---
_id: '10328'
abstract:
- lang: eng
text: We discus noise channels in coherent electro-optic up-conversion between microwave
and optical fields, in particular due to optical heating. We also report on a
novel configuration, which promises to be flexible and highly efficient.
alternative_title:
- OSA Technical Digest
article_number: QTu8A.1
article_processing_charge: No
author:
- first_name: Nicholas J.
full_name: Lambert, Nicholas J.
last_name: Lambert
- first_name: Sonia
full_name: Mobassem, Sonia
last_name: Mobassem
- first_name: Alfredo R
full_name: Rueda Sanchez, Alfredo R
id: 3B82B0F8-F248-11E8-B48F-1D18A9856A87
last_name: Rueda Sanchez
orcid: 0000-0001-6249-5860
- first_name: Harald G.L.
full_name: Schwefel, Harald G.L.
last_name: Schwefel
citation:
ama: 'Lambert NJ, Mobassem S, Rueda Sanchez AR, Schwefel HGL. New designs and noise
channels in electro-optic microwave to optical up-conversion. In: OSA Quantum
2.0 Conference. Optica Publishing Group; 2020. doi:10.1364/QUANTUM.2020.QTu8A.1'
apa: 'Lambert, N. J., Mobassem, S., Rueda Sanchez, A. R., & Schwefel, H. G.
L. (2020). New designs and noise channels in electro-optic microwave to optical
up-conversion. In OSA Quantum 2.0 Conference. Washington, DC, United States:
Optica Publishing Group. https://doi.org/10.1364/QUANTUM.2020.QTu8A.1'
chicago: Lambert, Nicholas J., Sonia Mobassem, Alfredo R Rueda Sanchez, and Harald
G.L. Schwefel. “New Designs and Noise Channels in Electro-Optic Microwave to Optical
up-Conversion.” In OSA Quantum 2.0 Conference. Optica Publishing Group,
2020. https://doi.org/10.1364/QUANTUM.2020.QTu8A.1.
ieee: N. J. Lambert, S. Mobassem, A. R. Rueda Sanchez, and H. G. L. Schwefel, “New
designs and noise channels in electro-optic microwave to optical up-conversion,”
in OSA Quantum 2.0 Conference, Washington, DC, United States, 2020.
ista: 'Lambert NJ, Mobassem S, Rueda Sanchez AR, Schwefel HGL. 2020. New designs
and noise channels in electro-optic microwave to optical up-conversion. OSA Quantum
2.0 Conference. OSA: Optical Society of America, OSA Technical Digest, , QTu8A.1.'
mla: Lambert, Nicholas J., et al. “New Designs and Noise Channels in Electro-Optic
Microwave to Optical up-Conversion.” OSA Quantum 2.0 Conference, QTu8A.1,
Optica Publishing Group, 2020, doi:10.1364/QUANTUM.2020.QTu8A.1.
short: N.J. Lambert, S. Mobassem, A.R. Rueda Sanchez, H.G.L. Schwefel, in:, OSA
Quantum 2.0 Conference, Optica Publishing Group, 2020.
conference:
end_date: 2020-09-17
location: Washington, DC, United States
name: 'OSA: Optical Society of America'
start_date: 2020-09-14
date_created: 2021-11-21T23:01:31Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2023-10-18T08:32:34Z
day: '01'
department:
- _id: JoFi
doi: 10.1364/QUANTUM.2020.QTu8A.1
language:
- iso: eng
month: '01'
oa_version: None
publication: OSA Quantum 2.0 Conference
publication_identifier:
isbn:
- 9-781-5575-2820-9
publication_status: published
publisher: Optica Publishing Group
quality_controlled: '1'
scopus_import: '1'
status: public
title: New designs and noise channels in electro-optic microwave to optical up-conversion
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2020'
...
