---
_id: '2320'
abstract:
- lang: eng
text: The binding of polarons, or its absence, is an old and subtle topic. After
defining the model we state some recent theorems of ours. First, the transition
from many-body collapse to the existence of a thermodynamic limit for N polarons
occurs precisely at U = 2α, where U is the electronic Coulomb repulsion and α
is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron
binding of any kind. We also discuss the Pekar-Tomasevich approximation to the
ground state energy, which is valid for large α. Finally, we derive exact results,
not reported before, about the one-dimensional toy model introduced by E. P. Gross.
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Lawrence
full_name: Thomas, Lawrence E
last_name: Thomas
citation:
ama: 'Frank R, Lieb É, Seiringer R, Thomas L. Binding, stability, and non-binding
of multi-polaron systems. In: World Scientific Publishing; 2011:21-32. doi:10.1142/9789814350365_0002'
apa: 'Frank, R., Lieb, É., Seiringer, R., & Thomas, L. (2011). Binding, stability,
and non-binding of multi-polaron systems (pp. 21–32). Presented at the QMath:
Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1142/9789814350365_0002'
chicago: Frank, Rupert, Élliott Lieb, Robert Seiringer, and Lawrence Thomas. “Binding,
Stability, and Non-Binding of Multi-Polaron Systems,” 21–32. World Scientific
Publishing, 2011. https://doi.org/10.1142/9789814350365_0002.
ieee: 'R. Frank, É. Lieb, R. Seiringer, and L. Thomas, “Binding, stability, and
non-binding of multi-polaron systems,” presented at the QMath: Mathematical Results
in Quantum Physics, 2011, pp. 21–32.'
ista: 'Frank R, Lieb É, Seiringer R, Thomas L. 2011. Binding, stability, and non-binding
of multi-polaron systems. QMath: Mathematical Results in Quantum Physics, 21–32.'
mla: Frank, Rupert, et al. Binding, Stability, and Non-Binding of Multi-Polaron
Systems. World Scientific Publishing, 2011, pp. 21–32, doi:10.1142/9789814350365_0002.
short: R. Frank, É. Lieb, R. Seiringer, L. Thomas, in:, World Scientific Publishing,
2011, pp. 21–32.
conference:
name: 'QMath: Mathematical Results in Quantum Physics'
date_created: 2018-12-11T11:56:58Z
date_published: 2011-05-26T00:00:00Z
date_updated: 2021-01-12T06:56:45Z
day: '26'
doi: 10.1142/9789814350365_0002
extern: 1
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1010.0737
month: '05'
oa: 1
page: 21 - 32
publication_status: published
publisher: World Scientific Publishing
publist_id: '4607'
quality_controlled: 0
status: public
title: Binding, stability, and non-binding of multi-polaron systems
type: conference
year: '2011'
...
---
_id: '2321'
abstract:
- lang: eng
text: We derive a sharp bound on the location of non-positive eigenvalues of Schrödinger
operators on the half-line with complex-valued potentials.
alternative_title:
- 'Operator Theory: Advances and Applications'
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Ari
full_name: Laptev, Ari
last_name: Laptev
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Frank R, Laptev A, Seiringer R. A sharp bound on eigenvalues of Schrödinger
operators on the halfline with complex-valued potentials. In: Vol 214. Springer;
2011:39-44. doi:10.1007/978-3-7643-9994-8_3'
apa: 'Frank, R., Laptev, A., & Seiringer, R. (2011). A sharp bound on eigenvalues
of Schrödinger operators on the halfline with complex-valued potentials (Vol.
214, pp. 39–44). Presented at the OTAMP: Operator Theory, Analysis and Mathematical
Physics, Springer. https://doi.org/10.1007/978-3-7643-9994-8_3'
chicago: Frank, Rupert, Ari Laptev, and Robert Seiringer. “ A Sharp Bound on Eigenvalues
of Schrödinger Operators on the Halfline with Complex-Valued Potentials,” 214:39–44.
Springer, 2011. https://doi.org/10.1007/978-3-7643-9994-8_3.
ieee: 'R. Frank, A. Laptev, and R. Seiringer, “ A sharp bound on eigenvalues of
Schrödinger operators on the halfline with complex-valued potentials,” presented
at the OTAMP: Operator Theory, Analysis and Mathematical Physics, 2011, vol. 214,
pp. 39–44.'
ista: 'Frank R, Laptev A, Seiringer R. 2011. A sharp bound on eigenvalues of Schrödinger
operators on the halfline with complex-valued potentials. OTAMP: Operator Theory,
Analysis and Mathematical Physics, Operator Theory: Advances and Applications,
vol. 214, 39–44.'
mla: Frank, Rupert, et al. A Sharp Bound on Eigenvalues of Schrödinger Operators
on the Halfline with Complex-Valued Potentials. Vol. 214, Springer, 2011,
pp. 39–44, doi:10.1007/978-3-7643-9994-8_3.
short: R. Frank, A. Laptev, R. Seiringer, in:, Springer, 2011, pp. 39–44.
conference:
name: 'OTAMP: Operator Theory, Analysis and Mathematical Physics'
date_created: 2018-12-11T11:56:59Z
date_published: 2011-03-31T00:00:00Z
date_updated: 2021-01-12T06:56:46Z
day: '31'
doi: 10.1007/978-3-7643-9994-8_3
extern: 1
intvolume: ' 214'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/0903.2053
month: '03'
oa: 1
page: 39 - 44
publication_status: published
publisher: Springer
publist_id: '4606'
quality_controlled: 0
status: public
title: ' A sharp bound on eigenvalues of Schrödinger operators on the halfline with
complex-valued potentials'
type: conference
volume: 214
year: '2011'
...
---
_id: '233'
abstract:
- lang: eng
text: 'For an irreducible polynomial in at most two variables the problem of representing
power-free integers is investigated. '
acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council"
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: Browning TD. Power-free values of polynomials. Archiv der Mathematik.
2011;96(2):139-150. doi:10.1007/s00013-011-0224-7
apa: Browning, T. D. (2011). Power-free values of polynomials. Archiv Der Mathematik.
Birkhäuser. https://doi.org/10.1007/s00013-011-0224-7
chicago: Browning, Timothy D. “Power-Free Values of Polynomials.” Archiv Der
Mathematik. Birkhäuser, 2011. https://doi.org/10.1007/s00013-011-0224-7.
ieee: T. D. Browning, “Power-free values of polynomials,” Archiv der Mathematik,
vol. 96, no. 2. Birkhäuser, pp. 139–150, 2011.
ista: Browning TD. 2011. Power-free values of polynomials. Archiv der Mathematik.
96(2), 139–150.
mla: Browning, Timothy D. “Power-Free Values of Polynomials.” Archiv Der Mathematik,
vol. 96, no. 2, Birkhäuser, 2011, pp. 139–50, doi:10.1007/s00013-011-0224-7.
short: T.D. Browning, Archiv Der Mathematik 96 (2011) 139–150.
date_created: 2018-12-11T11:45:21Z
date_published: 2011-02-19T00:00:00Z
date_updated: 2021-01-12T06:56:49Z
day: '19'
doi: 10.1007/s00013-011-0224-7
extern: 1
intvolume: ' 96'
issue: '2'
month: '02'
page: 139 - 150
publication: Archiv der Mathematik
publication_status: published
publisher: Birkhäuser
publist_id: '7670'
quality_controlled: 0
status: public
title: Power-free values of polynomials
type: journal_article
volume: 96
year: '2011'
...
---
_id: '234'
abstract:
- lang: eng
text: We investigate the average order of the divisor function at values of binary
cubic forms that are reducible over Q and discuss some applications.
