---
OA_place: publisher
OA_type: gold
_id: '21949'
abstract:
- lang: eng
text: "Cardiac T1 mapping provides critical quantitative insights into myocardial
tissue composition, enabling the assessment of pathologies such as fibrosis, inflammation,
and edema.\r\nHowever, the inherently dynamic nature of the heart imposes strict
limits on acquisition\r\ntimes, making high-resolution T1 mapping a persistent
challenge. Compressed sensing (CS)\r\napproaches have reduced scan durations by
undersampling k-space and reconstructing images from partial data, and recent
studies show that jointly optimizing the undersampling\r\npatterns with the reconstruction
network can substantially improve performance. Still,\r\nmost current T1 mapping
pipelines rely on static, hand-crafted masks that do not exploit\r\nthe full acceleration
and accuracy potential. Furthermore, most existing methods do not\r\nlevarage
the physical T1 decay model in optimization. In this work, we introduce T1-\r\nPILOT:
an end-to-end method that explicitly incorporates the T1 signal relaxation model\r\ninto
the sampling–reconstruction framework to guide the learning of non-Cartesian trajectories,
cross-frame alignment, and T1 decay estimation. Through extensive experiments\r\non
the CMRxRecon dataset, T1-PILOT significantly outperforms several baseline strategies
(including learned single-mask and fixed radial or golden-angle sampling schemes),\r\nachieving
higher T1 map fidelity at greater acceleration factors. In particular, we observe
consistent gains in PSNR and VIF relative to existing methods, along with marked\r\nimprovements
in delineating finer myocardial structures. Our results highlight that optimizing
sampling trajectories in tandem with the physical relaxation model leads to both\r\nenhanced
quantitative accuracy and reduced acquisition times. Code for reproducing all\r\nexperiments
and results is available at https://github.com/tamirshor7/T1-PILOT"
alternative_title:
- PMLR
article_processing_charge: No
author:
- first_name: Tamir
full_name: Shor, Tamir
last_name: Shor
- first_name: Moti
full_name: Freiman, Moti
last_name: Freiman
- first_name: Chaim
full_name: Baskin, Chaim
last_name: Baskin
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
citation:
ama: 'Shor T, Freiman M, Baskin C, Bronstein AM. T1-PILOT: Physics-informed learned
optimized trajectories for T1 mapping acceleration. In: Medical Imaging with
Deep Learning. Vol 315. ML Research Press; :1969-1982.'
apa: 'Shor, T., Freiman, M., Baskin, C., & Bronstein, A. M. (n.d.). T1-PILOT:
Physics-informed learned optimized trajectories for T1 mapping acceleration. In
Medical Imaging with Deep Learning (Vol. 315, pp. 1969–1982). Taipei, Taiwan:
ML Research Press.'
chicago: 'Shor, Tamir, Moti Freiman, Chaim Baskin, and Alex M. Bronstein. “T1-PILOT:
Physics-Informed Learned Optimized Trajectories for T1 Mapping Acceleration.”
In Medical Imaging with Deep Learning, 315:1969–82. ML Research Press,
n.d.'
ieee: 'T. Shor, M. Freiman, C. Baskin, and A. M. Bronstein, “T1-PILOT: Physics-informed
learned optimized trajectories for T1 mapping acceleration,” in Medical Imaging
with Deep Learning, Taipei, Taiwan, vol. 315, pp. 1969–1982.'
ista: 'Shor T, Freiman M, Baskin C, Bronstein AM. T1-PILOT: Physics-informed learned
optimized trajectories for T1 mapping acceleration. Medical Imaging with Deep
Learning. MIDL: Medical Imaging with Deep Learning, PMLR, vol. 315, 1969–1982.'
mla: 'Shor, Tamir, et al. “T1-PILOT: Physics-Informed Learned Optimized Trajectories
for T1 Mapping Acceleration.” Medical Imaging with Deep Learning, vol.
315, ML Research Press, pp. 1969–82.'
short: T. Shor, M. Freiman, C. Baskin, A.M. Bronstein, in:, Medical Imaging with
Deep Learning, ML Research Press, n.d., pp. 1969–1982.
conference:
end_date: 2026-07-10
location: Taipei, Taiwan
name: 'MIDL: Medical Imaging with Deep Learning'
start_date: 2026-07-08
corr_author: '1'
date_created: 2026-06-07T22:01:36Z
date_published: 2026-03-17T00:00:00Z
date_updated: 2026-06-08T08:05:24Z
day: '17'
ddc:
- '000'
department:
- _id: AlBr
has_accepted_license: '1'
intvolume: ' 315'
keyword:
- Cardiac T1 Mapping
- Trajectory Optimization and Reconstruction
- PhysicsInformed Deep-Learning
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
url: https://openreview.net/forum?id=nZaPtHbd6N#discussion
month: '03'
oa: 1
oa_version: Published Version
page: 1969-1982
publication: Medical Imaging with Deep Learning
publication_identifier:
eissn:
- 2640-3498
publication_status: accepted
publisher: ML Research Press
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/tamirshor7/T1-PILOT
scopus_import: '1'
status: public
title: 'T1-PILOT: Physics-informed learned optimized trajectories for T1 mapping acceleration'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 315
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '14703'
abstract:
- lang: eng
text: We present a discretization of the dynamic optimal transport problem for which
we can obtain the convergence rate for the value of the transport cost to its
continuous value when the temporal and spatial stepsize vanish. This convergence
result does not require any regularity assumption on the measures, though experiments
suggest that the rate is not sharp. Via an analysis of the duality gap we also
obtain the convergence rates for the gradient of the optimal potentials and the
velocity field under mild regularity assumptions. To obtain such rates we discretize
the dual formulation of the dynamic optimal transport problem and use the mature
literature related to the error due to discretizing the Hamilton-Jacobi equation.
