---
_id: '14499'
abstract:
- lang: eng
text: "An n-vertex graph is called C-Ramsey if it has no clique or independent set
of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper,
we study edge statistics in Ramsey graphs, in particular obtaining very precise
control of the distribution of the number of edges in a random vertex subset of
a C-Ramsey graph. This brings together two ongoing lines of research: the study
of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability
for low-degree polynomials of independent random variables.\r\n\r\nThe proof proceeds
via an ‘additive structure’ dichotomy on the degree sequence and involves a wide
range of different tools from Fourier analysis, random matrix theory, the theory
of Boolean functions, probabilistic combinatorics and low-rank approximation.
In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright
theorem on small-ball probability for polynomials of Gaussians, which we believe
is of independent interest. One of the consequences of our result is the resolution
of an old conjecture of Erdős and McKay, for which Erdős reiterated in several
of his open problem collections and for which he offered one of his notorious
monetary prizes."
acknowledgement: Kwan was supported for part of this work by ERC Starting Grant ‘RANDSTRUCT’
No. 101076777. Sah and Sawhney were supported by NSF Graduate Research Fellowship
Program DGE-2141064. Sah was supported by the PD Soros Fellowship. Sauermann was
supported by NSF Award DMS-2100157, and for part of this work by a Sloan Research
Fellowship.
article_number: e21
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Matthew Alan
full_name: Kwan, Matthew Alan
id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
last_name: Kwan
orcid: 0000-0002-4003-7567
- first_name: Ashwin
full_name: Sah, Ashwin
last_name: Sah
- first_name: Lisa
full_name: Sauermann, Lisa
last_name: Sauermann
- first_name: Mehtaab
full_name: Sawhney, Mehtaab
last_name: Sawhney
citation:
ama: Kwan MA, Sah A, Sauermann L, Sawhney M. Anticoncentration in Ramsey graphs
and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 2023;11.
doi:10.1017/fmp.2023.17
apa: Kwan, M. A., Sah, A., Sauermann, L., & Sawhney, M. (2023). Anticoncentration
in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics,
Pi. Cambridge University Press. https://doi.org/10.1017/fmp.2023.17
chicago: Kwan, Matthew Alan, Ashwin Sah, Lisa Sauermann, and Mehtaab Sawhney. “Anticoncentration
in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” Forum of Mathematics,
Pi. Cambridge University Press, 2023. https://doi.org/10.1017/fmp.2023.17.
ieee: M. A. Kwan, A. Sah, L. Sauermann, and M. Sawhney, “Anticoncentration in Ramsey
graphs and a proof of the Erdős–McKay conjecture,” Forum of Mathematics, Pi,
vol. 11. Cambridge University Press, 2023.
ista: Kwan MA, Sah A, Sauermann L, Sawhney M. 2023. Anticoncentration in Ramsey
graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 11,
e21.
mla: Kwan, Matthew Alan, et al. “Anticoncentration in Ramsey Graphs and a Proof
of the Erdős–McKay Conjecture.” Forum of Mathematics, Pi, vol. 11, e21,
Cambridge University Press, 2023, doi:10.1017/fmp.2023.17.
short: M.A. Kwan, A. Sah, L. Sauermann, M. Sawhney, Forum of Mathematics, Pi 11
(2023).
date_created: 2023-11-07T09:02:48Z
date_published: 2023-08-24T00:00:00Z
date_updated: 2023-11-07T09:18:57Z
day: '24'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.1017/fmp.2023.17
external_id:
arxiv:
- '2208.02874'
file:
- access_level: open_access
checksum: 54b824098d59073cc87a308d458b0a3e
content_type: application/pdf
creator: dernst
date_created: 2023-11-07T09:16:23Z
date_updated: 2023-11-07T09:16:23Z
file_id: '14500'
file_name: 2023_ForumMathematics_Kwan.pdf
file_size: 1218719
relation: main_file
success: 1
file_date_updated: 2023-11-07T09:16:23Z
has_accepted_license: '1'
intvolume: ' 11'
keyword:
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Mathematical Physics
- Statistics and Probability
- Algebra and Number Theory
- Analysis
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: bd95085b-d553-11ed-ba76-e55d3349be45
grant_number: '101076777'
name: Randomness and structure in combinatorics
publication: Forum of Mathematics, Pi
publication_identifier:
issn:
- 2050-5086
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture
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: 11
year: '2023'
...
---
_id: '14772'
abstract:
- lang: eng
text: "Many coupled evolution equations can be described via 2×2-block operator
matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with
possibly unbounded entries. Here, the case of diagonally dominant block operator
matrices is considered, that is, the case where the full operator A can be seen
as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D)
though with possibly large relative bound. For such operators the properties of
sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied,
and for these properties perturbation results for possibly large but structured
perturbations are derived. Thereby, the time dependent parabolic problem associated
with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied
to a wide range of problems such as different theories for liquid crystals, an
artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel
model."
acknowledgement: "We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for
valuable discussions. We also thank the anonymous referees for their helpful comments
and suggestions, and for the very accurate reading of the manuscript.\r\nThe first
author has been supported partially by the Nachwuchsring – Network for the promotion
of young scientists – at TU Kaiserslautern. Both authors have been supported by
MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative
of the Federal State of Rhineland-Palatinate, Germany."
article_number: '110146'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Amru
full_name: Hussein, Amru
last_name: Hussein
citation:
ama: Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator
matrices and applications. Journal of Functional Analysis. 2023;285(11).
doi:10.1016/j.jfa.2023.110146
apa: Agresti, A., & Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus
for block operator matrices and applications. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2023.110146
chicago: Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus
for Block Operator Matrices and Applications.” Journal of Functional Analysis.
Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110146.
ieee: A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block
operator matrices and applications,” Journal of Functional Analysis, vol.
285, no. 11. Elsevier, 2023.
ista: Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block
operator matrices and applications. Journal of Functional Analysis. 285(11), 110146.
mla: Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus
for Block Operator Matrices and Applications.” Journal of Functional Analysis,
vol. 285, no. 11, 110146, Elsevier, 2023, doi:10.1016/j.jfa.2023.110146.
short: A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).
date_created: 2024-01-10T09:15:18Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-10T11:24:56Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jfa.2023.110146
external_id:
arxiv:
- '2108.01962'
isi:
- '001081809000001'
file:
- access_level: open_access
checksum: eda98ca2aa73da91bd074baed34c2b3c
content_type: application/pdf
creator: dernst
date_created: 2024-01-10T11:23:57Z
date_updated: 2024-01-10T11:23:57Z
file_id: '14789'
file_name: 2023_JourFunctionalAnalysis_Agresti.pdf
file_size: 1120592
relation: main_file
success: 1
file_date_updated: 2024-01-10T11:23:57Z
has_accepted_license: '1'
intvolume: ' 285'
isi: 1
issue: '11'
keyword:
- Analysis
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maximal Lp-regularity and H∞-calculus for block operator matrices and applications
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: 285
year: '2023'
...
---
_id: '10850'
abstract:
- lang: eng
text: "We study two interacting quantum particles forming a bound state in d-dimensional
free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with
Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly
decreases upon going from k\r\nto k+1. This shows that the particles stick to
the corner where all boundary planes intersect.\r\nSecond, we show that for all
k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy,
has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes
the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020)
to dimensions d > 1."
acknowledgement: We thank Rupert Frank for contributing Appendix B. Funding from the
European Union's Horizon 2020 research and innovation programme under the ERC grant
agreement No. 694227 is gratefully acknowledged.
article_number: '109455'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal
of Functional Analysis. 2022;282(12). doi:10.1016/j.jfa.2022.109455
apa: Roos, B., & Seiringer, R. (2022). Two-particle bound states at interfaces
and corners. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109455
chicago: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces
and Corners.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109455.
ieee: B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,”
Journal of Functional Analysis, vol. 282, no. 12. Elsevier, 2022.
ista: Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners.
