---
_id: '3435'
abstract:
- lang: eng
text: We develop a new method for estimating effective population sizes, Ne, and
selection coefficients, s, from time-series data of allele frequencies sampled
from a single diallelic locus. The method is based on calculating transition probabilities,
using a numerical solution of the diffusion process, and assuming independent
binomial sampling from this diffusion process at each time point. We apply the
method in two example applications. First, we estimate selection coefficients
acting on the CCR5-Δ32 mutation on the basis of published samples of contemporary
and ancient human DNA. We show that the data are compatible with the assumption
of s = 0, although moderate amounts of selection acting on this mutation cannot
be excluded. In our second example, we estimate the selection coefficient acting
on a mutation segregating in an experimental phage population. We show that the
selection coefficient acting on this mutation is ~0.43.
author:
- first_name: Jonathan P
full_name: Jonathan Bollback
id: 2C6FA9CC-F248-11E8-B48F-1D18A9856A87
last_name: Bollback
orcid: 0000-0002-4624-4612
- first_name: Thomas
full_name: York, Thomas L
last_name: York
- first_name: Rasmus
full_name: Nielsen, Rasmus
last_name: Nielsen
citation:
ama: Bollback JP, York T, Nielsen R. Estimation of 2Nes From Temporal Allele Frequency
Data. *Genetics*. 2008;179(1):497-502. doi:10.1534/genetics.107.085019
apa: Bollback, J. P., York, T., & Nielsen, R. (2008). Estimation of 2Nes From
Temporal Allele Frequency Data. *Genetics*. Genetics Society of America.
https://doi.org/10.1534/genetics.107.085019
chicago: Bollback, Jonathan P, Thomas York, and Rasmus Nielsen. “Estimation of 2Nes
From Temporal Allele Frequency Data.” *Genetics*. Genetics Society of America,
2008. https://doi.org/10.1534/genetics.107.085019.
ieee: J. P. Bollback, T. York, and R. Nielsen, “Estimation of 2Nes From Temporal
Allele Frequency Data,” *Genetics*, vol. 179, no. 1. Genetics Society of
America, pp. 497–502, 2008.
ista: Bollback JP, York T, Nielsen R. 2008. Estimation of 2Nes From Temporal Allele
Frequency Data. Genetics. 179(1), 497–502.
mla: Bollback, Jonathan P., et al. “Estimation of 2Nes From Temporal Allele Frequency
Data.” *Genetics*, vol. 179, no. 1, Genetics Society of America, 2008, pp.
497–502, doi:10.1534/genetics.107.085019.
short: J.P. Bollback, T. York, R. Nielsen, Genetics 179 (2008) 497–502.
date_created: 2018-12-11T12:03:19Z
date_published: 2008-05-01T00:00:00Z
date_updated: 2021-01-12T07:43:27Z
day: '01'
doi: 10.1534/genetics.107.085019
extern: 1
intvolume: ' 179'
issue: '1'
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2390626
month: '05'
oa: 1
page: 497 - 502
publication: Genetics
publication_status: published
publisher: Genetics Society of America
publist_id: '2965'
quality_controlled: 0
status: public
title: Estimation of 2Nes From Temporal Allele Frequency Data
type: journal_article
volume: 179
year: '2008'
...
---
_id: '3504'
abstract:
- lang: eng
text: "Simulation and bisimulation metrics for stochastic systems provide a quantitative
gen- eralization of the classical simulation and bisimulation relations. These
metrics capture the similarity of states with respect to quantitative specifications
written in the quantitative μ-calculus and related probabilistic logics.\r\nWe
present algorithms for computing the metrics on Markov decision processes (MDPs),
turn- based stochastic games, and concurrent games. For turn-based games and MDPs,
we provide a polynomial-time algorithm based on linear programming for the computation
of the one-step metric distance between states. The algorithm improves on the
previously known exponential-time algo- rithm based on a reduction to the theory
of reals. We then present PSPACE algorithms for both the decision problem and
the problem of approximating the metric distance between two states, matching
the best known bound for Markov chains. For the bisimulation kernel of the metric,
which corresponds to probabilistic bisimulation, our algorithm works in time O(n4)
for both turn-based games and MDPs; improving the previously best known O(n9 ·
log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing
the exact distance between states is at least as hard as computing the value of
concurrent reachability games and the square-root-sum problem in computational
geometry. We show that checking whether the metric distance is bounded by a rational
r, can be accomplished via a reduction to the theory of real closed fields, involving
a\r\nformula with three quantifier alternations, yielding O(|G|O(|G|5)) time complexity,
improving the previously known reduction with O(|G|O(|G|7)) time complexity. These
algorithms can be iterated\r\nto approximate the metrics using binary search."
