---
_id: '2363'
abstract:
- lang: eng
text: ' We prove that the Gross-Pitaevskii equation correctly describes the
ground state energy and corresponding one-particle density matrix of rotating,
dilute, trapped Bose gases with repulsive two-body interactions. We also show
that there is 100% Bose-Einstein condensation. While a proof that the GP equation
correctly describes non-rotating or slowly rotating gases was known for some time,
the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground
state is not the lowest eigenstate of the Hamiltonian in this case. We have been
able to overcome this difficulty with the aid of coherent states. Our proof also
conceptually simplifies the previous proof for the slowly rotating case. In the
case of axially symmetric traps, our results show that the appearance of quantized
vortices causes spontaneous symmetry breaking in the ground state. '
author:
- 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: Lieb É, Seiringer R. Derivation of the Gross-Pitaevskii equation for rotating
Bose gases. Communications in Mathematical Physics. 2006;264(2):505-537.
doi:10.1007/s00220-006-1524-9
apa: Lieb, É., & Seiringer, R. (2006). Derivation of the Gross-Pitaevskii equation
for rotating Bose gases. Communications in Mathematical Physics. Springer.
https://doi.org/10.1007/s00220-006-1524-9
chicago: Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii
Equation for Rotating Bose Gases.” Communications in Mathematical Physics.
Springer, 2006. https://doi.org/10.1007/s00220-006-1524-9.
ieee: É. Lieb and R. Seiringer, “Derivation of the Gross-Pitaevskii equation for
rotating Bose gases,” Communications in Mathematical Physics, vol. 264,
no. 2. Springer, pp. 505–537, 2006.
ista: Lieb É, Seiringer R. 2006. Derivation of the Gross-Pitaevskii equation for
rotating Bose gases. Communications in Mathematical Physics. 264(2), 505–537.
mla: Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation
for Rotating Bose Gases.” Communications in Mathematical Physics, vol.
264, no. 2, Springer, 2006, pp. 505–37, doi:10.1007/s00220-006-1524-9.
short: É. Lieb, R. Seiringer, Communications in Mathematical Physics 264 (2006)
505–537.
date_created: 2018-12-11T11:57:13Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1007/s00220-006-1524-9
extern: 1
intvolume: ' 264'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0504042
month: '01'
oa: 1
page: 505 - 537
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4561'
quality_controlled: 0
status: public
title: Derivation of the Gross-Pitaevskii equation for rotating Bose gases
type: review
volume: 264
year: '2006'
...
---
_id: '2364'
abstract:
- lang: eng
text: We present an inequality that gives a lower bound on the expectation value
of certain two-body interaction potentials in a general state on Fock space in
terms of the corresponding expectation value for thermal equilibrium states of
non-interacting systems and the difference in the free energy. This bound can
be viewed as a rigorous version of first-order perturbation theory for many-body
systems at positive temperature. As an application, we give a proof of the first
two terms in a high density (and high temperature) expansion of the free energy
of jellium with Coulomb interactions, both in the fermionic and bosonic case.
For bosons, our method works above the transition temperature (for the non-interacting
gas) for Bose-Einstein condensation.
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. A correlation estimate for quantum many-body systems at positive
temperature. Reviews in Mathematical Physics. 2006;18(3):233-253. doi:10.1142/S0129055X06002632
apa: Seiringer, R. (2006). A correlation estimate for quantum many-body systems
at positive temperature. Reviews in Mathematical Physics. World Scientific
Publishing. https://doi.org/10.1142/S0129055X06002632
chicago: Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems
at Positive Temperature.” Reviews in Mathematical Physics. World Scientific
Publishing, 2006. https://doi.org/10.1142/S0129055X06002632.
ieee: R. Seiringer, “A correlation estimate for quantum many-body systems at positive
temperature,” Reviews in Mathematical Physics, vol. 18, no. 3. World Scientific
Publishing, pp. 233–253, 2006.
ista: Seiringer R. 2006. A correlation estimate for quantum many-body systems at
positive temperature. Reviews in Mathematical Physics. 18(3), 233–253.
mla: Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at
Positive Temperature.” Reviews in Mathematical Physics, vol. 18, no. 3,
World Scientific Publishing, 2006, pp. 233–53, doi:10.1142/S0129055X06002632.
short: R. Seiringer, Reviews in Mathematical Physics 18 (2006) 233–253.
date_created: 2018-12-11T11:57:14Z
date_published: 2006-04-01T00:00:00Z
date_updated: 2021-01-12T06:57:02Z
day: '01'
doi: 10.1142/S0129055X06002632
extern: 1
intvolume: ' 18'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0601051
month: '04'
oa: 1
page: 233 - 253
publication: Reviews in Mathematical Physics
publication_status: published
publisher: World Scientific Publishing
publist_id: '4562'
quality_controlled: 0
status: public
title: A correlation estimate for quantum many-body systems at positive temperature
type: journal_article
volume: 18
year: '2006'
...
---
_id: '2365'
abstract:
- lang: eng
text: We consider a gas of fermions with non-zero spin at temperature T and chemical
potential μ. We show that if the range of the interparticle interaction is small
compared to the mean particle distance, the thermodynamic pressure differs to
leading order from the corresponding expression for non-interacting particles
by a term proportional to the scattering length of the interparticle interaction.
This is true for any repulsive interaction, including hard cores. The result is
uniform in the temperature as long as T is of the same order as the Fermi temperature,
or smaller.
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 thermodynamic pressure of a dilute fermi gas. Communications
in Mathematical Physics. 2006;261(3):729-757. doi:10.1007/s00220-005-1433-3
apa: Seiringer, R. (2006). The thermodynamic pressure of a dilute fermi gas. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-005-1433-3
chicago: Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.”
Communications in Mathematical Physics. Springer, 2006. https://doi.org/10.1007/s00220-005-1433-3.
ieee: R. Seiringer, “The thermodynamic pressure of a dilute fermi gas,” Communications
in Mathematical Physics, vol. 261, no. 3. Springer, pp. 729–757, 2006.
ista: Seiringer R. 2006. The thermodynamic pressure of a dilute fermi gas. Communications
in Mathematical Physics. 261(3), 729–757.
mla: Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” Communications
in Mathematical Physics, vol. 261, no. 3, Springer, 2006, pp. 729–57, doi:10.1007/s00220-005-1433-3.
short: R. Seiringer, Communications in Mathematical Physics 261 (2006) 729–757.
date_created: 2018-12-11T11:57:14Z
date_published: 2006-02-01T00:00:00Z
date_updated: 2021-01-12T06:57:02Z
day: '01'
doi: 10.1007/s00220-005-1433-3
extern: 1
intvolume: ' 261'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0412086
month: '02'
oa: 1
page: 729 - 757
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4563'
quality_controlled: 0
status: public
title: The thermodynamic pressure of a dilute fermi gas
type: journal_article
volume: 261
year: '2006'
...
---
_id: '2366'
abstract:
- lang: eng
text: Inequalities are derived for power sums of the real part and the modulus of
the eigenvalues of a Schrödinger operator with a complex-valued potential.
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Ari
full_name: Laptev, Ari
last_name: Laptev
- 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, Laptev A, Lieb É, Seiringer R. Lieb-Thirring inequalities for Schrödinger
operators with complex-valued potentials. Letters in Mathematical Physics.
2006;77(3):309-316. doi:10.1007/s11005-006-0095-1
apa: Frank, R., Laptev, A., Lieb, É., & Seiringer, R. (2006). Lieb-Thirring
inequalities for Schrödinger operators with complex-valued potentials. Letters
in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-006-0095-1
chicago: Frank, Rupert, Ari Laptev, Élliott Lieb, and Robert Seiringer. “Lieb-Thirring
Inequalities for Schrödinger Operators with Complex-Valued Potentials.” Letters
in Mathematical Physics. Springer, 2006. https://doi.org/10.1007/s11005-006-0095-1.
ieee: R. Frank, A. Laptev, É. Lieb, and R. Seiringer, “Lieb-Thirring inequalities
for Schrödinger operators with complex-valued potentials,” Letters in Mathematical
Physics, vol. 77, no. 3. Springer, pp. 309–316, 2006.
ista: Frank R, Laptev A, Lieb É, Seiringer R. 2006. Lieb-Thirring inequalities for
Schrödinger operators with complex-valued potentials. Letters in Mathematical
Physics. 77(3), 309–316.
mla: Frank, Rupert, et al. “Lieb-Thirring Inequalities for Schrödinger Operators
with Complex-Valued Potentials.” Letters in Mathematical Physics, vol.