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: Browning TD. The divisor problem for binary cubic forms. Journal de Theorie
des Nombres de Bordeaux. 2011;23(3):579-602. doi:10.5802/jtnb.778
apa: Browning, T. D. (2011). The divisor problem for binary cubic forms. Journal
de Theorie Des Nombres de Bordeaux. Universite de Bordeaux. https://doi.org/10.5802/jtnb.778
chicago: Browning, Timothy D. “The Divisor Problem for Binary Cubic Forms.” Journal
de Theorie Des Nombres de Bordeaux. Universite de Bordeaux, 2011. https://doi.org/10.5802/jtnb.778.
ieee: T. D. Browning, “The divisor problem for binary cubic forms,” Journal de
Theorie des Nombres de Bordeaux, vol. 23, no. 3. Universite de Bordeaux, pp.
579–602, 2011.
ista: Browning TD. 2011. The divisor problem for binary cubic forms. Journal de
Theorie des Nombres de Bordeaux. 23(3), 579–602.
mla: Browning, Timothy D. “The Divisor Problem for Binary Cubic Forms.” Journal
de Theorie Des Nombres de Bordeaux, vol. 23, no. 3, Universite de Bordeaux,
2011, pp. 579–602, doi:10.5802/jtnb.778.
short: T.D. Browning, Journal de Theorie Des Nombres de Bordeaux 23 (2011) 579–602.
date_created: 2018-12-11T11:45:21Z
date_published: 2011-01-01T00:00:00Z
date_updated: 2021-01-12T06:56:53Z
day: '01'
doi: 10.5802/jtnb.778
extern: 1
intvolume: ' 23'
issue: '3'
month: '01'
page: 579 - 602
publication: Journal de Theorie des Nombres de Bordeaux
publication_status: published
publisher: Universite de Bordeaux
publist_id: '7671'
quality_controlled: 0
status: public
title: The divisor problem for binary cubic forms
type: journal_article
volume: 23
year: '2011'
...
---
_id: '235'
abstract:
- lang: eng
text: For given positive integers m and n, we consider the frequency of representations
of m/n as a sum of unit fractions.
article_processing_charge: No
article_type: original
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Christian
full_name: Elsholtz, Christian
last_name: Elsholtz
citation:
ama: Browning TD, Elsholtz C. The number of representations of rationals as a sum
of unit fractions. Illinois Journal of Mathematics. 2011;55(2):685-696.
apa: Browning, T. D., & Elsholtz, C. (2011). The number of representations of
rationals as a sum of unit fractions. Illinois Journal of Mathematics.
University of Illinois Press.
chicago: Browning, Timothy D, and Christian Elsholtz. “The Number of Representations
of Rationals as a Sum of Unit Fractions.” Illinois Journal of Mathematics.
University of Illinois Press, 2011.
ieee: T. D. Browning and C. Elsholtz, “The number of representations of rationals
as a sum of unit fractions,” Illinois Journal of Mathematics, vol. 55,
no. 2. University of Illinois Press, pp. 685–696, 2011.
ista: Browning TD, Elsholtz C. 2011. The number of representations of rationals
as a sum of unit fractions. Illinois Journal of Mathematics. 55(2), 685–696.
mla: Browning, Timothy D., and Christian Elsholtz. “The Number of Representations
of Rationals as a Sum of Unit Fractions.” Illinois Journal of Mathematics,
vol. 55, no. 2, University of Illinois Press, 2011, pp. 685–96.
short: T.D. Browning, C. Elsholtz, Illinois Journal of Mathematics 55 (2011) 685–696.
date_created: 2018-12-11T11:45:21Z
date_published: 2011-07-01T00:00:00Z
date_updated: 2021-01-12T06:56:57Z
day: '01'
extern: '1'
intvolume: ' 55'
issue: '2'
language:
- iso: eng
month: '07'
oa_version: None
page: 685 - 696
publication: Illinois Journal of Mathematics
publication_status: published
publisher: University of Illinois Press
publist_id: '7669'
quality_controlled: '1'
status: public
title: The number of representations of rationals as a sum of unit fractions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2011'
...
---
_id: '236'
abstract:
- lang: eng
text: An asymptotic formula is established for the number of Q-rational points of
bounded height on a nonsingular quartic Del Pezzo surface with a conic bundle
structure.
acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council"
author:
- first_name: Régis
full_name: de la Bretèche, Régis
last_name: De La Bretèche
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: De La Bretèche R, Browning TD. Manin’s conjecture for quartic Del Pezzo surfaces
with a conic fibration. Duke Mathematical Journal. 2011;160(1):1-69. doi:10.1215/00127094-1443466
apa: De La Bretèche, R., & Browning, T. D. (2011). Manin’s conjecture for quartic
Del Pezzo surfaces with a conic fibration. Duke Mathematical Journal. Duke
University Press. https://doi.org/10.1215/00127094-1443466
chicago: De La Bretèche, Régis, and Timothy D Browning. “Manin’s Conjecture for
Quartic Del Pezzo Surfaces with a Conic Fibration.” Duke Mathematical Journal.
Duke University Press, 2011. https://doi.org/10.1215/00127094-1443466.
ieee: R. De La Bretèche and T. D. Browning, “Manin’s conjecture for quartic Del
Pezzo surfaces with a conic fibration,” Duke Mathematical Journal, vol.
160, no. 1. Duke University Press, pp. 1–69, 2011.
ista: De La Bretèche R, Browning TD. 2011. Manin’s conjecture for quartic Del Pezzo
surfaces with a conic fibration. Duke Mathematical Journal. 160(1), 1–69.
mla: De La Bretèche, Régis, and Timothy D. Browning. “Manin’s Conjecture for Quartic
Del Pezzo Surfaces with a Conic Fibration.” Duke Mathematical Journal,
vol. 160, no. 1, Duke University Press, 2011, pp. 1–69, doi:10.1215/00127094-1443466.
short: R. De La Bretèche, T.D. Browning, Duke Mathematical Journal 160 (2011) 1–69.
date_created: 2018-12-11T11:45:21Z
date_published: 2011-09-27T00:00:00Z
date_updated: 2021-01-12T06:57:00Z
day: '27'
doi: 10.1215/00127094-1443466
extern: 1
intvolume: ' 160'
issue: '1'
month: '09'
page: 1 - 69
publication: Duke Mathematical Journal
publication_status: published
publisher: Duke University Press
publist_id: '7668'
quality_controlled: 0
status: public
title: Manin's conjecture for quartic Del Pezzo surfaces with a conic fibration
type: journal_article
volume: 160
year: '2011'
...