acknowledgement: 'The authors would like to thank Chris Wojtan for his continuous
support and several interesting discussions. Part of this research was performed
during two visits: one of SI to the BIDSA research center at Bocconi University,
and one of HL to the Institute of Science and Technology Austria. Both host institutions
are warmly acknowledged for the hospitality. HL is partially supported by the MUR-Prin
2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with Applications
to Optimization and Machine Learning”, funded by the European Union - Next Generation
EU. SI is supported in part by ERC Consolidator Grant 101045083 “CoDiNA” funded
by the European Research Council. Open access funding provided by Institute of Science
and Technology (IST Austria).'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
orcid: 0000-0002-3121-3100
- first_name: Hugo
full_name: Lavenant, Hugo
last_name: Lavenant
citation:
ama: Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic
optimal transport using the dual formulation. Foundations of Computational
Mathematics. 2026;26:349-384. doi:10.1007/s10208-024-09686-3
apa: Ishida, S., & Lavenant, H. (2026). Quantitative convergence of a discretization
of dynamic optimal transport using the dual formulation. Foundations of Computational
Mathematics. Springer Nature. https://doi.org/10.1007/s10208-024-09686-3
chicago: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” Foundations of Computational
Mathematics. Springer Nature, 2026. https://doi.org/10.1007/s10208-024-09686-3.
ieee: S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation,” Foundations of Computational
Mathematics, vol. 26. Springer Nature, pp. 349–384, 2026.
ista: Ishida S, Lavenant H. 2026. Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation. Foundations of Computational
Mathematics. 26, 349–384.
mla: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” Foundations of Computational
Mathematics, vol. 26, Springer Nature, 2026, pp. 349–84, doi:10.1007/s10208-024-09686-3.
short: S. Ishida, H. Lavenant, Foundations of Computational Mathematics 26 (2026)
349–384.
corr_author: '1'
das_tickbox: '0'
date_created: 2023-12-21T10:14:37Z
date_published: 2026-02-01T00:00:00Z
date_updated: 2026-07-23T05:39:38Z
day: '01'
ddc:
- '000'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1007/s10208-024-09686-3
external_id:
arxiv:
- '2312.12213'
isi:
- '001352503300001'
file:
- access_level: open_access
checksum: 30671f88e792e8b75ae3e698ac4c131c
content_type: application/pdf
creator: dernst
date_created: 2026-07-23T05:37:52Z
date_updated: 2026-07-23T05:37:52Z
file_id: '22384'
file_name: 2026_FoundCompMath_Ishida.pdf
file_size: 1240012
relation: main_file
success: 1
file_date_updated: 2026-07-23T05:37:52Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
keyword:
- Optimal transport
- Hamilton-Jacobi equation
- convex optimization
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 349-384
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Quantitative convergence of a discretization of dynamic optimal transport using
the dual formulation
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: 26
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '21528'
abstract:
- lang: eng
text: We present a framework for the end-to-end optimization of metasurface imaging
systems that reconstruct targets using compressed sensing, a technique for solving
underdetermined imaging problems when the target object exhibits sparsity (e.g.,
the object can be described by a small number of nonzero values, but the positions
of these values are unknown). We nest an iterative, unapproximated compressed
sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting
in an interpretable, data-efficient method for maximally leveraging metaoptics
to exploit object sparsity. We apply our framework to super-resolution imaging
and high-resolution depth imaging with a phase-change material. In both situations,
our end-to-end framework effectively optimizes metasurface structures for compressed
sensing recovery, automatically balancing a number of complicated design considerations
to select an imaging measurement matrix from a complex, physically constrained
manifold with millions of dimensions. The optimized metasurface imaging systems
are robust to noise, significantly improving over random scattering surfaces and
approaching the ideal compressed sensing performance of a Gaussian matrix, showing
how a physical metasurface system can demonstrably approach the mathematical limits
of compressed sensing.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gaurav
full_name: Arya, Gaurav
last_name: Arya
- first_name: William F.
full_name: Li, William F.
last_name: Li
- first_name: Charles
full_name: Roques-Carmes, Charles
id: e2e68fc9-6505-11ef-a541-eb4e72cc3e82
last_name: Roques-Carmes
- first_name: Marin
full_name: Soljačić, Marin
last_name: Soljačić
- first_name: Steven G.
full_name: Johnson, Steven G.
last_name: Johnson
- first_name: Zin
full_name: Lin, Zin
last_name: Lin
citation:
ama: Arya G, Li WF, Roques-Carmes C, Soljačić M, Johnson SG, Lin Z. End-to-end optimization
of metasurfaces for imaging with compressed sensing. ACS Photonics. 2024;11(5):2077-2087.
doi:10.1021/acsphotonics.4c00259
apa: Arya, G., Li, W. F., Roques-Carmes, C., Soljačić, M., Johnson, S. G., &
Lin, Z. (2024). End-to-end optimization of metasurfaces for imaging with compressed
sensing. ACS Photonics. American Chemical Society. https://doi.org/10.1021/acsphotonics.4c00259
chicago: Arya, Gaurav, William F. Li, Charles Roques-Carmes, Marin Soljačić, Steven
G. Johnson, and Zin Lin. “End-to-End Optimization of Metasurfaces for Imaging
with Compressed Sensing.” ACS Photonics. American Chemical Society, 2024.
https://doi.org/10.1021/acsphotonics.4c00259.
ieee: G. Arya, W. F. Li, C. Roques-Carmes, M. Soljačić, S. G. Johnson, and Z. Lin,
“End-to-end optimization of metasurfaces for imaging with compressed sensing,”
ACS Photonics, vol. 11, no. 5. American Chemical Society, pp. 2077–2087,
2024.
ista: Arya G, Li WF, Roques-Carmes C, Soljačić M, Johnson SG, Lin Z. 2024. End-to-end
optimization of metasurfaces for imaging with compressed sensing. ACS Photonics.
