---
_id: '217'
abstract:
- lang: eng
  text: We show that the number of nontrivial rational points of height at most B,
    which lie on the cubic surface x1 x2 x3 = x4 (x1 + x2 + x3)2, has order of magnitude
    B (log B)6. This agrees with Manin's conjecture.
acknowledgement: EPSRC GR/R93155/01
author:
- first_name: Timothy D
  full_name: Timothy Browning
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
citation:
  ama: Browning TD. The density of rational points on a certain singular cubic surface.
    <i>Journal of Number Theory</i>. 2005;119(2):242-283. doi:<a href="https://doi.org/10.1016/j.jnt.2005.11.007">10.1016/j.jnt.2005.11.007</a>
  apa: Browning, T. D. (2005). The density of rational points on a certain singular
    cubic surface. <i>Journal of Number Theory</i>. Elsevier. <a href="https://doi.org/10.1016/j.jnt.2005.11.007">https://doi.org/10.1016/j.jnt.2005.11.007</a>
  chicago: Browning, Timothy D. “The Density of Rational Points on a Certain Singular
    Cubic Surface.” <i>Journal of Number Theory</i>. Elsevier, 2005. <a href="https://doi.org/10.1016/j.jnt.2005.11.007">https://doi.org/10.1016/j.jnt.2005.11.007</a>.
  ieee: T. D. Browning, “The density of rational points on a certain singular cubic
    surface,” <i>Journal of Number Theory</i>, vol. 119, no. 2. Elsevier, pp. 242–283,
    2005.
  ista: Browning TD. 2005. The density of rational points on a certain singular cubic
    surface. Journal of Number Theory. 119(2), 242–283.
  mla: Browning, Timothy D. “The Density of Rational Points on a Certain Singular
    Cubic Surface.” <i>Journal of Number Theory</i>, vol. 119, no. 2, Elsevier, 2005,
    pp. 242–83, doi:<a href="https://doi.org/10.1016/j.jnt.2005.11.007">10.1016/j.jnt.2005.11.007</a>.
  short: T.D. Browning, Journal of Number Theory 119 (2005) 242–283.
date_created: 2018-12-11T11:45:16Z
date_published: 2005-12-27T00:00:00Z
date_updated: 2021-01-12T06:55:45Z
day: '27'
doi: 10.1016/j.jnt.2005.11.007
extern: 1
intvolume: '       119'
issue: '2'
month: '12'
page: 242 - 283
publication: Journal of Number Theory
publication_status: published
publisher: Elsevier
publist_id: '7695'
quality_controlled: 0
status: public
title: The density of rational points on a certain singular cubic surface
type: journal_article
volume: 119
year: '2005'
...
---
_id: '2307'
abstract:
- lang: eng
  text: The human norepinephrine (NE) transporter (hNET) attenuates neuronal signaling
    by rapid NE clearance from the synaptic cleft, and NET is a target for cocaine
    and amphetamines as well as therapeutics for depression, obsessive-compulsive
    disorder, and post-traumatic stress disorder. In spite of its central importance
    in the nervous system, little is known about how NET substrates, such as NE, 1-methyl-4-tetrahydropyridinium
    (MPP+), or amphetamine, interact with NET at the molecular level. Nor do we understand
    the mechanisms behind the transport rate. Previously we introduced a fluorescent
    substrate similar to MPP+, which allowed separate and simultaneous binding and
    transport measurement (Schwartz, J. W., Blakely, R. D., and DeFelice, L. J. (2003)
    J. Biol. Chem. 278, 9768-9777). Here we use this substrate, 4-(4-(dimethylamino)styrl)-N-methyl-pyridinium
    (ASP+), in combination with green fluorescent protein-tagged hNETs to measure
    substrate-transporter stoichiometry and substrate binding kinetics. Calibrated
    confocal microscopy and fluorescence correlation spectroscopy reveal that hNETs,
    which are homo-multimers, bind one substrate molecule per transporter subunit.