Journal of Functional Analysis. 282(12), 109455.
mla: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces
and Corners.” Journal of Functional Analysis, vol. 282, no. 12, 109455,
Elsevier, 2022, doi:10.1016/j.jfa.2022.109455.
short: B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).
date_created: 2022-03-16T08:41:53Z
date_published: 2022-06-15T00:00:00Z
date_updated: 2023-10-27T10:37:29Z
day: '15'
ddc:
- '510'
department:
- _id: GradSch
- _id: RoSe
doi: 10.1016/j.jfa.2022.109455
ec_funded: 1
external_id:
arxiv:
- '2105.04874'
isi:
- '000795160200009'
file:
- access_level: open_access
checksum: 63efcefaa1f2717244ef5407bd564426
content_type: application/pdf
creator: dernst
date_created: 2022-08-02T10:37:55Z
date_updated: 2022-08-02T10:37:55Z
file_id: '11720'
file_name: 2022_JourFunctionalAnalysis_Roos.pdf
file_size: 631391
relation: main_file
success: 1
file_date_updated: 2022-08-02T10:37:55Z
has_accepted_license: '1'
intvolume: ' 282'
isi: 1
issue: '12'
keyword:
- Analysis
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '14374'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Two-particle bound states at interfaces and corners
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: 282
year: '2022'
...
---
_id: '11556'
abstract:
- lang: eng
text: "We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation
kinetics and extend them for aggregation processes with collisional fragmentation
(shattering). We test the performance and accuracy of the extended methods and
compare their performance with efficient deterministic finite-difference method
applied to the same model. We validate the stochastic methods on the test problems
and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation
kinetics recently detected in deterministic simulations. We confirm the emergence
of steady oscillations of densities in such systems and prove the stability of
the\r\noscillations with respect to fluctuations and noise."
acknowledgement: Zhores supercomputer of Skolkovo Institute of Science and Technology
[68] has been used in the present research. S.A.M. was supported by Moscow Center
for Fundamental and Applied Mathematics (the agreement with the Ministry of Education
and Science of the Russian Federation No. 075-15-2019-1624). A.I.O. acknowledges
RFBR project No. 20-31-90022. N.V.B. acknowledges the support of the Analytical
Center (subsidy agreement 000000D730321P5Q0002, Grant No. 70-2021-00145 02.11.2021).
article_number: '111439'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Aleksei
full_name: Kalinov, Aleksei
id: 44b7120e-eb97-11eb-a6c2-e1557aa81d02
last_name: Kalinov
orcid: 0000-0003-2189-3904
- first_name: A.I.
full_name: Osinskiy, A.I.
last_name: Osinskiy
- first_name: S.A.
full_name: Matveev, S.A.
last_name: Matveev
- first_name: W.
full_name: Otieno, W.
last_name: Otieno
- first_name: N.V.
full_name: Brilliantov, N.V.
last_name: Brilliantov
citation:
ama: Kalinov A, Osinskiy AI, Matveev SA, Otieno W, Brilliantov NV. Direct simulation
Monte Carlo for new regimes in aggregation-fragmentation kinetics. Journal
of Computational Physics. 2022;467. doi:10.1016/j.jcp.2022.111439
apa: Kalinov, A., Osinskiy, A. I., Matveev, S. A., Otieno, W., & Brilliantov,
N. V. (2022). Direct simulation Monte Carlo for new regimes in aggregation-fragmentation
kinetics. Journal of Computational Physics. Elsevier. https://doi.org/10.1016/j.jcp.2022.111439
chicago: Kalinov, Aleksei, A.I. Osinskiy, S.A. Matveev, W. Otieno, and N.V. Brilliantov.
“Direct Simulation Monte Carlo for New Regimes in Aggregation-Fragmentation Kinetics.”
Journal of Computational Physics. Elsevier, 2022. https://doi.org/10.1016/j.jcp.2022.111439.
ieee: A. Kalinov, A. I. Osinskiy, S. A. Matveev, W. Otieno, and N. V. Brilliantov,
“Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics,”
Journal of Computational Physics, vol. 467. Elsevier, 2022.
ista: Kalinov A, Osinskiy AI, Matveev SA, Otieno W, Brilliantov NV. 2022. Direct
simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics.
Journal of Computational Physics. 467, 111439.
mla: Kalinov, Aleksei, et al. “Direct Simulation Monte Carlo for New Regimes in
Aggregation-Fragmentation Kinetics.” Journal of Computational Physics,
vol. 467, 111439, Elsevier, 2022, doi:10.1016/j.jcp.2022.111439.
short: A. Kalinov, A.I. Osinskiy, S.A. Matveev, W. Otieno, N.V. Brilliantov, Journal
of Computational Physics 467 (2022).
date_created: 2022-07-11T12:19:59Z
date_published: 2022-10-15T00:00:00Z
date_updated: 2023-08-03T11:55:06Z
day: '15'
ddc:
- '518'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1016/j.jcp.2022.111439
external_id:
arxiv:
- '2103.09481'
isi:
- '000917225500013'
intvolume: ' 467'
isi: 1
keyword:
- Computer Science Applications
- Physics and Astronomy (miscellaneous)
- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation
- Numerical Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2103.09481
month: '10'
oa: 1
oa_version: Preprint
publication: Journal of Computational Physics
publication_identifier:
issn:
- 0021-9991
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Direct simulation Monte Carlo for new regimes in aggregation-fragmentation
kinetics
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 467
year: '2022'
...
---
_id: '10643'
abstract:
- lang: eng
text: "We prove a generalised super-adiabatic theorem for extended fermionic systems
assuming a spectral gap only in the bulk. More precisely, we assume that the infinite
system has a unique ground state and that the corresponding Gelfand–Naimark–Segal
Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that
a similar adiabatic theorem also holds in the bulk of finite systems up to errors
that vanish faster than any inverse power of the system size, although the corresponding
finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"
acknowledgement: J.H. acknowledges partial financial support by the ERC Advanced Grant
‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft
and the Open Access Publishing Fund of the University of Tübingen is gratefully
acknowledged.
article_number: e4
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Stefan
full_name: Teufel, Stefan
last_name: Teufel
citation:
ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems
with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80'
apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic
limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2021.80'
chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2021.80.'
ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10.
Cambridge University Press, 2022.'
ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.'
mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol.
10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.'
short: S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).
date_created: 2022-01-18T16:18:51Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2023-08-02T13:53:11Z
day: '18'
ddc:
- '510'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1017/fms.2021.80
ec_funded: 1
external_id:
arxiv:
- '2012.15239'
isi:
- '000743615000001'
file:
- access_level: open_access
checksum: 87592a755adcef22ea590a99dc728dd3
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-19T09:27:43Z
date_updated: 2022-01-19T09:27:43Z
file_id: '10646'
file_name: 2022_ForumMathSigma_Henheik.pdf
file_size: 705323
relation: main_file
success: 1
file_date_updated: 2022-01-19T09:27:43Z
has_accepted_license: '1'
intvolume: ' 10'
isi: 1
keyword:
- computational mathematics
- discrete mathematics and combinatorics
- geometry and topology
- mathematical physics
- statistics and probability
- algebra and number theory
- theoretical computer science
- analysis
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk'
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: 10
year: '2022'
...