---
_id: '239'
abstract:
- lang: eng
text: An effective search bound is established for the least non-trivial integer
zero of an arbitrary cubic form C ε ℤ[X 1,...,X n], provided that n ≥ 17.
acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council"
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Rainer
full_name: Dietmann, Rainer
last_name: Dietmann
- first_name: Peter
full_name: Elliott, Peter
last_name: Elliott
citation:
ama: Browning TD, Dietmann R, Elliott P. Least zero of a cubic form. Mathematische
Annalen. 2011;352(3):745-778. doi:10.1007/s00208-011-0651-6
apa: Browning, T. D., Dietmann, R., & Elliott, P. (2011). Least zero of a cubic
form. Mathematische Annalen. Springer. https://doi.org/10.1007/s00208-011-0651-6
chicago: Browning, Timothy D, Rainer Dietmann, and Peter Elliott. “Least Zero of
a Cubic Form.” Mathematische Annalen. Springer, 2011. https://doi.org/10.1007/s00208-011-0651-6.
ieee: T. D. Browning, R. Dietmann, and P. Elliott, “Least zero of a cubic form,”
Mathematische Annalen, vol. 352, no. 3. Springer, pp. 745–778, 2011.
ista: Browning TD, Dietmann R, Elliott P. 2011. Least zero of a cubic form. Mathematische
Annalen. 352(3), 745–778.
mla: Browning, Timothy D., et al. “Least Zero of a Cubic Form.” Mathematische
Annalen, vol. 352, no. 3, Springer, 2011, pp. 745–78, doi:10.1007/s00208-011-0651-6.
short: T.D. Browning, R. Dietmann, P. Elliott, Mathematische Annalen 352 (2011)
745–778.
date_created: 2018-12-11T11:45:22Z
date_published: 2011-03-06T00:00:00Z
date_updated: 2021-01-12T06:57:11Z
day: '06'
doi: 10.1007/s00208-011-0651-6
extern: 1
intvolume: ' 352'
issue: '3'
month: '03'
page: 745 - 778
publication: Mathematische Annalen
publication_status: published
publisher: Springer
publist_id: '7665'
quality_controlled: 0
status: public
title: Least zero of a cubic form
type: journal_article
volume: 352
year: '2011'
...
---
_id: '2390'
abstract:
- lang: eng
text: 'We resolve several longstanding problems concerning the stability and the
absence of multi-particle binding for N≥2 polarons. Fröhlich''s 1937 polaron model
describes non-relativistic particles interacting with a scalar quantized field
with coupling √α, and with each other by Coulomb repulsion of strength U. We prove
the following: (i) While there is a known thermodynamic instability for U<2α,
stability of matter does hold for U>2α, that is, the ground state energy per
particle has a finite limit as N→∞. (ii) There is no binding of any kind if U
exceeds a critical value that depends on α but not on N. The same results are
shown to hold for the Pekar-Tomasevich model.'
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Lawrence
full_name: Thomas, Lawrence E
last_name: Thomas
citation:
ama: Frank R, Lieb É, Seiringer R, Thomas L. Stability and absence of binding for
multi-polaron systems. Publications Mathematiques de l Institut des Hautes
Etudes Scientifiques. 2011;113(1):39-67. doi:10.1007/s10240-011-0031-5
apa: Frank, R., Lieb, É., Seiringer, R., & Thomas, L. (2011). Stability and
absence of binding for multi-polaron systems. Publications Mathematiques de
l Institut Des Hautes Etudes Scientifiques. Springer. https://doi.org/10.1007/s10240-011-0031-5
chicago: Frank, Rupert, Élliott Lieb, Robert Seiringer, and Lawrence Thomas. “Stability
and Absence of Binding for Multi-Polaron Systems.” Publications Mathematiques
de l Institut Des Hautes Etudes Scientifiques. Springer, 2011. https://doi.org/10.1007/s10240-011-0031-5.
ieee: R. Frank, É. Lieb, R. Seiringer, and L. Thomas, “Stability and absence of
binding for multi-polaron systems,” Publications Mathematiques de l Institut
des Hautes Etudes Scientifiques, vol. 113, no. 1. Springer, pp. 39–67, 2011.
ista: Frank R, Lieb É, Seiringer R, Thomas L. 2011. Stability and absence of binding
for multi-polaron systems. Publications Mathematiques de l Institut des Hautes
Etudes Scientifiques. 113(1), 39–67.
mla: Frank, Rupert, et al. “Stability and Absence of Binding for Multi-Polaron Systems.”
Publications Mathematiques de l Institut Des Hautes Etudes Scientifiques,
vol. 113, no. 1, Springer, 2011, pp. 39–67, doi:10.1007/s10240-011-0031-5.
short: R. Frank, É. Lieb, R. Seiringer, L. Thomas, Publications Mathematiques de
l Institut Des Hautes Etudes Scientifiques 113 (2011) 39–67.
date_created: 2018-12-11T11:57:23Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:12Z
day: '01'
doi: 10.1007/s10240-011-0031-5
extern: 1
intvolume: ' 113'
issue: '1'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1004.4892
month: '06'
oa: 1
page: 39 - 67
publication: Publications Mathematiques de l Institut des Hautes Etudes Scientifiques
publication_status: published
publisher: Springer
publist_id: '4534'
quality_controlled: 0
status: public
title: Stability and absence of binding for multi-polaron systems
type: journal_article
volume: 113
year: '2011'
...
---
_id: '2391'
abstract:
- lang: eng
text: The change in energy of an ideal Fermi gas when a local one-body potential
is inserted into the system, or when the density is changed locally, are important
quantities in condensed matter physics. We show that they can be rigorously bounded
from below by a universal constant times the value given by the semiclassical
approximation.
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Frank R, Lewin M, Lieb É, Seiringer R. Energy cost to make a hole in the fermi
sea. Physical Review Letters. 2011;106(15). doi:10.1103/PhysRevLett.106.150402
apa: Frank, R., Lewin, M., Lieb, É., & Seiringer, R. (2011). Energy cost to
make a hole in the fermi sea. Physical Review Letters. American Physical
Society. https://doi.org/10.1103/PhysRevLett.106.150402
chicago: Frank, Rupert, Mathieu Lewin, Élliott Lieb, and Robert Seiringer. “Energy
Cost to Make a Hole in the Fermi Sea.” Physical Review Letters. American
Physical Society, 2011. https://doi.org/10.1103/PhysRevLett.106.150402.
ieee: R. Frank, M. Lewin, É. Lieb, and R. Seiringer, “Energy cost to make a hole
in the fermi sea,” Physical Review Letters, vol. 106, no. 15. American
Physical Society, 2011.
ista: Frank R, Lewin M, Lieb É, Seiringer R. 2011. Energy cost to make a hole in
the fermi sea. Physical Review Letters. 106(15).
mla: Frank, Rupert, et al. “Energy Cost to Make a Hole in the Fermi Sea.” Physical
Review Letters, vol. 106, no. 15, American Physical Society, 2011, doi:10.1103/PhysRevLett.106.150402.
short: R. Frank, M. Lewin, É. Lieb, R. Seiringer, Physical Review Letters 106 (2011).
date_created: 2018-12-11T11:57:24Z
date_published: 2011-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:12Z
day: '01'
doi: 10.1103/PhysRevLett.106.150402
extern: 1
intvolume: ' 106'
issue: '15'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1102.1414
month: '01'
oa: 1
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4535'
quality_controlled: 0
status: public
title: Energy cost to make a hole in the fermi sea
type: journal_article
volume: 106
year: '2011'
...
---
_id: '2393'
abstract:
- lang: eng
text: We investigate the low energy excitation spectrum of a Bose gas with weak,
long range repulsive interactions. In particular, we prove that the Bogoliubov
spectrum of elementary excitations with linear dispersion relation for small momentum
becomes exact in the mean-field limit.
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Seiringer R. The excitation spectrum for weakly interacting Bosons. Communications
in Mathematical Physics. 2011;306(2):565-578. doi:10.1007/s00220-011-1261-6
apa: Seiringer, R. (2011). The excitation spectrum for weakly interacting Bosons.
Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-011-1261-6
chicago: Seiringer, Robert. “The Excitation Spectrum for Weakly Interacting Bosons.”
Communications in Mathematical Physics. Springer, 2011. https://doi.org/10.1007/s00220-011-1261-6.
ieee: R. Seiringer, “The excitation spectrum for weakly interacting Bosons,” Communications
in Mathematical Physics, vol. 306, no. 2. Springer, pp. 565–578, 2011.
ista: Seiringer R. 2011. The excitation spectrum for weakly interacting Bosons.
Communications in Mathematical Physics. 306(2), 565–578.
mla: Seiringer, Robert. “The Excitation Spectrum for Weakly Interacting Bosons.”