    Substrate residence at the transporter, obtained from rapid on-off kinetics revealed
    in fluorescence correlation spectroscopy, is 526 μs. Substrate residence obtained
    by infinite dilution is 1000 times slower. This novel examination of substrate-transporter
    kinetics indicates that a single ASP + molecule binds and unbinds thousands of
    times before being transported or ultimately dissociated from hNET. Calibrated
    fluorescent images combined with mass spectroscopy give a transport rate of 0.06
    ASP +/hNET-protein/s, thus 36,000 on-off binding events (and 36 actual departures)
    occur for one transport event. Therefore binding has a low probability of resulting
    in transport. We interpret these data to mean that inefficient binding could contribute
    to slow transport rates.
author:
- first_name: Joel
  full_name: Schwartz, Joel W
  last_name: Schwartz
- first_name: Gaia
  full_name: Gaia Novarino
  id: 3E57A680-F248-11E8-B48F-1D18A9856A87
  last_name: Novarino
  orcid: 0000-0002-7673-7178
- first_name: David
  full_name: Piston, David W
  last_name: Piston
- first_name: Louis
  full_name: DeFelice, Louis J
  last_name: Defelice
citation:
  ama: Schwartz J, Novarino G, Piston D, Defelice L. Substrate binding stoichiometry
    and kinetics of the norepinephrine transporter. <i>Journal of Biological Chemistry</i>.
    2005;280(19):19177-19184. doi:<a href="https://doi.org/10.1074/jbc.M412923200">10.1074/jbc.M412923200</a>
  apa: Schwartz, J., Novarino, G., Piston, D., &#38; Defelice, L. (2005). Substrate
    binding stoichiometry and kinetics of the norepinephrine transporter. <i>Journal
    of Biological Chemistry</i>. American Society for Biochemistry and Molecular Biology.
    <a href="https://doi.org/10.1074/jbc.M412923200">https://doi.org/10.1074/jbc.M412923200</a>
  chicago: Schwartz, Joel, Gaia Novarino, David Piston, and Louis Defelice. “Substrate
    Binding Stoichiometry and Kinetics of the Norepinephrine Transporter.” <i>Journal
    of Biological Chemistry</i>. American Society for Biochemistry and Molecular Biology,
    2005. <a href="https://doi.org/10.1074/jbc.M412923200">https://doi.org/10.1074/jbc.M412923200</a>.
  ieee: J. Schwartz, G. Novarino, D. Piston, and L. Defelice, “Substrate binding stoichiometry
    and kinetics of the norepinephrine transporter,” <i>Journal of Biological Chemistry</i>,
    vol. 280, no. 19. American Society for Biochemistry and Molecular Biology, pp.
    19177–19184, 2005.
  ista: Schwartz J, Novarino G, Piston D, Defelice L. 2005. Substrate binding stoichiometry
    and kinetics of the norepinephrine transporter. Journal of Biological Chemistry.
    280(19), 19177–19184.
  mla: Schwartz, Joel, et al. “Substrate Binding Stoichiometry and Kinetics of the
    Norepinephrine Transporter.” <i>Journal of Biological Chemistry</i>, vol. 280,
    no. 19, American Society for Biochemistry and Molecular Biology, 2005, pp. 19177–84,
    doi:<a href="https://doi.org/10.1074/jbc.M412923200">10.1074/jbc.M412923200</a>.
  short: J. Schwartz, G. Novarino, D. Piston, L. Defelice, Journal of Biological Chemistry
    280 (2005) 19177–19184.
date_created: 2018-12-11T11:56:54Z
date_published: 2005-05-13T00:00:00Z
date_updated: 2021-01-12T06:56:40Z
day: '13'
doi: 10.1074/jbc.M412923200
extern: 1
intvolume: '       280'
issue: '19'
month: '05'
page: 19177 - 19184
publication: Journal of Biological Chemistry
publication_status: published
publisher: American Society for Biochemistry and Molecular Biology
publist_id: '4619'
quality_controlled: 0
status: public
title: Substrate binding stoichiometry and kinetics of the norepinephrine transporter
type: journal_article
volume: 280
year: '2005'
...
---
_id: '2335'
abstract:
- lang: eng
  text: This book contains a unique survey of the mathematically rigorous results
    about the quantum-mechanical many-body problem that have been obtained by the
    authors in the past seven years. It addresses a topic that is not only rich mathematically,
    using a large variety of techniques in mathematical analysis, but is also one
    with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein
    condensation. The book provides a pedagogical entry into an active area of ongoing
    research for both graduate students and researchers. It is an outgrowth of a course
    given by the authors for graduate students and post-doctoral researchers at the
    Oberwolfach Research Institute in 2004. The book also provides a coherent summary
    of the field and a reference for mathematicians and physicists active in research
    on quantum mechanics.
alternative_title:
- Oberwolfach Seminars
article_processing_charge: No
arxiv: 1
author:
- first_name: Élliott
  full_name: Lieb, Élliott
  last_name: Lieb
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
- first_name: Jakob
  full_name: Yngvason, Jakob
  last_name: Yngvason
citation:
  ama: 'Lieb É, Seiringer R, Solovej J, Yngvason J. <i>The Mathematics of the Bose
    Gas and Its Condensation</i>. Vol 34. Basel ; Berlin: Birkhäuser Verlag; 2005.
