---
_id: '9249'
abstract:
- lang: eng
text: Rhombic dodecahedron is a space filling polyhedron which represents the close
packing of spheres in 3D space and the Voronoi structures of the face centered
cubic (FCC) lattice. In this paper, we describe a new coordinate system where
every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid.
In order to illustrate the interest of the new coordinate system, we propose the
characterization of 3D digital plane with its topological features, such as the
interrelation between the thickness of the digital plane and the separability
constraint we aim to obtain. We also present the characterization of 3D digital
lines and study it as the intersection of multiple digital planes. Characterization
of 3D digital sphere with relevant topological features is proposed as well along
with the 48-symmetry appearing in the new coordinate system.
acknowledgement: "This work has been partially supported by the European Research
Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation
programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109,
‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no.
I 02979-N35. "
article_processing_charge: No
article_type: original
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic
dodecahedron grid. Mathematical Morphology - Theory and Applications. 2020;4(1):143-158.
doi:10.1515/mathm-2020-0106
apa: Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital
objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and
Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106
chicago: Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital
Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and
Applications. De Gruyter, 2020. https://doi.org/10.1515/mathm-2020-0106.
ieee: R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects
in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications,
vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.
ista: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in
rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications.
4(1), 143–158.
mla: Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical
Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp.
143–58, doi:10.1515/mathm-2020-0106.
short: R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology
- Theory and Applications 4 (2020) 143–158.
date_created: 2021-03-16T08:55:19Z
date_published: 2020-11-17T00:00:00Z
date_updated: 2021-03-22T09:01:50Z
day: '17'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/mathm-2020-0106
ec_funded: 1
file:
- access_level: open_access
checksum: 4a1043fa0548a725d464017fe2483ce0
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T08:56:37Z
date_updated: 2021-03-22T08:56:37Z
file_id: '9272'
file_name: 2020_MathMorpholTheoryAppl_Biswas.pdf
file_size: 3668725
relation: main_file
success: 1
file_date_updated: 2021-03-22T08:56:37Z
has_accepted_license: '1'
intvolume: ' 4'
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 143-158
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Mathematical Morphology - Theory and Applications
publication_identifier:
issn:
- 2353-3390
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: Digital objects in rhombic dodecahedron grid
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2020'
...
---
_id: '9299'
abstract:
- lang: eng
text: We call a multigraph non-homotopic if it can be drawn in the plane in such
a way that no two edges connecting the same pair of vertices can be continuously
transformed into each other without passing through a vertex, and no loop can
be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic
multigraph on n>1 vertices can have arbitrarily many edges. We prove that the
number of crossings between the edges of a non-homotopic multigraph with n vertices
and m>4n edges is larger than cm2n for some constant c>0 , and that this
bound is tight up to a polylogarithmic factor. We also show that the lower bound
is not asymptotically sharp as n is fixed and m⟶∞ .
acknowledgement: Supported by the National Research, Development and Innovation Office,
NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional
Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant
Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant
No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full
version can be found at https://arxiv.org/abs/2006.14908.
article_processing_charge: No
author:
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Gábor
full_name: Tardos, Gábor
last_name: Tardos
- first_name: Géza
full_name: Tóth, Géza
last_name: Tóth
citation:
ama: 'Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th
International Symposium on Graph Drawing and Network Visualization. Vol 12590.
LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28'
apa: 'Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic
edges. In 28th International Symposium on Graph Drawing and Network Visualization
(Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28'
chicago: Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic
Edges.” In 28th International Symposium on Graph Drawing and Network Visualization,
12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28.
ieee: J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,”
in 28th International Symposium on Graph Drawing and Network Visualization,
Virtual, Online, 2020, vol. 12590, pp. 359–371.
ista: 'Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th
International Symposium on Graph Drawing and Network Visualization. GD: Graph
Drawing and Network VisualizationLNCS vol. 12590, 359–371.'
mla: Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International
Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer
Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28.
short: J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing
and Network Visualization, Springer Nature, 2020, pp. 359–371.
conference:
end_date: 2020-09-18
location: Virtual, Online
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2020-09-16
date_created: 2021-03-28T22:01:44Z
date_published: 2020-09-20T00:00:00Z
date_updated: 2021-04-06T11:32:32Z
day: '20'
department:
- _id: HeEd
doi: 10.1007/978-3-030-68766-3_28
external_id:
arxiv:
- '2006.14908'
intvolume: ' 12590'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2006.14908
month: '09'
oa: 1
oa_version: Preprint
page: 359-371
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: 28th International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783030687656'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNCS
status: public
title: Crossings between non-homotopic edges
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12590
year: '2020'
...
---
_id: '9632'
abstract:
- lang: eng
text: "Second-order information, in the form of Hessian- or Inverse-Hessian-vector
products, is a fundamental tool for solving optimization problems. Recently, there
has been significant interest in utilizing this information in the context of
deep\r\nneural networks; however, relatively little is known about the quality
of existing approximations in this context. Our work examines this question, identifies
issues with existing approaches, and proposes a method called WoodFisher to compute
a faithful and efficient estimate of the inverse Hessian. Our main application
is to neural network compression, where we build on the classic Optimal Brain
Damage/Surgeon framework. We demonstrate that WoodFisher significantly outperforms
popular state-of-the-art methods for oneshot pruning. Further, even when iterative,
gradual pruning is allowed, our method results in a gain in test accuracy over
the state-of-the-art approaches, for standard image classification datasets such
as ImageNet ILSVRC. We examine how our method can be extended to take into account
first-order information, as well as\r\nillustrate its ability to automatically
set layer-wise pruning thresholds and perform compression in the limited-data
regime. The code is available at the following link, https://github.com/IST-DASLab/WoodFisher."
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 805223 ScaleML). Also, we would like to thank Alexander Shevchenko,
Alexandra Peste, and other members of the group for fruitful discussions.
article_processing_charge: No
author:
- first_name: Sidak Pal
full_name: Singh, Sidak Pal
id: DD138E24-D89D-11E9-9DC0-DEF6E5697425
last_name: Singh
- first_name: Dan-Adrian
full_name: Alistarh, Dan-Adrian
id: 4A899BFC-F248-11E8-B48F-1D18A9856A87
last_name: Alistarh
orcid: 0000-0003-3650-940X
citation:
ama: 'Singh SP, Alistarh D-A. WoodFisher: Efficient second-order approximation for
neural network compression. In: Advances in Neural Information Processing Systems.
Vol 33. Curran Associates; 2020:18098-18109.'
apa: 'Singh, S. P., & Alistarh, D.-A. (2020). WoodFisher: Efficient second-order
approximation for neural network compression. In Advances in Neural Information
Processing Systems (Vol. 33, pp. 18098–18109). Vancouver, Canada: Curran Associates.'
chicago: 'Singh, Sidak Pal, and Dan-Adrian Alistarh. “WoodFisher: Efficient Second-Order
Approximation for Neural Network Compression.” In Advances in Neural Information
Processing Systems, 33:18098–109. Curran Associates, 2020.'
ieee: 'S. P. Singh and D.-A. Alistarh, “WoodFisher: Efficient second-order approximation
for neural network compression,” in Advances in Neural Information Processing
Systems, Vancouver, Canada, 2020, vol. 33, pp. 18098–18109.'
ista: 'Singh SP, Alistarh D-A. 2020. WoodFisher: Efficient second-order approximation
for neural network compression. Advances in Neural Information Processing Systems.
