, NJ, USA , 2012, pp. 41–48.'
ista: 'Edelsbrunner H, Symonova O. 2012. The adaptive topology of a digital image.
ISVD: International Symposium on Voronoi Diagrams in Science and Engineering,
41–48.'
mla: Edelsbrunner, Herbert, and Olga Symonova. The Adaptive Topology of a Digital
Image. IEEE, 2012, pp. 41–48, doi:10.1109/ISVD.2012.11.
short: H. Edelsbrunner, O. Symonova, in:, IEEE, 2012, pp. 41–48.
conference:
end_date: 2012-06-29
location: 'New Brunswick, NJ, USA '
name: 'ISVD: International Symposium on Voronoi Diagrams in Science and Engineering'
start_date: 2012-06-27
corr_author: '1'
date_created: 2018-12-11T12:00:15Z
date_published: 2012-08-06T00:00:00Z
date_updated: 2024-10-09T20:54:57Z
day: '06'
ddc:
- '000'
department:
- _id: HeEd
- _id: MaJö
doi: 10.1109/ISVD.2012.11
file:
- access_level: open_access
checksum: 444869a4e8abf07834f88b6e5cb5e9c3
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:41Z
date_updated: 2020-07-14T12:45:52Z
file_id: '4765'
file_name: IST-2016-545-v1+1_2012-P-10-AdaptiveTopology.pdf
file_size: 760548
relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Submitted Version
page: 41 - 48
publication_status: published
publisher: IEEE
publist_id: '3844'
pubrep_id: '545'
quality_controlled: '1'
scopus_import: 1
status: public
title: The adaptive topology of a digital image
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '2904'
abstract:
- lang: eng
text: Generalized van der Corput sequences are onedimensional, infinite sequences
in the unit interval. They are generated from permutations in integer base b and
are the building blocks of the multi-dimensional Halton sequences. Motivated by
recent progress of Atanassov on the uniform distribution behavior of Halton sequences,
we study, among others, permutations of the form P(i) = ai (mod b) for coprime
integers a and b. We show that multipliers a that either divide b - 1 or b + 1
generate van der Corput sequences with weak distribution properties. We give explicit
lower bounds for the asymptotic distribution behavior of these sequences and relate
them to sequences generated from the identity permutation in smaller bases, which
are, due to Faure, the weakest distributed generalized van der Corput sequences.
- lang: fre
text: Les suites de Van der Corput généralisées sont dessuites unidimensionnelles
et infinies dans l’intervalle de l’unité.Elles sont générées par permutations
des entiers de la basebetsont les éléments constitutifs des suites multi-dimensionnelles
deHalton. Suites aux progrès récents d’Atanassov concernant le com-portement de
distribution uniforme des suites de Halton nous nousintéressons aux permutations
de la formuleP(i) =ai(modb)pour les entiers premiers entre euxaetb. Dans cet
article nousidentifions des multiplicateursagénérant des suites de Van derCorput
ayant une mauvaise distribution. Nous donnons les bornesinférieures explicites
pour cette distribution asymptotique asso-ciée à ces suites et relions ces dernières
aux suites générées parpermutation d’identité, qui sont, selon Faure, les moins
bien dis-tribuées des suites généralisées de Van der Corput dans une basedonnée.
article_processing_charge: No
article_type: original
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. Weak multipliers for generalized van der Corput sequences. Journal
de Theorie des Nombres des Bordeaux. 2012;24(3):729-749. doi:10.5802/jtnb.819
apa: Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences.
Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.819
chicago: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.”
Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux, 2012.
https://doi.org/10.5802/jtnb.819.
ieee: F. Pausinger, “Weak multipliers for generalized van der Corput sequences,”
Journal de Theorie des Nombres des Bordeaux, vol. 24, no. 3. Université
de Bordeaux, pp. 729–749, 2012.
ista: Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences.
Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.
mla: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.”