---
_id: '11916'
abstract:
- lang: eng
text: A domain is called Kac regular for a quadratic form on L2 if every functions
vanishing almost everywhere outside the domain can be approximated in form norm
by functions with compact support in the domain. It is shown that this notion
is stable under domination of quadratic forms. As applications measure perturbations
of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and
Schrödinger operators on manifolds are studied. Along the way a characterization
of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally
Riemannian metric measure spaces is obtained.
acknowledgement: "The author was supported by the German Academic Scholarship Foundation
(Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG)
via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement
during the author’s ongoing graduate studies and him as well as Marcel Schmidt for
fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu
and Peter Stollmann for valuable comments on a preliminary version of this article.
He would also like to thank the organizers of the conference Analysis and Geometry
on Graphs and Manifolds in Potsdam, where the initial motivation of this article
was conceived, and the organizers of the intense activity period Metric Measure
Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '38'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Wirth M. Kac regularity and domination of quadratic forms. Advances in Operator
Theory. 2022;7(3). doi:10.1007/s43036-022-00199-w
apa: Wirth, M. (2022). Kac regularity and domination of quadratic forms. Advances
in Operator Theory. Springer Nature. https://doi.org/10.1007/s43036-022-00199-w
chicago: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances
in Operator Theory. Springer Nature, 2022. https://doi.org/10.1007/s43036-022-00199-w.
ieee: M. Wirth, “Kac regularity and domination of quadratic forms,” Advances
in Operator Theory, vol. 7, no. 3. Springer Nature, 2022.
ista: Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances
in Operator Theory. 7(3), 38.
mla: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances
in Operator Theory, vol. 7, no. 3, 38, Springer Nature, 2022, doi:10.1007/s43036-022-00199-w.
short: M. Wirth, Advances in Operator Theory 7 (2022).
date_created: 2022-08-18T07:22:24Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-02-21T10:08:07Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s43036-022-00199-w
file:
- access_level: open_access
checksum: 913474844a1b38264fb710746d5e2e98
content_type: application/pdf
creator: dernst
date_created: 2022-08-18T08:02:34Z
date_updated: 2022-08-18T08:02:34Z
file_id: '11921'
file_name: 2022_AdvancesOperatorTheory_Wirth.pdf
file_size: 389060
relation: main_file
success: 1
file_date_updated: 2022-08-18T08:02:34Z
has_accepted_license: '1'
intvolume: ' 7'
issue: '3'
keyword:
- Algebra and Number Theory
- Analysis
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Advances in Operator Theory
publication_identifier:
eissn:
- 2538-225X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Kac regularity and domination of quadratic forms
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: 7
year: '2022'
...
---
_id: '12148'
abstract:
- lang: eng
text: 'We prove a general local law for Wigner matrices that optimally handles observables
of arbitrary rank and thus unifies the well-known averaged and isotropic local
laws. As an application, we prove a central limit theorem in quantum unique ergodicity
(QUE): that is, we show that the quadratic forms of a general deterministic matrix
A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation.
For the bulk spectrum, we thus generalise our previous result [17] as valid for
test matrices A of large rank as well as the result of Benigni and Lopatto [7]
as valid for specific small-rank observables.'
acknowledgement: L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.
D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation
and the ETH Zürich Foundation.
article_number: e96
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices.
Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local
law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University
Press. https://doi.org/10.1017/fms.2022.86
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform
Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2022.86.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner
matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press,
2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner
matrices. Forum of Mathematics, Sigma. 10, e96.
mla: Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum
of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).
date_created: 2023-01-12T12:07:30Z
date_published: 2022-10-27T00:00:00Z
date_updated: 2023-08-04T09:00:35Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2022.86
ec_funded: 1
external_id:
isi:
- '000873719200001'
file:
- access_level: open_access
checksum: 94a049aeb1eea5497aa097712a73c400
content_type: application/pdf
creator: dernst
date_created: 2023-01-24T10:02:40Z
date_updated: 2023-01-24T10:02:40Z
file_id: '12356'
file_name: 2022_ForumMath_Cipolloni.pdf
file_size: 817089
relation: main_file
success: 1
file_date_updated: 2023-01-24T10:02:40Z
has_accepted_license: '1'
intvolume: ' 10'
isi: 1
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Mathematical Physics
- Statistics and Probability
- Algebra and Number Theory
- Theoretical Computer Science
- Analysis
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
issn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rank-uniform local law for Wigner matrices
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: 10
year: '2022'
...
---
_id: '12179'
abstract:
- lang: eng
text: We derive an accurate lower tail estimate on the lowest singular value σ1(X−z)
of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z.
Such shift effectively changes the upper tail behavior of the condition number
κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices
to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away
from the real axis. This sharpens and resolves a recent conjecture in [J. Banks
et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of
the real Ginibre ensemble with a genuinely complex shift. As a consequence we
obtain an improved upper bound on the eigenvalue condition numbers (known also
as the eigenvector overlaps) for real Ginibre matrices. The main technical tool
is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys.,
1 (2020), pp. 101--146].
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. On the condition number of the shifted real
Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 2022;43(3):1469-1487.
doi:10.1137/21m1424408
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). On the condition number
of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications.
Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424408
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition
Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis
and Applications. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424408.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the
shifted real Ginibre ensemble,” SIAM Journal on Matrix Analysis and Applications,
vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487,
2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted
real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3),
1469–1487.
mla: Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre
Ensemble.” SIAM Journal on Matrix Analysis and Applications, vol. 43, no.
3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:10.1137/21m1424408.
short: G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and
Applications 43 (2022) 1469–1487.
date_created: 2023-01-12T12:12:38Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-01-27T06:56:06Z
day: '01'
department:
- _id: LaEr
doi: 10.1137/21m1424408
external_id:
arxiv:
- '2105.13719'
intvolume: ' 43'
issue: '3'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.13719
month: '07'
oa: 1
oa_version: Preprint
page: 1469-1487
publication: SIAM Journal on Matrix Analysis and Applications
publication_identifier:
eissn:
- 1095-7162
issn:
- 0895-4798
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the condition number of the shifted real Ginibre ensemble
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 43
year: '2022'
...
---
_id: '12216'
abstract:
- lang: eng
text: Many trace inequalities can be expressed either as concavity/convexity theorems
or as monotonicity theorems. A classic example is the joint convexity of the quantum
relative entropy which is equivalent to the Data Processing Inequality. The latter
says that quantum operations can never increase the relative entropy. The monotonicity
versions often have many advantages, and often have direct physical application,
as in the example just mentioned. Moreover, the monotonicity results are often
valid for a larger class of maps than, say, quantum operations (which are completely
positive). In this paper we prove several new monotonicity results, the first
of which is a monotonicity theorem that has as a simple corollary a celebrated
concavity theorem of Epstein. Our starting points are the monotonicity versions
of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs
of these in their general forms using interpolation. We then prove our new monotonicity
theorems by several duality arguments.
acknowledgement: Work partially supported by the Lise Meitner fellowship, Austrian
Science Fund (FWF) M3337.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Eric A.
full_name: Carlen, Eric A.
last_name: Carlen
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and
related inequalities. Linear Algebra and its Applications. 2022;654:289-310.
doi:10.1016/j.laa.2022.09.001
apa: Carlen, E. A., & Zhang, H. (2022). Monotonicity versions of Epstein’s concavity
theorem and related inequalities. Linear Algebra and Its Applications.
Elsevier. https://doi.org/10.1016/j.laa.2022.09.001
chicago: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s
Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications.
Elsevier, 2022. https://doi.org/10.1016/j.laa.2022.09.001.
ieee: E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem
and related inequalities,” Linear Algebra and its Applications, vol. 654.