NeurIPS: Conference on Neural Information Processing Systems vol. 33, 18098–18109.'
mla: 'Singh, Sidak Pal, and Dan-Adrian Alistarh. “WoodFisher: Efficient Second-Order
Approximation for Neural Network Compression.” Advances in Neural Information
Processing Systems, vol. 33, Curran Associates, 2020, pp. 18098–109.'
short: S.P. Singh, D.-A. Alistarh, in:, Advances in Neural Information Processing
Systems, Curran Associates, 2020, pp. 18098–18109.
conference:
end_date: 2020-12-12
location: Vancouver, Canada
name: 'NeurIPS: Conference on Neural Information Processing Systems'
start_date: 2020-12-06
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-06T00:00:00Z
date_updated: 2023-02-23T14:03:06Z
day: '06'
department:
- _id: DaAl
- _id: ToHe
ec_funded: 1
external_id:
arxiv:
- '2004.14340'
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://proceedings.neurips.cc/paper/2020/hash/d1ff1ec86b62cd5f3903ff19c3a326b2-Abstract.html
month: '12'
oa: 1
oa_version: Published Version
page: 18098-18109
project:
- _id: 268A44D6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '805223'
name: Elastic Coordination for Scalable Machine Learning
publication: Advances in Neural Information Processing Systems
publication_identifier:
isbn:
- '9781713829546'
issn:
- '10495258'
publication_status: published
publisher: Curran Associates
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'WoodFisher: Efficient second-order approximation for neural network compression'
type: conference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 33
year: '2020'
...
---
_id: '9630'
abstract:
- lang: eng
text: Various kinds of data are routinely represented as discrete probability distributions.
Examples include text documents summarized by histograms of word occurrences and
images represented as histograms of oriented gradients. Viewing a discrete probability
distribution as a point in the standard simplex of the appropriate dimension,
we can understand collections of such objects in geometric and topological terms. Importantly,
instead of using the standard Euclidean distance, we look into dissimilarity measures
with information-theoretic justification, and we develop the theory needed for
applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable the usage of existing computational topology software
in this context.
acknowledgement: This research is partially supported by the Office of Naval Research,
through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
the Austrian Science Fund (FWF).
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7
apa: Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis
in information space. Journal of Computational Geometry. Carleton University.
https://doi.org/10.20382/jocg.v11i2a7
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
Analysis in Information Space.” Journal of Computational Geometry. Carleton
University, 2020. https://doi.org/10.20382/jocg.v11i2a7.
ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University,
pp. 162–182, 2020.
ista: Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information
space. Journal of Computational Geometry. 11(2), 162–182.
mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
Journal of Computational Geometry, vol. 11, no. 2, Carleton University,
2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.
short: H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11
(2020) 162–182.
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2021-08-11T12:26:34Z
day: '14'
ddc:
- '510'
- '000'
department:
- _id: HeEd
doi: 10.20382/jocg.v11i2a7
file:
- access_level: open_access
checksum: f02d0b2b3838e7891a6c417fc34ffdcd
content_type: application/pdf
creator: asandaue
date_created: 2021-08-11T11:55:11Z
date_updated: 2021-08-11T11:55:11Z
file_id: '9882'
file_name: 2020_JournalOfComputationalGeometry_Edelsbrunner.pdf
file_size: 1449234
relation: main_file
success: 1
file_date_updated: 2021-08-11T11:55:11Z
has_accepted_license: '1'
intvolume: ' 11'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '12'
oa: 1
oa_version: Published Version
page: 162-182
project:
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
publication: Journal of Computational Geometry
publication_identifier:
eissn:
- 1920180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological data analysis in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 11
year: '2020'
...
---
_id: '9631'
abstract:
- lang: eng
text: The ability to leverage large-scale hardware parallelism has been one of the
key enablers of the accelerated recent progress in machine learning. Consequently,
there has been considerable effort invested into developing efficient parallel
variants of classic machine learning algorithms. However, despite the wealth of
knowledge on parallelization, some classic machine learning algorithms often prove
hard to parallelize efficiently while maintaining convergence. In this paper,
we focus on efficient parallel algorithms for the key machine learning task of
inference on graphical models, in particular on the fundamental belief propagation
algorithm. We address the challenge of efficiently parallelizing this classic
paradigm by showing how to leverage scalable relaxed schedulers in this context.