acknowledgement: This research was supported in part by the NSF grants CCR-0132780
and CNS-0720884.
alternative_title:
- LIPIcs
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Luca
full_name: De Alfaro, Luca
last_name: De Alfaro
- first_name: Ritankar
full_name: Majumdar, Ritankar
last_name: Majumdar
- first_name: Vishwanath
full_name: Raman, Vishwanath
last_name: Raman
citation:
ama: 'Chatterjee K, De Alfaro L, Majumdar R, Raman V. Algorithms for game metrics.
In: Vol 2. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2008:107-118. doi:10.4230/LIPIcs.FSTTCS.2008.1745'
apa: 'Chatterjee, K., De Alfaro, L., Majumdar, R., & Raman, V. (2008). Algorithms
for game metrics (Vol. 2, pp. 107–118). Presented at the FSTTCS: Foundations of
Software Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1745'
chicago: Chatterjee, Krishnendu, Luca De Alfaro, Ritankar Majumdar, and Vishwanath
Raman. “Algorithms for Game Metrics,” 2:107–18. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2008. https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1745.
ieee: 'K. Chatterjee, L. De Alfaro, R. Majumdar, and V. Raman, “Algorithms for game
metrics,” presented at the FSTTCS: Foundations of Software Technology and Theoretical
Computer Science, 2008, vol. 2, pp. 107–118.'
ista: 'Chatterjee K, De Alfaro L, Majumdar R, Raman V. 2008. Algorithms for game
metrics. FSTTCS: Foundations of Software Technology and Theoretical Computer Science,
LIPIcs, vol. 2, 107–118.'
mla: Chatterjee, Krishnendu, et al. *Algorithms for Game Metrics*. Vol. 2,
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2008, pp. 107–18, doi:10.4230/LIPIcs.FSTTCS.2008.1745.
short: K. Chatterjee, L. De Alfaro, R. Majumdar, V. Raman, in:, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2008, pp. 107–118.
conference:
name: 'FSTTCS: Foundations of Software Technology and Theoretical Computer Science'
date_created: 2018-12-11T12:03:40Z
date_published: 2008-12-05T00:00:00Z
date_updated: 2021-01-12T07:52:48Z
day: '05'
ddc:
- '000'
doi: 10.4230/LIPIcs.FSTTCS.2008.1745
extern: '1'
file:
- access_level: open_access
checksum: 0a447454a24e273f7ddf51dbfe47f877
content_type: application/pdf
creator: dernst
date_created: 2019-05-10T10:01:21Z
date_updated: 2020-07-14T12:46:12Z
file_id: '6398'
file_name: 2008_LIPIcs_Chatterjee.pdf
file_size: 442139
relation: main_file
file_date_updated: 2020-07-14T12:46:12Z
has_accepted_license: '1'
intvolume: ' 2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 107 - 118
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '2883'
quality_controlled: '1'
related_material:
record:
- id: '3868'
relation: later_version
status: public
status: public
title: Algorithms for game metrics
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2008'
...
---
_id: '9457'
abstract:
- lang: eng
text: Eukaryotic chromatin is separated into functional domains differentiated by
posttranslational histone modifications, histone variants, and DNA methylation1–6.
Methylation is associated with repression of transcriptional initiation in plants
and animals, and is frequently found in transposable elements. Proper methylation
patterns are critical for eukaryotic development4,5, and aberrant methylation-induced
silencing of tumor suppressor genes is a common feature of human cancer7. In contrast
to methylation, the histone variant H2A.Z is preferentially deposited by the Swr1
ATPase complex near 5′ ends of genes where it promotes transcriptional competence8–20.
How DNA methylation and H2A.Z influence transcription remains largely unknown.