77, no. 3, Springer, 2006, pp. 309–16, doi:10.1007/s11005-006-0095-1.
short: R. Frank, A. Laptev, É. Lieb, R. Seiringer, Letters in Mathematical Physics
77 (2006) 309–316.
date_created: 2018-12-11T11:57:15Z
date_published: 2006-09-01T00:00:00Z
date_updated: 2021-01-12T06:57:03Z
day: '01'
doi: 10.1007/s11005-006-0095-1
extern: 1
intvolume: ' 77'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0605017
month: '09'
oa: 1
page: 309 - 316
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4560'
quality_controlled: 0
status: public
title: Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
type: journal_article
volume: 77
year: '2006'
...
---
_id: '2368'
abstract:
- lang: eng
text: The recent experimental success in creating Bose-Einstein condensates of alkali
atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest
in the mathematical description of interacting Bose gases.
alternative_title:
- LNP
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. Dilute, trapped Bose gases and Bose-Einstein condensation. In:
Dereziński J, Siedentop H, eds. Large Coulomb Systems. Vol 695. Springer;
2006:249-274. doi:10.1007/3-540-32579-4_6'
apa: Seiringer, R. (2006). Dilute, trapped Bose gases and Bose-Einstein condensation.
In J. Dereziński & H. Siedentop (Eds.), Large Coulomb Systems (Vol.
695, pp. 249–274). Springer. https://doi.org/10.1007/3-540-32579-4_6
chicago: Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.”
In Large Coulomb Systems, edited by Jan Dereziński and Heinz Siedentop,
695:249–74. Springer, 2006. https://doi.org/10.1007/3-540-32579-4_6.
ieee: R. Seiringer, “Dilute, trapped Bose gases and Bose-Einstein condensation,”
in Large Coulomb Systems, vol. 695, J. Dereziński and H. Siedentop, Eds.
Springer, 2006, pp. 249–274.
ista: 'Seiringer R. 2006.Dilute, trapped Bose gases and Bose-Einstein condensation.
In: Large Coulomb Systems. LNP, vol. 695, 249–274.'
mla: Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.”
Large Coulomb Systems, edited by Jan Dereziński and Heinz Siedentop, vol.
695, Springer, 2006, pp. 249–74, doi:10.1007/3-540-32579-4_6.
short: R. Seiringer, in:, J. Dereziński, H. Siedentop (Eds.), Large Coulomb Systems,
Springer, 2006, pp. 249–274.
date_created: 2018-12-11T11:57:15Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:03Z
day: '01'
doi: 10.1007/3-540-32579-4_6
editor:
- first_name: Jan
full_name: Dereziński, Jan
last_name: Dereziński
- first_name: Heinz
full_name: Siedentop, Heinz
last_name: Siedentop
extern: 1
intvolume: ' 695'
month: '01'
page: 249 - 274
publication: Large Coulomb Systems
publication_status: published
publisher: Springer
publist_id: '4558'
quality_controlled: 0
status: public
title: Dilute, trapped Bose gases and Bose-Einstein condensation
type: book_chapter
volume: 695
year: '2006'
...
---
_id: '2369'
abstract:
- lang: eng
text: One of the most remarkable recent developments in the study of ultracold Bose
gases is the observation of a reversible transition from a Bose Einstein condensate
to a state composed of localized atoms as the strength of a periodic, optical
trapping potential is varied. In [1] a model of this phenomenon has been analyzed
rigorously. The gas is a hard core lattice gas and the optical lattice is modeled
by a periodic potential of strength λ. For small λ and temperature Bose- Einstein
condensation (BEC) is proved to occur, while at large λ BEC disappears, even in
the ground state, which is a Mott-insulator state with a characteristic gap. The
inter-particle interaction is essential for this effect. This contribution gives
a pedagogical survey of these results.
alternative_title:
- LNP
author:
- first_name: Michael
full_name: Aizenman, Michael
last_name: Aizenman
- 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: Jan
full_name: Solovej, Jan P
last_name: Solovej
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: 'Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. Bose-Einstein condensation
as a quantum phase transition in an optical lattice. In: Asch J, Joye A, eds.
Mathematical Physics of Quantum Mechanics. Vol 690. Springer; 2006:199-215.
doi:10.1007/b11573432'
apa: Aizenman, M., Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2006).
Bose-Einstein condensation as a quantum phase transition in an optical lattice.
In J. Asch & A. Joye (Eds.), Mathematical Physics of Quantum Mechanics
(Vol. 690, pp. 199–215). Springer. https://doi.org/10.1007/b11573432
chicago: Aizenman, Michael, Élliott Lieb, Robert Seiringer, Jan Solovej, and Jakob
Yngvason. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical
Lattice.” In Mathematical Physics of Quantum Mechanics, edited by Joachim
Asch and Alain Joye, 690:199–215. Springer, 2006. https://doi.org/10.1007/b11573432.
ieee: M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “Bose-Einstein
condensation as a quantum phase transition in an optical lattice,” in Mathematical
Physics of Quantum Mechanics, vol. 690, J. Asch and A. Joye, Eds. Springer,
2006, pp. 199–215.
ista: 'Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. 2006.Bose-Einstein
condensation as a quantum phase transition in an optical lattice. In: Mathematical
Physics of Quantum Mechanics. LNP, vol. 690, 199–215.'
mla: Aizenman, Michael, et al. “Bose-Einstein Condensation as a Quantum Phase Transition
in an Optical Lattice.” Mathematical Physics of Quantum Mechanics, edited
by Joachim Asch and Alain Joye, vol. 690, Springer, 2006, pp. 199–215, doi:10.1007/b11573432.
short: M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, in:, J. Asch,
A. Joye (Eds.), Mathematical Physics of Quantum Mechanics, Springer, 2006, pp.
199–215.
date_created: 2018-12-11T11:57:16Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:04Z
day: '01'
doi: 10.1007/b11573432
editor:
- first_name: Joachim
full_name: Asch, Joachim
last_name: Asch
- first_name: Alain
full_name: Joye, Alain
last_name: Joye
extern: 1
intvolume: ' 690'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0412034
month: '01'
oa: 1
page: 199 - 215
publication: Mathematical Physics of Quantum Mechanics
publication_status: published
publisher: Springer
publist_id: '4559'
quality_controlled: 0
status: public
title: Bose-Einstein condensation as a quantum phase transition in an optical lattice
type: book_chapter
volume: 690
year: '2006'
...
---
_id: '2416'
alternative_title:
- Algorithms and Combinatorics
author:
- first_name: Jørgen
full_name: Bang-Jensen, Jørgen
last_name: Bang Jensen
- first_name: Bruce
full_name: Reed, Bruce
last_name: Reed
- first_name: Bruce
full_name: Schacht, Bruce
last_name: Schacht
- first_name: Robert
full_name: Šámal, Robert
last_name: Šámal
- first_name: Bjarne
full_name: Toft, Bjarne
last_name: Toft
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Bang Jensen J, Reed B, Schacht B, Šámal R, Toft B, Wagner U. On six problems
posed by Jarik Nešetřil. In: Topics in Discrete Mathematics. Vol 26. Springer;
2006:613-627. doi:10.1007/3-540-33700-8_30'
apa: Bang Jensen, J., Reed, B., Schacht, B., Šámal, R., Toft, B., & Wagner,
U. (2006). On six problems posed by Jarik Nešetřil. In Topics in Discrete Mathematics
(Vol. 26, pp. 613–627). Springer. https://doi.org/10.1007/3-540-33700-8_30
chicago: Bang Jensen, Jørgen, Bruce Reed, Bruce Schacht, Robert Šámal, Bjarne Toft,
and Uli Wagner. “On Six Problems Posed by Jarik Nešetřil.” In Topics in Discrete
Mathematics, 26:613–27. Springer, 2006. https://doi.org/10.1007/3-540-33700-8_30.
ieee: J. Bang Jensen, B. Reed, B. Schacht, R. Šámal, B. Toft, and U. Wagner, “On
six problems posed by Jarik Nešetřil,” in Topics in Discrete Mathematics,
vol. 26, Springer, 2006, pp. 613–627.
ista: 'Bang Jensen J, Reed B, Schacht B, Šámal R, Toft B, Wagner U. 2006.On six
problems posed by Jarik Nešetřil. In: Topics in Discrete Mathematics. Algorithms
and Combinatorics, vol. 26, 613–627.'
mla: Bang Jensen, Jørgen, et al. “On Six Problems Posed by Jarik Nešetřil.” Topics
in Discrete Mathematics, vol. 26, Springer, 2006, pp. 613–27, doi:10.1007/3-540-33700-8_30.
short: J. Bang Jensen, B. Reed, B. Schacht, R. Šámal, B. Toft, U. Wagner, in:, Topics
in Discrete Mathematics, Springer, 2006, pp. 613–627.
date_created: 2018-12-11T11:57:32Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:21Z
day: '01'
doi: 10.1007/3-540-33700-8_30
extern: 1
intvolume: ' 26'
month: '01'
page: 613 - 627
publication: Topics in Discrete Mathematics
publication_status: published
publisher: Springer
publist_id: '4509'
quality_controlled: 0
status: public
title: On six problems posed by Jarik Nešetřil
type: book_chapter
volume: 26
year: '2006'
...