    doi:<a href="https://doi.org/10.1007/b137508">10.1007/b137508</a>'
  apa: 'Lieb, É., Seiringer, R., Solovej, J., &#38; Yngvason, J. (2005). <i>The Mathematics
    of the Bose gas and its Condensation</i> (Vol. 34). Basel ; Berlin: Birkhäuser
    Verlag. <a href="https://doi.org/10.1007/b137508">https://doi.org/10.1007/b137508</a>'
  chicago: 'Lieb, Élliott, Robert Seiringer, Jan Solovej, and Jakob Yngvason. <i>The
    Mathematics of the Bose Gas and Its Condensation</i>. Vol. 34. Basel ; Berlin:
    Birkhäuser Verlag, 2005. <a href="https://doi.org/10.1007/b137508">https://doi.org/10.1007/b137508</a>.'
  ieee: 'É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, <i>The Mathematics of
    the Bose gas and its Condensation</i>, vol. 34. Basel ; Berlin: Birkhäuser Verlag,
    2005.'
  ista: 'Lieb É, Seiringer R, Solovej J, Yngvason J. 2005. The Mathematics of the
    Bose gas and its Condensation, Basel ; Berlin: Birkhäuser Verlag, VIII, 203p.'
  mla: Lieb, Élliott, et al. <i>The Mathematics of the Bose Gas and Its Condensation</i>.
    Vol. 34, Birkhäuser Verlag, 2005, doi:<a href="https://doi.org/10.1007/b137508">10.1007/b137508</a>.
  short: É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, The Mathematics of the Bose
    Gas and Its Condensation, Birkhäuser Verlag, Basel ; Berlin, 2005.
date_created: 2018-12-11T11:57:03Z
date_published: 2005-01-01T00:00:00Z
date_updated: 2021-12-22T08:04:00Z
day: '01'
doi: 10.1007/b137508
extern: '1'
external_id:
  arxiv:
  - cond-mat/0610117
intvolume: '        34'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/cond-mat/0610117
month: '01'
oa: 1
oa_version: Preprint
page: VIII, 203
place: Basel ; Berlin
publication_identifier:
  isbn:
  - 978-3-7643-7336-8
publication_status: published
publisher: Birkhäuser Verlag
publist_id: '4591'
quality_controlled: '1'
status: public
title: The Mathematics of the Bose gas and its Condensation
type: book
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 34
year: '2005'
...
---
_id: '2336'
abstract:
- lang: eng
  text: |2-


    Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, ρ, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4–5 decades ago, and to explore new regimes not treated before. For systems with repulsive (i.e. positive) interaction potentials the experimental low temperature state and the ground state are effectively synonymous — and this fact is used in all modeling. In such cases, the leading term in the energy/particle is 2πħ2 aρ/m where a is the scattering length of the two-body potential. Owing to the delicate and peculiar nature of bosonic correlations (such as the strange N 7/5 law for charged bosons), four decades of research failed to establish this plausible formula rigorously. The only previous lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct asymptotic formula has been obtained by us and this work will be presented. The reason behind the mathematical difficulties will be emphasized. A different formula, postulated as late as 1971 by Schick, holds in two dimensions and this, too, will be shown to be correct. With the aid of the methodology developed to prove the lower bound for the homogeneous gas, several other problems have been successfully addressed. One is the proof by us that the Gross-Pitaevskii equation correctly describes the ground state in the ‘traps’ actually used in the experiments. For this system it is also possible to prove complete Bose condensation and superfluidity as we have shown. On the frontier of experimental developments is the possibility that a dilute gas in an elongated trap will behave like a one-dimensional system; we have proved this mathematically. Another topic is a proof that Foldy’s 1961 theory of a high density Bose gas of charged particles correctly describes its ground state energy; using this we can also prove the N 7/5 formula for the ground state energy of the two-component charged Bose gas proposed by Dyson in 1967. All of this is quite recent work and it is hoped that the mathematical methodology might be useful, ultimately, to solve more complex problems connected with these interesting systems.