Elsevier, pp. 289–310, 2022.
ista: Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem
and related inequalities. Linear Algebra and its Applications. 654, 289–310.
mla: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity
Theorem and Related Inequalities.” Linear Algebra and Its Applications,
vol. 654, Elsevier, 2022, pp. 289–310, doi:10.1016/j.laa.2022.09.001.
short: E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.
date_created: 2023-01-16T09:46:38Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-04T09:24:51Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1016/j.laa.2022.09.001
external_id:
isi:
- '000860689600014'
file:
- access_level: open_access
checksum: cf3cb7e7e34baa967849f01d8f0c1ae4
content_type: application/pdf
creator: dernst
date_created: 2023-01-27T08:08:39Z
date_updated: 2023-01-27T08:08:39Z
file_id: '12415'
file_name: 2022_LinearAlgebra_Carlen.pdf
file_size: 441184
relation: main_file
success: 1
file_date_updated: 2023-01-27T08:08:39Z
has_accepted_license: '1'
intvolume: ' 654'
isi: 1
keyword:
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Numerical Analysis
- Algebra and Number Theory
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 289-310
project:
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
publication: Linear Algebra and its Applications
publication_identifier:
issn:
- 0024-3795
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Monotonicity versions of Epstein's concavity theorem and related inequalities
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: 654
year: '2022'
...
---
_id: '12304'
abstract:
- lang: eng
text: 'We establish sharp criteria for the instantaneous propagation of free boundaries
in solutions to the thin-film equation. The criteria are formulated in terms of
the initial distribution of mass (as opposed to previous almost-optimal results),
reflecting the fact that mass is a locally conserved quantity for the thin-film
equation. In the regime of weak slippage, our criteria are at the same time necessary
and sufficient. The proof of our upper bounds on free boundary propagation is
based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial
scales: We combine estimates on the local mass and estimates on energies to show
that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially
smaller space-time cylinder with the same time horizon. The derivation of our
lower bounds on free boundary propagation is based on a combination of a monotone
quantity and almost optimal estimates established previously by the second author
with a new estimate connecting motion of mass to entropy production.'
acknowledgement: N. De Nitti acknowledges the kind hospitality of IST Austria within
the framework of the ISTernship Summer Program 2018, during which most of the present
article was written. N. DeNitti has received funding by The Austrian Agency for
International Cooperation in Education &Research (OeAD-GmbH) via its financial support
of the ISTernship Summer Program 2018. N.De Nitti would also like to thank Giuseppe
Coclite, Giuseppe Devillanova, Giuseppe Florio, Sebastian Hensel, and Francesco
Maddalena for several helpful conversations on topics related to this work.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicola
full_name: De Nitti, Nicola
last_name: De Nitti
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: De Nitti N, Fischer JL. Sharp criteria for the waiting time phenomenon in solutions
to the thin-film equation. Communications in Partial Differential Equations.
2022;47(7):1394-1434. doi:10.1080/03605302.2022.2056702
apa: De Nitti, N., & Fischer, J. L. (2022). Sharp criteria for the waiting time
phenomenon in solutions to the thin-film equation. Communications in Partial
Differential Equations. Taylor & Francis. https://doi.org/10.1080/03605302.2022.2056702
chicago: De Nitti, Nicola, and Julian L Fischer. “Sharp Criteria for the Waiting
Time Phenomenon in Solutions to the Thin-Film Equation.” Communications in
Partial Differential Equations. Taylor & Francis, 2022. https://doi.org/10.1080/03605302.2022.2056702.
ieee: N. De Nitti and J. L. Fischer, “Sharp criteria for the waiting time phenomenon
in solutions to the thin-film equation,” Communications in Partial Differential
Equations, vol. 47, no. 7. Taylor & Francis, pp. 1394–1434, 2022.
ista: De Nitti N, Fischer JL. 2022. Sharp criteria for the waiting time phenomenon
in solutions to the thin-film equation. Communications in Partial Differential
Equations. 47(7), 1394–1434.
mla: De Nitti, Nicola, and Julian L. Fischer. “Sharp Criteria for the Waiting Time
Phenomenon in Solutions to the Thin-Film Equation.” Communications in Partial
Differential Equations, vol. 47, no. 7, Taylor & Francis, 2022, pp. 1394–434,
doi:10.1080/03605302.2022.2056702.
short: N. De Nitti, J.L. Fischer, Communications in Partial Differential Equations
47 (2022) 1394–1434.
date_created: 2023-01-16T10:06:50Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-08-04T10:34:31Z
day: '01'
department:
- _id: JuFi
doi: 10.1080/03605302.2022.2056702
external_id:
arxiv:
- '1907.05342'
isi:
- '000805689800001'
intvolume: ' 47'
isi: 1
issue: '7'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1907.05342'
month: '07'
oa: 1
oa_version: Preprint
page: 1394-1434
publication: Communications in Partial Differential Equations
publication_identifier:
eissn:
- 1532-4133
issn:
- 0360-5302
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sharp criteria for the waiting time phenomenon in solutions to the thin-film
equation
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 47
year: '2022'
...
---
_id: '12305'
abstract:
- lang: eng
text: This paper is concerned with the sharp interface limit for the Allen--Cahn
equation with a nonlinear Robin boundary condition in a bounded smooth domain
Ω⊂\R2. We assume that a diffuse interface already has developed and that it is
in contact with the boundary ∂Ω. The boundary condition is designed in such a
way that the limit problem is given by the mean curvature flow with constant α-contact
angle. For α close to 90° we prove a local in time convergence result for well-prepared
initial data for times when a smooth solution to the limit problem exists. Based
on the latter we construct a suitable curvilinear coordinate system and carry
out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear
Robin boundary condition. Moreover, we show a spectral estimate for the corresponding
linearized Allen--Cahn operator and with its aid we derive strong norm estimates
for the difference of the exact and approximate solutions using a Gronwall-type
argument.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Helmut
full_name: Abels, Helmut
last_name: Abels
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°.
SIAM Journal on Mathematical Analysis. 2022;54(1):114-172. doi:10.1137/21m1424925
apa: Abels, H., & Moser, M. (2022). Convergence of the Allen--Cahn equation
with a nonlinear Robin boundary condition to mean curvature flow with contact
angle close to 90°. SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424925
chicago: Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation
with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact
Angle Close to 90°.” SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424925.
ieee: H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°,”
SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial
and Applied Mathematics, pp. 114–172, 2022.
ista: Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°.
SIAM Journal on Mathematical Analysis. 54(1), 114–172.
mla: Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation
with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact
Angle Close to 90°.” SIAM Journal on Mathematical Analysis, vol. 54, no.
1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:10.1137/21m1424925.
short: H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172.
date_created: 2023-01-16T10:07:00Z
date_published: 2022-01-04T00:00:00Z
date_updated: 2023-08-04T10:34:56Z
day: '04'
department:
- _id: JuFi
doi: 10.1137/21m1424925
external_id:
arxiv:
- '2105.08434'
isi:
- '000762768000004'
intvolume: ' 54'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2105.08434'
month: '01'
oa: 1
oa_version: Preprint
page: 114-172
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition
to mean curvature flow with contact angle close to 90°
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '10856'
abstract:
- lang: eng
text: "We study the properties of the maximal volume k-dimensional sections of the
n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a
k-dimensional subspace to be a local maximizer of the volume of such sections,
which we formulate in a geometric way. We estimate the length of the projection
of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes
the volume of the intersection. We \x1Cnd the optimal upper bound on the volume
of a planar section of the cube [−1, 1]n , n ≥ 2."
acknowledgement: "The authors acknowledge the support of the grant of the Russian
Government N 075-15-\r\n2019-1926. G.I.was supported also by the SwissNational Science
Foundation grant 200021-179133. The authors are very grateful to the anonymous reviewer
for valuable remarks."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
- first_name: Igor
full_name: Tsiutsiurupa, Igor
last_name: Tsiutsiurupa
citation:
ama: Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. Analysis
and Geometry in Metric Spaces. 2021;9(1):1-18. doi:10.1515/agms-2020-0103
apa: Ivanov, G., & Tsiutsiurupa, I. (2021). On the volume of sections of the
cube. Analysis and Geometry in Metric Spaces. De Gruyter. https://doi.org/10.1515/agms-2020-0103
chicago: Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the
Cube.” Analysis and Geometry in Metric Spaces. De Gruyter, 2021. https://doi.org/10.1515/agms-2020-0103.
ieee: G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” Analysis
and Geometry in Metric Spaces, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021.
ista: Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis
and Geometry in Metric Spaces. 9(1), 1–18.
mla: Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.”