11(5), 2077–2087.
mla: Arya, Gaurav, et al. “End-to-End Optimization of Metasurfaces for Imaging with
Compressed Sensing.” ACS Photonics, vol. 11, no. 5, American Chemical Society,
2024, pp. 2077–87, doi:10.1021/acsphotonics.4c00259.
short: G. Arya, W.F. Li, C. Roques-Carmes, M. Soljačić, S.G. Johnson, Z. Lin, ACS
Photonics 11 (2024) 2077–2087.
date_created: 2026-03-30T12:22:47Z
date_published: 2024-04-23T00:00:00Z
date_updated: 2026-04-27T09:03:21Z
day: '23'
ddc:
- '530'
doi: 10.1021/acsphotonics.4c00259
extern: '1'
external_id:
arxiv:
- '2201.12348'
intvolume: ' 11'
issue: '5'
keyword:
- end-to-end
- optimization
- metasurface
- imaging
- compressed sensing
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2201.12348
month: '04'
oa: 1
oa_version: Preprint
page: 2077-2087
publication: ACS Photonics
publication_identifier:
eissn:
- 2330-4022
publication_status: published
publisher: American Chemical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: End-to-end optimization of metasurfaces for imaging with compressed sensing
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 11
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '21672'
abstract:
- lang: eng
text: We present a framework for the end-to-end optimization of metasurface imaging
systems that reconstruct targets using compressed sensing, a technique for solving
underdetermined imaging problems when the target object exhibits sparsity (i.e.
the object can be described by a small number of non-zero values, but the positions
of these values are unknown). We nest an iterative, unapproximated compressed
sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting
in an interpretable, data-efficient method for maximally leveraging metaoptics
to exploit object sparsity. We apply our framework to super-resolution imaging
and high-resolution depth imaging with a phase-change material. In both situations,
our end-to-end framework computationally discovers optimal metasurface structures
for compressed sensing recovery, automatically balancing a number of complicated
design considerations to select an imaging measurement matrix from a complex,
physically constrained manifold with millions ofdimensions. The optimized metasurface
imaging systems are robust to noise, significantly improving over random scattering
surfaces and approaching the ideal compressed sensing performance of a Gaussian
matrix, showing how a physical metasurface system can demonstrably approach the
mathematical limits of compressed sensing.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gaurav
full_name: Arya, Gaurav
last_name: Arya
- first_name: William F.
full_name: Li, William F.
last_name: Li
- first_name: Charles
full_name: Roques-Carmes, Charles
id: e2e68fc9-6505-11ef-a541-eb4e72cc3e82
last_name: Roques-Carmes
- first_name: Marin
full_name: Soljačić, Marin
last_name: Soljačić
- first_name: Steven G.
full_name: Johnson, Steven G.
last_name: Johnson
- first_name: Zin
full_name: Lin, Zin
last_name: Lin
citation:
ama: Arya G, Li WF, Roques-Carmes C, Soljačić M, Johnson SG, Lin Z. End-to-end optimization
of metasurfaces for imaging with compressed sensing. ACS Photonics. 2024.
doi:10.1021/acsphotonics.4c00259
apa: Arya, G., Li, W. F., Roques-Carmes, C., Soljačić, M., Johnson, S. G., &
Lin, Z. (2024). End-to-end optimization of metasurfaces for imaging with compressed
sensing. ACS Photonics. American Chemical Society. https://doi.org/10.1021/acsphotonics.4c00259
chicago: Arya, Gaurav, William F. Li, Charles Roques-Carmes, Marin Soljačić, Steven
G. Johnson, and Zin Lin. “End-to-End Optimization of Metasurfaces for Imaging
with Compressed Sensing.” ACS Photonics. American Chemical Society, 2024.
https://doi.org/10.1021/acsphotonics.4c00259.
ieee: G. Arya, W. F. Li, C. Roques-Carmes, M. Soljačić, S. G. Johnson, and Z. Lin,
“End-to-end optimization of metasurfaces for imaging with compressed sensing,”
ACS Photonics. American Chemical Society, 2024.
ista: Arya G, Li WF, Roques-Carmes C, Soljačić M, Johnson SG, Lin Z. 2024. End-to-end
optimization of metasurfaces for imaging with compressed sensing. ACS Photonics.
mla: Arya, Gaurav, et al. “End-to-End Optimization of Metasurfaces for Imaging with
Compressed Sensing.” ACS Photonics, American Chemical Society, 2024, doi:10.1021/acsphotonics.4c00259.
short: G. Arya, W.F. Li, C. Roques-Carmes, M. Soljačić, S.G. Johnson, Z. Lin, ACS
Photonics (2024).
date_created: 2026-04-09T09:10:41Z
date_published: 2024-04-23T00:00:00Z
date_updated: 2026-04-27T09:23:04Z
day: '23'
ddc:
- '530'
doi: 10.1021/acsphotonics.4c00259
extern: '1'
external_id:
arxiv:
- '2201.12348'
keyword:
- end-to-end
- optimization
- metasurface
- imaging
- compressed sensing
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2201.12348
month: '04'
oa: 1
oa_version: Preprint
publication: ACS Photonics
publication_identifier:
eissn:
- 2330-4022
publication_status: published
publisher: American Chemical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: End-to-end optimization of metasurfaces for imaging with compressed sensing
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
_id: '17203'
abstract:
- lang: eng
text: "The behavior of a rigid body primarily depends on its mass moments, which
consist of the mass, center of mass, and moments of inertia. It is possible to
manipulate these quantities without altering the geometric appearance of an object
by introducing cavities in its interior. Algorithms that find cavities of suitable
shapes and sizes have enabled the computational design of spinning tops, yo-yos,
wheels, buoys, and statically balanced objects. Previous work is based, for example,
on topology optimization on voxel grids, which introduces a large number of optimization
variables and box constraints, or offset surface computation, which cannot guarantee
that solutions to a feasible problem will always be found.\r\n\r\nIn this work,
we provide a mathematical analysis of constrained topology optimization problems
that depend only on mass moments. This class of problems covers, among others,
all applications mentioned above. Our main result is to show that no matter the
outer shape of the rigid body to be optimized or the optimization objective and
constraints considered, the optimal solution always features a quadric-shaped
interface between material and cavities. This proves that optimal interfaces are
always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases,
such as planes.\r\n\r\nThis insight lets us replace a difficult topology optimization
problem with a provably equivalent non-linear equation system in a small number
(<10) of variables, which represent the coefficients of the quadric. This system
can be solved in a few seconds for most examples, provides insights into the geometric
structure of many specific applications, and lets us describe their solution properties.
Finally, our method integrates seamlessly into modern fabrication workflows because
our solutions are analytical surfaces that are native to the CAD domain."
acknowledgement: We thank Gianmarco Cherchi for his help in tailoring the Mesh Booleans
code for this project, Stefan Jeschke for his help with the photographs, Malina
Strugaru and Aleksei Kalinov for their help with the samples, and the anonymous
reviewers as well as the members of the ISTA Visual Computing Group for their feedback.
