---
_id: '181'
abstract:
- lang: eng
text: We consider large random matrices X with centered, independent entries but
possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for
f, g functions analytic on the spectrum of X. We use these results to compute
the long time asymptotics for systems of coupled di erential equations with random
coe cients. We show that when the coupling is critical, the norm squared of the
solution decays like t−1/2.
acknowledgement: The work of the second author was also partially supported by the
Hausdorff Center of Mathematics.
article_processing_charge: No
author:
- 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
- first_name: David T
full_name: Renfrew, David T
id: 4845BF6A-F248-11E8-B48F-1D18A9856A87
last_name: Renfrew
orcid: 0000-0003-3493-121X
citation:
ama: Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled
differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290.
doi:10.1137/17M1143125
apa: Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for
systems of randomly coupled differential equations. SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125
chicago: Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for
Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.
ieee: L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of
randomly coupled differential equations,” SIAM Journal on Mathematical Analysis,
vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290,
2018.
ista: Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly
coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3),
3271–3290.
mla: Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential
Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society
for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.
short: L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis
50 (2018) 3271–3290.
date_created: 2018-12-11T11:45:03Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2023-09-15T12:05:52Z
day: '01'
department:
- _id: LaEr
doi: 10.1137/17M1143125
ec_funded: 1
external_id:
arxiv:
- '1708.01546'
isi:
- '000437018500032'
intvolume: ' 50'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.01546
month: '01'
oa: 1
oa_version: Published Version
page: 3271 - 3290
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 258F40A4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02080
name: Structured Non-Hermitian Random Matrices
publication: SIAM Journal on Mathematical Analysis
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7740'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Power law decay for systems of randomly coupled differential equations
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 50
year: '2018'
...
---
_id: '322'
abstract:
- lang: eng
text: We construct quantizations of multiplicative hypertoric varieties using an
algebra of q-difference operators on affine space, where q is a root of unity
in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the
multiplicative hypertoric variety and admits an explicit finite étale splitting.
The global sections of this Azumaya algebra is a hypertoric quantum group, and
we prove a localization theorem. We introduce a general framework of Frobenius
quantum moment maps and their Hamiltonian reductions; our results shed light on
an instance of this framework.
acknowledgement: "National Science Foundation: Graduate Research Fellowship and grant
No.0932078000; ERC Advanced Grant “Arithmetic and Physics of Higgs moduli spaces”
No. 320593 \r\nThe author is grateful to David Jordan for suggesting this project
and providing guidance throughout, particularly for the formulation of Frobenius
quantum moment maps and key ideas in the proofs of Theorems 3.12 and 4.8. Special
thanks to David Ben-Zvi (the author's PhD advisor) for numerous discussions and
constant encouragement, and for suggesting the term ‘hypertoric quantum group.’
Many results appearing in the current paper were proven independently by Nicholas
Cooney; the author is grateful to Nicholas for sharing his insight on various topics,
including Proposition 3.8. The author also thanks Nicholas Proudfoot for relating
the definition of multiplicative hypertoric varieties, as well as the content of
Remark 2.14. The author also benefited immensely from the close reading and detailed
comments of an anonymous referee, and from conversations with Justin Hilburn, Kobi
Kremnitzer, Michael McBreen, Tom Nevins, Travis Schedler, and Ben Webster. \r\n\r\n\r\n\r\n"
article_processing_charge: No
author:
- first_name: Iordan V
full_name: Ganev, Iordan V
id: 447491B8-F248-11E8-B48F-1D18A9856A87
last_name: Ganev
citation:
ama: Ganev IV. Quantizations of multiplicative hypertoric varieties at a root of
unity. Journal of Algebra. 2018;506:92-128. doi:10.1016/j.jalgebra.2018.03.015
apa: Ganev, I. V. (2018). Quantizations of multiplicative hypertoric varieties at
a root of unity. Journal of Algebra. World Scientific Publishing. https://doi.org/10.1016/j.jalgebra.2018.03.015
chicago: Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties
at a Root of Unity.” Journal of Algebra. World Scientific Publishing, 2018.
https://doi.org/10.1016/j.jalgebra.2018.03.015.
ieee: I. V. Ganev, “Quantizations of multiplicative hypertoric varieties at a root
of unity,” Journal of Algebra, vol. 506. World Scientific Publishing, pp.