---
_id: '2429'
abstract:
- lang: eng
text: 'We show, with an elementary proof, that the number of halving simplices in
a set of n points in 4 in general position is O(n4-2/45). This improves the previous
bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number
of halving simplices intersecting a fixed 2-plane. '
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Shakhar
full_name: Smorodinsky, Shakhar
last_name: Smorodinsky
- 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, Sharir M, Smorodinsky S, Wagner U. K-sets in four dimensions. Discrete
& Computational Geometry. 2006;35(2):177-191. doi:10.1007/s00454-005-1200-4
apa: Matoušek, J., Sharir, M., Smorodinsky, S., & Wagner, U. (2006). K-sets
in four dimensions. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-005-1200-4
chicago: Matoušek, Jiří, Micha Sharir, Shakhar Smorodinsky, and Uli Wagner. “K-Sets
in Four Dimensions.” Discrete & Computational Geometry. Springer, 2006.
https://doi.org/10.1007/s00454-005-1200-4.
ieee: J. Matoušek, M. Sharir, S. Smorodinsky, and U. Wagner, “K-sets in four dimensions,”
Discrete & Computational Geometry, vol. 35, no. 2. Springer, pp. 177–191,
2006.
ista: Matoušek J, Sharir M, Smorodinsky S, Wagner U. 2006. K-sets in four dimensions.
Discrete & Computational Geometry. 35(2), 177–191.
mla: Matoušek, Jiří, et al. “K-Sets in Four Dimensions.” Discrete & Computational
Geometry, vol. 35, no. 2, Springer, 2006, pp. 177–91, doi:10.1007/s00454-005-1200-4.
short: J. Matoušek, M. Sharir, S. Smorodinsky, U. Wagner, Discrete & Computational
Geometry 35 (2006) 177–191.
date_created: 2018-12-11T11:57:37Z
date_published: 2006-02-01T00:00:00Z
date_updated: 2021-01-12T06:57:26Z
day: '01'
doi: 10.1007/s00454-005-1200-4
extern: 1
intvolume: ' 35'
issue: '2'
month: '02'
page: 177 - 191
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '4495'
quality_controlled: 0
status: public
title: K-sets in four dimensions
type: journal_article
volume: 35
year: '2006'
...
---
_id: '2430'
abstract:
- lang: eng
text: We consider an online version of the conflict-free coloring of a set of points
on the line, where each newly inserted point must be assigned a color upon insertion,
and at all times the coloring has to be conflict-free, in the sense that in every
interval I there is a color that appears exactly once in I. We present deterministic
and randomized algorithms for achieving this goal, and analyze their performance,
that is, the maximum number of colors that they need to use, as a function of
the number n of inserted points. We first show that a natural and simple (deterministic)
approach may perform rather poorly, requiring Ω(√̃) colors in the worst case.
We then derive two efficient variants of this simple algorithm. The first is deterministic
and uses O(log 2 n) colors, and the second is randomized and uses O(log n) colors
with high probability. We also show that the O(log 2 n) bound on the number of
colors used by our deterministic algorithm is tight on the worst case. We also
analyze the performance of the simplest proposed algorithm when the points are
inserted in a random order and present an incomplete analysis that indicates that,
with high probability, it uses only O(log n) colors. Finally, we show that in
the extension of this problem to two dimensions, where the relevant ranges are
disks, n colors may be required in the worst case.
author:
- first_name: Ke
full_name: Chent, Ke
last_name: Chent
- first_name: Amos
full_name: Fiat, Amos
last_name: Fiat
- first_name: Haim
full_name: Kaplan, Haim
last_name: Kaplan
- first_name: Meital
full_name: Levy, Meital B
last_name: Levy
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Elchanan
full_name: Mossel, Elchanan
last_name: Mossel
- first_name: János
full_name: Pach, János
last_name: Pach
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Shakhar
full_name: Smorodinsky, Shakhar
last_name: Smorodinsky
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
- first_name: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Chent K, Fiat A, Kaplan H, et al. Online conflict-free coloring for intervals.
SIAM Journal on Computing. 2006;36(5):1342-1359. doi:10.1137/S0097539704446682
apa: Chent, K., Fiat, A., Kaplan, H., Levy, M., Matoušek, J., Mossel, E., … Welzl,
E. (2006). Online conflict-free coloring for intervals. SIAM Journal on Computing.
SIAM. https://doi.org/10.1137/S0097539704446682
chicago: Chent, Ke, Amos Fiat, Haim Kaplan, Meital Levy, Jiří Matoušek, Elchanan
Mossel, János Pach, et al. “Online Conflict-Free Coloring for Intervals.” SIAM
Journal on Computing. SIAM, 2006. https://doi.org/10.1137/S0097539704446682.
ieee: K. Chent et al., “Online conflict-free coloring for intervals,” SIAM
Journal on Computing, vol. 36, no. 5. SIAM, pp. 1342–1359, 2006.
ista: Chent K, Fiat A, Kaplan H, Levy M, Matoušek J, Mossel E, Pach J, Sharir M,
Smorodinsky S, Wagner U, Welzl E. 2006. Online conflict-free coloring for intervals.
SIAM Journal on Computing. 36(5), 1342–1359.
mla: Chent, Ke, et al. “Online Conflict-Free Coloring for Intervals.” SIAM Journal
on Computing, vol. 36, no. 5, SIAM, 2006, pp. 1342–59, doi:10.1137/S0097539704446682.
short: K. Chent, A. Fiat, H. Kaplan, M. Levy, J. Matoušek, E. Mossel, J. Pach, M.
Sharir, S. Smorodinsky, U. Wagner, E. Welzl, SIAM Journal on Computing 36 (2006)
1342–1359.
date_created: 2018-12-11T11:57:37Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:26Z
day: '01'
doi: 10.1137/S0097539704446682
extern: 1
intvolume: ' 36'
issue: '5'
month: '01'
page: 1342 - 1359
publication: SIAM Journal on Computing
publication_status: published
publisher: SIAM
publist_id: '4490'
quality_controlled: 0
status: public
title: Online conflict-free coloring for intervals
type: journal_article
volume: 36
year: '2006'
...
---
_id: '2431'
abstract:
- lang: eng
text: We prove an upper bound, tight up to a factor of 2, for the number of vertices
of level at most t in an arrangement of n halfspaces in R , for arbitrary n and
d (in particular, the dimension d is not considered constant). This partially
settles a conjecture of Eckhoff, Linhart, and Welzl. Up to the factor of 2, the
result generalizes McMullen's Upper Bound Theorem for convex polytopes (the case
ℓ = O) and extends a theorem of Linhart for the case d ≤ 4. Moreover, the bound
sharpens asymptotic estimates obtained by Clarkson and Shor. The proof is based
on the h-matrix of the arrangement (a generalization, introduced by Mulmuley,
of the h-vector of a convex polytope). We show that bounding appropriate sums
of entries of this matrix reduces to a lemma about quadrupels of sets with certain
intersection properties, and we prove this lemma, up to a factor of 2, using tools
from multilinear algebra. This extends an approach of Alon and Kalai, who used
linear algebra methods for an alternative proof of the classical Upper Bound Theorem.
The bounds for the entries of the h-matrix also imply bounds for the number of
i-dimensional faces, i > 0, at level at most ℓ. Furthermore, we discuss a connection
with crossing numbers of graphs that was one of the main motivations for investigating
exact bounds that are valid for arbitrary dimensions.
alternative_title:
- IEEE Conference Proceedings
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. On a geometric generalization of the Upper Bound Theorem. In: IEEE;
2006:635-645. doi:10.1109/FOCS.2006.53'
apa: 'Wagner, U. (2006). On a geometric generalization of the Upper Bound Theorem
(pp. 635–645). Presented at the FOCS: Foundations of Computer Science, IEEE. https://doi.org/10.1109/FOCS.2006.53'
chicago: Wagner, Uli. “On a Geometric Generalization of the Upper Bound Theorem,”
635–45. IEEE, 2006. https://doi.org/10.1109/FOCS.2006.53.
ieee: 'U. Wagner, “On a geometric generalization of the Upper Bound Theorem,” presented
at the FOCS: Foundations of Computer Science, 2006, pp. 635–645.'
ista: 'Wagner U. 2006. On a geometric generalization of the Upper Bound Theorem.
FOCS: Foundations of Computer Science, IEEE Conference Proceedings, , 635–645.'
mla: Wagner, Uli. On a Geometric Generalization of the Upper Bound Theorem.