Here we show that in the plant Arabidopsis thaliana, regions of DNA methylation
are quantitatively deficient in H2A.Z. Exclusion of H2A.Z is seen at sites of
DNA methylation in the bodies of actively transcribed genes and in methylated
transposons. Mutation of the MET1 DNA methyltransferase, which causes both losses
and gains of DNA methylation4,5, engenders opposite changes in H2A.Z deposition,
while mutation of the PIE1 subunit of the Swr1 complex that deposits H2A.Z17 leads
to genome-wide hypermethylation. Our findings indicate that DNA methylation can
influence chromatin structure and effect gene silencing by excluding H2A.Z, and
that H2A.Z protects genes from DNA methylation.
article_processing_charge: No
article_type: letter_note
author:
- first_name: Daniel
full_name: ZILBERMAN, Daniel
id: 6973db13-dd5f-11ea-814e-b3e5455e9ed1
last_name: ZILBERMAN
- first_name: Devin
full_name: Coleman-Derr, Devin
last_name: Coleman-Derr
- first_name: Tracy
full_name: Ballinger, Tracy
last_name: Ballinger
- first_name: Steven
full_name: Henikoff, Steven
last_name: Henikoff
citation:
ama: ZILBERMAN D, Coleman-Derr D, Ballinger T, Henikoff S. Histone H2A.Z and DNA
methylation are mutually antagonistic chromatin marks. *Nature*. 2008;456(7218):125-129.
doi:10.1038/nature07324
apa: ZILBERMAN, D., Coleman-Derr, D., Ballinger, T., & Henikoff, S. (2008).
Histone H2A.Z and DNA methylation are mutually antagonistic chromatin marks. *Nature*.
Springer Nature. https://doi.org/10.1038/nature07324
chicago: ZILBERMAN, Daniel, Devin Coleman-Derr, Tracy Ballinger, and Steven Henikoff.
“Histone H2A.Z and DNA Methylation Are Mutually Antagonistic Chromatin Marks.”
*Nature*. Springer Nature, 2008. https://doi.org/10.1038/nature07324.
ieee: D. ZILBERMAN, D. Coleman-Derr, T. Ballinger, and S. Henikoff, “Histone H2A.Z
and DNA methylation are mutually antagonistic chromatin marks,” *Nature*,
vol. 456, no. 7218. Springer Nature, pp. 125–129, 2008.
ista: ZILBERMAN D, Coleman-Derr D, Ballinger T, Henikoff S. 2008. Histone H2A.Z
and DNA methylation are mutually antagonistic chromatin marks. Nature. 456(7218),
125–129.
mla: ZILBERMAN, Daniel, et al. “Histone H2A.Z and DNA Methylation Are Mutually Antagonistic
Chromatin Marks.” *Nature*, vol. 456, no. 7218, Springer Nature, 2008, pp.
125–29, doi:10.1038/nature07324.
short: D. ZILBERMAN, D. Coleman-Derr, T. Ballinger, S. Henikoff, Nature 456 (2008)
125–129.
date_created: 2021-06-04T11:49:32Z
date_published: 2008-11-06T00:00:00Z
date_updated: 2021-06-08T09:42:26Z
day: '06'
doi: 10.1038/nature07324
extern: '1'
external_id:
pmid:
- '18815594'
intvolume: ' 456'
issue: '7218'
keyword:
- Multidisciplinary
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2877514/
month: '11'
oa: 1
oa_version: Submitted Version
page: 125-129
pmid: 1
publication: Nature
publication_identifier:
eissn:
- 1476-4687
issn:
- 0028-0836
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Histone H2A.Z and DNA methylation are mutually antagonistic chromatin marks
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 456
year: '2008'
...
---
_id: '2367'
abstract:
- lang: eng
text: It was recently shown by Hansen that the Wigner-Yanase entropy is, for general
states of quantum systems, not subadditive with respect to decomposition into
two subsystems, although this property is known to hold for pure states. We investigate
the question whether the weaker property of subadditivity for pure states with
respect to decomposition into more than two subsystems holds. This property would
have interesting applications in quantum chemistry. We show, however, that it
does not hold in general, and provide a counterexample.
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. On the failure of subadditivity of the Wigner-Yanase entropy.
*Letters in Mathematical Physics*. 2007;80(3):285-288. doi:10.1007/s11005-007-0159-x
apa: Seiringer, R. (2007). On the failure of subadditivity of the Wigner-Yanase
entropy. *Letters in Mathematical Physics*. Springer. https://doi.org/10.1007/s11005-007-0159-x
chicago: Seiringer, Robert. “On the Failure of Subadditivity of the Wigner-Yanase
Entropy.” *Letters in Mathematical Physics*. Springer, 2007. https://doi.org/10.1007/s11005-007-0159-x.
ieee: R. Seiringer, “On the failure of subadditivity of the Wigner-Yanase entropy,”
*Letters in Mathematical Physics*, vol. 80, no. 3. Springer, pp. 285–288,
2007.
ista: Seiringer R. 2007. On the failure of subadditivity of the Wigner-Yanase entropy.