Communications in Mathematical Physics, vol. 306, no. 2, Springer, 2011,
pp. 565–78, doi:10.1007/s00220-011-1261-6.
short: R. Seiringer, Communications in Mathematical Physics 306 (2011) 565–578.
date_created: 2018-12-11T11:57:24Z
date_published: 2011-09-01T00:00:00Z
date_updated: 2021-01-12T06:57:13Z
day: '01'
doi: 10.1007/s00220-011-1261-6
extern: 1
intvolume: ' 306'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1008.5349
month: '09'
oa: 1
page: 565 - 578
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4533'
quality_controlled: 0
status: public
title: The excitation spectrum for weakly interacting Bosons
type: journal_article
volume: 306
year: '2011'
...
---
_id: '2436'
abstract:
- lang: eng
text: 'Let EMBEDk→d be the following algorithmic problem: Given a finite simplicial
complex K of dimension at most k, does there exist a (piecewise linear) embedding
of K into Rd? Known results easily imply the polynomiality of EMBEDk→2 (k = 1;
2; the case k = 1, d = 2 is graph planarity) and of EMBEDk→2k for all k ≥ 3. We
show that the celebrated result of Novikov on the algorithmic unsolvability of
recognizing the 5-sphere implies that EMBEDd→d and EMBED (d-1)→d are undecidable
for each d ≥ 5. Our main result is the NP-hardness of EMBED2→4 and, more generally,
of EMBED k→d for all k; d with d ≥ 4 and d ≥ k ≥ (2d - 2)/3. These dimensions
fall outside the metastable range of a theorem of Haefliger and Weber, which characterizes
embeddability using the deleted product obstruction. Our reductions are based
on examples, due to Segal, Spież, Freedman, Krushkal, Teichner, and Skopenkov,
showing that outside the metastable range the deleted product obstruction is not
sufficient to characterize embeddability. '
acknowledgement: |-
We would like to thank Colin Rourke for explanations concerning PL topology and for examples showing the difference between PL embeddability and topological embeddability
mentioned in Section 2. We also thank Michael Joswig, Gil Kalai, Frank Lutz, Alexander Nabutovsky, and Robin Thomas for kindly answering our questions. The second author would also like to thank Sergio Cabello for helpful discussions regarding linear-time algorithms for EMBED2!2.
Finally, we are grateful to two anonymous referees for careful reading and valuable suggestions.
Research of U.Wagner was supported by the Swiss National Science Foundation (SNF Projects
200021-116741 and 200021-125309).
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Martin
full_name: Martin Tancer
id: 38AC689C-F248-11E8-B48F-1D18A9856A87
last_name: Tancer
orcid: 0000-0002-1191-6714
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Matoušek J, Tancer M, Wagner U. Hardness of embedding simplicial complexes
in Rd. Journal of the European Mathematical Society. 2011;13(2):259-295.
doi:10.4171/JEMS/252
apa: Matoušek, J., Tancer, M., & Wagner, U. (2011). Hardness of embedding simplicial
complexes in Rd. Journal of the European Mathematical Society. European
Mathematical Society. https://doi.org/10.4171/JEMS/252
chicago: Matoušek, Jiří, Martin Tancer, and Uli Wagner. “Hardness of Embedding Simplicial
Complexes in Rd.” Journal of the European Mathematical Society. European
Mathematical Society, 2011. https://doi.org/10.4171/JEMS/252.
ieee: J. Matoušek, M. Tancer, and U. Wagner, “Hardness of embedding simplicial complexes
in Rd,” Journal of the European Mathematical Society, vol. 13, no. 2. European
Mathematical Society, pp. 259–295, 2011.
ista: Matoušek J, Tancer M, Wagner U. 2011. Hardness of embedding simplicial complexes
in Rd. Journal of the European Mathematical Society. 13(2), 259–295.
mla: Matoušek, Jiří, et al. “Hardness of Embedding Simplicial Complexes in Rd.”
Journal of the European Mathematical Society, vol. 13, no. 2, European
Mathematical Society, 2011, pp. 259–95, doi:10.4171/JEMS/252.
short: J. Matoušek, M. Tancer, U. Wagner, Journal of the European Mathematical Society
13 (2011) 259–295.
date_created: 2018-12-11T11:57:39Z
date_published: 2011-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:28Z
day: '01'
doi: 10.4171/JEMS/252
extern: 1
intvolume: ' 13'
issue: '2'
month: '01'
page: 259 - 295
publication: Journal of the European Mathematical Society
publication_status: published
publisher: European Mathematical Society
publist_id: '4470'
quality_controlled: 0
status: public
title: Hardness of embedding simplicial complexes in Rd
type: journal_article
volume: 13
year: '2011'
...
---
_id: '2437'
abstract:
- lang: eng
text: We introduce a new notion of minors for simplicial complexes (hypergraphs),
so-called homological minors. Our motivation is to propose a general approach
to attack certain extremal problems for sparse simplicial complexes and the corresponding
threshold problems for random complexes. In this paper, we focus on threshold
problems. The basic model for random complexes is the Linial-Meshulam model Xk(n,
p). By definition, such a complex has n vertices, a complete (k -1)-dimensional
skeleton, and every possible k-dimensional simplex is chosen independently with
probability p. We show that for every k, t≥ 1, there is a constant C = C(k, t)
such that for p≥ C/n, the random complex Xk(n, p) asymptotically almost surely
contains K tk (the complete k-dimensional complex on t vertices) as a homological
minor. As corollary, the threshold for (topological) embeddability of Xk(n, p)
into R2k is at p = θ(1/n). The method can be extended to other models of random
complexes (for which the lower skeleta are not necessarily complete) and also
to more general Tverberg-type problems, where instead of continuous maps without
doubly covered image points (embeddings), we consider maps without qfold covered
image points.
author:
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Wagner U. Minors in random and expanding hypergraphs. In: ACM; 2011:351-360.
doi:10.1145/1998196.1998256'
apa: 'Wagner, U. (2011). Minors in random and expanding hypergraphs (pp. 351–360).
Presented at the SGC: Symposuim on Computational Geometry, ACM. https://doi.org/10.1145/1998196.1998256'
chicago: Wagner, Uli. “Minors in Random and Expanding Hypergraphs,” 351–60. ACM,
2011. https://doi.org/10.1145/1998196.1998256.
ieee: 'U. Wagner, “Minors in random and expanding hypergraphs,” presented at the
SGC: Symposuim on Computational Geometry, 2011, pp. 351–360.'
ista: 'Wagner U. 2011. Minors in random and expanding hypergraphs. SGC: Symposuim
on Computational Geometry, 351–360.'
mla: Wagner, Uli. Minors in Random and Expanding Hypergraphs. ACM, 2011,
pp. 351–60, doi:10.1145/1998196.1998256.
short: U. Wagner, in:, ACM, 2011, pp. 351–360.
conference:
name: 'SGC: Symposuim on Computational Geometry'
date_created: 2018-12-11T11:57:39Z
date_published: 2011-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:29Z
day: '01'
doi: 10.1145/1998196.1998256
extern: 1
month: '01'
page: 351 - 360
publication_status: published
publisher: ACM
publist_id: '4469'
quality_controlled: 0
status: public
title: Minors in random and expanding hypergraphs
type: conference
year: '2011'
...