IEEE, 2006, pp. 635–45, doi:10.1109/FOCS.2006.53.
short: U. Wagner, in:, IEEE, 2006, pp. 635–645.
conference:
name: 'FOCS: Foundations of Computer Science'
date_created: 2018-12-11T11:57:37Z
date_published: 2006-06-08T00:00:00Z
date_updated: 2021-01-12T06:57:27Z
day: '08'
doi: 10.1109/FOCS.2006.53
extern: 1
month: '06'
page: 635 - 645
publication_status: published
publisher: IEEE
publist_id: '4489'
quality_controlled: 0
status: public
title: On a geometric generalization of the Upper Bound Theorem
type: conference
year: '2006'
...
---
_id: '2657'
abstract:
- lang: eng
text: The highest densities of the two metabotropic GABA subunits, GABA B1 and GABAB2,
have been reported as occurring around the glutamatergic synapses between Purkinje
cell spines and parallel fibre varicosities. In order to determine how this distribution
is achieved during development, we investigated the expression pattern and the
cellular and subcellular localization of the GABAB1 and GABAB2 subunits in the
rat cerebellum during postnatal development. At the light microscopic level, immunoreactivity
for the GABAB1 and GABAB2 subunits was very prominent in the developing molecular
layer, especially in Purkinje cells. Using double immunofluorescence, we demonstrated
that GABAB1 was transiently expressed in glial cells. At the electron microscopic
level, immunoreactivity for GABAB receptors was always detected both pre- and
postsynaptically. Presynaptically, GABAB1 and GABAB2 were localized in the extrasynaptic
membrane of parallel fibres at all ages, and only rarely in GABAergic axons. Postsynaptically,
GABAB receptors were localized to the extrasynaptic and perisynaptic plasma membrane
of Purkinje cell dendrites and spines throughout development. Quantitative analysis
and three-dimensional reconstructions further revealed a progressive developmental
movement of the GABAB1 subunit on the surface of Purkinje cells from dendritic
shafts to its final destination, the dendritic spines. Together, these results
indicate that GABAB receptors undergo dynamic regulation during cerebellar development
in association with the establishment and maturation of glutamatergic synapses
to Purkinje cells.
author:
- first_name: Rafael
full_name: Luján, Rafael
last_name: Luján
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
citation:
ama: Luján R, Shigemoto R. Localization of metabotropic GABA receptor subunits GABAB1
and GABAB2 relative to synaptic sites in the rat developing cerebellum. European
Journal of Neuroscience. 2006;23(6):1479-1490. doi:10.1111/j.1460-9568.2006.04669.x
apa: Luján, R., & Shigemoto, R. (2006). Localization of metabotropic GABA receptor
subunits GABAB1 and GABAB2 relative to synaptic sites in the rat developing cerebellum.
European Journal of Neuroscience. Wiley-Blackwell. https://doi.org/10.1111/j.1460-9568.2006.04669.x
chicago: Luján, Rafael, and Ryuichi Shigemoto. “Localization of Metabotropic GABA
Receptor Subunits GABAB1 and GABAB2 Relative to Synaptic Sites in the Rat Developing
Cerebellum.” European Journal of Neuroscience. Wiley-Blackwell, 2006. https://doi.org/10.1111/j.1460-9568.2006.04669.x.
ieee: R. Luján and R. Shigemoto, “Localization of metabotropic GABA receptor subunits
GABAB1 and GABAB2 relative to synaptic sites in the rat developing cerebellum,”
European Journal of Neuroscience, vol. 23, no. 6. Wiley-Blackwell, pp.
1479–1490, 2006.
ista: Luján R, Shigemoto R. 2006. Localization of metabotropic GABA receptor subunits
GABAB1 and GABAB2 relative to synaptic sites in the rat developing cerebellum.
European Journal of Neuroscience. 23(6), 1479–1490.
mla: Luján, Rafael, and Ryuichi Shigemoto. “Localization of Metabotropic GABA Receptor
Subunits GABAB1 and GABAB2 Relative to Synaptic Sites in the Rat Developing Cerebellum.”
European Journal of Neuroscience, vol. 23, no. 6, Wiley-Blackwell, 2006,
pp. 1479–90, doi:10.1111/j.1460-9568.2006.04669.x.
short: R. Luján, R. Shigemoto, European Journal of Neuroscience 23 (2006) 1479–1490.
date_created: 2018-12-11T11:58:54Z
date_published: 2006-03-01T00:00:00Z
date_updated: 2021-01-12T06:58:52Z
day: '01'
doi: 10.1111/j.1460-9568.2006.04669.x
extern: 1
intvolume: ' 23'
issue: '6'
month: '03'
page: 1479 - 1490
publication: European Journal of Neuroscience
publication_status: published
publisher: Wiley-Blackwell
publist_id: '4239'
quality_controlled: 0
status: public
title: Localization of metabotropic GABA receptor subunits GABAB1 and GABAB2 relative
to synaptic sites in the rat developing cerebellum
type: journal_article
volume: 23
year: '2006'
...
---
_id: '2659'
abstract:
- lang: eng
text: Transmembrane AMPA receptor regulatory proteins (TARPs), including stargazin/γ-2,
are associated with AMPA receptors and participate in their surface delivery and
anchoring at the postsynaptic membrane. TARPs may also act as a positive modulator
of the AMPA receptor ion channel function; however, little is known about other
TARP members except for stargazin/γ-2. We examined the synaptic localization of
stargazin/γ-2 and γ-8 by immunoelectron microscopy and biochemical analysis. The
analysis of sodium dodecyl sulfate-digested freeze-fracture replica labeling revealed
that stargazin/γ-2 was concentrated in the postsynaptic area, whereas γ-8 was
distributed both in synaptic and extra-synaptic plasma membranes of the hippocampal
neuron. When a synaptic plasma membrane-enriched brain fraction was treated with
Triton X-100 and separated by sucrose density gradient ultracentrifugation, a
large proportion of NMDA receptor and stargazin/γ-2 was accumulated in raft-enriched
fractions, whereas AMPA receptor and γ-8 were distributed in both the raft-enriched
fractions and other Triton-insoluble fractions. Phosphorylation of stargazin/γ-2
and γ-8 was regulated by different sets of kinases and phosphatases in cultured
cortical neurons. These results suggested that stargazin/γ-2 and γ-8 have distinct
roles in postsynaptic membranes under the regulation of different intracellular
signaling pathways.
author:
- first_name: Mihoko
full_name: Inamura, Mihoko
last_name: Inamura
- first_name: Makoto
full_name: Itakura, Makoto
last_name: Itakura
- first_name: Hirotsugu
full_name: Okamoto, Hirotsugu
last_name: Okamoto
- first_name: Sumio
full_name: Hoka, Sumio
last_name: Hoka
- first_name: Akira
full_name: Mizoguchi, Akira
last_name: Mizoguchi
- 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: Saori
full_name: Yamamori, Saori
last_name: Yamamori
- first_name: Masami
full_name: Takahashi, Masami
last_name: Takahashi
citation:
ama: Inamura M, Itakura M, Okamoto H, et al. Differential localization and regulation
of stargazin-like protein, γ-8 and stargazin in the plasma membrane of hippocampal
and cortical neurons. Neuroscience Research. 2006;55(1):45-53. doi:10.1016/j.neures.2006.01.004
apa: Inamura, M., Itakura, M., Okamoto, H., Hoka, S., Mizoguchi, A., Fukazawa, Y.,
… Takahashi, M. (2006). Differential localization and regulation of stargazin-like
protein, γ-8 and stargazin in the plasma membrane of hippocampal and cortical
neurons. Neuroscience Research. Elsevier. https://doi.org/10.1016/j.neures.2006.01.004
chicago: Inamura, Mihoko, Makoto Itakura, Hirotsugu Okamoto, Sumio Hoka, Akira Mizoguchi,
Yugo Fukazawa, Ryuichi Shigemoto, Saori Yamamori, and Masami Takahashi. “ Differential
Localization and Regulation of Stargazin-like Protein, γ-8 and Stargazin in the
Plasma Membrane of Hippocampal and Cortical Neurons.” Neuroscience Research.