Analysis and Geometry in Metric Spaces, vol. 9, no. 1, De Gruyter, 2021,
pp. 1–18, doi:10.1515/agms-2020-0103.
short: G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021)
1–18.
date_created: 2022-03-18T09:25:14Z
date_published: 2021-01-29T00:00:00Z
date_updated: 2023-08-17T07:07:58Z
day: '29'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1515/agms-2020-0103
external_id:
arxiv:
- '2004.02674'
isi:
- '000734286800001'
file:
- access_level: open_access
checksum: 7e615ac8489f5eae580b6517debfdc53
content_type: application/pdf
creator: dernst
date_created: 2022-03-18T09:31:59Z
date_updated: 2022-03-18T09:31:59Z
file_id: '10857'
file_name: 2021_AnalysisMetricSpaces_Ivanov.pdf
file_size: 789801
relation: main_file
success: 1
file_date_updated: 2022-03-18T09:31:59Z
has_accepted_license: '1'
intvolume: ' 9'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Geometry and Topology
- Analysis
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 1-18
publication: Analysis and Geometry in Metric Spaces
publication_identifier:
issn:
- 2299-3274
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the volume of sections of the cube
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: 9
year: '2021'
...
---
_id: '11608'
abstract:
- lang: eng
text: 'In order to understand stellar evolution, it is crucial to efficiently determine
stellar surface rotation periods. Indeed, while they are of great importance in
stellar models, angular momentum transport processes inside stars are still poorly
understood today. Surface rotation, which is linked to the age of the star, is
one of the constraints needed to improve the way those processes are modelled.
Statistics of the surface rotation periods for a large sample of stars of different
spectral types are thus necessary. An efficient tool to automatically determine
reliable rotation periods is needed when dealing with large samples of stellar
photometric datasets. The objective of this work is to develop such a tool. For
this purpose, machine learning classifiers constitute relevant bases to build
our new methodology. Random forest learning abilities are exploited to automate
the extraction of rotation periods in Kepler light curves. Rotation periods and
complementary parameters are obtained via three different methods: a wavelet analysis,
the autocorrelation function of the light curve, and the composite spectrum. We
trained three different classifiers: one to detect if rotational modulations are
present in the light curve, one to flag close binary or classical pulsators candidates
that can bias our rotation period determination, and finally one classifier to
provide the final rotation period. We tested our machine learning pipeline on
23 431 stars of the Kepler K and M dwarf reference rotation catalogue for which
60% of the stars have been visually inspected. For the sample of 21 707 stars
where all the input parameters are provided to the algorithm, 94.2% of them are
correctly classified (as rotating or not). Among the stars that have a rotation
period in the reference catalogue, the machine learning provides a period that
agrees within 10% of the reference value for 95.3% of the stars. Moreover, the
yield of correct rotation periods is raised to 99.5% after visually inspecting
25.2% of the stars. Over the two main analysis steps, rotation classification
and period selection, the pipeline yields a global agreement with the reference
values of 92.1% and 96.9% before and after visual inspection. Random forest classifiers
are efficient tools to determine reliable rotation periods in large samples of
stars. The methodology presented here could be easily adapted to extract surface
rotation periods for stars with different spectral types or observed by other
instruments such as K2, TESS or by PLATO in the near future.'
acknowledgement: 'We thank Suzanne Aigrain and Joe Llama for providing us with the
simulated data used in Aigrain et al. (2015). S. N. B., L. B. and R. A. G. acknowledge
the support from PLATO and GOLF CNES grants. A. R. G. S. acknowledges the support
from NASA under grant NNX17AF27G. S. M. acknowledges the support from the Spanish
Ministry of Science and Innovation with the Ramon y Cajal fellowship number RYC-2015-17697.
P. L. P. and S. M. acknowledge support from the Spanish Ministry of Science and
Innovation with the grant number PID2019-107187GB-I00. This research has made use
of the NASA Exoplanet Archive, which is operated by the California Institute of
Technology, under contract with the National Aeronautics and Space Administration
under the Exoplanet Exploration Program. Software: Python (Van Rossum & Drake 2009),
numpy (Oliphant 2006), pandas (The pandas development team 2020; McKinney 2010),
matplotlib (Hunter 2007), scikit-learn (Pedregosa et al. 2011). The source code
used to obtain the present results can be found at: https://gitlab.com/sybreton/pushkin
; https://gitlab.com/sybreton/ml_surface_rotation_paper .'
article_number: A125
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: S. N.
full_name: Breton, S. N.
last_name: Breton
- first_name: A. R. G.
full_name: Santos, A. R. G.
last_name: Santos
- first_name: Lisa Annabelle
full_name: Bugnet, Lisa Annabelle
id: d9edb345-f866-11ec-9b37-d119b5234501
last_name: Bugnet
orcid: 0000-0003-0142-4000
- first_name: S.
full_name: Mathur, S.
last_name: Mathur
- first_name: R. A.
full_name: García, R. A.
last_name: García
- first_name: P. L.
full_name: Pallé, P. L.
last_name: Pallé
citation:
ama: 'Breton SN, Santos ARG, Bugnet LA, Mathur S, García RA, Pallé PL. ROOSTER:
A machine-learning analysis tool for Kepler stellar rotation periods. Astronomy
& Astrophysics. 2021;647. doi:10.1051/0004-6361/202039947'
apa: 'Breton, S. N., Santos, A. R. G., Bugnet, L. A., Mathur, S., García, R. A.,
& Pallé, P. L. (2021). ROOSTER: A machine-learning analysis tool for Kepler
stellar rotation periods. Astronomy & Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/202039947'
chicago: 'Breton, S. N., A. R. G. Santos, Lisa Annabelle Bugnet, S. Mathur, R. A.
García, and P. L. Pallé. “ROOSTER: A Machine-Learning Analysis Tool for Kepler
Stellar Rotation Periods.” Astronomy & Astrophysics. EDP Sciences,
2021. https://doi.org/10.1051/0004-6361/202039947.'
ieee: 'S. N. Breton, A. R. G. Santos, L. A. Bugnet, S. Mathur, R. A. García, and
P. L. Pallé, “ROOSTER: A machine-learning analysis tool for Kepler stellar rotation
periods,” Astronomy & Astrophysics, vol. 647. EDP Sciences, 2021.'
ista: 'Breton SN, Santos ARG, Bugnet LA, Mathur S, García RA, Pallé PL. 2021. ROOSTER:
A machine-learning analysis tool for Kepler stellar rotation periods. Astronomy
& Astrophysics. 647, A125.'
mla: 'Breton, S. N., et al. “ROOSTER: A Machine-Learning Analysis Tool for Kepler
Stellar Rotation Periods.” Astronomy & Astrophysics, vol. 647, A125,
EDP Sciences, 2021, doi:10.1051/0004-6361/202039947.'
short: S.N. Breton, A.R.G. Santos, L.A. Bugnet, S. Mathur, R.A. García, P.L. Pallé,
Astronomy & Astrophysics 647 (2021).
date_created: 2022-07-18T12:21:32Z
date_published: 2021-03-19T00:00:00Z
date_updated: 2022-08-22T08:47:47Z
day: '19'
doi: 10.1051/0004-6361/202039947
extern: '1'
external_id:
arxiv:
- '2101.10152'
intvolume: ' 647'
keyword:
- Space and Planetary Science
- Astronomy and Astrophysics
- 'methods: data analysis / stars: solar-type / stars: activity / stars: rotation
/ starspots'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2101.10152
month: '03'
oa: 1
oa_version: Preprint
publication: Astronomy & Astrophysics
publication_identifier:
eissn:
- 1432-0746
issn:
- 0004-6361
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'ROOSTER: A machine-learning analysis tool for Kepler stellar rotation periods'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 647
year: '2021'
...