---
_id: '2454'
abstract:
- lang: eng
text: Within a multicellular tissue cells may coordinately form a singular or multiple
polar axes, but it is unclear whether a common mechanism governs different types
of polar axis formation. The phosphorylation status of PIN proteins, which is
directly affected by the PINOID (PID) protein kinase and the PP2A protein phosphatase,
is known to regulate the apical-basal polarity of PIN localization in bipolar
cells of roots and shoot apices. Here, we provide evidence that the phosphorylation
status-mediated PIN polarity switch is widely used to modulate cellular processes
in Arabidopsis including multipolar pavement cells (PC) with interdigitated lobes
and indentations. The degree of PC interdigitation was greatly reduced either
when the FYPP1 gene, which encodes a PP2A called phytochrome-associated serine/threonine
protein phosphatase, was knocked out or when the PID gene was overexpressed (35S:PID).
These genetic modifications caused PIN1 localization to switch from lobe to indentation
regions. The PP2A and PID mediated switching of PIN1 localization is strikingly
similar to their regulation of the apical-basal polarity switch of PIN proteins
in other cells. Our findings suggest a common mechanism for the regulation of
PIN1 polarity formation, a fundamental cellular process that is crucial for pattern
formation both at the tissue/organ and cellular levels.
author:
- first_name: Hongjiang
full_name: Hongjiang Li
id: 33CA54A6-F248-11E8-B48F-1D18A9856A87
last_name: Li
orcid: 0000-0001-5039-9660
- first_name: Deshu
full_name: Lin, Deshu
last_name: Lin
- first_name: Pankaj
full_name: Dhonukshe, Pankaj B
last_name: Dhonukshe
- first_name: Shingo
full_name: Nagawa, Shingo
last_name: Nagawa
- first_name: Dandan
full_name: Chen, Dandan
last_name: Chen
- first_name: Jirí
full_name: Jirí Friml
id: 4159519E-F248-11E8-B48F-1D18A9856A87
last_name: Friml
orcid: 0000-0002-8302-7596
- first_name: Ben
full_name: Scheres, Ben
last_name: Scheres
- first_name: Hongwei
full_name: Guo, Hongwei
last_name: Guo
- first_name: Zhenbiao
full_name: Yang, Zhenbiao
last_name: Yang
citation:
ama: Li H, Lin D, Dhonukshe P, et al. Phosphorylation switch modulates the interdigitated
pattern of PIN1 localization and cell expansion in Arabidopsis leaf epidermis.
Cell Research. 2011;21(6):970-978. doi:10.1038/cr.2011.49
apa: Li, H., Lin, D., Dhonukshe, P., Nagawa, S., Chen, D., Friml, J., … Yang, Z.
(2011). Phosphorylation switch modulates the interdigitated pattern of PIN1 localization
and cell expansion in Arabidopsis leaf epidermis. Cell Research. Nature
Publishing Group. https://doi.org/10.1038/cr.2011.49
chicago: Li, Hongjiang, Deshu Lin, Pankaj Dhonukshe, Shingo Nagawa, Dandan Chen,
Jiří Friml, Ben Scheres, Hongwei Guo, and Zhenbiao Yang. “Phosphorylation Switch
Modulates the Interdigitated Pattern of PIN1 Localization and Cell Expansion in
Arabidopsis Leaf Epidermis.” Cell Research. Nature Publishing Group, 2011.
https://doi.org/10.1038/cr.2011.49.
ieee: H. Li et al., “Phosphorylation switch modulates the interdigitated
pattern of PIN1 localization and cell expansion in Arabidopsis leaf epidermis,”
Cell Research, vol. 21, no. 6. Nature Publishing Group, pp. 970–978, 2011.
ista: Li H, Lin D, Dhonukshe P, Nagawa S, Chen D, Friml J, Scheres B, Guo H, Yang
Z. 2011. Phosphorylation switch modulates the interdigitated pattern of PIN1 localization
and cell expansion in Arabidopsis leaf epidermis. Cell Research. 21(6), 970–978.
mla: Li, Hongjiang, et al. “Phosphorylation Switch Modulates the Interdigitated
Pattern of PIN1 Localization and Cell Expansion in Arabidopsis Leaf Epidermis.”
Cell Research, vol. 21, no. 6, Nature Publishing Group, 2011, pp. 970–78,
doi:10.1038/cr.2011.49.
short: H. Li, D. Lin, P. Dhonukshe, S. Nagawa, D. Chen, J. Friml, B. Scheres, H.
Guo, Z. Yang, Cell Research 21 (2011) 970–978.
date_created: 2018-12-11T11:57:45Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:35Z
day: '01'
doi: 10.1038/cr.2011.49
extern: 1
intvolume: ' 21'
issue: '6'
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3203702/
month: '06'
oa: 1
page: 970 - 978
publication: Cell Research
publication_status: published
publisher: Nature Publishing Group
publist_id: '4449'
quality_controlled: 0
status: public
title: Phosphorylation switch modulates the interdigitated pattern of PIN1 localization
and cell expansion in Arabidopsis leaf epidermis
type: journal_article
volume: 21
year: '2011'
...
---
_id: '2460'
abstract:
- lang: eng
text: In unicellular and multicellular organisms, cell polarity is essential for
a wide range of biological processes. An important feature of cell polarity is
the asymmetric distribution of proteins in or at the plasma membrane. In plants
such polar localized proteins play various specific roles ranging from organizing
cell morphogenesis, asymmetric cell division, pathogen defense, nutrient transport
and establishment of hormone gradients for developmental patterning. Moreover,
flexible respecification of cell polarities enables plants to adjust their physiology
and development to environmental changes. Having evolved multicellularity independently
and lacking major cell polarity mechanisms of animal cells, plants came up with
alternative solutions to generate and respecify cell polarity as well as to regulate
polar domains at the plasma membrane.
author:
- first_name: Jan
full_name: Dettmer, Jan
last_name: Dettmer
- first_name: Jirí
full_name: Friml, Jirí
id: 4159519E-F248-11E8-B48F-1D18A9856A87
last_name: Friml
orcid: 0000-0002-8302-7596
citation:
ama: 'Dettmer J, Friml J. Cell polarity in plants: When two do the same, it is not
the same... Current Opinion in Cell Biology. 2011;23(6):686-696. doi:10.1016/j.ceb.2011.09.006'
apa: 'Dettmer, J., & Friml, J. (2011). Cell polarity in plants: When two do
the same, it is not the same... Current Opinion in Cell Biology. Elsevier.
https://doi.org/10.1016/j.ceb.2011.09.006'
chicago: 'Dettmer, Jan, and Jiří Friml. “Cell Polarity in Plants: When Two Do the
Same, It Is Not the Same...” Current Opinion in Cell Biology. Elsevier,
2011. https://doi.org/10.1016/j.ceb.2011.09.006.'
ieee: 'J. Dettmer and J. Friml, “Cell polarity in plants: When two do the same,
it is not the same...,” Current Opinion in Cell Biology, vol. 23, no. 6.
Elsevier, pp. 686–696, 2011.'
ista: 'Dettmer J, Friml J. 2011. Cell polarity in plants: When two do the same,
it is not the same... Current Opinion in Cell Biology. 23(6), 686–696.'
mla: 'Dettmer, Jan, and Jiří Friml. “Cell Polarity in Plants: When Two Do the Same,
It Is Not the Same...” Current Opinion in Cell Biology, vol. 23, no. 6,
Elsevier, 2011, pp. 686–96, doi:10.1016/j.ceb.2011.09.006.'
short: J. Dettmer, J. Friml, Current Opinion in Cell Biology 23 (2011) 686–696.
date_created: 2018-12-11T11:57:47Z
date_published: 2011-12-01T00:00:00Z
date_updated: 2021-01-12T06:57:37Z
day: '01'
doi: 10.1016/j.ceb.2011.09.006
extern: '1'
intvolume: ' 23'
issue: '6'
language:
- iso: eng
month: '12'
oa_version: None
page: 686 - 696
publication: Current Opinion in Cell Biology
publication_status: published
publisher: Elsevier
publist_id: '4443'
quality_controlled: '1'
status: public
title: 'Cell polarity in plants: When two do the same, it is not the same...'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2011'
...