---
_id: '9633'
abstract:
- lang: eng
text: The search for biologically faithful synaptic plasticity rules has resulted
in a large body of models. They are usually inspired by – and fitted to – experimental
data, but they rarely produce neural dynamics that serve complex functions. These
failures suggest that current plasticity models are still under-constrained by
existing data. Here, we present an alternative approach that uses meta-learning
to discover plausible synaptic plasticity rules. Instead of experimental data,
the rules are constrained by the functions they implement and the structure they
are meant to produce. Briefly, we parameterize synaptic plasticity rules by a
Volterra expansion and then use supervised learning methods (gradient descent
or evolutionary strategies) to minimize a problem-dependent loss function that
quantifies how effectively a candidate plasticity rule transforms an initially
random network into one with the desired function. We first validate our approach
by re-discovering previously described plasticity rules, starting at the single-neuron
level and “Oja’s rule”, a simple Hebbian plasticity rule that captures the direction
of most variability of inputs to a neuron (i.e., the first principal component).
We expand the problem to the network level and ask the framework to find Oja’s
rule together with an anti-Hebbian rule such that an initially random two-layer
firing-rate network will recover several principal components of the input space
after learning. Next, we move to networks of integrate-and-fire neurons with plastic
inhibitory afferents. We train for rules that achieve a target firing rate by
countering tuned excitation. Our algorithm discovers a specific subset of the
manifold of rules that can solve this task. Our work is a proof of principle of
an automated and unbiased approach to unveil synaptic plasticity rules that obey
biological constraints and can solve complex functions.
acknowledgement: We would like to thank Chaitanya Chintaluri, Georgia Christodoulou,
Bill Podlaski and Merima Šabanovic for useful discussions and comments. This work
was supported by a Wellcome Trust ´ Senior Research Fellowship (214316/Z/18/Z),
a BBSRC grant (BB/N019512/1), an ERC consolidator Grant (SYNAPSEEK), a Leverhulme
Trust Project Grant (RPG-2016-446), and funding from École Polytechnique, Paris.
article_processing_charge: No
author:
- first_name: Basile J
full_name: Confavreux, Basile J
id: C7610134-B532-11EA-BD9F-F5753DDC885E
last_name: Confavreux
- first_name: Friedemann
full_name: Zenke, Friedemann
last_name: Zenke
- first_name: Everton J.
full_name: Agnes, Everton J.
last_name: Agnes
- first_name: Timothy
full_name: Lillicrap, Timothy
last_name: Lillicrap
- first_name: Tim P
full_name: Vogels, Tim P
id: CB6FF8D2-008F-11EA-8E08-2637E6697425
last_name: Vogels
orcid: 0000-0003-3295-6181
citation:
ama: 'Confavreux BJ, Zenke F, Agnes EJ, Lillicrap T, Vogels TP. A meta-learning
approach to (re)discover plasticity rules that carve a desired function into a
neural network. In: Advances in Neural Information Processing Systems.
Vol 33. ; 2020:16398-16408.'
apa: Confavreux, B. J., Zenke, F., Agnes, E. J., Lillicrap, T., & Vogels, T.
P. (2020). A meta-learning approach to (re)discover plasticity rules that carve
a desired function into a neural network. In Advances in Neural Information
Processing Systems (Vol. 33, pp. 16398–16408). Vancouver, Canada.
chicago: Confavreux, Basile J, Friedemann Zenke, Everton J. Agnes, Timothy Lillicrap,
and Tim P Vogels. “A Meta-Learning Approach to (Re)Discover Plasticity Rules That
Carve a Desired Function into a Neural Network.” In Advances in Neural Information
Processing Systems, 33:16398–408, 2020.
ieee: B. J. Confavreux, F. Zenke, E. J. Agnes, T. Lillicrap, and T. P. Vogels, “A
meta-learning approach to (re)discover plasticity rules that carve a desired function
into a neural network,” in Advances in Neural Information Processing Systems,
Vancouver, Canada, 2020, vol. 33, pp. 16398–16408.
ista: 'Confavreux BJ, Zenke F, Agnes EJ, Lillicrap T, Vogels TP. 2020. A meta-learning
approach to (re)discover plasticity rules that carve a desired function into a
neural network. Advances in Neural Information Processing Systems. NeurIPS: Conference
on Neural Information Processing Systems vol. 33, 16398–16408.'
mla: Confavreux, Basile J., et al. “A Meta-Learning Approach to (Re)Discover Plasticity
Rules That Carve a Desired Function into a Neural Network.” Advances in Neural
Information Processing Systems, vol. 33, 2020, pp. 16398–408.