---
_id: '10045'
abstract:
- lang: eng
text: "Given a fixed finite metric space (V,μ), the {\\em minimum 0-extension problem},
denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize
function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative
costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational
complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai:
if metric μ is {\\em orientable modular} then 0-Ext[μ] can be solved in polynomial
time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed
a theory of discrete convex functions on orientable modular graphs generalizing
several known classes of functions in discrete convex analysis, such as L♮-convex
functions. We consider a more general version of the problem in which unary functions
fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where
set F⊆(V2) is fixed. We extend the complexity classification above by providing
an explicit condition on (μ,F) for the problem to be tractable. In order to prove
the tractability part, we generalize Hirai's theory and define a larger class
of discrete convex functions. It covers, in particular, another well-known class
of functions, namely submodular functions on an integer lattice. Finally, we improve
the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs.\r\n"
article_number: '2109.10203'
article_processing_charge: No
arxiv: 1
author:
- first_name: Martin
full_name: Dvorak, Martin
id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425
last_name: Dvorak
orcid: 0000-0001-5293-214X
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete
convexity. arXiv. doi:10.48550/arXiv.2109.10203
apa: Dvorak, M., & Kolmogorov, V. (n.d.). Generalized minimum 0-extension problem
and discrete convexity. arXiv. https://doi.org/10.48550/arXiv.2109.10203
chicago: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension
Problem and Discrete Convexity.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2109.10203.
ieee: M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and
discrete convexity,” arXiv. .
ista: Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete
convexity. arXiv, 2109.10203.
mla: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem
and Discrete Convexity.” ArXiv, 2109.10203, doi:10.48550/arXiv.2109.10203.
short: M. Dvorak, V. Kolmogorov, ArXiv (n.d.).
date_created: 2021-09-27T10:48:23Z
date_published: 2021-09-21T00:00:00Z
date_updated: 2023-05-03T10:40:16Z
day: '21'
ddc:
- '004'
department:
- _id: GradSch
- _id: VlKo
doi: 10.48550/arXiv.2109.10203
external_id:
arxiv:
- '2109.10203'
file:
- access_level: open_access
checksum: e7e83065f7bc18b9c188bf93b5ca5db6
content_type: application/pdf
creator: mdvorak
date_created: 2021-09-27T10:54:51Z
date_updated: 2021-09-27T10:54:51Z
file_id: '10046'
file_name: Generalized-0-Ext.pdf
file_size: 603672
relation: main_file
success: 1
file_date_updated: 2021-09-27T10:54:51Z
has_accepted_license: '1'
keyword:
- minimum 0-extension problem
- metric labeling problem
- discrete metric spaces
- metric extensions
- computational complexity
- valued constraint satisfaction problems
- discrete convex analysis
- L-convex functions
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2109.10203'
month: '09'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Generalized minimum 0-extension problem and discrete convexity
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '10211'
abstract:
- lang: eng
text: "We study the problem of recovering an unknown signal \U0001D465\U0001D465
given measurements obtained from a generalized linear model with a Gaussian sensing
matrix. Two popular solutions are based on a linear estimator \U0001D465\U0001D465^L
and a spectral estimator \U0001D465\U0001D465^s. The former is a data-dependent
linear combination of the columns of the measurement matrix, and its analysis
is quite simple. The latter is the principal eigenvector of a data-dependent matrix,
and a recent line of work has studied its performance. In this paper, we show
how to optimally combine \U0001D465\U0001D465^L and \U0001D465\U0001D465^s. At
the heart of our analysis is the exact characterization of the empirical joint
distribution of (\U0001D465\U0001D465,\U0001D465\U0001D465^L,\U0001D465\U0001D465^s)
in the high-dimensional limit. This allows us to compute the Bayes-optimal combination
of \U0001D465\U0001D465^L and \U0001D465\U0001D465^s, given the limiting distribution
of the signal \U0001D465\U0001D465. When the distribution of the signal is Gaussian,
then the Bayes-optimal combination has the form \U0001D703\U0001D465\U0001D465^L+\U0001D465\U0001D465^s
and we derive the optimal combination coefficient. In order to establish the limiting
distribution of (\U0001D465\U0001D465,\U0001D465\U0001D465^L,\U0001D465\U0001D465^s),
we design and analyze an approximate message passing algorithm whose iterates
give \U0001D465\U0001D465^L and approach \U0001D465\U0001D465^s. Numerical simulations
demonstrate the improvement of the proposed combination with respect to the two
methods considered separately."
acknowledgement: M. Mondelli would like to thank Andrea Montanari for helpful discussions.
All the authors would like to thank the anonymous reviewers for their helpful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Christos
full_name: Thrampoulidis, Christos
last_name: Thrampoulidis
- first_name: Ramji
full_name: Venkataramanan, Ramji
last_name: Venkataramanan
citation:
ama: Mondelli M, Thrampoulidis C, Venkataramanan R. Optimal combination of linear
and spectral estimators for generalized linear models. Foundations of Computational
Mathematics. 2021. doi:10.1007/s10208-021-09531-x
apa: Mondelli, M., Thrampoulidis, C., & Venkataramanan, R. (2021). Optimal combination
of linear and spectral estimators for generalized linear models. Foundations
of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-021-09531-x
chicago: Mondelli, Marco, Christos Thrampoulidis, and Ramji Venkataramanan. “Optimal
Combination of Linear and Spectral Estimators for Generalized Linear Models.”
Foundations of Computational Mathematics. Springer, 2021. https://doi.org/10.1007/s10208-021-09531-x.
ieee: M. Mondelli, C. Thrampoulidis, and R. Venkataramanan, “Optimal combination
of linear and spectral estimators for generalized linear models,” Foundations
of Computational Mathematics. Springer, 2021.
ista: Mondelli M, Thrampoulidis C, Venkataramanan R. 2021. Optimal combination of
linear and spectral estimators for generalized linear models. Foundations of Computational
Mathematics.
mla: Mondelli, Marco, et al. “Optimal Combination of Linear and Spectral Estimators
for Generalized Linear Models.” Foundations of Computational Mathematics,
Springer, 2021, doi:10.1007/s10208-021-09531-x.
short: M. Mondelli, C. Thrampoulidis, R. Venkataramanan, Foundations of Computational
Mathematics (2021).