Letters in Mathematical Physics. 80(3), 285–288.
mla: Seiringer, Robert. “On the Failure of Subadditivity of the Wigner-Yanase Entropy.”
*Letters in Mathematical Physics*, vol. 80, no. 3, Springer, 2007, pp. 285–88,
doi:10.1007/s11005-007-0159-x.
short: R. Seiringer, Letters in Mathematical Physics 80 (2007) 285–288.
date_created: 2018-12-11T11:57:15Z
date_published: 2007-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:03Z
day: '01'
doi: 10.1007/s11005-007-0159-x
extern: 1
intvolume: ' 80'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/0704.1435
month: '06'
oa: 1
page: 285 - 288
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4557'
quality_controlled: 0
status: public
title: On the failure of subadditivity of the Wigner-Yanase entropy
type: journal_article
volume: 80
year: '2007'
...
---
_id: '2370'
abstract:
- lang: eng
text: After recalling briefly the connection between spontaneous symmetry breaking
and off-diagonal long-range order for models of magnets a general proof of spontaneous
breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented.
The proof is based on a rigorous validation of Bogoliubov's c-number substitution
for the k = 0 mode operator α0.
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
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Lieb É, Seiringer R, Yngvason J. Bose-Einstein condensation and spontaneous
symmetry breaking. *Reports on Mathematical Physics*. 2007;59(3):389-399.
doi:10.1016/S0034-4877(07)80074-7
apa: Lieb, É., Seiringer, R., & Yngvason, J. (2007). Bose-Einstein condensation
and spontaneous symmetry breaking. *Reports on Mathematical Physics*. Elsevier.
https://doi.org/10.1016/S0034-4877(07)80074-7
chicago: Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Bose-Einstein Condensation
and Spontaneous Symmetry Breaking.” *Reports on Mathematical Physics*. Elsevier,
2007. https://doi.org/10.1016/S0034-4877(07)80074-7.
ieee: É. Lieb, R. Seiringer, and J. Yngvason, “Bose-Einstein condensation and spontaneous
symmetry breaking,” *Reports on Mathematical Physics*, vol. 59, no. 3. Elsevier,
pp. 389–399, 2007.
ista: Lieb É, Seiringer R, Yngvason J. 2007. Bose-Einstein condensation and spontaneous
symmetry breaking. Reports on Mathematical Physics. 59(3), 389–399.
mla: Lieb, Élliott, et al. “Bose-Einstein Condensation and Spontaneous Symmetry
Breaking.” *Reports on Mathematical Physics*, vol. 59, no. 3, Elsevier, 2007,
pp. 389–99, doi:10.1016/S0034-4877(07)80074-7.
short: É. Lieb, R. Seiringer, J. Yngvason, Reports on Mathematical Physics 59 (2007)
389–399.
date_created: 2018-12-11T11:57:16Z
date_published: 2007-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:04Z
day: '01'
doi: 10.1016/S0034-4877(07)80074-7
extern: 1
intvolume: ' 59'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0610034
month: '06'
oa: 1
page: 389 - 399
publication: Reports on Mathematical Physics
publication_status: published
publisher: Elsevier
publist_id: '4556'
quality_controlled: 0
status: public
title: Bose-Einstein condensation and spontaneous symmetry breaking
type: journal_article
volume: 59
year: '2007'
...
---
_id: '2371'
abstract:
- lang: eng
text: We give a proof of stability of relativistic matter with magnetic fields all
the way up to the critical value of the nuclear charge Zα = 2/π.