Elsevier, 2006. https://doi.org/10.1016/j.neures.2006.01.004.
ieee: M. Inamura et al., “ Differential localization and regulation of stargazin-like
protein, γ-8 and stargazin in the plasma membrane of hippocampal and cortical
neurons,” Neuroscience Research, vol. 55, no. 1. Elsevier, pp. 45–53, 2006.
ista: Inamura M, Itakura M, Okamoto H, Hoka S, Mizoguchi A, Fukazawa Y, Shigemoto
R, Yamamori S, Takahashi M. 2006. Differential localization and regulation of
stargazin-like protein, γ-8 and stargazin in the plasma membrane of hippocampal
and cortical neurons. Neuroscience Research. 55(1), 45–53.
mla: Inamura, Mihoko, et al. “ Differential Localization and Regulation of Stargazin-like
Protein, γ-8 and Stargazin in the Plasma Membrane of Hippocampal and Cortical
Neurons.” Neuroscience Research, vol. 55, no. 1, Elsevier, 2006, pp. 45–53,
doi:10.1016/j.neures.2006.01.004.
short: M. Inamura, M. Itakura, H. Okamoto, S. Hoka, A. Mizoguchi, Y. Fukazawa, R.
Shigemoto, S. Yamamori, M. Takahashi, Neuroscience Research 55 (2006) 45–53.
date_created: 2018-12-11T11:58:55Z
date_published: 2006-05-01T00:00:00Z
date_updated: 2021-01-12T06:58:52Z
day: '01'
doi: 10.1016/j.neures.2006.01.004
extern: 1
intvolume: ' 55'
issue: '1'
month: '05'
page: 45 - 53
publication: Neuroscience Research
publication_status: published
publisher: Elsevier
publist_id: '4238'
quality_controlled: 0
status: public
title: ' Differential localization and regulation of stargazin-like protein, γ-8 and
stargazin in the plasma membrane of hippocampal and cortical neurons'
type: journal_article
volume: 55
year: '2006'
...
---
_id: '2660'
abstract:
- lang: eng
text: Pavlovian fear conditioning, a simple form of associative learning, is thought
to involve the induction of associative, NMDA receptor-dependent long-term potentiation
(LTP) in the lateral amygdala. Using a combined genetic and electrophysiological
approach, we show here that lack of a specific GABAB receptor subtype, GABAB(1a,2),
unmasks a nonassociative, NMDA receptor-independent form of presynaptic LTP at
cortico-amygdala afferents. Moreover, the level of presynaptic GABA B(1a,2) receptor
activation, and hence the balance between associative and nonassociative forms
of LTP, can be dynamically modulated by local inhibitory activity. At the behavioral
level, genetic loss of GABA B(1a) results in a generalization of conditioned fear
to nonconditioned stimuli. Our findings indicate that presynaptic inhibition through
GABAB(1a,2) receptors serves as an activity-dependent constraint on the induction
of homosynaptic plasticity, which may be important to prevent the generalization
of conditioned fear.
author:
- first_name: Hamdy
full_name: Shaban, Hamdy
last_name: Shaban
- first_name: Yann
full_name: Humeau, Yann
last_name: Humeau
- first_name: Cyril
full_name: Herry, Cyril
last_name: Herry
- first_name: Guillaume
full_name: Cassasus, Guillaume
last_name: Cassasus
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
- first_name: Stéphane
full_name: Ciocchi, Stéphane
last_name: Ciocchi
- first_name: Samuel
full_name: Barbieri, Samuel
last_name: Barbieri
- first_name: Herman
full_name: Van Der Putten, Herman V
last_name: Van Der Putten
- first_name: Klemens
full_name: Kaupmann, Klemens
last_name: Kaupmann
- first_name: Bernhard
full_name: Bettler, Bernhard
last_name: Bettler
- first_name: Andreas
full_name: Lüthi, Andreas
last_name: Lüthi
citation:
ama: Shaban H, Humeau Y, Herry C, et al. Generalization of amygdala LTP and conditioned
fear in the absence of presynaptic inhibition. Nature Neuroscience. 2006;9(8):1028-1035.
doi:10.1038/nn1732
apa: Shaban, H., Humeau, Y., Herry, C., Cassasus, G., Shigemoto, R., Ciocchi, S.,
… Lüthi, A. (2006). Generalization of amygdala LTP and conditioned fear in the
absence of presynaptic inhibition. Nature Neuroscience. Nature Publishing
Group. https://doi.org/10.1038/nn1732
chicago: Shaban, Hamdy, Yann Humeau, Cyril Herry, Guillaume Cassasus, Ryuichi Shigemoto,
Stéphane Ciocchi, Samuel Barbieri, et al. “Generalization of Amygdala LTP and
Conditioned Fear in the Absence of Presynaptic Inhibition.” Nature Neuroscience.
Nature Publishing Group, 2006. https://doi.org/10.1038/nn1732.
ieee: H. Shaban et al., “Generalization of amygdala LTP and conditioned fear
in the absence of presynaptic inhibition,” Nature Neuroscience, vol. 9,
no. 8. Nature Publishing Group, pp. 1028–1035, 2006.
ista: Shaban H, Humeau Y, Herry C, Cassasus G, Shigemoto R, Ciocchi S, Barbieri
S, Van Der Putten H, Kaupmann K, Bettler B, Lüthi A. 2006. Generalization of amygdala
LTP and conditioned fear in the absence of presynaptic inhibition. Nature Neuroscience.
9(8), 1028–1035.
mla: Shaban, Hamdy, et al. “Generalization of Amygdala LTP and Conditioned Fear
in the Absence of Presynaptic Inhibition.” Nature Neuroscience, vol. 9,
no. 8, Nature Publishing Group, 2006, pp. 1028–35, doi:10.1038/nn1732.
short: H. Shaban, Y. Humeau, C. Herry, G. Cassasus, R. Shigemoto, S. Ciocchi, S.
Barbieri, H. Van Der Putten, K. Kaupmann, B. Bettler, A. Lüthi, Nature Neuroscience
9 (2006) 1028–1035.
date_created: 2018-12-11T11:58:55Z
date_published: 2006-08-01T00:00:00Z
date_updated: 2021-01-12T06:58:53Z
day: '01'
doi: 10.1038/nn1732
extern: 1
intvolume: ' 9'
issue: '8'
month: '08'
page: 1028 - 1035
publication: Nature Neuroscience
publication_status: published
publisher: Nature Publishing Group
publist_id: '4236'
quality_controlled: 0
status: public
title: Generalization of amygdala LTP and conditioned fear in the absence of presynaptic
inhibition
type: journal_article
volume: 9
year: '2006'
...
---
_id: '2661'
abstract:
- lang: eng
text: GABAB receptors are the G protein-coupled receptors for the main inhibitory
neurotransmitter in the brain, γ-aminobutyric acid (GABA). Molecular diversity
in the GABAB system arises from the GABAB1a and GABAB1b subunit isoforms that
solely differ in their ectodomains by a pair of sushi repeats that is unique to
GABAB1a. Using a combined genetic, physiological, and morphological approach,
we now demonstrate that GABAB1 isoforms localize to distinct synaptic sites and
convey separate functions in vivo. At hippocampal CA3-to-CA1 synapses, GABAB1a
assembles heteroreceptors inhibiting glutamate release, while predominantly GABAB1b
mediates postsynaptic inhibition. Electron microscopy reveals a synaptic distribution
of GABAB1 isoforms that agrees with the observed functional differences. Transfected
CA3 neurons selectively express GABAB1a in distal axons, suggesting that the sushi
repeats, a conserved protein interaction motif, specify heteroreceptor localization.
The constitutive absence of GABAB1a but not GABAB1b results in impaired synaptic
plasticity and hippocampus-dependent memory, emphasizing molecular differences
in synaptic GABAB functions.
author:
- first_name: Réjan
full_name: Vigot, Réjan
last_name: Vigot
- first_name: Samuel
full_name: Barbieri, Samuel
last_name: Barbieri
- first_name: Hans
full_name: Bräuner-Osborne, Hans
last_name: Bräuner Osborne
- first_name: Rostislav
full_name: Tureček, Rostislav
last_name: Tureček
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
- first_name: Yan
full_name: Zhang, Yan Ping
last_name: Zhang
- first_name: Rafael
full_name: Luján, Rafael
last_name: Luján
- first_name: Laura
full_name: Jacobson, Laura H
last_name: Jacobson
- first_name: Barbara
full_name: Biermann, Barbara
last_name: Biermann
- first_name: Jean
full_name: Fritschy, Jean-Marc
last_name: Fritschy
- first_name: Claire
full_name: Vacher, Claire-Marie
last_name: Vacher
- first_name: Matthias
full_name: Müller, Matthias P
last_name: Müller
- first_name: Gilles
full_name: Sansig, Gilles
last_name: Sansig
- first_name: Nicole
full_name: Guetg, Nicole
last_name: Guetg
- first_name: John
full_name: Cryan, John F
last_name: Cryan
- first_name: Klemens
full_name: Kaupmann, Klemens
last_name: Kaupmann
- first_name: Martin
full_name: Gassmann, Martin
last_name: Gassmann
- first_name: Thomas
full_name: Oertner, Thomas G
last_name: Oertner
- first_name: Bernhard
full_name: Bettler, Bernhard
last_name: Bettler
citation:
ama: Vigot R, Barbieri S, Bräuner Osborne H, et al. Differential Compartmentalization
and Distinct Functions of GABAB Receptor Variants. Neuron. 2006;50(4):589-601.