Journal de Theorie Des Nombres Des Bordeaux, vol. 24, no. 3, Université
de Bordeaux, 2012, pp. 729–49, doi:10.5802/jtnb.819.
short: F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749.
date_created: 2018-12-11T12:00:15Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2025-09-30T08:18:15Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.5802/jtnb.819
external_id:
isi:
- '000315243100011'
file:
- access_level: open_access
checksum: 6954bfe9d7f4119fbdda7a11cf0f5c67
content_type: application/pdf
creator: dernst
date_created: 2020-05-11T12:40:39Z
date_updated: 2020-07-14T12:45:52Z
file_id: '7819'
file_name: JTNB_2012__24_3_729_0.pdf
file_size: 819275
relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
issue: '3'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 729 - 749
publication: Journal de Theorie des Nombres des Bordeaux
publication_identifier:
eissn:
- 2118-8572
issn:
- 1246-7405
publication_status: published
publisher: Université de Bordeaux
publist_id: '3843'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weak multipliers for generalized van der Corput sequences
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 24
year: '2012'
...
---
_id: '2912'
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: Nataliya
full_name: Strelkova, Nataliya
last_name: Strelkova
citation:
ama: Edelsbrunner H, Strelkova N. On the configuration space for the shortest networks.
Russian Mathematical Surveys. 2012;67(6):1167–1168. doi:10.4213/rm9503
apa: Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space for
the shortest networks. Russian Mathematical Surveys. Russian Academy of
Sciences. https://doi.org/10.4213/rm9503
chicago: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space
for the Shortest Networks.” Russian Mathematical Surveys. Russian Academy
of Sciences, 2012. https://doi.org/10.4213/rm9503.
ieee: H. Edelsbrunner and N. Strelkova, “On the configuration space for the shortest
networks,” Russian Mathematical Surveys, vol. 67, no. 6. Russian Academy
of Sciences, pp. 1167–1168, 2012.
ista: Edelsbrunner H, Strelkova N. 2012. On the configuration space for the shortest
networks. Russian Mathematical Surveys. 67(6), 1167–1168.
mla: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space
for the Shortest Networks.” Russian Mathematical Surveys, vol. 67, no.
6, Russian Academy of Sciences, 2012, pp. 1167–1168, doi:10.4213/rm9503.
short: H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168.
date_created: 2018-12-11T12:00:18Z
date_published: 2012-10-01T00:00:00Z
date_updated: 2023-10-17T11:40:39Z
day: '01'
department:
- _id: HeEd
doi: 10.4213/rm9503
intvolume: ' 67'
issue: '6'
language:
- iso: eng
month: '10'
oa_version: None
page: 1167–1168
publication: Russian Mathematical Surveys
publication_status: published
publisher: Russian Academy of Sciences
publist_id: '3831'
quality_controlled: '1'
status: public
title: On the configuration space for the shortest networks
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 67
year: '2012'
...
---
_id: '2941'
article_processing_charge: No
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: Oleg
full_name: Musin, Oleg
last_name: Musin
citation:
ama: Dolbilin N, Edelsbrunner H, Musin O. On the optimality of functionals over
triangulations of Delaunay sets. Russian Mathematical Surveys. 2012;67(4):781-783.
doi:10.1070/RM2012v067n04ABEH004807
apa: Dolbilin, N., Edelsbrunner, H., & Musin, O. (2012). On the optimality of
functionals over triangulations of Delaunay sets. Russian Mathematical Surveys.
IOP Publishing. https://doi.org/10.1070/RM2012v067n04ABEH004807
chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, and Oleg Musin. “On the Optimality
of Functionals over Triangulations of Delaunay Sets.” Russian Mathematical
Surveys. IOP Publishing, 2012. https://doi.org/10.1070/RM2012v067n04ABEH004807.
ieee: N. Dolbilin, H. Edelsbrunner, and O. Musin, “On the optimality of functionals
over triangulations of Delaunay sets,” Russian Mathematical Surveys, vol.