92–128, 2018.
ista: Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a
root of unity. Journal of Algebra. 506, 92–128.
mla: Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a
Root of Unity.” Journal of Algebra, vol. 506, World Scientific Publishing,
2018, pp. 92–128, doi:10.1016/j.jalgebra.2018.03.015.
short: I.V. Ganev, Journal of Algebra 506 (2018) 92–128.
date_created: 2018-12-11T11:45:49Z
date_published: 2018-07-15T00:00:00Z
date_updated: 2023-09-15T12:08:38Z
day: '15'
department:
- _id: TaHa
doi: 10.1016/j.jalgebra.2018.03.015
ec_funded: 1
external_id:
arxiv:
- '1412.7211'
isi:
- '000433270600005'
intvolume: ' 506'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1412.7211
month: '07'
oa: 1
oa_version: Preprint
page: 92 - 128
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Journal of Algebra
publication_status: published
publisher: World Scientific Publishing
publist_id: '7543'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantizations of multiplicative hypertoric varieties at a root of unity
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 506
year: '2018'
...
---
_id: '9831'
abstract:
- lang: eng
text: 'Implementation of the inference method in Matlab, including three applications
of the method: The first one for the model of ant motion, the second one for bacterial
chemotaxis, and the third one for the motion of fish.'
article_processing_charge: No
author:
- first_name: Katarína
full_name: Bod’Ová, Katarína
last_name: Bod’Ová
- first_name: Gabriel
full_name: Mitchell, Gabriel
id: 315BCD80-F248-11E8-B48F-1D18A9856A87
last_name: Mitchell
- first_name: Roy
full_name: Harpaz, Roy
last_name: Harpaz
- first_name: Elad
full_name: Schneidman, Elad
last_name: Schneidman
- first_name: Gašper
full_name: Tkačik, Gašper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkačik
orcid: 0000-0002-6699-1455
citation:
ama: Bod’Ová K, Mitchell G, Harpaz R, Schneidman E, Tkačik G. Implementation of
the inference method in Matlab. 2018. doi:10.1371/journal.pone.0193049.s001
apa: Bod’Ová, K., Mitchell, G., Harpaz, R., Schneidman, E., & Tkačik, G. (2018).
Implementation of the inference method in Matlab. Public Library of Science. https://doi.org/10.1371/journal.pone.0193049.s001
chicago: Bod’Ová, Katarína, Gabriel Mitchell, Roy Harpaz, Elad Schneidman, and Gašper
Tkačik. “Implementation of the Inference Method in Matlab.” Public Library of
Science, 2018. https://doi.org/10.1371/journal.pone.0193049.s001.
ieee: K. Bod’Ová, G. Mitchell, R. Harpaz, E. Schneidman, and G. Tkačik, “Implementation
of the inference method in Matlab.” Public Library of Science, 2018.
ista: Bod’Ová K, Mitchell G, Harpaz R, Schneidman E, Tkačik G. 2018. Implementation
of the inference method in Matlab, Public Library of Science, 10.1371/journal.pone.0193049.s001.
mla: Bod’Ová, Katarína, et al. Implementation of the Inference Method in Matlab.
Public Library of Science, 2018, doi:10.1371/journal.pone.0193049.s001.
short: K. Bod’Ová, G. Mitchell, R. Harpaz, E. Schneidman, G. Tkačik, (2018).
date_created: 2021-08-09T07:01:24Z
date_published: 2018-03-07T00:00:00Z
date_updated: 2023-09-15T12:06:18Z
day: '07'
department:
- _id: GaTk
doi: 10.1371/journal.pone.0193049.s001
month: '03'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '406'
relation: used_in_publication
status: public
status: public
title: Implementation of the inference method in Matlab
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2018'
...
---
_id: '142'
abstract:
- lang: eng
text: We address the problem of analyzing the reachable set of a polynomial nonlinear
continuous system by over-approximating the flowpipe of its dynamics. The common
approach to tackle this problem is to perform a numerical integration over a given
time horizon based on Taylor expansion and interval arithmetic. However, this
method results to be very conservative when there is a large difference in speed
between trajectories as time progresses. In this paper, we propose to use combinations
of barrier functions, which we call piecewise barrier tube (PBT), to over-approximate
flowpipe. The basic idea of PBT is that for each segment of a flowpipe, a coarse
box which is big enough to contain the segment is constructed using sampled simulation
and then in the box we compute by linear programming a set of barrier functions
(called barrier tube or BT for short) which work together to form a tube surrounding
the flowpipe. The benefit of using PBT is that (1) BT is independent of time and
hence can avoid being stretched and deformed by time; and (2) a small number of
BTs can form a tight over-approximation for the flowpipe, which means that the
computation required to decide whether the BTs intersect the unsafe set can be
reduced significantly. We implemented a prototype called PBTS in C++. Experiments
on some benchmark systems show that our approach is effective.