short: B.J. Confavreux, F. Zenke, E.J. Agnes, T. Lillicrap, T.P. Vogels, in:, Advances
in Neural Information Processing Systems, 2020, pp. 16398–16408.
conference:
end_date: 2020-12-12
location: Vancouver, Canada
name: 'NeurIPS: Conference on Neural Information Processing Systems'
start_date: 2020-12-06
date_created: 2021-07-04T22:01:27Z
date_published: 2020-12-06T00:00:00Z
date_updated: 2023-10-18T09:20:55Z
day: '06'
department:
- _id: TiVo
ec_funded: 1
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://proceedings.neurips.cc/paper/2020/hash/bdbd5ebfde4934142c8a88e7a3796cd5-Abstract.html
month: '12'
oa: 1
oa_version: Published Version
page: 16398-16408
project:
- _id: c084a126-5a5b-11eb-8a69-d75314a70a87
grant_number: 214316/Z/18/Z
name: What’s in a memory? Spatiotemporal dynamics in strongly coupled recurrent
neuronal networks.
- _id: 0aacfa84-070f-11eb-9043-d7eb2c709234
call_identifier: H2020
grant_number: '819603'
name: Learning the shape of synaptic plasticity rules for neuronal architectures
and function through machine learning.
publication: Advances in Neural Information Processing Systems
publication_identifier:
issn:
- 1049-5258
publication_status: published
quality_controlled: '1'
related_material:
link:
- relation: is_continued_by
url: https://doi.org/10.1101/2020.10.24.353409
record:
- id: '14422'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: A meta-learning approach to (re)discover plasticity rules that carve a desired
function into a neural network
type: conference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 33
year: '2020'
...
---
_id: '8943'
abstract:
- lang: eng
text: The widely used non-steroidal anti-inflammatory drugs (NSAIDs) are derivatives
of the phytohormone salicylic acid (SA). SA is well known to regulate plant immunity
and development, whereas there have been few reports focusing on the effects of
NSAIDs in plants. Our studies here reveal that NSAIDs exhibit largely overlapping
physiological activities to SA in the model plant Arabidopsis. NSAID treatments
lead to shorter and agravitropic primary roots and inhibited lateral root organogenesis.
Notably, in addition to the SA-like action, which in roots involves binding to
the protein phosphatase 2A (PP2A), NSAIDs also exhibit PP2A-independent effects.
Cell biological and biochemical analyses reveal that many NSAIDs bind directly
to and inhibit the chaperone activity of TWISTED DWARF1, thereby regulating actin
cytoskeleton dynamics and subsequent endosomal trafficking. Our findings uncover
an unexpected bioactivity of human pharmaceuticals in plants and provide insights
into the molecular mechanism underlying the cellular action of this class of anti-inflammatory
compounds.
acknowledged_ssus:
- _id: LifeSc
- _id: Bio
acknowledgement: "We thank Drs. Sebastian Bednarek (University of Wisconsin-Madison),
Niko Geldner (University of Lausanne), and Karin Schumacher (Heidelberg University)
for kindly sharing published Arabidopsis lines; Dr. Satoshi Naramoto for the pPIN2::PIN2-GFP;
pVHA-a1::VHA-a1-mRFP reporter; the staff at the Life Science Facility and Bioimaging
Facility, Monika Hrtyan, and Dorota Jaworska at IST Austria for technical support;
and Drs. Su Tang (Texas A&M University),\r\nMelinda Abas (BOKU), Eva Benkova´ (IST
Austria), Christian Luschnig (BOKU), Bartel Vanholme (Gent University), and the
Friml group for valuable discussions. The research leading to these findings was
funded by the European Union’s Horizon 2020 program (ERC grant agreement no. 742985,
to J.F.), the People Programme (Marie Curie Actions) of the European Union’s Seventh
Framework Programme (FP7/2007-2013) under REA grant agreement no.\r\n291734, the
Swiss National Funds (31003A_165877, to M.G.), the Ministry of Education, Youth,
and Sports of the Czech Republic (project no. CZ.02.1.01/0.0/0.0/16_019/0000738,
EU Operational Programme ‘‘Research, development and education and Centre for Plant
Experimental Biology’’), and the EU Operational Programme Prague - Competitiveness
(project no. CZ.2.16/3.1.00/21519). S.T. was funded by a European Molecular Biology
Organization (EMBO) long-term postdoctoral fellowship (ALTF 723-2015). X.Z. was
partly supported by a PhD scholarship from the China Scholarship Council."