This project was funded in part by the European Research Council (ERC Consolidator
Grant 101045083 CoDiNA).
article_number: '78'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Christian
full_name: Hafner, Christian
id: 400429CC-F248-11E8-B48F-1D18A9856A87
last_name: Hafner
- first_name: Mickaël
full_name: Ly, Mickaël
id: 6340d7f0-b48d-11eb-b10d-b7487e71d9f1
last_name: Ly
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: 'Hafner C, Ly M, Wojtan C. Spin-it faster: Quadrics solve all topology optimization
problems that depend only on mass moments. Transactions on Graphics. 2024;43(4).
doi:10.1145/3658194'
apa: 'Hafner, C., Ly, M., & Wojtan, C. (2024). Spin-it faster: Quadrics solve
all topology optimization problems that depend only on mass moments. Transactions
on Graphics. Denver, Colorado: Association for Computing Machinery. https://doi.org/10.1145/3658194'
chicago: 'Hafner, Christian, Mickaël Ly, and Chris Wojtan. “Spin-It Faster: Quadrics
Solve All Topology Optimization Problems That Depend Only on Mass Moments.” Transactions
on Graphics. Association for Computing Machinery, 2024. https://doi.org/10.1145/3658194.'
ieee: 'C. Hafner, M. Ly, and C. Wojtan, “Spin-it faster: Quadrics solve all topology
optimization problems that depend only on mass moments,” Transactions on Graphics,
vol. 43, no. 4. Association for Computing Machinery, 2024.'
ista: 'Hafner C, Ly M, Wojtan C. 2024. Spin-it faster: Quadrics solve all topology
optimization problems that depend only on mass moments. Transactions on Graphics.
43(4), 78.'
mla: 'Hafner, Christian, et al. “Spin-It Faster: Quadrics Solve All Topology Optimization
Problems That Depend Only on Mass Moments.” Transactions on Graphics, vol.
43, no. 4, 78, Association for Computing Machinery, 2024, doi:10.1145/3658194.'
short: C. Hafner, M. Ly, C. Wojtan, Transactions on Graphics 43 (2024).
conference:
end_date: 2024-08-01
location: Denver, Colorado
start_date: 2024-07-28
corr_author: '1'
date_created: 2024-07-05T12:08:57Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-08T08:29:09Z
day: '01'
ddc:
- '516'
department:
- _id: ChWo
doi: 10.1145/3658194
external_id:
isi:
- '001289270900045'
file:
- access_level: open_access
checksum: 0dc9f5a6422b8a49a79026900f349ee5
content_type: application/pdf
creator: chafner
date_created: 2024-07-05T12:05:17Z
date_updated: 2024-07-05T12:05:17Z
file_id: '17204'
file_name: sif-final.pdf
file_size: 7225150
relation: main_file
success: 1
- access_level: open_access
checksum: cde433c6a40688d5f1187fb5721f6f94
content_type: application/pdf
creator: chafner
date_created: 2024-07-05T12:06:03Z
date_updated: 2024-07-05T12:06:03Z
file_id: '17205'
file_name: sif-supp-final.pdf
file_size: 397262
relation: supplementary_material
- access_level: open_access
checksum: c0457a09c2ab9a1c2935c995dcc84907
content_type: video/mp4
creator: chafner
date_created: 2024-07-17T09:29:13Z
date_updated: 2024-07-17T09:29:13Z
file_id: '17276'
file_name: sif-video-final.mp4
file_size: 170001305
relation: supplementary_material
title: Submission Video
file_date_updated: 2024-07-17T09:29:13Z
has_accepted_license: '1'
intvolume: ' 43'
isi: 1
issue: '4'
keyword:
- Topology Optimization
- Mass Moments
- Computational Geometry
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
- 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Spin-it faster: Quadrics solve all topology optimization problems that depend
only on mass moments'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 43
year: '2024'
...
---
OA_place: publisher
_id: '17208'
abstract:
- lang: eng
text: "Can current quantum computers provide a speedup over their classical counterparts
for some kinds of problems? In this thesis, with a focus on ground state search/preparation,
we address some of the challenges that both quantum annealing and variational
quantum algorithms suffer from, hindering any possible practical speedup in comparison
to the best classical counterparts. \r\n\r\nIn the first part of the thesis, we
study the performance of quantum annealing for solving a particular combinatorial
optimization problem called 3-XOR satisfability (3-XORSAT). The classical problem
is mapped into a ground state search of a 3-local classical Hamiltonian $H_C$.
We consider how modifying the initial problem, by adding more interaction terms
to the corresponding Hamiltonian, leads to the emergence of a first-order phase
transition during the annealing process. This phenomenon causes the total annealing
duration, $T$, required to prepare the ground state of $H_C$ with a high probability
to increase exponentially with the size of the problem. Our findings indicate
that with the growing complexity of problem instances, the likelihood of encountering
first-order phase transitions also increases, making quantum annealing an impractical
solution for these types of combinatorial optimization problems.\r\n\r\nIn the
second part, we focus on the problem of barren plateaus in generic variational
quantum algorithms. Barren plateaus correspond to flat regions in the parameter
space where the gradient of the cost function is zero in expectation, and with
the variance decaying exponentially with the system size, thus obstructing an
efficient parameter optimization. We propose an algorithm to circumvent Barren
Plateaus by monitoring the entanglement entropy of k-local reduced density matrices,
alongside a method for estimating entanglement entropy via classical shadow tomography.
We illustrate the approach with the paradigmatic example of the variational quantum
eigensolver, and show that our algorithm effectively avoids barren plateaus in
the initialization as well as during the optimization stage. \r\n\r\nLastly, in
the last two Chapters of this thesis, we focus on the quantum approximate optimization
algorithm (QAOA), originally introduced as an algorithm for solving generic combinatorial
optimization problems in near-term quantum devices. Specifically, we focus on
how to develop rigorous initialization strategies with guarantee improvement.