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
citation:
ama: Frank R, Lieb É, Seiringer R. Stability of relativistic matter with magnetic
fields for nuclear charges up to the critical value. *Communications in Mathematical
Physics*. 2007;275(2):479-489. doi:10.1007/s00220-007-0307-2
apa: Frank, R., Lieb, É., & Seiringer, R. (2007). Stability of relativistic
matter with magnetic fields for nuclear charges up to the critical value. *Communications
in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-007-0307-2
chicago: Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Stability of Relativistic
Matter with Magnetic Fields for Nuclear Charges up to the Critical Value.” *Communications
in Mathematical Physics*. Springer, 2007. https://doi.org/10.1007/s00220-007-0307-2.
ieee: R. Frank, É. Lieb, and R. Seiringer, “Stability of relativistic matter with
magnetic fields for nuclear charges up to the critical value,” *Communications
in Mathematical Physics*, vol. 275, no. 2. Springer, pp. 479–489, 2007.
ista: Frank R, Lieb É, Seiringer R. 2007. Stability of relativistic matter with
magnetic fields for nuclear charges up to the critical value. Communications in
Mathematical Physics. 275(2), 479–489.
mla: Frank, Rupert, et al. “Stability of Relativistic Matter with Magnetic Fields
for Nuclear Charges up to the Critical Value.” *Communications in Mathematical
Physics*, vol. 275, no. 2, Springer, 2007, pp. 479–89, doi:10.1007/s00220-007-0307-2.
short: R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 275
(2007) 479–489.
date_created: 2018-12-11T11:57:16Z
date_published: 2007-10-01T00:00:00Z
date_updated: 2021-01-12T06:57:05Z
day: '01'
doi: 10.1007/s00220-007-0307-2
extern: 1
intvolume: ' 275'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0610062
month: '10'
oa: 1
page: 479 - 489
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4555'
quality_controlled: 0
status: public
title: Stability of relativistic matter with magnetic fields for nuclear charges up
to the critical value
type: journal_article
volume: 275
year: '2007'
...
---
_id: '2372'
abstract:
- lang: eng
text: The increasing interest in the Müller density-matrix-functional theory has
led us to a systematic mathematical investigation of its properties. This functional
is similar to the Hartree-Fock (HF) functional, but with a modified exchange term
in which the square of the density matrix γ(x, x′) is replaced by the square of
γ1 2 (x, x′). After an extensive introductory discussion of density-matrix-functional
theory we show, among other things, that this functional is convex (unlike the
HF functional) and that energy minimizing γ 's have unique densities ρ(r), which
is a physically desirable property often absent in HF theory. We show that minimizers
exist if N≤Z, and derive various properties of the minimal energy and the corresponding
minimizers. We also give a precise statement about the equation for the orbitals
of γ, which is more complex than for HF theory. We state some open mathematical
questions about the theory together with conjectured solutions.
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: Heinz
full_name: Siedentop, Heinz K
last_name: Siedentop
citation:
ama: Frank R, Lieb É, Seiringer R, Siedentop H. Müller’s exchange-correlation energy
in density-matrix-functional theory. *Physical Review A - Atomic, Molecular,
and Optical Physics*. 2007;76(5). doi:10.1103/PhysRevA.76.052517
apa: Frank, R., Lieb, É., Seiringer, R., & Siedentop, H. (2007). Müller’s exchange-correlation
energy in density-matrix-functional theory. *Physical Review A - Atomic, Molecular,
and Optical Physics*. American Physical Society. https://doi.org/10.1103/PhysRevA.76.052517
chicago: Frank, Rupert, Élliott Lieb, Robert Seiringer, and Heinz Siedentop. “Müller’s
Exchange-Correlation Energy in Density-Matrix-Functional Theory.” *Physical
Review A - Atomic, Molecular, and Optical Physics*. American Physical Society,
2007. https://doi.org/10.1103/PhysRevA.76.052517.
ieee: R. Frank, É. Lieb, R. Seiringer, and H. Siedentop, “Müller’s exchange-correlation
energy in density-matrix-functional theory,” *Physical Review A - Atomic, Molecular,
and Optical Physics*, vol. 76, no. 5. American Physical Society, 2007.
ista: Frank R, Lieb É, Seiringer R, Siedentop H. 2007. Müller’s exchange-correlation
energy in density-matrix-functional theory. Physical Review A - Atomic, Molecular,
and Optical Physics. 76(5).
mla: Frank, Rupert, et al. “Müller’s Exchange-Correlation Energy in Density-Matrix-Functional
Theory.” *Physical Review A - Atomic, Molecular, and Optical Physics*, vol.