acknowledgement: 'Austrian Science Fund FWF: S11402-N23, S11405-N23, Z211-N32'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Hui
full_name: Kong, Hui
id: 3BDE25AA-F248-11E8-B48F-1D18A9856A87
last_name: Kong
orcid: 0000-0002-3066-6941
- first_name: Ezio
full_name: Bartocci, Ezio
last_name: Bartocci
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Kong H, Bartocci E, Henzinger TA. Reachable set over-approximation for nonlinear
systems using piecewise barrier tubes. In: Vol 10981. Springer; 2018:449-467.
doi:10.1007/978-3-319-96145-3_24'
apa: 'Kong, H., Bartocci, E., & Henzinger, T. A. (2018). Reachable set over-approximation
for nonlinear systems using piecewise barrier tubes (Vol. 10981, pp. 449–467).
Presented at the CAV: Computer Aided Verification, Oxford, United Kingdom: Springer.
https://doi.org/10.1007/978-3-319-96145-3_24'
chicago: Kong, Hui, Ezio Bartocci, and Thomas A Henzinger. “Reachable Set Over-Approximation
for Nonlinear Systems Using Piecewise Barrier Tubes,” 10981:449–67. Springer,
2018. https://doi.org/10.1007/978-3-319-96145-3_24.
ieee: 'H. Kong, E. Bartocci, and T. A. Henzinger, “Reachable set over-approximation
for nonlinear systems using piecewise barrier tubes,” presented at the CAV: Computer
Aided Verification, Oxford, United Kingdom, 2018, vol. 10981, pp. 449–467.'
ista: 'Kong H, Bartocci E, Henzinger TA. 2018. Reachable set over-approximation
for nonlinear systems using piecewise barrier tubes. CAV: Computer Aided Verification,
LNCS, vol. 10981, 449–467.'
mla: Kong, Hui, et al. Reachable Set Over-Approximation for Nonlinear Systems
Using Piecewise Barrier Tubes. Vol. 10981, Springer, 2018, pp. 449–67, doi:10.1007/978-3-319-96145-3_24.
short: H. Kong, E. Bartocci, T.A. Henzinger, in:, Springer, 2018, pp. 449–467.
conference:
end_date: 2018-07-17
location: Oxford, United Kingdom
name: 'CAV: Computer Aided Verification'
start_date: 2018-07-14
date_created: 2018-12-11T11:44:51Z
date_published: 2018-07-18T00:00:00Z
date_updated: 2023-09-15T12:12:08Z
day: '18'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-319-96145-3_24
external_id:
isi:
- '000491481600024'
file:
- access_level: open_access
checksum: fd95e8026deacef3dc752a733bb9355f
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T15:57:06Z
date_updated: 2020-07-14T12:44:53Z
file_id: '5718'
file_name: 2018_LNCS_Kong.pdf
file_size: 5591566
relation: main_file
file_date_updated: 2020-07-14T12:44:53Z
has_accepted_license: '1'
intvolume: ' 10981'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 449 - 467
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication_status: published
publisher: Springer
publist_id: '7781'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Reachable set over-approximation for nonlinear systems using piecewise barrier
tubes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 10981
year: '2018'
...
---
_id: '427'
abstract:
- lang: eng
text: We investigate the quantum interference induced shifts between energetically
close states in highly charged ions, with the energy structure being observed
by laser spectroscopy. In this work, we focus on hyperfine states of lithiumlike
heavy-Z isotopes and quantify how much quantum interference changes the observed
transition frequencies. The process of photon excitation and subsequent photon
decay for the transition 2s→2p→2s is implemented with fully relativistic and full-multipole
frameworks, which are relevant for such relativistic atomic systems. We consider
the isotopes Pb79+207 and Bi80+209 due to experimental interest, as well as other
examples of isotopes with lower Z, namely Pr56+141 and Ho64+165. We conclude that
quantum interference can induce shifts up to 11% of the linewidth in the measurable
resonances of the considered isotopes, if interference between resonances is neglected.