Our motivation for this study lies in that for random initialization, the optimization
typically leads to local minima with poor performance. Our main result corresponds
to the analytical construction of index-1 saddle points or transition states,
stationary points with a single direction of descent, as a tool for systematically
exploring the QAOA optimization landscape. This leads us to propose a novel greedy
parameter initialization strategy that guarantees for the energy to decrease with
an increasing number of circuit layers. Furthermore, with precise estimates for
the negative Hessian eigenvalue and its eigenvector, we establish a lower bound
for energy improvement following a QAOA iteration."
acknowledged_ssus:
- _id: ScienComp
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Raimel A
full_name: Medina Ramos, Raimel A
id: CE680B90-D85A-11E9-B684-C920E6697425
last_name: Medina Ramos
orcid: 0000-0002-5383-2869
citation:
ama: Medina Ramos RA. Exploring the optimization landscape of variational quantum
algorithms. 2024. doi:10.15479/at:ista:17208
apa: Medina Ramos, R. A. (2024). Exploring the optimization landscape of variational
quantum algorithms. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17208
chicago: Medina Ramos, Raimel A. “Exploring the Optimization Landscape of Variational
Quantum Algorithms.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17208.
ieee: R. A. Medina Ramos, “Exploring the optimization landscape of variational quantum
algorithms,” Institute of Science and Technology Austria, 2024.
ista: Medina Ramos RA. 2024. Exploring the optimization landscape of variational
quantum algorithms. Institute of Science and Technology Austria.
mla: Medina Ramos, Raimel A. Exploring the Optimization Landscape of Variational
Quantum Algorithms. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17208.
short: R.A. Medina Ramos, Exploring the Optimization Landscape of Variational Quantum
Algorithms, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-07-09T09:14:24Z
date_published: 2024-07-09T00:00:00Z
date_updated: 2026-04-07T12:43:22Z
day: '09'
ddc:
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: MaSe
doi: 10.15479/at:ista:17208
ec_funded: 1
file:
- access_level: closed
checksum: 6f45273d04f4418bc2adc018baed0525
content_type: application/zip
creator: rmedinar
date_created: 2024-07-09T09:21:44Z
date_updated: 2024-07-10T11:34:09Z
file_id: '17212'
file_name: Raimel_Thesis-Final.zip
file_size: '14218691'
relation: source_file
- access_level: open_access
checksum: 6724a95bec772dbabc0111b9f08a805e
content_type: application/pdf
creator: rmedinar
date_created: 2024-07-17T09:23:24Z
date_updated: 2024-07-17T09:23:24Z
file_id: '17275'
file_name: Raimel_Thesis-20_pdfa.pdf
file_size: 11253627
relation: main_file
success: 1
file_date_updated: 2024-07-17T09:23:24Z
has_accepted_license: '1'
keyword:
- Quantum computing
- Variational Quantum Algorithms
- Optimization
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '133'
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '850899'
name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10545'
relation: part_of_dissertation
status: public
- id: '10067'
relation: part_of_dissertation
status: public
- id: '17222'
relation: part_of_dissertation
status: public
- id: '13125'
relation: part_of_dissertation
status: public
- id: '11471'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
title: Exploring the optimization landscape of variational quantum algorithms
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
_id: '12984'
abstract:
- lang: eng
text: Tattoos are a highly popular medium, with both artistic and medical applications.
Although the mechanical process of tattoo application has evolved historically,
the results are reliant on the artisanal skill of the artist. This can be especially
challenging for some skin tones, or in cases where artists lack experience. We
provide the first systematic overview of tattooing as a computational fabrication
technique. We built an automated tattooing rig and a recipe for the creation of
silicone sheets mimicking realistic skin tones, which allowed us to create an
accurate model predicting tattoo appearance. This enables several exciting applications
including tattoo previewing, color retargeting, novel ink spectra optimization,
color-accurate prosthetics, and more.
acknowledged_ssus:
- _id: M-Shop
acknowledgement: We thank Todor Asenov and the Miba Machine Shop for their help in
assembling the tattoo machine and manufacturing the substrates. We thank Geysler
Rodrigues for the insightful discussions on tattooing practices from a professional
artist's perspective. We thank Maria Fernanda Portugal for sharing a doctor's perspective
on medical applications of tattoos. This work is graciously supported by the FWF
Lise Meitner (Grant M 3319).
article_number: '67'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Michael
full_name: Piovarci, Michael
id: 62E473F4-5C99-11EA-A40E-AF823DDC885E
last_name: Piovarci
orcid: 0000-0002-5062-4474
- first_name: Alexandre
full_name: Chapiro, Alexandre
last_name: Chapiro
- first_name: Bernd
full_name: Bickel, Bernd
id: 49876194-F248-11E8-B48F-1D18A9856A87
last_name: Bickel
orcid: 0000-0001-6511-9385
citation:
ama: 'Piovarci M, Chapiro A, Bickel B. Skin-Screen: A computational fabrication
framework for color tattoos. ACM Transactions on Graphics. 2023;42(4).
doi:10.1145/3592432'
apa: 'Piovarci, M., Chapiro, A., & Bickel, B. (2023). Skin-Screen: A computational
fabrication framework for color tattoos. ACM Transactions on Graphics.
Los Angeles, CA, United States: Association for Computing Machinery. https://doi.org/10.1145/3592432'
chicago: 'Piovarci, Michael, Alexandre Chapiro, and Bernd Bickel. “Skin-Screen:
A Computational Fabrication Framework for Color Tattoos.” ACM Transactions
on Graphics. Association for Computing Machinery, 2023. https://doi.org/10.1145/3592432.'
ieee: 'M. Piovarci, A. Chapiro, and B. Bickel, “Skin-Screen: A computational fabrication
framework for color tattoos,” ACM Transactions on Graphics, vol. 42, no.