76, no. 5, American Physical Society, 2007, doi:10.1103/PhysRevA.76.052517.
short: R. Frank, É. Lieb, R. Seiringer, H. Siedentop, Physical Review A - Atomic,
Molecular, and Optical Physics 76 (2007).
date_created: 2018-12-11T11:57:17Z
date_published: 2007-11-30T00:00:00Z
date_updated: 2021-01-12T06:57:05Z
day: '30'
doi: 10.1103/PhysRevA.76.052517
extern: 1
intvolume: ' 76'
issue: '5'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/0705.1587
month: '11'
oa: 1
publication: Physical Review A - Atomic, Molecular, and Optical Physics
publication_status: published
publisher: American Physical Society
publist_id: '4554'
quality_controlled: 0
status: public
title: Müller's exchange-correlation energy in density-matrix-functional theory
type: journal_article
volume: 76
year: '2007'
...
---
_id: '2373'
abstract:
- lang: eng
text: For the BCS equation with local two-body interaction λV(x), we give a rigorous
analysis of the asymptotic behavior of the critical temperature as γ"0. We
derive necessary and sufficient conditions onV(x) for the existence of a nontrivial
solution for all values of γ>0.
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Serguei
full_name: Naboko, Serguei N
last_name: Naboko
- 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, Hainzl C, Naboko S, Seiringer R. The critical temperature for the
BCS equation at weak coupling. *Journal of Geometric Analysis*. 2007;17(4):559-567.
doi:10.1007/BF02937429
apa: Frank, R., Hainzl, C., Naboko, S., & Seiringer, R. (2007). The critical
temperature for the BCS equation at weak coupling. *Journal of Geometric Analysis*.
Springer. https://doi.org/10.1007/BF02937429
chicago: Frank, Rupert, Christian Hainzl, Serguei Naboko, and Robert Seiringer.
“The Critical Temperature for the BCS Equation at Weak Coupling.” *Journal of
Geometric Analysis*. Springer, 2007. https://doi.org/10.1007/BF02937429.
ieee: R. Frank, C. Hainzl, S. Naboko, and R. Seiringer, “The critical temperature
for the BCS equation at weak coupling,” *Journal of Geometric Analysis*,
vol. 17, no. 4. Springer, pp. 559–567, 2007.
ista: Frank R, Hainzl C, Naboko S, Seiringer R. 2007. The critical temperature for
the BCS equation at weak coupling. Journal of Geometric Analysis. 17(4), 559–567.
mla: Frank, Rupert, et al. “The Critical Temperature for the BCS Equation at Weak
Coupling.” *Journal of Geometric Analysis*, vol. 17, no. 4, Springer, 2007,
pp. 559–67, doi:10.1007/BF02937429.
short: R. Frank, C. Hainzl, S. Naboko, R. Seiringer, Journal of Geometric Analysis
17 (2007) 559–567.
date_created: 2018-12-11T11:57:17Z
date_published: 2007-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:05Z
day: '01'
doi: 10.1007/BF02937429
extern: 1
intvolume: ' 17'
issue: '4'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/0704.3564
month: '01'
oa: 1
page: 559 - 567
publication: Journal of Geometric Analysis
publication_status: published
publisher: Springer
publist_id: '4553'
quality_controlled: 0
status: public
title: The critical temperature for the BCS equation at weak coupling
type: journal_article
volume: 17
year: '2007'
...
---
_id: '2375'
abstract:
- lang: eng
text: We give a Cwikel-Lieb-Rozenblum type bound on the number of bound states of
Schrödinger operators with matrix-valued potentials using the functional integral
method of Lieb. This significantly improves the constant in this inequality obtained
earlier by Hundertmark.
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
citation:
ama: Frank R, Lieb É, Seiringer R. Number of bound states of Schrödinger operators
with matrix-valued potentials. *Letters in Mathematical Physics*. 2007;82(2-3):107-116.
doi:10.1007/s11005-007-0211-x
apa: Frank, R., Lieb, É., & Seiringer, R. (2007). Number of bound states of
Schrödinger operators with matrix-valued potentials. *Letters in Mathematical
Physics*. Springer. https://doi.org/10.1007/s11005-007-0211-x
chicago: Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Number of Bound States
of Schrödinger Operators with Matrix-Valued Potentials.” *Letters in Mathematical
Physics*. Springer, 2007. https://doi.org/10.1007/s11005-007-0211-x.
ieee: R. Frank, É. Lieb, and R. Seiringer, “Number of bound states of Schrödinger
operators with matrix-valued potentials,” *Letters in Mathematical Physics*,
vol. 82, no. 2–3. Springer, pp. 107–116, 2007.
ista: Frank R, Lieb É, Seiringer R. 2007. Number of bound states of Schrödinger
operators with matrix-valued potentials. Letters in Mathematical Physics. 82(2–3),
107–116.
mla: Frank, Rupert, et al. “Number of Bound States of Schrödinger Operators with
Matrix-Valued Potentials.” *Letters in Mathematical Physics*, vol. 82, no.