---
_id: '2511'
abstract:
- lang: eng
text: Parkinson's disease is a common neurodegenerative disorder characterized by
a profound motor disability that is traceable to the emergence of synchronous,
rhythmic spiking in neurons of the external segment of the globus pallidus (GPe).
The origins of this pathophysiology are poorly defined for the generation of pacemaking.
After the induction of a parkinsonian state in mice, there was a progressive decline
in autonomous GPe pacemaking, which normally serves to desynchronize activity.
The loss was attributable to the downregulation of an ion channel that is essential
in pacemaking, the hyperpolarization and cyclic nucleotide-gated (HCN) channel.
Viral delivery of HCN2 subunits restored pacemaking and reduced burst spiking
in GPe neurons. However, the motor disability induced by dopamine (DA) depletion
was not reversed, suggesting that the loss of pacemaking was a consequence, rather
than a cause, of key network pathophysiology, a conclusion that is consistent
with the ability of L-type channel antagonists to attenuate silencing after DA
depletion.
author:
- first_name: Savio
full_name: Chan, Savio
last_name: Chan
- first_name: Kelly
full_name: Glajch, Kelly E
last_name: Glajch
- first_name: Tracy
full_name: Gertler, Tracy S
last_name: Gertler
- first_name: Jaime
full_name: Guzmán, Jaime N
last_name: Guzmán
- first_name: Jeff
full_name: Mercer, Jeff N
last_name: Mercer
- first_name: Alan
full_name: Lewis, Alan S
last_name: Lewis
- first_name: Alan
full_name: Goldberg, Alan B
last_name: Goldberg
- first_name: Tatiana
full_name: Tkatch, Tatiana
last_name: Tkatch
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
- first_name: Sheila
full_name: Fleming, Sheila M
last_name: Fleming
- first_name: Dane
full_name: Chetkovich, Dane M
last_name: Chetkovich
- first_name: Pavel
full_name: Osten, Pavel
last_name: Osten
- first_name: Hitoshi
full_name: Kita, Hitoshi
last_name: Kita
- first_name: James
full_name: Surmeier, James D
last_name: Surmeier
citation:
ama: Chan S, Glajch K, Gertler T, et al. HCN channelopathy in external globus pallidus
neurons in models of Parkinson s disease. Nature Neuroscience. 2011;14(1):85-94.
doi:10.1038/nn.2692
apa: Chan, S., Glajch, K., Gertler, T., Guzmán, J., Mercer, J., Lewis, A., … Surmeier,
J. (2011). HCN channelopathy in external globus pallidus neurons in models of
Parkinson s disease. Nature Neuroscience. Nature Publishing Group. https://doi.org/10.1038/nn.2692
chicago: Chan, Savio, Kelly Glajch, Tracy Gertler, Jaime Guzmán, Jeff Mercer, Alan
Lewis, Alan Goldberg, et al. “HCN Channelopathy in External Globus Pallidus Neurons
in Models of Parkinson s Disease.” Nature Neuroscience. Nature Publishing
Group, 2011. https://doi.org/10.1038/nn.2692.
ieee: S. Chan et al., “HCN channelopathy in external globus pallidus neurons
in models of Parkinson s disease,” Nature Neuroscience, vol. 14, no. 1.
Nature Publishing Group, pp. 85–94, 2011.
ista: Chan S, Glajch K, Gertler T, Guzmán J, Mercer J, Lewis A, Goldberg A, Tkatch
T, Shigemoto R, Fleming S, Chetkovich D, Osten P, Kita H, Surmeier J. 2011. HCN
channelopathy in external globus pallidus neurons in models of Parkinson s disease.
Nature Neuroscience. 14(1), 85–94.
mla: Chan, Savio, et al. “HCN Channelopathy in External Globus Pallidus Neurons
in Models of Parkinson s Disease.” Nature Neuroscience, vol. 14, no. 1,
Nature Publishing Group, 2011, pp. 85–94, doi:10.1038/nn.2692.
short: S. Chan, K. Glajch, T. Gertler, J. Guzmán, J. Mercer, A. Lewis, A. Goldberg,
T. Tkatch, R. Shigemoto, S. Fleming, D. Chetkovich, P. Osten, H. Kita, J. Surmeier,
Nature Neuroscience 14 (2011) 85–94.
date_created: 2018-12-11T11:58:06Z
date_published: 2011-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:56Z
day: '01'
doi: 10.1038/nn.2692
extern: 1
intvolume: ' 14'
issue: '1'
month: '01'
page: 85 - 94
publication: Nature Neuroscience
publication_status: published
publisher: Nature Publishing Group
publist_id: '4390'
quality_controlled: 0
status: public
title: HCN channelopathy in external globus pallidus neurons in models of Parkinson
s disease
type: journal_article
volume: 14
year: '2011'
...
---
_id: '2512'
abstract:
- lang: eng
text: GABAergic inhibition plays a central role in the control of pyramidal cell
ensemble activities; thus, any signaling mechanism that regulates inhibition is
able to fine-tune network patterns. Here, we provide evidence that the retrograde
nitric oxide (NO)- cGMP cascade triggered by NMDA receptor (NMDAR) activation
plays a role in the control of hippocampal GABAergic transmission in mice. GABAergic
synapses express neuronal nitric oxide synthase (nNOS) postsynaptically and NO
receptors (NO-sensitive guanylyl cyclase) in the presynaptic terminals. We hypothesized
that-similar to glutamatergic synapses-the Ca 2+ transients required to activate
nNOS were provided by NMDA receptor activation. Indeed, administration of 5 μm
NMDA induced a robust nNOS-dependent cGMP production in GABAergic terminals, selectively
in the CA1 and CA3c areas. Furthermore, using preembedding, postembedding, and
SDS-digested freeze-fracture replica immunogold labeling, we provided quantitative
immunocytochemical evidence that NMDAR subunits GluN1, GluN2A, and GluN2B were
present in most somatic GABAergic synapses postsynaptically. These data indicate
that NMDARs can modulate hippocampal GABAergic inhibition via NO- cGMP signaling
in an activity-dependent manner and that this effect is subregion specific in
the mouse hippocampus.
author:
- first_name: Eszter
full_name: Szabadits, Eszter
last_name: Szabadits
- first_name: Csaba
full_name: Cserép, Csaba
last_name: Cserép
- first_name: András
full_name: Szonyi, András
last_name: Szonyi
- first_name: Yugo
full_name: Fukazawa, Yugo
last_name: Fukazawa
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
- first_name: Masahiko
full_name: Watanabe, Masahiko
last_name: Watanabe
- first_name: Shigeyoshi
full_name: Itohara, Shigeyoshi
last_name: Itohara
- first_name: Tamás
full_name: Freund, Tamás F
last_name: Freund
- first_name: Gábor
full_name: Nyíri, Gábor
last_name: Nyíri
citation:
ama: Szabadits E, Cserép C, Szonyi A, et al. NMDA receptors in hippocampal GABAergic
synapses and their role in nitric oxide signaling. Journal of Neuroscience.
2011;31(16):5893-5904. doi:10.1523/JNEUROSCI.5938-10.2011
apa: Szabadits, E., Cserép, C., Szonyi, A., Fukazawa, Y., Shigemoto, R., Watanabe,
M., … Nyíri, G. (2011). NMDA receptors in hippocampal GABAergic synapses and their
role in nitric oxide signaling. Journal of Neuroscience. Society for Neuroscience.
https://doi.org/10.1523/JNEUROSCI.5938-10.2011
chicago: Szabadits, Eszter, Csaba Cserép, András Szonyi, Yugo Fukazawa, Ryuichi
Shigemoto, Masahiko Watanabe, Shigeyoshi Itohara, Tamás Freund, and Gábor Nyíri.