article_number: '108463'
article_processing_charge: Yes
article_type: original
author:
- first_name: Shutang
full_name: Tan, Shutang
id: 2DE75584-F248-11E8-B48F-1D18A9856A87
last_name: Tan
orcid: 0000-0002-0471-8285
- first_name: Martin
full_name: Di Donato, Martin
last_name: Di Donato
- first_name: Matous
full_name: Glanc, Matous
id: 1AE1EA24-02D0-11E9-9BAA-DAF4881429F2
last_name: Glanc
orcid: 0000-0003-0619-7783
- first_name: Xixi
full_name: Zhang, Xixi
id: 61A66458-47E9-11EA-85BA-8AEAAF14E49A
last_name: Zhang
orcid: 0000-0001-7048-4627
- first_name: Petr
full_name: Klíma, Petr
last_name: Klíma
- first_name: Jie
full_name: Liu, Jie
last_name: Liu
- first_name: Aurélien
full_name: Bailly, Aurélien
last_name: Bailly
- first_name: Noel
full_name: Ferro, Noel
last_name: Ferro
- first_name: Jan
full_name: Petrášek, Jan
last_name: Petrášek
- first_name: Markus
full_name: Geisler, Markus
last_name: Geisler
- first_name: Jiří
full_name: Friml, Jiří
id: 4159519E-F248-11E8-B48F-1D18A9856A87
last_name: Friml
orcid: 0000-0002-8302-7596
citation:
ama: Tan S, Di Donato M, Glanc M, et al. Non-steroidal anti-inflammatory drugs target
TWISTED DWARF1-regulated actin dynamics and auxin transport-mediated plant development.
Cell Reports. 2020;33(9). doi:10.1016/j.celrep.2020.108463
apa: Tan, S., Di Donato, M., Glanc, M., Zhang, X., Klíma, P., Liu, J., … Friml,
J. (2020). Non-steroidal anti-inflammatory drugs target TWISTED DWARF1-regulated
actin dynamics and auxin transport-mediated plant development. Cell Reports.
Elsevier. https://doi.org/10.1016/j.celrep.2020.108463
chicago: Tan, Shutang, Martin Di Donato, Matous Glanc, Xixi Zhang, Petr Klíma, Jie
Liu, Aurélien Bailly, et al. “Non-Steroidal Anti-Inflammatory Drugs Target TWISTED
DWARF1-Regulated Actin Dynamics and Auxin Transport-Mediated Plant Development.”
Cell Reports. Elsevier, 2020. https://doi.org/10.1016/j.celrep.2020.108463.
ieee: S. Tan et al., “Non-steroidal anti-inflammatory drugs target TWISTED
DWARF1-regulated actin dynamics and auxin transport-mediated plant development,”
Cell Reports, vol. 33, no. 9. Elsevier, 2020.
ista: Tan S, Di Donato M, Glanc M, Zhang X, Klíma P, Liu J, Bailly A, Ferro N, Petrášek
J, Geisler M, Friml J. 2020. Non-steroidal anti-inflammatory drugs target TWISTED
DWARF1-regulated actin dynamics and auxin transport-mediated plant development.
Cell Reports. 33(9), 108463.
mla: Tan, Shutang, et al. “Non-Steroidal Anti-Inflammatory Drugs Target TWISTED
DWARF1-Regulated Actin Dynamics and Auxin Transport-Mediated Plant Development.”
Cell Reports, vol. 33, no. 9, 108463, Elsevier, 2020, doi:10.1016/j.celrep.2020.108463.
short: S. Tan, M. Di Donato, M. Glanc, X. Zhang, P. Klíma, J. Liu, A. Bailly, N.