67, no. 4. IOP Publishing, pp. 781–783, 2012.
ista: Dolbilin N, Edelsbrunner H, Musin O. 2012. On the optimality of functionals
over triangulations of Delaunay sets. Russian Mathematical Surveys. 67(4), 781–783.
mla: Dolbilin, Nikolai, et al. “On the Optimality of Functionals over Triangulations
of Delaunay Sets.” Russian Mathematical Surveys, vol. 67, no. 4, IOP Publishing,
2012, pp. 781–83, doi:10.1070/RM2012v067n04ABEH004807.
short: N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012)
781–783.
date_created: 2018-12-11T12:00:28Z
date_published: 2012-11-01T00:00:00Z
date_updated: 2025-09-30T08:13:48Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1070/RM2012v067n04ABEH004807
external_id:
isi:
- '000310789000005'
file:
- access_level: open_access
checksum: 389a5ae53d6347de36c3468034f2821d
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:49Z
date_updated: 2020-07-14T12:45:55Z
file_id: '5239'
file_name: IST-2013-132-v1+1_2012-J-04-Functional-E.pdf
file_size: 253816
relation: main_file
file_date_updated: 2020-07-14T12:45:55Z
has_accepted_license: '1'
intvolume: ' 67'
isi: 1
issue: '4'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Submitted Version
page: 781 - 783
publication: Russian Mathematical Surveys
publication_status: published
publisher: IOP Publishing
publist_id: '3792'
pubrep_id: '132'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the optimality of functionals over triangulations of Delaunay sets
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 67
year: '2012'
...
---
OA_type: closed access
_id: '2971'
abstract:
- lang: eng
text: 'We study the task of interactive semantic labeling of a segmentation hierarchy.
To this end we propose a framework interleaving two components: an automatic labeling
step, based on a Conditional Random Field whose dependencies are defined by the
inclusion tree of the segmentation hierarchy, and an interaction step that integrates
incremental input from a human user. Evaluated on two distinct datasets, the proposed
interactive approach efficiently integrates human interventions and illustrates
the advantages of structured prediction in an interactive framework. '
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Georg
full_name: Zankl, Georg
last_name: Zankl
- first_name: Yll
full_name: Haxhimusa, Yll
last_name: Haxhimusa
- first_name: Adrian
full_name: Ion, Adrian
id: 29F89302-F248-11E8-B48F-1D18A9856A87
last_name: Ion
citation:
ama: 'Zankl G, Haxhimusa Y, Ion A. Interactive labeling of image segmentation hierarchies.
In: 34th DAGM and 36th OAGM Symposium. Vol 7476. Springer; 2012:11-20.
doi:10.1007/978-3-642-32717-9_2'
apa: 'Zankl, G., Haxhimusa, Y., & Ion, A. (2012). Interactive labeling of image
segmentation hierarchies. In 34th DAGM and 36th OAGM Symposium (Vol. 7476,
pp. 11–20). Graz, Austria: Springer. https://doi.org/10.1007/978-3-642-32717-9_2'
chicago: Zankl, Georg, Yll Haxhimusa, and Adrian Ion. “Interactive Labeling of Image
Segmentation Hierarchies.” In 34th DAGM and 36th OAGM Symposium, 7476:11–20.
Springer, 2012. https://doi.org/10.1007/978-3-642-32717-9_2.
ieee: G. Zankl, Y. Haxhimusa, and A. Ion, “Interactive labeling of image segmentation
hierarchies,” in 34th DAGM and 36th OAGM Symposium, Graz, Austria, 2012,
vol. 7476, pp. 11–20.
ista: Zankl G, Haxhimusa Y, Ion A. 2012. Interactive labeling of image segmentation
hierarchies. 34th DAGM and 36th OAGM Symposium. Pattern Recognition, LNCS, vol.
7476, 11–20.
mla: Zankl, Georg, et al. “Interactive Labeling of Image Segmentation Hierarchies.”
34th DAGM and 36th OAGM Symposium, vol. 7476, Springer, 2012, pp. 11–20,
doi:10.1007/978-3-642-32717-9_2.
short: G. Zankl, Y. Haxhimusa, A. Ion, in:, 34th DAGM and 36th OAGM Symposium, Springer,
2012, pp. 11–20.
conference:
end_date: 2012-08-31
location: Graz, Austria
name: Pattern Recognition
start_date: 2012-08-28
date_created: 2018-12-11T12:00:37Z
date_published: 2012-08-01T00:00:00Z
date_updated: 2025-05-20T07:21:42Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-642-32717-9_2
intvolume: ' 7476'
language:
- iso: eng
month: '08'
oa_version: None
page: 11 - 20
publication: 34th DAGM and 36th OAGM Symposium
publication_identifier:
eisbn:
- '9783642327179'
eissn:
- 1611-3349
publication_status: published
publisher: Springer
publist_id: '3737'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Interactive labeling of image segmentation hierarchies
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7476
year: '2012'
...