4. Association for Computing Machinery, 2023.'
ista: 'Piovarci M, Chapiro A, Bickel B. 2023. Skin-Screen: A computational fabrication
framework for color tattoos. ACM Transactions on Graphics. 42(4), 67.'
mla: 'Piovarci, Michael, et al. “Skin-Screen: A Computational Fabrication Framework
for Color Tattoos.” ACM Transactions on Graphics, vol. 42, no. 4, 67, Association
for Computing Machinery, 2023, doi:10.1145/3592432.'
short: M. Piovarci, A. Chapiro, B. Bickel, ACM Transactions on Graphics 42 (2023).
conference:
end_date: 2023-08-10
location: Los Angeles, CA, United States
name: 'SIGGRAPH: Computer Graphics and Interactive Techniques Conference'
start_date: 2023-08-06
corr_author: '1'
date_created: 2023-05-16T09:39:14Z
date_published: 2023-07-26T00:00:00Z
date_updated: 2025-04-15T07:43:53Z
day: '26'
ddc:
- '004'
department:
- _id: BeBi
doi: 10.1145/3592432
external_id:
isi:
- '001044671300033'
file:
- access_level: open_access
checksum: 5f0a6867689e025a661bd0b4fd90b821
content_type: application/pdf
creator: mpiovarc
date_created: 2023-05-16T09:38:25Z
date_updated: 2023-05-16T09:38:25Z
file_id: '12985'
file_name: Piovarci2023.pdf
file_size: 30817343
relation: main_file
success: 1
- access_level: open_access
checksum: 6dd371de5b517e5f184f9c2cbea4b8b3
content_type: application/pdf
creator: dernst
date_created: 2024-04-16T05:52:18Z
date_updated: 2024-04-16T05:52:18Z
file_id: '15324'
file_name: 2023_ACM_Piovarci.pdf
file_size: 30281676
relation: main_file
success: 1
file_date_updated: 2024-04-16T05:52:18Z
has_accepted_license: '1'
intvolume: ' 42'
isi: 1
issue: '4'
keyword:
- appearance
- modeling
- reproduction
- tattoo
- skin color
- gamut mapping
- ink-optimization
- prosthetic
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: eb901961-77a9-11ec-83b8-f5c883a62027
grant_number: M03319
name: Perception-Aware Appearance Fabrication
publication: ACM Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
- 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Skin-Screen: A computational fabrication framework for color tattoos'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 42
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '21527'
abstract:
- lang: eng
text: Optical metasurfaces have been heralded as the platform to integrate multiple
functionalities in a compact form-factor, with the potential to replace bulky
optical components. A central stepping stone toward realizing this promise is
the demonstration of multifunctionality under several constraints (e.g., at multiple
incident wavelengths and/or angles) in a single device, an achievement being hampered
by design limitations inherent to single-layer planar geometries. Here, we propose
a framework for the inverse design of multilayer metaoptics via topology optimization,
showing that even few-wavelength thick devices can achieve high-efficiency multifunctionality,
such as multiangle light concentration and plan-achromaticity. We embody our framework
in multiple closely spaced patterned layers of a low-index polymer, with fabrication
constraints specific to this platform enforced in the optimization process. We
experimentally demonstrate our approach with an inverse-designed 3D-printed light
concentrator working at five different nonparaxial angles of incidence. Our framework
paves the way toward realizing multifunctional ultracompact 3D nanophotonic devices.
article_processing_charge: No
article_type: letter_note
arxiv: 1
author:
- first_name: Charles
full_name: Roques-Carmes, Charles
id: e2e68fc9-6505-11ef-a541-eb4e72cc3e82
last_name: Roques-Carmes
- first_name: Zin
full_name: Lin, Zin
last_name: Lin
- first_name: Rasmus E.
full_name: Christiansen, Rasmus E.
last_name: Christiansen
- first_name: Yannick
full_name: Salamin, Yannick
last_name: Salamin
- first_name: Steven E.
full_name: Kooi, Steven E.
last_name: Kooi
- first_name: John D.
full_name: Joannopoulos, John D.
last_name: Joannopoulos
- first_name: Steven G.
full_name: Johnson, Steven G.
last_name: Johnson
- first_name: Marin
full_name: Soljačić, Marin
last_name: Soljačić
citation:
ama: Roques-Carmes C, Lin Z, Christiansen RE, et al. Toward 3D-printed inverse-designed
metaoptics. ACS Photonics. 2022;9(1):43-51. doi:10.1021/acsphotonics.1c01442
apa: Roques-Carmes, C., Lin, Z., Christiansen, R. E., Salamin, Y., Kooi, S. E.,
Joannopoulos, J. D., … Soljačić, M. (2022). Toward 3D-printed inverse-designed
metaoptics. ACS Photonics. American Chemical Society. https://doi.org/10.1021/acsphotonics.1c01442
chicago: Roques-Carmes, Charles, Zin Lin, Rasmus E. Christiansen, Yannick Salamin,
Steven E. Kooi, John D. Joannopoulos, Steven G. Johnson, and Marin Soljačić. “Toward
3D-Printed Inverse-Designed Metaoptics.” ACS Photonics. American Chemical
Society, 2022. https://doi.org/10.1021/acsphotonics.1c01442.
ieee: C. Roques-Carmes et al., “Toward 3D-printed inverse-designed metaoptics,”
ACS Photonics, vol. 9, no. 1. American Chemical Society, pp. 43–51, 2022.
ista: Roques-Carmes C, Lin Z, Christiansen RE, Salamin Y, Kooi SE, Joannopoulos
JD, Johnson SG, Soljačić M. 2022. Toward 3D-printed inverse-designed metaoptics.
ACS Photonics. 9(1), 43–51.
mla: Roques-Carmes, Charles, et al. “Toward 3D-Printed Inverse-Designed Metaoptics.”
ACS Photonics, vol. 9, no. 1, American Chemical Society, 2022, pp. 43–51,
doi:10.1021/acsphotonics.1c01442.
short: C. Roques-Carmes, Z. Lin, R.E. Christiansen, Y. Salamin, S.E. Kooi, J.D.
Joannopoulos, S.G. Johnson, M. Soljačić, ACS Photonics 9 (2022) 43–51.
date_created: 2026-03-30T12:22:47Z
date_published: 2022-01-07T00:00:00Z
date_updated: 2026-04-27T09:14:46Z
day: '07'
ddc:
- '530'
doi: 10.1021/acsphotonics.1c01442
extern: '1'
external_id:
arxiv:
- '2105.11326'
intvolume: ' 9'
issue: '1'
keyword:
- metasurfaces
- inverse design
- multilayered metaoptics
- 3D printing
- topology optimization
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.11326
month: '01'
oa: 1
oa_version: Preprint
page: 43-51
publication: ACS Photonics
publication_identifier:
eissn:
- 2330-4022
publication_status: published
publisher: American Chemical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Toward 3D-printed inverse-designed metaoptics
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 9
year: '2022'
...