The inclusion of relativity decreases the cross section by 35%, mainly due to
the complete retardation form of the electric dipole multipole. However, the contribution
of the next higher multipoles (e.g., magnetic quadrupole) to the cross section
is negligible. This makes the contribution of relativity and higher-order multipoles
to the quantum interference induced shifts a minor effect, even for heavy-Z elements.
acknowledgement: "This work was funded by the Portuguese Fundação para a Ciência e
a Tecnologia (FCT/MCTES/PIDDAC) under Grant No. UID/FIS/04559/2013 (LIBPhys). P.A.
acknowledges the support of the FCT, under Contract No. SFRH/BPD/92329/2013. L.S.
acknowledges financial support from the People Programme (Marie Curie Actions) of
the European Union's Seventh Framework Programme (FP7/2007-2013) under REA Grant
Agreement No. (291734). Laboratoire Kastler Brossel (LKB) is “Unité Mixte de Recherche
de Sorbonne Université, de ENS-PSL Research University, du Collège de France et
du CNRS No. 8552.” APPENDIX:\r\n"
article_number: '022510'
article_processing_charge: No
article_type: original
author:
- first_name: Pedro
full_name: Amaro, Pedro
last_name: Amaro
- first_name: Ulisses
full_name: Loureiro, Ulisses
last_name: Loureiro
- first_name: Laleh
full_name: Safari, Laleh
id: 3C325E5E-F248-11E8-B48F-1D18A9856A87
last_name: Safari
- first_name: Filippo
full_name: Fratini, Filippo
last_name: Fratini
- first_name: Paul
full_name: Indelicato, Paul
last_name: Indelicato
- first_name: Thomas
full_name: Stöhlker, Thomas
last_name: Stöhlker
- first_name: José
full_name: Santos, José
last_name: Santos
citation:
ama: Amaro P, Loureiro U, Safari L, et al. Quantum interference in laser spectroscopy
of highly charged lithiumlike ions. Physical Review A - Atomic, Molecular,
and Optical Physics. 2018;97(2). doi:10.1103/PhysRevA.97.022510
apa: Amaro, P., Loureiro, U., Safari, L., Fratini, F., Indelicato, P., Stöhlker,
T., & Santos, J. (2018). Quantum interference in laser spectroscopy of highly
charged lithiumlike ions. Physical Review A - Atomic, Molecular, and Optical
Physics. American Physical Society. https://doi.org/10.1103/PhysRevA.97.022510
chicago: Amaro, Pedro, Ulisses Loureiro, Laleh Safari, Filippo Fratini, Paul Indelicato,
Thomas Stöhlker, and José Santos. “Quantum Interference in Laser Spectroscopy
of Highly Charged Lithiumlike Ions.” Physical Review A - Atomic, Molecular,
and Optical Physics. American Physical Society, 2018. https://doi.org/10.1103/PhysRevA.97.022510.
ieee: P. Amaro et al., “Quantum interference in laser spectroscopy of highly
charged lithiumlike ions,” Physical Review A - Atomic, Molecular, and Optical
Physics, vol. 97, no. 2. American Physical Society, 2018.
ista: Amaro P, Loureiro U, Safari L, Fratini F, Indelicato P, Stöhlker T, Santos
J. 2018. Quantum interference in laser spectroscopy of highly charged lithiumlike
ions. Physical Review A - Atomic, Molecular, and Optical Physics. 97(2), 022510.
mla: Amaro, Pedro, et al. “Quantum Interference in Laser Spectroscopy of Highly
Charged Lithiumlike Ions.” Physical Review A - Atomic, Molecular, and Optical
Physics, vol. 97, no. 2, 022510, American Physical Society, 2018, doi:10.1103/PhysRevA.97.022510.
short: P. Amaro, U. Loureiro, L. Safari, F. Fratini, P. Indelicato, T. Stöhlker,
J. Santos, Physical Review A - Atomic, Molecular, and Optical Physics 97 (2018).
date_created: 2018-12-11T11:46:25Z
date_published: 2018-02-21T00:00:00Z
date_updated: 2023-09-15T12:09:35Z
day: '21'
department:
- _id: MiLe
doi: 10.1103/PhysRevA.97.022510
ec_funded: 1
external_id:
arxiv:
- '1802.07920'
isi:
- '000425601000004'
intvolume: ' 97'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1802.07920
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: ' Physical Review A - Atomic, Molecular, and Optical Physics'
publication_status: published
publisher: American Physical Society
publist_id: '7396'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantum interference in laser spectroscopy of highly charged lithiumlike ions
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 97
year: '2018'
...