---
OA_place: publisher
_id: '6588'
abstract:
- lang: eng
text: First we note that the best polynomial approximation to vertical bar x vertical
bar on the set, which consists of an interval on the positive half-axis and a
point on the negative half-axis, can be given by means of the classical Chebyshev
polynomials. Then we explore the cases when a solution of the related problem
on two intervals can be given in elementary functions.
acknowledgement: "This work is supported by the Austrian Science Fund (FWF), Project
P22025-N18.\r\n"
article_processing_charge: No
article_type: original
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. Elementary solutions of the Bernstein problem on two intervals.
Journal of Mathematical Physics, Analysis, Geometry. 2012;8(1):63-78.
apa: Pausinger, F. (2012). Elementary solutions of the Bernstein problem on two
intervals. Journal of Mathematical Physics, Analysis, Geometry. B. Verkin
Institute for Low Temperature Physics and Engineering.
chicago: Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two
Intervals.” Journal of Mathematical Physics, Analysis, Geometry. B. Verkin
Institute for Low Temperature Physics and Engineering, 2012.
ieee: F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals,”
Journal of Mathematical Physics, Analysis, Geometry, vol. 8, no. 1. B.
Verkin Institute for Low Temperature Physics and Engineering, pp. 63–78, 2012.
ista: Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals.
Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78.
mla: Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.”
Journal of Mathematical Physics, Analysis, Geometry, vol. 8, no. 1, B.
Verkin Institute for Low Temperature Physics and Engineering, 2012, pp. 63–78.
short: F. Pausinger, Journal of Mathematical Physics, Analysis, Geometry 8 (2012)
63–78.
corr_author: '1'
date_created: 2019-06-27T08:16:56Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2026-06-18T19:08:51Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
external_id:
isi:
- '000301173600004'
intvolume: ' 8'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mathnet.ru/eng/jmag525
month: '01'
oa: 1
oa_version: Published Version
page: 63-78
publication: Journal of Mathematical Physics, Analysis, Geometry
publication_identifier:
issn:
- 1812-9471
publication_status: published
publisher: B. Verkin Institute for Low Temperature Physics and Engineering
quality_controlled: '1'
scopus_import: '1'
status: public
title: Elementary solutions of the Bernstein problem on two intervals
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2012'
...
---
_id: '3115'
abstract:
- lang: eng
text: 'We consider the offset-deconstruction problem: Given a polygonal shape Q
with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance,
as the Minkowski sum of another polygonal shape P with a disk of fixed radius?
If it does, we also seek a preferably simple-looking solution P; then, P''s offset
constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We
give an O(nlogn)-time exact decision algorithm that handles any polygonal shape,
assuming the real-RAM model of computation. A variant of the algorithm, which
we have implemented using the cgal library, is based on rational arithmetic and
answers the same deconstruction problem up to an uncertainty parameter δ its running
time additionally depends on δ. If the input shape is found to be approximable,
this algorithm also computes an approximate solution for the problem. It also
allows us to solve parameter-optimization problems induced by the offset-deconstruction
problem. For convex shapes, the complexity of the exact decision algorithm drops
to O(n), which is also the time required to compute a solution P with at most
one more vertex than a vertex-minimal one.'