---
_id: '9817'
abstract:
- lang: eng
text: Elastic bending of initially flat slender elements allows the realization
and economic fabrication of intriguing curved shapes. In this work, we derive
an intuitive but rigorous geometric characterization of the design space of plane
elastic rods with variable stiffness. It enables designers to determine which
shapes are physically viable with active bending by visual inspection alone. Building
on these insights, we propose a method for efficiently designing the geometry
of a flat elastic rod that realizes a target equilibrium curve, which only requires
solving a linear program. We implement this method in an interactive computational
design tool that gives feedback about the feasibility of a design, and computes
the geometry of the structural elements necessary to realize it within an instant.
The tool also offers an iterative optimization routine that improves the fabricability
of a model while modifying it as little as possible. In addition, we use our geometric
characterization to derive an algorithm for analyzing and recovering the stability
of elastic curves that would otherwise snap out of their unstable equilibrium
shapes by buckling. We show the efficacy of our approach by designing and manufacturing
several physical models that are assembled from flat elements.
acknowledgement: "We thank the anonymous reviewers for their generous feedback, and
Michal Piovarči for his help in producing the supplemental video. 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 715767).\r\n"
article_number: '126'
article_processing_charge: No
article_type: original
author:
- first_name: Christian
full_name: Hafner, Christian
id: 400429CC-F248-11E8-B48F-1D18A9856A87
last_name: Hafner
- first_name: Bernd
full_name: Bickel, Bernd
id: 49876194-F248-11E8-B48F-1D18A9856A87
last_name: Bickel
orcid: 0000-0001-6511-9385
citation:
ama: Hafner C, Bickel B. The design space of plane elastic curves. ACM Transactions
on Graphics. 2021;40(4). doi:10.1145/3450626.3459800
apa: 'Hafner, C., & Bickel, B. (2021). The design space of plane elastic curves.
ACM Transactions on Graphics. Virtual: Association for Computing Machinery.
https://doi.org/10.1145/3450626.3459800'
chicago: Hafner, Christian, and Bernd Bickel. “The Design Space of Plane Elastic
Curves.” ACM Transactions on Graphics. Association for Computing Machinery,
2021. https://doi.org/10.1145/3450626.3459800.
ieee: C. Hafner and B. Bickel, “The design space of plane elastic curves,” ACM
Transactions on Graphics, vol. 40, no. 4. Association for Computing Machinery,
2021.
ista: Hafner C, Bickel B. 2021. The design space of plane elastic curves. ACM Transactions
on Graphics. 40(4), 126.
mla: Hafner, Christian, and Bernd Bickel. “The Design Space of Plane Elastic Curves.”
ACM Transactions on Graphics, vol. 40, no. 4, 126, Association for Computing
Machinery, 2021, doi:10.1145/3450626.3459800.
short: C. Hafner, B. Bickel, ACM Transactions on Graphics 40 (2021).
conference:
end_date: 2021-08-13
location: Virtual
name: 'SIGGRAF: Special Interest Group on Computer Graphics and Interactive Techniques'
start_date: 2021-08-09
date_created: 2021-08-08T22:01:26Z
date_published: 2021-07-19T00:00:00Z
date_updated: 2026-08-21T22:30:05Z
day: '19'
ddc:
- '516'
department:
- _id: BeBi
doi: 10.1145/3450626.3459800
ec_funded: 1
external_id:
isi:
- '000674930900091'
file:
- access_level: open_access
checksum: 7e5d08ce46b0451b3102eacd3d00f85f
content_type: application/pdf
creator: chafner
date_created: 2021-10-18T10:42:15Z
date_updated: 2021-10-18T10:42:15Z
file_id: '10150'
file_name: elastic-curves-paper.pdf
file_size: 17064290
relation: main_file
success: 1
- access_level: open_access
checksum: 0088643478be7c01a703b5b10767348f
content_type: application/pdf
creator: chafner
date_created: 2021-10-18T10:42:22Z
date_updated: 2021-10-18T10:42:22Z
file_id: '10151'
file_name: elastic-curves-supp.pdf
file_size: 547156
relation: supplementary_material
file_date_updated: 2021-10-18T10:42:22Z
has_accepted_license: '1'
intvolume: ' 40'
isi: 1
issue: '4'
keyword:
- Computing methodologies
- shape modeling
- modeling and simulation
- theory of computation
- computational geometry
- mathematics of computing
- mathematical optimization
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 24F9549A-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '715767'
name: 'MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and
Modeling'
publication: ACM Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
- 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
related_material:
link:
- description: News on IST Website
relation: press_release
url: https://ist.ac.at/en/news/designing-with-elastic-structures/
record:
- id: '12897'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: The design space of plane elastic curves
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 40
year: '2021'
...
---
_id: '7130'
abstract:
- lang: eng
text: "We show that statistical criticality, i.e. the occurrence of power law frequency
distributions, arises in samples that are maximally informative about the underlying
generating process. In order to reach this conclusion, we first identify the frequency
with which different outcomes occur in a sample, as the variable carrying useful
information on the generative process. The entropy of the frequency, that we call
relevance, provides an upper bound to the number of informative bits. This differs
from the entropy of the data, that we take as a measure of resolution. Samples
that maximise relevance at a given resolution—that we call maximally informative
samples—exhibit statistical criticality. In particular, Zipf's law arises at the
optimal trade-off between resolution (i.e. compression) and relevance. As a byproduct,
we derive a bound of the maximal number of parameters that can be estimated from
a dataset, in the absence of prior knowledge on the generative model.\r\n\r\nFurthermore,
we relate criticality to the statistical properties of the representation of the
data generating process. We show that, as a consequence of the concentration property
of the asymptotic equipartition property, representations that are maximally informative
about the data generating process are characterised by an exponential distribution
of energy levels. This arises from a principle of minimal entropy, that is conjugate
of the maximum entropy principle in statistical mechanics. This explains why statistical
criticality requires no parameter fine tuning in maximally informative samples."
acknowledgement: We acknowledge interesting discussions with M Abbott, E Aurell, J
Barbier, R Monasson, T Mora, I Nemenman, N Tishby and R Zecchina. This research
was supported by the Kavli Foundation and the Centre of Excellence scheme of the
Research Council of Norway (Centre for Neural Computation) (RJC and YR), by the
Basic Science Research Program through the National Research Foundation of Korea
(NRF), funded by the Ministry of Education (2016R1D1A1B03932264) (JJ), and, in part,
by the ICTP through the OEA-AC-98 (JS).