doi:10.1016/j.neuron.2006.04.014
apa: Vigot, R., Barbieri, S., Bräuner Osborne, H., Tureček, R., Shigemoto, R., Zhang,
Y., … Bettler, B. (2006). Differential Compartmentalization and Distinct Functions
of GABAB Receptor Variants. Neuron. Elsevier. https://doi.org/10.1016/j.neuron.2006.04.014
chicago: Vigot, Réjan, Samuel Barbieri, Hans Bräuner Osborne, Rostislav Tureček,
Ryuichi Shigemoto, Yan Zhang, Rafael Luján, et al. “Differential Compartmentalization
and Distinct Functions of GABAB Receptor Variants.” Neuron. Elsevier, 2006.
https://doi.org/10.1016/j.neuron.2006.04.014.
ieee: R. Vigot et al., “Differential Compartmentalization and Distinct Functions
of GABAB Receptor Variants,” Neuron, vol. 50, no. 4. Elsevier, pp. 589–601,
2006.
ista: Vigot R, Barbieri S, Bräuner Osborne H, Tureček R, Shigemoto R, Zhang Y, Luján
R, Jacobson L, Biermann B, Fritschy J, Vacher C, Müller M, Sansig G, Guetg N,
Cryan J, Kaupmann K, Gassmann M, Oertner T, Bettler B. 2006. Differential Compartmentalization
and Distinct Functions of GABAB Receptor Variants. Neuron. 50(4), 589–601.
mla: Vigot, Réjan, et al. “Differential Compartmentalization and Distinct Functions
of GABAB Receptor Variants.” Neuron, vol. 50, no. 4, Elsevier, 2006, pp.
589–601, doi:10.1016/j.neuron.2006.04.014.
short: R. Vigot, S. Barbieri, H. Bräuner Osborne, R. Tureček, R. Shigemoto, Y. Zhang,
R. Luján, L. Jacobson, B. Biermann, J. Fritschy, C. Vacher, M. Müller, G. Sansig,
N. Guetg, J. Cryan, K. Kaupmann, M. Gassmann, T. Oertner, B. Bettler, Neuron 50
(2006) 589–601.
date_created: 2018-12-11T11:58:56Z
date_published: 2006-05-18T00:00:00Z
date_updated: 2021-01-12T06:58:54Z
day: '18'
doi: 10.1016/j.neuron.2006.04.014
extern: 1
intvolume: ' 50'
issue: '4'
month: '05'
page: 589 - 601
publication: Neuron
publication_status: published
publisher: Elsevier
publist_id: '4237'
quality_controlled: 0
status: public
title: Differential Compartmentalization and Distinct Functions of GABAB Receptor
Variants
type: journal_article
volume: 50
year: '2006'
...
---
_id: '2662'
abstract:
- lang: eng
text: G-protein-coupled inwardly rectifying K+ channels (Kir3 channels) coupled
to metabotropic GABAB receptors are essential for the control of neuronal excitation.
To determine the distribution of Kir3 channels and their spatial relationship
to GABAB receptors on hippocampal pyramidal cells, we used a high-resolution immunocytochemical
approach. Immunoreactivity for the Kir3.2 subunit was most abundant postsynaptically
and localized to the extrasynaptic plasma membrane of dendritic shafts and spines
of principal cells. Quantitative analysis of immunogold particles for Kir3.2 revealed
an enrichment of the protein around putative glutamatergic synapses on dendritic
spines, similar to that of GABA B1. Consistent with this observation, a high degree
of coclustering of Kir3.2 and GABAB1 was revealed around excitatory synapses by
the highly sensitive SDS-digested freeze-fracture replica immunolabeling. In contrast,
in dendritic shafts receptors and channels were found to be mainly segregated.
These results suggest that Kir3.2-containing K+ channels on dendritic spines preferentially
mediate the effect of GABA, whereas channels on dendritic shafts are likely to
be activated by other neurotransmitters as well. Thus, Kir3 channels, localized
to different subcellular compartments of hippocampal principal cells, appear to
be differentially involved in synaptic integration in pyramidal cell dendrites.
author:
- first_name: Ákos
full_name: Kulik, Ákos
last_name: Kulik
- first_name: Imre
full_name: Vida, Imre
last_name: Vida
- first_name: Yugo
full_name: Fukazawa, Yugo
last_name: Fukazawa
- first_name: Nicole
full_name: Guetg, Nicole
last_name: Guetg
- first_name: Yu
full_name: Kasugai, Yu
last_name: Kasugai
- first_name: Cheryl
full_name: Marker, Cheryl L
last_name: Marker
- first_name: Franck
full_name: Rigato, Franck
last_name: Rigato
- first_name: Bernhard
full_name: Bettler, Bernhard
last_name: Bettler
- first_name: Kevin
full_name: Wickman, Kevin D
last_name: Wickman
- first_name: Michael
full_name: Frotscher, Michael
last_name: Frotscher
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
citation:
ama: Kulik Á, Vida I, Fukazawa Y, et al. Compartment-dependent colocalization of
Kir3.2-containing K+ channels and GABAB receptors in hippocampal pyramidal cells.
Journal of Neuroscience. 2006;26(16):4289-4297. doi:10.1523/JNEUROSCI.4178-05.2006
apa: Kulik, Á., Vida, I., Fukazawa, Y., Guetg, N., Kasugai, Y., Marker, C., … Shigemoto,
R. (2006). Compartment-dependent colocalization of Kir3.2-containing K+ channels
and GABAB receptors in hippocampal pyramidal cells. Journal of Neuroscience.
Society for Neuroscience. https://doi.org/10.1523/JNEUROSCI.4178-05.2006
chicago: Kulik, Ákos, Imre Vida, Yugo Fukazawa, Nicole Guetg, Yu Kasugai, Cheryl
Marker, Franck Rigato, et al. “Compartment-Dependent Colocalization of Kir3.2-Containing
K+ Channels and GABAB Receptors in Hippocampal Pyramidal Cells.” Journal of
Neuroscience. Society for Neuroscience, 2006. https://doi.org/10.1523/JNEUROSCI.4178-05.2006.
ieee: Á. Kulik et al., “Compartment-dependent colocalization of Kir3.2-containing
K+ channels and GABAB receptors in hippocampal pyramidal cells,” Journal of
Neuroscience, vol. 26, no. 16. Society for Neuroscience, pp. 4289–4297, 2006.
ista: Kulik Á, Vida I, Fukazawa Y, Guetg N, Kasugai Y, Marker C, Rigato F, Bettler
B, Wickman K, Frotscher M, Shigemoto R. 2006. Compartment-dependent colocalization
of Kir3.2-containing K+ channels and GABAB receptors in hippocampal pyramidal
cells. Journal of Neuroscience. 26(16), 4289–4297.
mla: Kulik, Ákos, et al. “Compartment-Dependent Colocalization of Kir3.2-Containing
K+ Channels and GABAB Receptors in Hippocampal Pyramidal Cells.” Journal of
Neuroscience, vol. 26, no. 16, Society for Neuroscience, 2006, pp. 4289–97,
doi:10.1523/JNEUROSCI.4178-05.2006.
short: Á. Kulik, I. Vida, Y. Fukazawa, N. Guetg, Y. Kasugai, C. Marker, F. Rigato,
B. Bettler, K. Wickman, M. Frotscher, R. Shigemoto, Journal of Neuroscience 26
(2006) 4289–4297.
date_created: 2018-12-11T11:58:56Z
date_published: 2006-04-19T00:00:00Z
date_updated: 2021-01-12T06:58:54Z
day: '19'
doi: 10.1523/JNEUROSCI.4178-05.2006
extern: 1
intvolume: ' 26'
issue: '16'
month: '04'
page: 4289 - 4297
publication: Journal of Neuroscience
publication_status: published
publisher: Society for Neuroscience
publist_id: '4235'
quality_controlled: 0
status: public
title: Compartment-dependent colocalization of Kir3.2-containing K+ channels and GABAB
receptors in hippocampal pyramidal cells
type: journal_article
volume: 26
year: '2006'
...