Ferro, J. Petrášek, M. Geisler, J. Friml, Cell Reports 33 (2020).
date_created: 2020-12-13T23:01:21Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2023-11-16T13:03:31Z
day: '01'
ddc:
- '580'
department:
- _id: JiFr
doi: 10.1016/j.celrep.2020.108463
ec_funded: 1
external_id:
isi:
- '000595658100018'
pmid:
- '33264621'
file:
- access_level: open_access
checksum: ed18cba0fb48ed2e789381a54cc21904
content_type: application/pdf
creator: dernst
date_created: 2020-12-14T07:33:39Z
date_updated: 2020-12-14T07:33:39Z
file_id: '8948'
file_name: 2020_CellReports_Tan.pdf
file_size: 8056434
relation: main_file
success: 1
file_date_updated: 2020-12-14T07:33:39Z
has_accepted_license: '1'
intvolume: ' 33'
isi: 1
issue: '9'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 261099A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '742985'
name: Tracing Evolution of Auxin Transport and Polarity in Plants
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 256FEF10-B435-11E9-9278-68D0E5697425
grant_number: 723-2015
name: Long Term Fellowship
publication: Cell Reports
publication_identifier:
eissn:
- '22111247'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/plants-on-aspirin/
scopus_import: '1'
status: public
title: Non-steroidal anti-inflammatory drugs target TWISTED DWARF1-regulated actin
dynamics and auxin transport-mediated plant development
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: 33
year: '2020'
...
---
_id: '7932'
abstract:
- lang: eng
text: Pulsating flows through tubular geometries are laminar provided that velocities
are moderate. This in particular is also believed to apply to cardiovascular flows
where inertial forces are typically too low to sustain turbulence. On the other
hand, flow instabilities and fluctuating shear stresses are held responsible for
a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism
for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates.
Geometrical distortions of small, yet finite, amplitude are found to excite a
state consisting of helical vortices during flow deceleration. The resulting flow
pattern grows rapidly in magnitude, breaks down into turbulence, and eventually
returns to laminar when the flow accelerates. This scenario causes shear stress
fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions
can adversely affect blood vessels and have been shown to promote inflammation
and dysfunction of the shear stress-sensitive endothelial cell layer.
article_processing_charge: No
article_type: original
author:
- first_name: Duo
full_name: Xu, Duo
id: 3454D55E-F248-11E8-B48F-1D18A9856A87
last_name: Xu
- first_name: Atul
full_name: Varshney, Atul
id: 2A2006B2-F248-11E8-B48F-1D18A9856A87
last_name: Varshney
orcid: 0000-0002-3072-5999
- first_name: Xingyu
full_name: Ma, Xingyu
id: 34BADBA6-F248-11E8-B48F-1D18A9856A87
last_name: Ma
orcid: 0000-0002-0179-9737
- first_name: Baofang
full_name: Song, Baofang
last_name: Song
- first_name: Michael
full_name: Riedl, Michael
id: 3BE60946-F248-11E8-B48F-1D18A9856A87
last_name: Riedl
orcid: 0000-0003-4844-6311
- first_name: Marc
full_name: Avila, Marc
last_name: Avila
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: Xu D, Varshney A, Ma X, et al. Nonlinear hydrodynamic instability and turbulence
in pulsatile flow. Proceedings of the National Academy of Sciences of the United
States of America. 2020;117(21):11233-11239. doi:10.1073/pnas.1913716117
apa: Xu, D., Varshney, A., Ma, X., Song, B., Riedl, M., Avila, M., & Hof, B.
(2020). Nonlinear hydrodynamic instability and turbulence in pulsatile flow. Proceedings
of the National Academy of Sciences of the United States of America. National
Academy of Sciences. https://doi.org/10.1073/pnas.1913716117
chicago: Xu, Duo, Atul Varshney, Xingyu Ma, Baofang Song, Michael Riedl, Marc Avila,
and Björn Hof. “Nonlinear Hydrodynamic Instability and Turbulence in Pulsatile
Flow.” Proceedings of the National Academy of Sciences of the United States
of America. National Academy of Sciences, 2020. https://doi.org/10.1073/pnas.1913716117.
ieee: D. Xu et al., “Nonlinear hydrodynamic instability and turbulence in
pulsatile flow,” Proceedings of the National Academy of Sciences of the United
States of America, vol. 117, no. 21. National Academy of Sciences, pp. 11233–11239,
2020.
ista: Xu D, Varshney A, Ma X, Song B, Riedl M, Avila M, Hof B. 2020. Nonlinear hydrodynamic
instability and turbulence in pulsatile flow. Proceedings of the National Academy
of Sciences of the United States of America. 117(21), 11233–11239.