date_created: 2021-11-03T10:59:08Z
date_published: 2021-08-17T00:00:00Z
date_updated: 2023-09-05T14:13:57Z
day: '17'
ddc:
- '510'
department:
- _id: MaMo
doi: 10.1007/s10208-021-09531-x
external_id:
arxiv:
- '2008.03326'
isi:
- '000685721000001'
file:
- access_level: open_access
checksum: 9ea12dd8045a0678000a3a59295221cb
content_type: application/pdf
creator: alisjak
date_created: 2021-12-13T15:47:54Z
date_updated: 2021-12-13T15:47:54Z
file_id: '10542'
file_name: 2021_Springer_Mondelli.pdf
file_size: 2305731
relation: main_file
success: 1
file_date_updated: 2021-12-13T15:47:54Z
has_accepted_license: '1'
isi: 1
keyword:
- Applied Mathematics
- Computational Theory and Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal combination of linear and spectral estimators for generalized linear
models
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '10549'
abstract:
- lang: eng
text: We derive optimal-order homogenization rates for random nonlinear elliptic
PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely,
for a random monotone operator on \mathbb {R}^d with stationary law (that is spatially
homogeneous statistics) and fast decay of correlations on scales larger than the
microscale \varepsilon >0, we establish homogenization error estimates of the
order \varepsilon in case d\geqq 3, and of the order \varepsilon |\log \varepsilon
|^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have
been limited to a small algebraic rate of convergence \varepsilon ^\delta . We
also establish error estimates for the approximation of the homogenized operator
by the method of representative volumes of the order (L/\varepsilon )^{-d/2} for
a representative volume of size L. Our results also hold in the case of systems
for which a (small-scale) C^{1,\alpha } regularity theory is available.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) – project number 405009441.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Stefan
full_name: Neukamm, Stefan
last_name: Neukamm
citation:
ama: Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization
of nonlinear uniformly elliptic equations and systems. Archive for Rational
Mechanics and Analysis. 2021;242(1):343-452. doi:10.1007/s00205-021-01686-9
apa: Fischer, J. L., & Neukamm, S. (2021). Optimal homogenization rates in stochastic
homogenization of nonlinear uniformly elliptic equations and systems. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01686-9
chicago: Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in
Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.”
Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01686-9.
ieee: J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic
homogenization of nonlinear uniformly elliptic equations and systems,” Archive
for Rational Mechanics and Analysis, vol. 242, no. 1. Springer Nature, pp.
343–452, 2021.
ista: Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization
of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics
and Analysis. 242(1), 343–452.
mla: Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic
Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive
for Rational Mechanics and Analysis, vol. 242, no. 1, Springer Nature, 2021,
pp. 343–452, doi:10.1007/s00205-021-01686-9.
short: J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242
(2021) 343–452.
date_created: 2021-12-16T12:12:33Z
date_published: 2021-06-30T00:00:00Z
date_updated: 2023-08-17T06:23:21Z
day: '30'
ddc:
- '530'
department:
- _id: JuFi
doi: 10.1007/s00205-021-01686-9
external_id:
arxiv:
- '1908.02273'
isi:
- '000668431200001'
file:
- access_level: open_access
checksum: cc830b739aed83ca2e32c4e0ce266a4c
content_type: application/pdf
creator: cchlebak
date_created: 2021-12-16T14:58:08Z
date_updated: 2021-12-16T14:58:08Z
file_id: '10558'
file_name: 2021_ArchRatMechAnalysis_Fischer.pdf
file_size: 1640121
relation: main_file
success: 1
file_date_updated: 2021-12-16T14:58:08Z
has_accepted_license: '1'
intvolume: ' 242'
isi: 1
issue: '1'
keyword:
- Mechanical Engineering
- Mathematics (miscellaneous)
- Analysis
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 343-452
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal homogenization rates in stochastic homogenization of nonlinear uniformly
elliptic equations and systems
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: 242
year: '2021'
...
---
_id: '10862'
abstract:
- lang: eng
text: We consider the sum of two large Hermitian matrices A and B with a Haar unitary
conjugation bringing them into a general relative position. We prove that the
eigenvalue density on the scale slightly above the local eigenvalue spacing is
asymptotically given by the free additive convolution of the laws of A and B as
the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues
and optimal rate of convergence in Voiculescu's theorem. Our previous works [4],
[5] established these results in the bulk spectrum, the current paper completely
settles the problem at the spectral edges provided they have the typical square-root
behavior. The key element of our proof is to compensate the deterioration of the
stability of the subordination equations by sharp error estimates that properly
account for the local density near the edge. Our results also hold if the Haar
unitary matrix is replaced by the Haar orthogonal matrix.
acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804.
article_number: '108639'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
last_name: Schnelli
citation:
ama: Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices
at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639
apa: Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition
of random matrices at the regular edge. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2020.108639
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for
Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis.
Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108639.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random
matrices at the regular edge,” Journal of Functional Analysis, vol. 279,
no. 7. Elsevier, 2020.
ista: Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random
matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.
mla: Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at
the Regular Edge.” Journal of Functional Analysis, vol. 279, no. 7, 108639,
Elsevier, 2020, doi:10.1016/j.jfa.2020.108639.
short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).
date_created: 2022-03-18T10:18:59Z
date_published: 2020-10-15T00:00:00Z
date_updated: 2023-08-24T14:08:42Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2020.108639
ec_funded: 1
external_id:
arxiv:
- '1708.01597'
isi:
- '000559623200009'
intvolume: ' 279'
isi: 1
issue: '7'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.01597
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral rigidity for addition of random matrices at the regular edge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 279
year: '2020'
...
---
_id: '8691'
abstract:
- lang: eng
text: Given l>2ν>2d≥4, we prove the persistence of a Cantor--family of KAM tori
of measure O(ε1/2−ν/l) for any non--degenerate nearly integrable Hamiltonian system
of class Cl(D×Td), where D⊂Rd is a bounded domain, provided that the size ε of
the perturbation is sufficiently small. This extends a result by D. Salamon in
\cite{salamon2004kolmogorov} according to which we do have the persistence of
a single KAM torus in the same framework. Moreover, it is well--known that, for
the persistence of a single torus, the regularity assumption can not be improved.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Edmond
full_name: Koudjinan, Edmond
id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
last_name: Koudjinan
orcid: 0000-0003-2640-4049
citation:
ama: Koudjinan E. A KAM theorem for finitely differentiable Hamiltonian systems.
Journal of Differential Equations. 2020;269(6):4720-4750. doi:10.1016/j.jde.2020.03.044
apa: Koudjinan, E. (2020). A KAM theorem for finitely differentiable Hamiltonian
systems. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2020.03.044
chicago: Koudjinan, Edmond. “A KAM Theorem for Finitely Differentiable Hamiltonian
Systems.” Journal of Differential Equations. Elsevier, 2020. https://doi.org/10.1016/j.jde.2020.03.044.
ieee: E. Koudjinan, “A KAM theorem for finitely differentiable Hamiltonian systems,”
Journal of Differential Equations, vol. 269, no. 6. Elsevier, pp. 4720–4750,
2020.
ista: Koudjinan E. 2020. A KAM theorem for finitely differentiable Hamiltonian systems.
Journal of Differential Equations. 269(6), 4720–4750.
mla: Koudjinan, Edmond. “A KAM Theorem for Finitely Differentiable Hamiltonian Systems.”
Journal of Differential Equations, vol. 269, no. 6, Elsevier, 2020, pp.
4720–50, doi:10.1016/j.jde.2020.03.044.
short: E. Koudjinan, Journal of Differential Equations 269 (2020) 4720–4750.
date_created: 2020-10-21T15:03:05Z
date_published: 2020-09-05T00:00:00Z
date_updated: 2021-01-12T08:20:33Z
day: '05'
doi: 10.1016/j.jde.2020.03.044
extern: '1'
external_id:
arxiv:
- '1909.04099'
intvolume: ' 269'
issue: '6'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1909.04099
month: '09'
oa: 1
oa_version: Preprint
page: 4720-4750
publication: Journal of Differential Equations
publication_identifier:
issn:
- 0022-0396
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: A KAM theorem for finitely differentiable Hamiltonian systems
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 269
year: '2020'
...