---
_id: '2663'
abstract:
- lang: eng
text: The rocker mice are hereditary ataxic mutants that carry a point mutation
in the gene encoding the CaV2.1 (P/Q-type) Ca2+ channel α1 subunit, and show the
mildest symptoms among the reported CaV2.1 mutant mice. We studied the basic characteristics
of the rocker mutant Ca2+ channel and their impacts on excitatory synaptic transmission
in cerebellar Purkinje cells (PCs). In acutely dissociated PC somas, the rocker
mutant channel showed a moderate reduction in Ca2+ channel current density, whereas
its kinetics and voltage dependency of gating remained nearly normal. Despite
the small changes in channel function, synaptic transmission in the parallel fiber
(PF)-PC synapses was severely impaired. The climbing fiber inputs onto PCs showed
a moderate impairment but could elicit normal complex spikes. Presynaptic function
of the PF-PC synapses, however, was unexpectedly almost normal in terms of paired-pulse
facilitation, sensitivity to extracellular Ca2+ concentration and glutamate concentration
in synaptic clefts. Electron microscopic analyses including freeze-fracture replica
labeling revealed that both the number and density of postsynaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic
acid (AMPA) receptors substantially decreased without gross structural changes
of the PF-PC synapses. We also observed an abnormal arborization of PC dendrites
in young adult rocker mice (∼ 1 month old). These lines of evidence suggest that
even a moderate dysfunction of CaV2.1 Ca2+ channel can cause substantial changes
in postsynaptic molecular composition of the PF-PC synapses and dendritic structure
of PCs.
author:
- first_name: Takashi
full_name: Kodama, Takashi
last_name: Kodama
- first_name: Yuko
full_name: Itsukaichi-Nishida, Yuko
last_name: Itsukaichi Nishida
- first_name: Yugo
full_name: Fukazawa, Yugo
last_name: Fukazawa
- first_name: Minoru
full_name: Wakamori, Minoru
last_name: Wakamori
- first_name: Mariko
full_name: Miyata, Mariko
last_name: Miyata
- first_name: Elek
full_name: Molnár, Elek
last_name: Molnár
- first_name: Yasuo
full_name: Mori, Yasuo
last_name: Mori
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
- first_name: Keiji
full_name: Imoto, Keiji
last_name: Imoto
citation:
ama: Kodama T, Itsukaichi Nishida Y, Fukazawa Y, et al. A CaV2.1 calcium channel
mutation rocker reduces the number of postsynaptic AMPA receptors in parallel
fiber-Purkinje cell synapses. European Journal of Neuroscience. 2006;24(11):2993-3007.
doi:10.1111/j.1460-9568.2006.05191.x
apa: Kodama, T., Itsukaichi Nishida, Y., Fukazawa, Y., Wakamori, M., Miyata, M.,
Molnár, E., … Imoto, K. (2006). A CaV2.1 calcium channel mutation rocker reduces
the number of postsynaptic AMPA receptors in parallel fiber-Purkinje cell synapses.
European Journal of Neuroscience. Wiley-Blackwell. https://doi.org/10.1111/j.1460-9568.2006.05191.x
chicago: Kodama, Takashi, Yuko Itsukaichi Nishida, Yugo Fukazawa, Minoru Wakamori,
Mariko Miyata, Elek Molnár, Yasuo Mori, Ryuichi Shigemoto, and Keiji Imoto. “A
CaV2.1 Calcium Channel Mutation Rocker Reduces the Number of Postsynaptic AMPA
Receptors in Parallel Fiber-Purkinje Cell Synapses.” European Journal of Neuroscience.
Wiley-Blackwell, 2006. https://doi.org/10.1111/j.1460-9568.2006.05191.x.
ieee: T. Kodama et al., “A CaV2.1 calcium channel mutation rocker reduces
the number of postsynaptic AMPA receptors in parallel fiber-Purkinje cell synapses,”
European Journal of Neuroscience, vol. 24, no. 11. Wiley-Blackwell, pp.
2993–3007, 2006.
ista: Kodama T, Itsukaichi Nishida Y, Fukazawa Y, Wakamori M, Miyata M, Molnár E,
Mori Y, Shigemoto R, Imoto K. 2006. A CaV2.1 calcium channel mutation rocker reduces
the number of postsynaptic AMPA receptors in parallel fiber-Purkinje cell synapses.
European Journal of Neuroscience. 24(11), 2993–3007.
mla: Kodama, Takashi, et al. “A CaV2.1 Calcium Channel Mutation Rocker Reduces the
Number of Postsynaptic AMPA Receptors in Parallel Fiber-Purkinje Cell Synapses.”
European Journal of Neuroscience, vol. 24, no. 11, Wiley-Blackwell, 2006,
pp. 2993–3007, doi:10.1111/j.1460-9568.2006.05191.x.
short: T. Kodama, Y. Itsukaichi Nishida, Y. Fukazawa, M. Wakamori, M. Miyata, E.
Molnár, Y. Mori, R. Shigemoto, K. Imoto, European Journal of Neuroscience 24 (2006)
2993–3007.
date_created: 2018-12-11T11:58:56Z
date_published: 2006-12-01T00:00:00Z
date_updated: 2021-01-12T06:58:54Z
day: '01'
doi: 10.1111/j.1460-9568.2006.05191.x
extern: 1
intvolume: ' 24'
issue: '11'
month: '12'
page: 2993 - 3007
publication: European Journal of Neuroscience
publication_status: published
publisher: Wiley-Blackwell
publist_id: '4233'
quality_controlled: 0
status: public
title: A CaV2.1 calcium channel mutation rocker reduces the number of postsynaptic
AMPA receptors in parallel fiber-Purkinje cell synapses
type: journal_article
volume: 24
year: '2006'
...
---
_id: '2664'
abstract:
- lang: eng
text: Metabotropic glutamate receptors (mGlus) are a family of G-protein-coupled
receptors activated by the neurotransmitter glutamate. Molecular cloning has revealed
eight different subtypes (mGlu1-8) with distinct molecular and pharmacological
properties. Multiplicity in this receptor family is further generated through
alternative splicing. mGlus activate a multitude of signalling pathways important
for modulating neuronal excitability, synaptic plasticity and feedback regulation
of neurotransmitter release. In this review, we summarize anatomical findings
(from our work and that of other laboratories) describing their distribution in
the central nervous system. Recent evidence regarding the localization of these
receptors in peripheral tissues will also be examined. The distinct regional,
cellular and subcellular distribution of mGlus in the brain will be discussed
in view of their relationship to neurotransmitter release sites and of possible
functional implications.
author:
- first_name: Francesco
full_name: Ferraguti, Francesco
last_name: Ferraguti
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
citation:
ama: Ferraguti F, Shigemoto R. Metabotropic glutamate receptors. Cell and Tissue
Research. 2006;326(2):483-504. doi:10.1007/s00441-006-0266-5
apa: Ferraguti, F., & Shigemoto, R. (2006). Metabotropic glutamate receptors.
Cell and Tissue Research. Springer. https://doi.org/10.1007/s00441-006-0266-5
chicago: Ferraguti, Francesco, and Ryuichi Shigemoto. “Metabotropic Glutamate Receptors.”
Cell and Tissue Research. Springer, 2006. https://doi.org/10.1007/s00441-006-0266-5.
ieee: F. Ferraguti and R. Shigemoto, “Metabotropic glutamate receptors,” Cell
and Tissue Research, vol. 326, no. 2. Springer, pp. 483–504, 2006.
ista: Ferraguti F, Shigemoto R. 2006. Metabotropic glutamate receptors. Cell and
Tissue Research. 326(2), 483–504.
mla: Ferraguti, Francesco, and Ryuichi Shigemoto. “Metabotropic Glutamate Receptors.”
Cell and Tissue Research, vol. 326, no. 2, Springer, 2006, pp. 483–504,
doi:10.1007/s00441-006-0266-5.
short: F. Ferraguti, R. Shigemoto, Cell and Tissue Research 326 (2006) 483–504.
date_created: 2018-12-11T11:58:57Z
date_published: 2006-11-01T00:00:00Z
date_updated: 2020-07-14T12:45:44Z
day: '01'
doi: 10.1007/s00441-006-0266-5
extern: 1
intvolume: ' 326'
issue: '2'
month: '11'
page: 483 - 504
publication: Cell and Tissue Research
publication_status: published
publisher: Springer
publist_id: '4234'
quality_controlled: 0
status: public
title: Metabotropic glutamate receptors
type: review
volume: 326
year: '2006'
...
---
_id: '2745'
abstract:
- lang: eng
text: 'We consider the dynamics of N boson systems interacting through a pair potential
N -1 V a (x i -x j ) where V a (x)=a -3 V(x/a). We denote the solution to the
N-particle Schrödinger equation by Ψ N, t . Recall that the Gross-Pitaevskii (GP)
equation is a nonlinear Schrödinger equation and the GP hierarchy is an infinite
BBGKY hierarchy of equations so that if u t solves the GP equation, then the family
of k-particle density matrices [InlineMediaObject not available: see fulltext.]
solves the GP hierarchy. Under the assumption that a = Nε for 0 < ε < 3/5,
we prove that as N→∞ the limit points of the k-particle density matrices of Ψ
N, t are solutions of the GP hierarchy with the coupling constant in the nonlinear
term of the GP equation given by ∫ V (x)dx. The uniqueness of the solutions of
this hierarchy remains an open question.'
author:
- first_name: Alexander
full_name: Elgart, Alexander
last_name: Elgart
- 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: Elgart A, Erdös L, Schlein B, Yau H. Gross-Pitaevskii equation as the mean
field limit of weakly coupled bosons. Archive for Rational Mechanics and Analysis.