2–3, Springer, 2007, pp. 107–16, doi:10.1007/s11005-007-0211-x.
short: R. Frank, É. Lieb, R. Seiringer, Letters in Mathematical Physics 82 (2007)
107–116.
date_created: 2018-12-11T11:57:18Z
date_published: 2007-12-01T00:00:00Z
date_updated: 2021-01-12T06:57:06Z
day: '01'
doi: 10.1007/s11005-007-0211-x
extern: 1
intvolume: ' 82'
issue: 2-3
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/0710.1877
month: '12'
oa: 1
page: 107 - 116
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4552'
quality_controlled: 0
status: public
title: Number of bound states of Schrödinger operators with matrix-valued potentials
type: journal_article
volume: 82
year: '2007'
...
---
_id: '2705'
alternative_title:
- Proceedings of Symposia in Pure Mathematics
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. Recent developments in quantum mechanics with magnetic fields. In:
Gesztesy F, Deift P, Galvez P, Perry P, Schlag W, eds. *Spectral Theory and
Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday *.
Vol 76. American Mathematical Society; 2007:401-428.'
apa: 'Erdös, L. (2007). Recent developments in quantum mechanics with magnetic fields.
In F. Gesztesy, P. Deift, P. Galvez, P. Perry, & W. Schlag (Eds.), *Spectral
Theory and Mathematical Physics: a Festschrift in Honor of Barry Simon’s 60th
Birthday * (Vol. 76, pp. 401–428). American Mathematical Society.'
chicago: 'Erdös, László. “Recent Developments in Quantum Mechanics with Magnetic
Fields.” In *Spectral Theory and Mathematical Physics: A Festschrift in Honor
of Barry Simon’s 60th Birthday *, edited by Fritz Gesztesy, Percy Deift, Percy
Galvez, Peter Perry, and Wilhelm Schlag, 76:401–28. American Mathematical Society,
2007.'
ieee: 'L. Erdös, “Recent developments in quantum mechanics with magnetic fields,”
in *Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry
Simon’s 60th Birthday *, vol. 76, F. Gesztesy, P. Deift, P. Galvez, P. Perry,
and W. Schlag, Eds. American Mathematical Society, 2007, pp. 401–428.'
ista: 'Erdös L. 2007.Recent developments in quantum mechanics with magnetic fields.
In: Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry
Simon’s 60th Birthday . Proceedings of Symposia in Pure Mathematics, vol. 76,
401–428.'
mla: 'Erdös, László. “Recent Developments in Quantum Mechanics with Magnetic Fields.”
*Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s
60th Birthday *, edited by Fritz Gesztesy et al., vol. 76, American Mathematical
Society, 2007, pp. 401–28.'
short: 'L. Erdös, in:, F. Gesztesy, P. Deift, P. Galvez, P. Perry, W. Schlag (Eds.),
Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s
60th Birthday , American Mathematical Society, 2007, pp. 401–428.'
date_created: 2018-12-11T11:59:10Z
date_published: 2007-03-30T00:00:00Z
date_updated: 2021-01-12T06:59:10Z
day: '30'
editor:
- first_name: Fritz
full_name: Gesztesy, Fritz
last_name: Gesztesy
- first_name: Percy
full_name: Deift, Percy
last_name: Deift
- first_name: Percy
full_name: Galvez, Percy
last_name: Galvez
- first_name: Peter
full_name: Perry, Peter
last_name: Perry
- first_name: Wilhelm
full_name: Schlag, Wilhelm
last_name: Schlag
extern: 1
intvolume: ' 76'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0510055v2
month: '03'
oa: 1
page: 401 - 428
publication: 'Spectral Theory and Mathematical Physics: a Festschrift in Honor of
Barry Simon''s 60th Birthday '
publication_status: published
publisher: American Mathematical Society
publist_id: '4191'
quality_controlled: 0
status: public
title: Recent developments in quantum mechanics with magnetic fields
type: book_chapter
volume: 76
year: '2007'
...