---
_id: '7369'
abstract:
- lang: eng
text: Neuronal responses to complex stimuli and tasks can encompass a wide range
of time scales. Understanding these responses requires measures that characterize
how the information on these response patterns are represented across multiple
temporal resolutions. In this paper we propose a metric – which we call multiscale
relevance (MSR) – to capture the dynamical variability of the activity of single
neurons across different time scales. The MSR is a non-parametric, fully featureless
indicator in that it uses only the time stamps of the firing activity without
resorting to any a priori covariate or invoking any specific structure in the
tuning curve for neural activity. When applied to neural data from the mEC and
from the ADn and PoS regions of freely-behaving rodents, we found that neurons
having low MSR tend to have low mutual information and low firing sparsity across
the correlates that are believed to be encoded by the region of the brain where
the recordings were made. In addition, neurons with high MSR contain significant
information on spatial navigation and allow to decode spatial position or head
direction as efficiently as those neurons whose firing activity has high mutual
information with the covariate to be decoded and significantly better than the
set of neurons with high local variations in their interspike intervals. Given
these results, we propose that the MSR can be used as a measure to rank and select
neurons for their information content without the need to appeal to any a priori
covariate.
acknowledgement: 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 is currently receiving funding from the European Union’s Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.
article_processing_charge: Yes (via OA deal)
article_type: original
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: Matteo
full_name: Marsili, Matteo
last_name: Marsili
- first_name: Yasser
full_name: Roudi, Yasser
last_name: Roudi
citation:
ama: Cubero RJ, Marsili M, Roudi Y. Multiscale relevance and informative encoding
in neuronal spike trains. Journal of Computational Neuroscience. 2020;48:85-102.
doi:10.1007/s10827-020-00740-x
apa: Cubero, R. J., Marsili, M., & Roudi, Y. (2020). Multiscale relevance and
informative encoding in neuronal spike trains. Journal of Computational Neuroscience.
Springer Nature. https://doi.org/10.1007/s10827-020-00740-x
chicago: Cubero, Ryan J, Matteo Marsili, and Yasser Roudi. “Multiscale Relevance
and Informative Encoding in Neuronal Spike Trains.” Journal of Computational
Neuroscience. Springer Nature, 2020. https://doi.org/10.1007/s10827-020-00740-x.
ieee: R. J. Cubero, M. Marsili, and Y. Roudi, “Multiscale relevance and informative
encoding in neuronal spike trains,” Journal of Computational Neuroscience,
vol. 48. Springer Nature, pp. 85–102, 2020.
ista: Cubero RJ, Marsili M, Roudi Y. 2020. Multiscale relevance and informative
encoding in neuronal spike trains. Journal of Computational Neuroscience. 48,
85–102.
mla: Cubero, Ryan J., et al. “Multiscale Relevance and Informative Encoding in Neuronal
Spike Trains.” Journal of Computational Neuroscience, vol. 48, Springer
Nature, 2020, pp. 85–102, doi:10.1007/s10827-020-00740-x.
short: R.J. Cubero, M. Marsili, Y. Roudi, Journal of Computational Neuroscience
48 (2020) 85–102.
date_created: 2020-01-28T10:34:00Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2023-08-17T14:35:22Z
day: '01'
ddc:
- '004'
- '519'
- '570'
department:
- _id: SaSi
doi: 10.1007/s10827-020-00740-x
ec_funded: 1
external_id:
isi:
- '000515321800006'
file:
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creator: rcubero
date_created: 2020-01-28T09:31:09Z
date_updated: 2020-07-14T12:47:56Z
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file_name: 10827_2020_740_MOESM1_ESM.pdf
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file_size: 3257880
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file_date_updated: 2020-07-14T12:47:56Z
has_accepted_license: '1'
intvolume: ' 48'
isi: 1
keyword:
- Time series analysis
- Multiple time scale analysis
- Spike train data
- Information theory
- Bayesian decoding
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 85-102
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Computational Neuroscience
publication_identifier:
eissn:
- 1573-6873
issn:
- 0929-5313
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multiscale relevance and informative encoding in neuronal spike trains
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: 48
year: '2020'
...
---
_id: '7383'
abstract:
- lang: eng
text: Organisms cope with change by employing transcriptional regulators. However,
when faced with rare environments, the evolution of transcriptional regulators
and their promoters may be too slow. We ask whether the intrinsic instability
of gene duplication and amplification provides a generic alternative to canonical
gene regulation. By real-time monitoring of gene copy number mutations in E. coli,
we show that gene duplications and amplifications enable adaptation to fluctuating
environments by rapidly generating copy number, and hence expression level, polymorphism.
This ‘amplification-mediated gene expression tuning’ occurs on timescales similar
to canonical gene regulation and can deal with rapid environmental changes. Mathematical
modeling shows that amplifications also tune gene expression in stochastic environments
where transcription factor-based schemes are hard to evolve or maintain. The fleeting
nature of gene amplifications gives rise to a generic population-level mechanism
that relies on genetic heterogeneity to rapidly tune expression of any gene, without
leaving any genomic signature.
article_processing_charge: No
author:
- first_name: Rok
full_name: Grah, Rok
id: 483E70DE-F248-11E8-B48F-1D18A9856A87
last_name: Grah
orcid: 0000-0003-2539-3560
citation:
ama: 'Grah R. Matlab scripts for the Paper: Gene Amplification as a Form of Population-Level
Gene Expression regulation. 2020. doi:10.15479/AT:ISTA:7383'
apa: 'Grah, R. (2020). Matlab scripts for the Paper: Gene Amplification as a Form
of Population-Level Gene Expression regulation. Institute of Science and Technology
Austria. https://doi.org/10.15479/AT:ISTA:7383'
chicago: 'Grah, Rok. “Matlab Scripts for the Paper: Gene Amplification as a Form
of Population-Level Gene Expression Regulation.” Institute of Science and Technology
Austria, 2020. https://doi.org/10.15479/AT:ISTA:7383.'
ieee: 'R. Grah, “Matlab scripts for the Paper: Gene Amplification as a Form of Population-Level
Gene Expression regulation.” Institute of Science and Technology Austria, 2020.'
ista: 'Grah R. 2020. Matlab scripts for the Paper: Gene Amplification as a Form
of Population-Level Gene Expression regulation, Institute of Science and Technology
Austria, 10.15479/AT:ISTA:7383.'
mla: 'Grah, Rok. Matlab Scripts for the Paper: Gene Amplification as a Form of
Population-Level Gene Expression Regulation. Institute of Science and Technology
Austria, 2020, doi:10.15479/AT:ISTA:7383.'
short: R. Grah, (2020).
contributor:
- contributor_type: project_leader
first_name: Calin C
id: 47F8433E-F248-11E8-B48F-1D18A9856A87
last_name: Guet
orcid: 0000-0001-6220-2052
date_created: 2020-01-28T10:41:49Z
date_published: 2020-01-28T00:00:00Z
date_updated: 2024-02-21T12:42:31Z
day: '28'
department:
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- _id: GaTk
doi: 10.15479/AT:ISTA:7383
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file_name: READ_ME_MAIN.txt
file_size: 962
relation: main_file
file_date_updated: 2020-07-14T12:47:57Z
has_accepted_license: '1'
keyword:
- Matlab scripts
- analysis of microfluidics
- mathematical model
month: '01'
oa: 1
oa_version: Published Version
publisher: Institute of Science and Technology Austria
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status: public
title: 'Matlab scripts for the Paper: Gene Amplification as a Form of Population-Level
Gene Expression regulation'
type: research_data
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2020'
...