2006;179(2):265-283. doi:10.1007/s00205-005-0388-z
apa: Elgart, A., Erdös, L., Schlein, B., & Yau, H. (2006). Gross-Pitaevskii
equation as the mean field limit of weakly coupled bosons. Archive for Rational
Mechanics and Analysis. Springer. https://doi.org/10.1007/s00205-005-0388-z
chicago: Elgart, Alexander, László Erdös, Benjamin Schlein, and Horng Yau. “Gross-Pitaevskii
Equation as the Mean Field Limit of Weakly Coupled Bosons.” Archive for Rational
Mechanics and Analysis. Springer, 2006. https://doi.org/10.1007/s00205-005-0388-z.
ieee: A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Gross-Pitaevskii equation as
the mean field limit of weakly coupled bosons,” Archive for Rational Mechanics
and Analysis, vol. 179, no. 2. Springer, pp. 265–283, 2006.
ista: Elgart A, Erdös L, Schlein B, Yau H. 2006. Gross-Pitaevskii equation as the
mean field limit of weakly coupled bosons. Archive for Rational Mechanics and
Analysis. 179(2), 265–283.
mla: Elgart, Alexander, et al. “Gross-Pitaevskii Equation as the Mean Field Limit
of Weakly Coupled Bosons.” Archive for Rational Mechanics and Analysis,
vol. 179, no. 2, Springer, 2006, pp. 265–83, doi:10.1007/s00205-005-0388-z.
short: A. Elgart, L. Erdös, B. Schlein, H. Yau, Archive for Rational Mechanics and
Analysis 179 (2006) 265–283.
date_created: 2018-12-11T11:59:22Z
date_published: 2006-02-01T00:00:00Z
date_updated: 2021-01-12T06:59:25Z
day: '01'
doi: 10.1007/s00205-005-0388-z
extern: 1
intvolume: ' 179'
issue: '2'
month: '02'
page: 265 - 283
publication: Archive for Rational Mechanics and Analysis
publication_status: published
publisher: Springer
publist_id: '4147'
quality_controlled: 0
status: public
title: Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons
type: journal_article
volume: 179
year: '2006'
...
---
_id: '2746'
abstract:
- lang: eng
text: We consider random Schrödinger equations on Rd or Zd for d ≥ 3 with uncorrelated,
identically distributed random potential. Denote by λ the coupling constant and
ψt the solution with initial data ψ0.
alternative_title:
- LNP
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Manfred
full_name: Salmhofer, Manfred
last_name: Salmhofer
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: 'Erdös L, Salmhofer M, Yau H. Towards the quantum Brownian motion. In: Vol
690. World Scientific Publishing; 2006:233-257. doi:10.1007/3-540-34273-7_18'
apa: 'Erdös, L., Salmhofer, M., & Yau, H. (2006). Towards the quantum Brownian
motion (Vol. 690, pp. 233–257). Presented at the QMath: Mathematical Results in
Quantum Physics, World Scientific Publishing. https://doi.org/10.1007/3-540-34273-7_18'
chicago: Erdös, László, Manfred Salmhofer, and Horng Yau. “Towards the Quantum Brownian
Motion,” 690:233–57. World Scientific Publishing, 2006. https://doi.org/10.1007/3-540-34273-7_18.
ieee: 'L. Erdös, M. Salmhofer, and H. Yau, “Towards the quantum Brownian motion,”
presented at the QMath: Mathematical Results in Quantum Physics, 2006, vol. 690,
pp. 233–257.'
ista: 'Erdös L, Salmhofer M, Yau H. 2006. Towards the quantum Brownian motion. QMath:
Mathematical Results in Quantum Physics, LNP, vol. 690, 233–257.'
mla: Erdös, László, et al. Towards the Quantum Brownian Motion. Vol. 690,
World Scientific Publishing, 2006, pp. 233–57, doi:10.1007/3-540-34273-7_18.
short: L. Erdös, M. Salmhofer, H. Yau, in:, World Scientific Publishing, 2006, pp.
233–257.
conference:
name: 'QMath: Mathematical Results in Quantum Physics'
date_created: 2018-12-11T11:59:23Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2021-01-12T06:59:25Z
day: '01'
doi: 10.1007/3-540-34273-7_18
extern: 1
intvolume: ' 690'
month: '01'
page: 233 - 257
publication_status: published
publisher: World Scientific Publishing
publist_id: '4146'
quality_controlled: 0
status: public
title: Towards the quantum Brownian motion
type: conference
volume: 690
year: '2006'
...
---
_id: '2747'
abstract:
- lang: eng
text: Consider a system of N bosons on the three-dimensional unit torus interacting
via a pair potential N 2V(N(x i - x j)) where x = (x i, . . ., x N) denotes the
positions of the particles. Suppose that the initial data ψ N,0 satisfies the
condition 〈ψ N,0, H 2 Nψ N,0) ≤ C N 2 where H N is the Hamiltonian of the Bose
system. This condition is satisfied if ψ N,0 = W Nφ N,t where W N is an approximate
ground state to H N and φ N,0 is regular. Let ψ N,t denote the solution to the
Schrödinger equation with Hamiltonian H N. Gross and Pitaevskii proposed to model
the dynamics of such a system by a nonlinear Schrödinger equation, the Gross-Pitaevskii
(GP) equation. The GP hierarchy is an infinite BBGKY hierarchy of equations so
that if u t solves the GP equation, then the family of k-particle density matrices
⊗ k |u t?〉 〈 t | solves the GP hierarchy. We prove that as N → ∞ the limit points
of the k-particle density matrices of ψ N,t are solutions of the GP hierarchy.
Our analysis requires that the N-boson dynamics be described by a modified Hamiltonian
that cuts off the pair interactions whenever at least three particles come into
a region with diameter much smaller than the typical interparticle distance. Our
proof can be extended to a modified Hamiltonian that only forbids at least n particles
from coming close together for any fixed n.
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. Derivation of the Gross-Pitaevskii hierarchy for
the dynamics of Bose-Einstein condensate. Communications on Pure and Applied
Mathematics. 2006;59(12):1659-1741. doi:10.1002/cpa.20123
apa: Erdös, L., Schlein, B., & Yau, H. (2006). Derivation of the Gross-Pitaevskii
hierarchy for the dynamics of Bose-Einstein condensate. Communications on Pure
and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.20123
chicago: Erdös, László, Benjamin Schlein, and Horng Yau. “Derivation of the Gross-Pitaevskii
Hierarchy for the Dynamics of Bose-Einstein Condensate.” Communications on
Pure and Applied Mathematics. Wiley-Blackwell, 2006. https://doi.org/10.1002/cpa.20123.
ieee: L. Erdös, B. Schlein, and H. Yau, “Derivation of the Gross-Pitaevskii hierarchy
for the dynamics of Bose-Einstein condensate,” Communications on Pure and Applied
Mathematics, vol. 59, no. 12. Wiley-Blackwell, pp. 1659–1741, 2006.
ista: Erdös L, Schlein B, Yau H. 2006. Derivation of the Gross-Pitaevskii hierarchy
for the dynamics of Bose-Einstein condensate. Communications on Pure and Applied
Mathematics. 59(12), 1659–1741.
mla: Erdös, László, et al. “Derivation of the Gross-Pitaevskii Hierarchy for the
Dynamics of Bose-Einstein Condensate.” Communications on Pure and Applied Mathematics,
vol. 59, no. 12, Wiley-Blackwell, 2006, pp. 1659–741, doi:10.1002/cpa.20123.
short: L. Erdös, B. Schlein, H. Yau, Communications on Pure and Applied Mathematics
59 (2006) 1659–1741.
date_created: 2018-12-11T11:59:23Z
date_published: 2006-12-01T00:00:00Z
date_updated: 2021-01-12T06:59:26Z
day: '01'
doi: 10.1002/cpa.20123
extern: 1
intvolume: ' 59'
issue: '12'
month: '12'
page: 1659 - 1741
publication: Communications on Pure and Applied Mathematics
publication_status: published
publisher: Wiley-Blackwell
publist_id: '4145'
quality_controlled: 0
status: public
title: Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein
condensate
type: journal_article
volume: 59
year: '2006'
...