article_number: '063402'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ryan J
full_name: Cubero, Ryan J
id: 850B2E12-9CD4-11E9-837F-E719E6697425
last_name: Cubero
orcid: 0000-0003-0002-1867
- first_name: Junghyo
full_name: Jo, Junghyo
last_name: Jo
- first_name: Matteo
full_name: Marsili, Matteo
last_name: Marsili
- first_name: Yasser
full_name: Roudi, Yasser
last_name: Roudi
- first_name: Juyong
full_name: Song, Juyong
last_name: Song
citation:
ama: 'Cubero RJ, Jo J, Marsili M, Roudi Y, Song J. Statistical criticality arises
in most informative representations. Journal of Statistical Mechanics: Theory
and Experiment. 2019;2019(6). doi:10.1088/1742-5468/ab16c8'
apa: 'Cubero, R. J., Jo, J., Marsili, M., Roudi, Y., & Song, J. (2019). Statistical
criticality arises in most informative representations. Journal of Statistical
Mechanics: Theory and Experiment. IOP Publishing. https://doi.org/10.1088/1742-5468/ab16c8'
chicago: 'Cubero, Ryan J, Junghyo Jo, Matteo Marsili, Yasser Roudi, and Juyong Song.
“Statistical Criticality Arises in Most Informative Representations.” Journal
of Statistical Mechanics: Theory and Experiment. IOP Publishing, 2019. https://doi.org/10.1088/1742-5468/ab16c8.'
ieee: 'R. J. Cubero, J. Jo, M. Marsili, Y. Roudi, and J. Song, “Statistical criticality
arises in most informative representations,” Journal of Statistical Mechanics:
Theory and Experiment, vol. 2019, no. 6. IOP Publishing, 2019.'
ista: 'Cubero RJ, Jo J, Marsili M, Roudi Y, Song J. 2019. Statistical criticality
arises in most informative representations. Journal of Statistical Mechanics:
Theory and Experiment. 2019(6), 063402.'
mla: 'Cubero, Ryan J., et al. “Statistical Criticality Arises in Most Informative
Representations.” Journal of Statistical Mechanics: Theory and Experiment,
vol. 2019, no. 6, 063402, IOP Publishing, 2019, doi:10.1088/1742-5468/ab16c8.'
short: 'R.J. Cubero, J. Jo, M. Marsili, Y. Roudi, J. Song, Journal of Statistical
Mechanics: Theory and Experiment 2019 (2019).'
date_created: 2019-11-26T22:36:09Z
date_published: 2019-06-17T00:00:00Z
date_updated: 2021-01-12T08:11:57Z
day: '17'
doi: 10.1088/1742-5468/ab16c8
extern: '1'
external_id:
arxiv:
- '1808.00249'
intvolume: ' 2019'
issue: '6'
keyword:
- optimization under uncertainty
- source coding
- large deviation
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1808.00249
month: '06'
oa: 1
oa_version: Preprint
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
issn:
- 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: Statistical criticality arises in most informative representations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2019
year: '2019'
...
---
_id: '11683'
abstract:
- lang: eng
text: The vertex connectivity κ of a graph is the smallest number of vertices whose
deletion separates the graph or makes it trivial. We present the fastest known
deterministic algorithm for finding the vertex connectivity and a corresponding
separator. The time for a digraph having n vertices and m edges is O(min{κ3 +
n, κn}m); for an undirected graph the term m can be replaced by κn. A randomized
algorithm finds κ with error probability 1/2 in time O(nm). If the vertices have
nonnegative weights the weighted vertex connectivity is found in time O(κ1nmlog(n2/m))
where κ1 ≤ m/n is the unweighted vertex connectivity or in expected time O(nmlog(n2/m))
with error probability 1/2. The main algorithm combines two previous vertex connectivity
algorithms and a generalization of the preflow-push algorithm of Hao and Orlin
(1994, J. Algorithms17, 424–446) that computes edge connectivity.
article_processing_charge: No
article_type: original
author:
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Satish
full_name: Rao, Satish
last_name: Rao
- first_name: Harold N.
full_name: Gabow, Harold N.
last_name: Gabow
citation:
ama: 'Henzinger M, Rao S, Gabow HN. Computing vertex connectivity: New bounds from
old techniques. Journal of Algorithms. 2000;34(2):222-250. doi:10.1006/jagm.1999.1055'
apa: 'Henzinger, M., Rao, S., & Gabow, H. N. (2000). Computing vertex connectivity:
New bounds from old techniques. Journal of Algorithms. Elsevier. https://doi.org/10.1006/jagm.1999.1055'
chicago: 'Henzinger, Monika, Satish Rao, and Harold N. Gabow. “Computing Vertex
Connectivity: New Bounds from Old Techniques.” Journal of Algorithms. Elsevier,
2000. https://doi.org/10.1006/jagm.1999.1055.'
ieee: 'M. Henzinger, S. Rao, and H. N. Gabow, “Computing vertex connectivity: New
bounds from old techniques,” Journal of Algorithms, vol. 34, no. 2. Elsevier,
pp. 222–250, 2000.'
ista: 'Henzinger M, Rao S, Gabow HN. 2000. Computing vertex connectivity: New bounds
from old techniques. Journal of Algorithms. 34(2), 222–250.'
mla: 'Henzinger, Monika, et al. “Computing Vertex Connectivity: New Bounds from
Old Techniques.” Journal of Algorithms, vol. 34, no. 2, Elsevier, 2000,
pp. 222–50, doi:10.1006/jagm.1999.1055.'
short: M. Henzinger, S. Rao, H.N. Gabow, Journal of Algorithms 34 (2000) 222–250.
date_created: 2022-07-28T08:56:10Z
date_published: 2000-02-01T00:00:00Z
date_updated: 2024-11-04T11:42:08Z
day: '01'
doi: 10.1006/jagm.1999.1055
extern: '1'
intvolume: ' 34'
issue: '2'
keyword:
- Computational Theory and Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
month: '02'
oa_version: None
page: 222-250
publication: Journal of Algorithms
publication_identifier:
issn:
- 0196-6774
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Computing vertex connectivity: New bounds from old techniques'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2000'
...