acknowledgement: "We thank Eyal Flato (Plataine Ltd.) for raising the offset-deconstruction
problem in connection with wood cutting. We also thank Tim Bretl (UIUC) for suggesting
the digital-pen offset-deconstruction problem. This work has been supported in part
by the Israel Science Foundation (grant no. 1102/11), by the German–Israeli Foundation
(grant no. 969/07), by the Hermann Minkowski–Minerva Center for Geometry at Tel
Aviv University, and by the EU Project under Contract No. 255827 (CGL—Computational
Geometry Learning).\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Eric
full_name: Berberich, Eric
last_name: Berberich
- first_name: Dan
full_name: Halperin, Dan
last_name: Halperin
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Roza
full_name: Pogalnikova, Roza
last_name: Pogalnikova
citation:
ama: Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate
offsets. Discrete & Computational Geometry. 2012;48(4):964-989. doi:10.1007/s00454-012-9441-5
apa: Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2012). Deconstructing
approximate offsets. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-012-9441-5
chicago: Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing
Approximate Offsets.” Discrete & Computational Geometry. Springer,
2012. https://doi.org/10.1007/s00454-012-9441-5.
ieee: E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing
approximate offsets,” Discrete & Computational Geometry, vol. 48, no.
4. Springer, pp. 964–989, 2012.
ista: Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate
offsets. Discrete & Computational Geometry. 48(4), 964–989.
mla: Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Discrete &
Computational Geometry, vol. 48, no. 4, Springer, 2012, pp. 964–89, doi:10.1007/s00454-012-9441-5.
short: E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete & Computational
Geometry 48 (2012) 964–989.
corr_author: '1'
date_created: 2018-12-11T12:01:28Z
date_published: 2012-12-01T00:00:00Z
date_updated: 2025-09-30T08:01:36Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-012-9441-5
external_id:
arxiv:
- '1109.2158'
isi:
- '000311503200006'
intvolume: ' 48'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1109.2158
month: '12'
oa: 1
oa_version: Preprint
page: 964 - 989
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '3584'
quality_controlled: '1'
related_material:
record:
- id: '3329'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Deconstructing approximate offsets
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 48
year: '2012'
...
---
_id: '3120'
abstract:
- lang: eng
text: We introduce a strategy based on Kustin-Miller unprojection that allows us
to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions
(that is, nine equations and sixteen first syzygies). Our two basic games are
called Tom and Jerry; the main application is the biregular construction of most
of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There
are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type
I projection. In every case, at least one Tom and one Jerry construction works,
providing at least two deformation families of quasismooth Fano 3-folds having
the same numerics but different topology. © 2012 Copyright Foundation Compositio
Mathematica.
acknowledgement: This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.
article_processing_charge: No
arxiv: 1
author:
- first_name: Gavin
full_name: Brown, Gavin
last_name: Brown
- first_name: Michael
full_name: Kerber, Michael
id: 36E4574A-F248-11E8-B48F-1D18A9856A87
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Miles
full_name: Reid, Miles
last_name: Reid
citation:
ama: Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part
I. Compositio Mathematica. 2012;148(4):1171-1194. doi:10.1112/S0010437X11007226
apa: Brown, G., Kerber, M., & Reid, M. (2012). Fano 3 folds in codimension 4
Tom and Jerry Part I. Compositio Mathematica. Cambridge University Press.
https://doi.org/10.1112/S0010437X11007226
chicago: Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension
4 Tom and Jerry Part I.” Compositio Mathematica. Cambridge University Press,
2012. https://doi.org/10.1112/S0010437X11007226.
ieee: G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry
Part I,” Compositio Mathematica, vol. 148, no. 4. Cambridge University
Press, pp. 1171–1194, 2012.
ista: Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry
Part I. Compositio Mathematica. 148(4), 1171–1194.
mla: Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.”
Compositio Mathematica, vol. 148, no. 4, Cambridge University Press, 2012,
pp. 1171–94, doi:10.1112/S0010437X11007226.
short: G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194.
date_created: 2018-12-11T12:01:30Z
date_published: 2012-07-01T00:00:00Z
date_updated: 2025-09-30T07:59:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/S0010437X11007226
external_id:
arxiv:
- '1009.4313'
isi:
- '000307176400007'
intvolume: ' 148'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1009.4313
month: '07'
oa: 1
oa_version: Preprint
page: 1171 - 1194
publication: Compositio Mathematica
publication_status: published
publisher: Cambridge University Press
publist_id: '3579'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fano 3 folds in codimension 4 Tom and Jerry Part I
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 148
year: '2012'
...