“NMDA Receptors in Hippocampal GABAergic Synapses and Their Role in Nitric Oxide
Signaling.” Journal of Neuroscience. Society for Neuroscience, 2011. https://doi.org/10.1523/JNEUROSCI.5938-10.2011.
ieee: E. Szabadits et al., “NMDA receptors in hippocampal GABAergic synapses
and their role in nitric oxide signaling,” Journal of Neuroscience, vol.
31, no. 16. Society for Neuroscience, pp. 5893–5904, 2011.
ista: Szabadits E, Cserép C, Szonyi A, Fukazawa Y, Shigemoto R, Watanabe M, Itohara
S, Freund T, Nyíri G. 2011. NMDA receptors in hippocampal GABAergic synapses and
their role in nitric oxide signaling. Journal of Neuroscience. 31(16), 5893–5904.
mla: Szabadits, Eszter, et al. “NMDA Receptors in Hippocampal GABAergic Synapses
and Their Role in Nitric Oxide Signaling.” Journal of Neuroscience, vol.
31, no. 16, Society for Neuroscience, 2011, pp. 5893–904, doi:10.1523/JNEUROSCI.5938-10.2011.
short: E. Szabadits, C. Cserép, A. Szonyi, Y. Fukazawa, R. Shigemoto, M. Watanabe,
S. Itohara, T. Freund, G. Nyíri, Journal of Neuroscience 31 (2011) 5893–5904.
date_created: 2018-12-11T11:58:06Z
date_published: 2011-04-20T00:00:00Z
date_updated: 2021-01-12T06:57:56Z
day: '20'
doi: 10.1523/JNEUROSCI.5938-10.2011
extern: 1
intvolume: ' 31'
issue: '16'
month: '04'
page: 5893 - 5904
publication: Journal of Neuroscience
publication_status: published
publisher: Society for Neuroscience
publist_id: '4389'
quality_controlled: 0
status: public
title: NMDA receptors in hippocampal GABAergic synapses and their role in nitric oxide
signaling
type: journal_article
volume: 31
year: '2011'
...
---
_id: '2513'
abstract:
- lang: eng
text: 'SK2-containing channels are expressed in the postsynaptic density (PSD) of
dendritic spines on mouse hippocampal area CA1 pyramidal neurons and influence
synaptic responses, plasticity and learning. The Sk2 gene (also known as Kcnn2)
encodes two isoforms that differ only in the length of their N-terminal domains.
SK2-long (SK2-L) and SK2-short (SK2-S) are coexpressed in CA1 pyramidal neurons
and likely form heteromeric channels. In mice lacking SK2-L (SK2-S only mice),
SK2-S-containing channels were expressed in the extrasynaptic membrane, but were
excluded from the PSD. The SK channel contribution to excitatory postsynaptic
potentials was absent in SK2-S only mice and was restored by SK2-L re-expression.
Blocking SK channels increased the amount of long-term potentiation induced in
area CA1 in slices from wild-type mice but had no effect in slices from SK2-S
only mice. Furthermore, SK2-S only mice outperformed wild-type mice in the novel
object recognition task. These results indicate that SK2-L directs synaptic SK2-containing
channel expression and is important for normal synaptic signaling, plasticity
and learning. '
author:
- first_name: Duane
full_name: Allen, Duane H
last_name: Allen
- first_name: Chris
full_name: Bond, Chris T
last_name: Bond
- first_name: Rafael
full_name: Luján, Rafael
last_name: Luján
- first_name: Carmen
full_name: Ballesteros-Merino, Carmen
last_name: Ballesteros Merino
- first_name: Michael
full_name: Lin, Michael T
last_name: Lin
- first_name: Kang
full_name: Wang, Kang
last_name: Wang
- first_name: Nathan
full_name: Klett, Nathan
last_name: Klett
- first_name: Masahiko
full_name: Watanabe, Masahiko
last_name: Watanabe
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
- first_name: Robert
full_name: Stackman, Robert W
last_name: Stackman
- first_name: James
full_name: Maylie, James G
last_name: Maylie
- first_name: John
full_name: Adelman, John P
last_name: Adelman
citation:
ama: Allen D, Bond C, Luján R, et al. The SK2-long isoform directs synaptic localization
and function of SK2-containing channels. Nature Neuroscience. 2011;14(6):744-749.
doi:10.1038/nn.2832
apa: Allen, D., Bond, C., Luján, R., Ballesteros Merino, C., Lin, M., Wang, K.,
… Adelman, J. (2011). The SK2-long isoform directs synaptic localization and function
of SK2-containing channels. Nature Neuroscience. Nature Publishing Group.
https://doi.org/10.1038/nn.2832
chicago: Allen, Duane, Chris Bond, Rafael Luján, Carmen Ballesteros Merino, Michael
Lin, Kang Wang, Nathan Klett, et al. “The SK2-Long Isoform Directs Synaptic Localization
and Function of SK2-Containing Channels.” Nature Neuroscience. Nature Publishing
Group, 2011. https://doi.org/10.1038/nn.2832.
ieee: D. Allen et al., “The SK2-long isoform directs synaptic localization
and function of SK2-containing channels,” Nature Neuroscience, vol. 14,
no. 6. Nature Publishing Group, pp. 744–749, 2011.
ista: Allen D, Bond C, Luján R, Ballesteros Merino C, Lin M, Wang K, Klett N, Watanabe
M, Shigemoto R, Stackman R, Maylie J, Adelman J. 2011. The SK2-long isoform directs
synaptic localization and function of SK2-containing channels. Nature Neuroscience.
14(6), 744–749.
mla: Allen, Duane, et al. “The SK2-Long Isoform Directs Synaptic Localization and
Function of SK2-Containing Channels.” Nature Neuroscience, vol. 14, no.
6, Nature Publishing Group, 2011, pp. 744–49, doi:10.1038/nn.2832.
short: D. Allen, C. Bond, R. Luján, C. Ballesteros Merino, M. Lin, K. Wang, N. Klett,
M. Watanabe, R. Shigemoto, R. Stackman, J. Maylie, J. Adelman, Nature Neuroscience
14 (2011) 744–749.
date_created: 2018-12-11T11:58:07Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:56Z
day: '01'
doi: 10.1038/nn.2832
extern: 1
intvolume: ' 14'
issue: '6'
month: '06'
page: 744 - 749
publication: Nature Neuroscience
publication_status: published
publisher: Nature Publishing Group
publist_id: '4388'
quality_controlled: 0
status: public
title: The SK2-long isoform directs synaptic localization and function of SK2-containing
channels
type: journal_article
volume: 14
year: '2011'
...
---
_id: '2717'
abstract:
- lang: eng
text: 'We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions.
The matrix elements H xy, indexed by, are independent, uniformly distributed random
variables if {pipe}x-y{pipe} is less than the band width W, and zero otherwise.
We prove that the time evolution of a quantum particle subject to the Hamiltonian
H is diffusive on time scales. We also show that the localization length of the
eigenvectors of H is larger than a factor W d/6 times the band width. All results
are uniform in the size of the matrix. '
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Antti
full_name: Knowles, Antti
last_name: Knowles
citation:
ama: Erdös L, Knowles A. Quantum diffusion and eigenfunction delocalization in a
random band matrix model. Communications in Mathematical Physics. 2011;303(2):509-554.
doi:10.1007/s00220-011-1204-2
apa: Erdös, L., & Knowles, A. (2011). Quantum diffusion and eigenfunction delocalization
in a random band matrix model. Communications in Mathematical Physics.
