---
_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: 2023-02-23T10:15:15Z
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: '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.
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
- 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: 2021-01-12T06:59:58Z
day: '30'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1073/pnas.1304354110
external_id:
pmid:
- '25673779'
intvolume: ' 110'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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: 2023-02-23T10:35:00Z
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: '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.
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. 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, 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, 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,
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.
date_created: 2018-12-11T11:59:58Z
date_published: 2013-05-01T00:00:00Z
date_updated: 2021-01-12T07:00:18Z
day: '01'
department:
- _id: HeEd
doi: 10.4310/HHA.2013.v15.n1.a3
external_id:
arxiv:
- '1102.3389'
intvolume: ' 15'
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
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: '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: 2021-01-12T07:00:29Z
day: '12'
department:
- _id: HeEd
doi: 10.1073/pnas.1222821110
external_id:
pmid:
- '23362379'
intvolume: ' 110'
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: '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:
- ' JMLR: W&CP'
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: Vol 31. JMLR; 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 (Vol. 31, pp. 161–169).
Presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence,
Scottsdale, AZ, United States: JMLR.'
chicago: Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph
Lampert. “Computing the M Most Probable Modes of a Graphical Model,” 31:161–69.
JMLR, 2013.
ieee: 'C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, and C. Lampert, “Computing the
M most probable modes of a graphical model,” presented at the AISTATS: Conference
on Uncertainty in Artificial Intelligence, 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. AISTATS: Conference on Uncertainty
in Artificial Intelligence, JMLR: W&CP, vol. 31, 161–169.'
mla: Chen, Chao, et al. Computing the M Most Probable Modes of a Graphical Model.
Vol. 31, JMLR, 2013, pp. 161–69.
short: C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, JMLR, 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
date_created: 2018-12-11T12:00:14Z
date_published: 2013-01-01T00:00:00Z
date_updated: 2021-01-12T07:00:35Z
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_status: published
publisher: JMLR
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: '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
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 of 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
of 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 of 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 of 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 of 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
date_created: 2018-12-11T12:00:16Z
date_published: 2013-01-01T00:00:00Z
date_updated: 2021-01-12T07:00:36Z
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 of 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: '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.
date_created: 2018-12-11T11:59:44Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2023-02-23T11:13:49Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-013-9517-x
intvolume: ' 49'
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: '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.
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.'
date_created: 2018-12-11T12:00:27Z
date_published: 2013-05-01T00:00:00Z
date_updated: 2023-02-23T11:24:10Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2012.02.010
intvolume: ' 46'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 46
year: '2013'
...
---
_id: '10897'
abstract:
- lang: eng
text: Taking images is an efficient way to collect data about the physical world.
It can be done fast and in exquisite detail. By definition, image processing is
the field that concerns itself with the computation aimed at harnessing the information
contained in images [10]. This talk is concerned with topological information.
Our main thesis is that persistent homology [5] is a useful method to quantify
and summarize topological information, building a bridge that connects algebraic
topology with applications. We provide supporting evidence for this thesis by
touching upon four technical developments in the overlap between persistent homology
and image processing.
acknowledgement: This research is partially supported by the European Science Foundation
(ESF) under the Research Network Programme, the European Union under the Toposys
Project FP7-ICT-318493-STREP, the Russian Government under the Mega Project 11.G34.31.0053.
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Edelsbrunner H. Persistent homology in image processing. In: Graph-Based
Representations in Pattern Recognition. Vol 7877. LNCS. Berlin, Heidelberg:
Springer Nature; 2013:182-183. doi:10.1007/978-3-642-38221-5_19'
apa: 'Edelsbrunner, H. (2013). Persistent homology in image processing. In Graph-Based
Representations in Pattern Recognition (Vol. 7877, pp. 182–183). Berlin, Heidelberg:
Springer Nature. https://doi.org/10.1007/978-3-642-38221-5_19'
chicago: 'Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” In Graph-Based
Representations in Pattern Recognition, 7877:182–83. LNCS. Berlin, Heidelberg:
Springer Nature, 2013. https://doi.org/10.1007/978-3-642-38221-5_19.'
ieee: H. Edelsbrunner, “Persistent homology in image processing,” in Graph-Based
Representations in Pattern Recognition, Vienna, Austria, 2013, vol. 7877,
pp. 182–183.
ista: 'Edelsbrunner H. 2013. Persistent homology in image processing. Graph-Based
Representations in Pattern Recognition. GbRPR: Graph-based Representations in
Pattern RecognitionLNCS vol. 7877, 182–183.'
mla: Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” Graph-Based
Representations in Pattern Recognition, vol. 7877, Springer Nature, 2013,
pp. 182–83, doi:10.1007/978-3-642-38221-5_19.
short: H. Edelsbrunner, in:, Graph-Based Representations in Pattern Recognition,
Springer Nature, Berlin, Heidelberg, 2013, pp. 182–183.
conference:
end_date: 2013-05-17
location: Vienna, Austria
name: 'GbRPR: Graph-based Representations in Pattern Recognition'
start_date: 2013-05-15
date_created: 2022-03-21T07:30:33Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2023-09-05T15:10:20Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-642-38221-5_19
ec_funded: 1
intvolume: ' 7877'
language:
- iso: eng
month: '06'
oa_version: None
page: 182-183
place: Berlin, Heidelberg
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Graph-Based Representations in Pattern Recognition
publication_identifier:
eisbn:
- '9783642382215'
eissn:
- 1611-3349
isbn:
- '9783642382208'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNCS
status: public
title: Persistent homology in image processing
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 7877
year: '2013'
...