We present an extensive empirical study, showing that our approach outperforms
previous parallel belief propagation implementations both in terms of scalability
and in terms of wall-clock convergence time, on a range of practical applications.
acknowledgement: "We thank Marco Mondelli for discussions related to LDPC decoding,
and Giorgi Nadiradze for discussions on analysis of relaxed schedulers. This project
has received funding from the European Research Council (ERC) under the European\r\nUnion’s
Horizon 2020 research and innovation programme (grant agreement No 805223 ScaleML)."
article_processing_charge: No
author:
- first_name: Vitaly
full_name: Aksenov, Vitaly
last_name: Aksenov
- first_name: Dan-Adrian
full_name: Alistarh, Dan-Adrian
id: 4A899BFC-F248-11E8-B48F-1D18A9856A87
last_name: Alistarh
orcid: 0000-0003-3650-940X
- first_name: Janne
full_name: Korhonen, Janne
id: C5402D42-15BC-11E9-A202-CA2BE6697425
last_name: Korhonen
citation:
ama: 'Aksenov V, Alistarh D-A, Korhonen J. Scalable belief propagation via relaxed
scheduling. In: Advances in Neural Information Processing Systems. Vol
33. Curran Associates; 2020:22361-22372.'
apa: 'Aksenov, V., Alistarh, D.-A., & Korhonen, J. (2020). Scalable belief propagation
via relaxed scheduling. In Advances in Neural Information Processing Systems
(Vol. 33, pp. 22361–22372). Vancouver, Canada: Curran Associates.'
chicago: Aksenov, Vitaly, Dan-Adrian Alistarh, and Janne Korhonen. “Scalable Belief
Propagation via Relaxed Scheduling.” In Advances in Neural Information Processing
Systems, 33:22361–72. Curran Associates, 2020.
ieee: V. Aksenov, D.-A. Alistarh, and J. Korhonen, “Scalable belief propagation
via relaxed scheduling,” in Advances in Neural Information Processing Systems,
Vancouver, Canada, 2020, vol. 33, pp. 22361–22372.
ista: 'Aksenov V, Alistarh D-A, Korhonen J. 2020. Scalable belief propagation via
relaxed scheduling. Advances in Neural Information Processing Systems. NeurIPS:
Conference on Neural Information Processing Systems vol. 33, 22361–22372.'
mla: Aksenov, Vitaly, et al. “Scalable Belief Propagation via Relaxed Scheduling.”
Advances in Neural Information Processing Systems, vol. 33, Curran Associates,
2020, pp. 22361–72.
short: V. Aksenov, D.-A. Alistarh, J. Korhonen, in:, Advances in Neural Information
Processing Systems, Curran Associates, 2020, pp. 22361–22372.
conference:
end_date: 2020-12-12
location: Vancouver, Canada
name: 'NeurIPS: Conference on Neural Information Processing Systems'
start_date: 2020-12-06
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-06T00:00:00Z
date_updated: 2023-02-23T14:03:03Z
day: '06'
department:
- _id: DaAl
ec_funded: 1
external_id:
arxiv:
- '2002.11505'
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://proceedings.neurips.cc/paper/2020/hash/fdb2c3bab9d0701c4a050a4d8d782c7f-Abstract.html
month: '12'
oa: 1
oa_version: Published Version
page: 22361-22372
project:
- _id: 268A44D6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '805223'
name: Elastic Coordination for Scalable Machine Learning
publication: Advances in Neural Information Processing Systems
publication_identifier:
isbn:
- '9781713829546'
issn:
- '10495258'
publication_status: published
publisher: Curran Associates
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scalable belief propagation via relaxed scheduling
type: conference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 33
year: '2020'
...