mla: Xu, Duo, et al. “Nonlinear Hydrodynamic Instability and Turbulence in Pulsatile
Flow.” Proceedings of the National Academy of Sciences of the United States
of America, vol. 117, no. 21, National Academy of Sciences, 2020, pp. 11233–39,
doi:10.1073/pnas.1913716117.
short: D. Xu, A. Varshney, X. Ma, B. Song, M. Riedl, M. Avila, B. Hof, Proceedings
of the National Academy of Sciences of the United States of America 117 (2020)
11233–11239.
date_created: 2020-06-07T22:00:51Z
date_published: 2020-05-26T00:00:00Z
date_updated: 2023-11-30T10:55:13Z
day: '26'
department:
- _id: BjHo
doi: 10.1073/pnas.1913716117
ec_funded: 1
external_id:
arxiv:
- '2005.11190'
isi:
- '000536797100014'
intvolume: ' 117'
isi: 1
issue: '21'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2005.11190
month: '05'
oa: 1
oa_version: Preprint
page: 11233-11239
project:
- _id: 238B8092-32DE-11EA-91FC-C7463DDC885E
call_identifier: FWF
grant_number: I04188
name: Instabilities in pulsating pipe flow of Newtonian and complex fluids
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Proceedings of the National Academy of Sciences of the United States
of America
publication_identifier:
eissn:
- '10916490'
issn:
- '00278424'
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/blood-flows-more-turbulent-than-previously-expected/
record:
- id: '12726'
relation: dissertation_contains
status: public
- id: '14530'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Nonlinear hydrodynamic instability and turbulence in pulsatile flow
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 117
year: '2020'
...
---
_id: '14694'
abstract:
- lang: eng
text: We study the unique solution m of the Dyson equation \( -m(z)^{-1} = z\1 -
a + S[m(z)] \) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies
in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving
linear operator on A. We show that m is the Stieltjes transform of a compactly
supported A-valued measure on R. Under suitable assumptions, we establish that
this measure has a uniformly 1/3-Hölder continuous density with respect to the
Lebesgue measure, which is supported on finitely many intervals, called bands.
In fact, the density is analytic inside the bands with a square-root growth at
the edges and internal cubic root cusps whenever the gap between two bands vanishes.
The shape of these singularities is universal and no other singularity may occur.
We give a precise asymptotic description of m near the singular points. These
asymptotics generalize the analysis at the regular edges given in the companion
paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated
random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020;
Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality
at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1,
No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math.
Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite
dimensional band mass formula from [the first author et al., loc. cit.] to the
von Neumann algebra setting by showing that the spectral mass of the bands is
topologically rigid under deformations and we conclude that these masses are quantized
in some important cases.
article_processing_charge: Yes
article_type: original
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral
bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780'
apa: 'Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear
self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS
Press. https://doi.org/10.4171/dm/780'
chicago: 'Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation
with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica.
EMS Press, 2020. https://doi.org/10.4171/dm/780.'
ieee: 'J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy:
Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press,
pp. 1421–1539, 2020.'
ista: 'Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy:
Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.'
mla: 'Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral
Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020,
pp. 1421–539, doi:10.4171/dm/780.'
short: J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.
date_created: 2023-12-18T10:37:43Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2023-12-18T10:46:09Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.4171/dm/780
external_id:
arxiv:
- '1804.07752'
file:
- access_level: open_access
checksum: 12aacc1d63b852ff9a51c1f6b218d4a6
content_type: application/pdf
creator: dernst
date_created: 2023-12-18T10:42:32Z
date_updated: 2023-12-18T10:42:32Z
file_id: '14695'
file_name: 2020_DocumentaMathematica_Alt.pdf
file_size: 1374708
relation: main_file
success: 1
file_date_updated: 2023-12-18T10:42:32Z
has_accepted_license: '1'
intvolume: ' 25'
keyword:
- General Mathematics
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1421-1539
publication: Documenta Mathematica
publication_identifier:
eissn:
- 1431-0643
issn:
- 1431-0635
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '6183'
relation: earlier_version
status: public
status: public
title: 'The Dyson equation with linear self-energy: Spectral bands, edges and cusps'
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: 25
year: '2020'
...