Springer. https://doi.org/10.1007/s00220-011-1204-2
chicago: Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction
Delocalization in a Random Band Matrix Model.” Communications in Mathematical
Physics. Springer, 2011. https://doi.org/10.1007/s00220-011-1204-2.
ieee: L. Erdös and A. Knowles, “Quantum diffusion and eigenfunction delocalization
in a random band matrix model,” Communications in Mathematical Physics,
vol. 303, no. 2. Springer, pp. 509–554, 2011.
ista: Erdös L, Knowles A. 2011. Quantum diffusion and eigenfunction delocalization
in a random band matrix model. Communications in Mathematical Physics. 303(2),
509–554.
mla: Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction Delocalization
in a Random Band Matrix Model.” Communications in Mathematical Physics,
vol. 303, no. 2, Springer, 2011, pp. 509–54, doi:10.1007/s00220-011-1204-2.
short: L. Erdös, A. Knowles, Communications in Mathematical Physics 303 (2011) 509–554.
date_created: 2018-12-11T11:59:14Z
date_published: 2011-04-01T00:00:00Z
date_updated: 2021-01-12T06:59:15Z
day: '01'
doi: 10.1007/s00220-011-1204-2
extern: 1
intvolume: ' 303'
issue: '2'
month: '04'
page: 509 - 554
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4175'
quality_controlled: 0
status: public
title: Quantum diffusion and eigenfunction delocalization in a random band matrix
model
type: journal_article
volume: 303
year: '2011'
...
---
_id: '2764'
abstract:
- lang: eng
text: Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds
to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion
self-dual ensembles. For any β≥1, we prove that the relaxation time to local equilibrium
for the Dyson Brownian motion is bounded above by N -ζ for some ζ> 0. The proof
is based on an estimate of the entropy flow of the Dyson Brownian motion w. r.
t. a "pseudo equilibrium measure". As an application of this estimate,
we prove that the eigenvalue spacing statistics in the bulk of the spectrum for
N×N symmetric Wigner ensemble is the same as that of the Gaussian Orthogonal Ensemble
(GOE) in the limit N→∞. The assumptions on the probability distribution of the
matrix elements of the Wigner ensemble are a subexponential decay and some minor
restriction on the support.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: Erdös L, Schlein B, Yau H. Universality of random matrices and local relaxation
flow. Inventiones Mathematicae. 2011;185(1):75-119. doi:10.1007/s00222-010-0302-7
apa: Erdös, L., Schlein, B., & Yau, H. (2011). Universality of random matrices
and local relaxation flow. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-010-0302-7
chicago: Erdös, László, Benjamin Schlein, and Horng Yau. “Universality of Random
Matrices and Local Relaxation Flow.” Inventiones Mathematicae. Springer,
2011. https://doi.org/10.1007/s00222-010-0302-7.
ieee: L. Erdös, B. Schlein, and H. Yau, “Universality of random matrices and local
relaxation flow,” Inventiones Mathematicae, vol. 185, no. 1. Springer,
pp. 75–119, 2011.
ista: Erdös L, Schlein B, Yau H. 2011. Universality of random matrices and local
relaxation flow. Inventiones Mathematicae. 185(1), 75–119.
mla: Erdös, László, et al. “Universality of Random Matrices and Local Relaxation
Flow.” Inventiones Mathematicae, vol. 185, no. 1, Springer, 2011, pp. 75–119,
doi:10.1007/s00222-010-0302-7.
short: L. Erdös, B. Schlein, H. Yau, Inventiones Mathematicae 185 (2011) 75–119.
date_created: 2018-12-11T11:59:29Z
date_published: 2011-07-01T00:00:00Z
date_updated: 2021-01-12T06:59:32Z
day: '01'
doi: 10.1007/s00222-010-0302-7
extern: 1
intvolume: ' 185'
issue: '1'
month: '07'
page: 75 - 119
publication: Inventiones Mathematicae
publication_status: published
publisher: Springer
publist_id: '4126'
quality_controlled: 0
status: public
title: Universality of random matrices and local relaxation flow
type: journal_article
volume: 185
year: '2011'
...
---
_id: '2765'
abstract:
- lang: eng
text: 'This is a study of the universality of spectral statistics for large random
matrices. Considered are N×N symmetric, Hermitian, or quaternion self-dual random
matrices with independent identically distributed entries (Wigner matrices), where
the probability distribution of each matrix element is given by a measure v with
zero expectation and with subexponential decay. The main result is that the correlation
functions of the local eigenvalue statistics in the bulk of the spectrum coincide
with those of the Gaussian Orthogonal Ensemble (GOE), the Gaussian Unitary Ensemble
(GUE), and the Gaussian Symplectic Ensemble (GSE), respectively, in the limit
as N → ∞. This approach is based on a study of the Dyson Brownian motion via a
related new dynamics, the local relaxation flow. As a main input, it is established
that the density of the eigenvalues converges to the Wigner semicircle law, and
this holds even down to the smallest possible scale. Moreover, it is shown that
the eigenvectors are completely delocalized. These results hold even without the
condition that the matrix elements are identically distributed: only independence
is used. In fact, for the matrix elements of the Green function strong estimates
are given that imply that the local statistics of any two ensembles in the bulk
are identical if the first four moments of the matrix elements match. Universality
at the spectral edges requires matching only two moments. A Wigner-type estimate
is also proved, and it is shown that the eigenvalues repel each other on arbitrarily
small scales.'
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: 'Erdös L. Universality of Wigner random matrices: A survey of recent results.
Russian Mathematical Surveys. 2011;66(3):507-626. doi:10.1070/RM2011v066n03ABEH004749'
apa: 'Erdös, L. (2011). Universality of Wigner random matrices: A survey of recent
results. Russian Mathematical Surveys. IOP Publishing Ltd. https://doi.org/10.1070/RM2011v066n03ABEH004749'
chicago: 'Erdös, László. “Universality of Wigner Random Matrices: A Survey of Recent
Results.” Russian Mathematical Surveys. IOP Publishing Ltd., 2011. https://doi.org/10.1070/RM2011v066n03ABEH004749.'
ieee: 'L. Erdös, “Universality of Wigner random matrices: A survey of recent results,”
Russian Mathematical Surveys, vol. 66, no. 3. IOP Publishing Ltd., pp.
507–626, 2011.'
ista: 'Erdös L. 2011. Universality of Wigner random matrices: A survey of recent
results. Russian Mathematical Surveys. 66(3), 507–626.'
mla: 'Erdös, László. “Universality of Wigner Random Matrices: A Survey of Recent
Results.” Russian Mathematical Surveys, vol. 66, no. 3, IOP Publishing
Ltd., 2011, pp. 507–626, doi:10.1070/RM2011v066n03ABEH004749.'
short: L. Erdös, Russian Mathematical Surveys 66 (2011) 507–626.
date_created: 2018-12-11T11:59:29Z
date_published: 2011-01-01T00:00:00Z
date_updated: 2019-04-26T07:22:20Z
day: '01'
doi: 10.1070/RM2011v066n03ABEH004749
extern: 1
intvolume: ' 66'
issue: '3'
main_file_link:
- open_access: '0'
url: http://arxiv.org/abs/1004.0861
month: '01'
page: 507 - 626
publication: Russian Mathematical Surveys
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '4125'
quality_controlled: 0
status: public
title: 'Universality of Wigner random matrices: A survey of recent results'
type: review
volume: 66
year: '2011'
...