alternative_title:
- Mathematical Physics Studies
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: Jan
  full_name: Solovej, Jan P
  last_name: Solovej
- first_name: Jakob
  full_name: Yngvason, Jakob
  last_name: Yngvason
citation:
  ama: 'Lieb É, Seiringer R, Solovej J, Yngvason J. The quantum-mechanical many-body
    problem: The Bose gas. In: Benedicks M, Jones P, Smirnov S, Winckler B, eds. <i>Perspectives
    in Analysis</i>. Vol 27. Springer; 2005:97-183. doi:<a href="https://doi.org/10.1007/3-540-30434-7_9">10.1007/3-540-30434-7_9</a>'
  apa: 'Lieb, É., Seiringer, R., Solovej, J., &#38; Yngvason, J. (2005). The quantum-mechanical
    many-body problem: The Bose gas. In M. Benedicks, P. Jones, S. Smirnov, &#38;
    B. Winckler (Eds.), <i>Perspectives in Analysis</i> (Vol. 27, pp. 97–183). Springer.
    <a href="https://doi.org/10.1007/3-540-30434-7_9">https://doi.org/10.1007/3-540-30434-7_9</a>'
  chicago: 'Lieb, Élliott, Robert Seiringer, Jan Solovej, and Jakob Yngvason. “The
    Quantum-Mechanical Many-Body Problem: The Bose Gas.” In <i>Perspectives in Analysis</i>,
    edited by Michael Benedicks, Peter Jones, Stanislav Smirnov, and Björn Winckler,
    27:97–183. Springer, 2005. <a href="https://doi.org/10.1007/3-540-30434-7_9">https://doi.org/10.1007/3-540-30434-7_9</a>.'
  ieee: 'É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “The quantum-mechanical
    many-body problem: The Bose gas,” in <i>Perspectives in Analysis</i>, vol. 27,
    M. Benedicks, P. Jones, S. Smirnov, and B. Winckler, Eds. Springer, 2005, pp.
    97–183.'
  ista: 'Lieb É, Seiringer R, Solovej J, Yngvason J. 2005.The quantum-mechanical many-body
    problem: The Bose gas. In: Perspectives in Analysis. Mathematical Physics Studies,
    vol. 27, 97–183.'
  mla: 'Lieb, Élliott, et al. “The Quantum-Mechanical Many-Body Problem: The Bose
    Gas.” <i>Perspectives in Analysis</i>, edited by Michael Benedicks et al., vol.
    27, Springer, 2005, pp. 97–183, doi:<a href="https://doi.org/10.1007/3-540-30434-7_9">10.1007/3-540-30434-7_9</a>.'
  short: É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, in:, M. Benedicks, P. Jones,
    S. Smirnov, B. Winckler (Eds.), Perspectives in Analysis, Springer, 2005, pp.
    97–183.
date_created: 2018-12-11T11:57:04Z
date_published: 2005-01-01T00:00:00Z
date_updated: 2021-01-12T06:56:52Z
day: '01'
doi: 10.1007/3-540-30434-7_9
editor:
- first_name: Michael
  full_name: Benedicks, Michael
  last_name: Benedicks
- first_name: Peter
  full_name: Jones, Peter W
  last_name: Jones
- first_name: Stanislav
  full_name: Smirnov, Stanislav
  last_name: Smirnov
- first_name: Björn
  full_name: Winckler, Björn
  last_name: Winckler
extern: 1
intvolume: '        27'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0405004
month: '01'
oa: 1
page: 97 - 183
publication: Perspectives in Analysis
publication_status: published
publisher: Springer
publist_id: '4590'
quality_controlled: 0
status: public
title: 'The quantum-mechanical many-body problem: The Bose gas'
type: book_chapter
volume: 27
year: '2005'
...
---
_id: '2359'
abstract:
- lang: eng
  text: The validity of substituting a c-number z for the k = 0 mode operator a0 is
    established rigorously in full generality, thereby verifying one aspect of Bogoliubov's
    1947 theory. This substitution not only yields the correct value of thermodynamic
    quantities such as the pressure or ground state energy, but also the value of
    |z|2 that maximizes the partition function equals the true amount of condensation
    in the presence of a gauge-symmetry-breaking term. This point had previously been
    elusive.
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. Justification of c-number substitutions in
    bosonic hamiltonians. <i>Physical Review Letters</i>. 2005;94(8). doi:<a href="https://doi.org/10.1103/PhysRevLett.94.080401">10.1103/PhysRevLett.94.080401</a>
  apa: Lieb, É., Seiringer, R., &#38; Yngvason, J. (2005). Justification of c-number
    substitutions in bosonic hamiltonians. <i>Physical Review Letters</i>. American
    Physical Society. <a href="https://doi.org/10.1103/PhysRevLett.94.080401">https://doi.org/10.1103/PhysRevLett.94.080401</a>
  chicago: Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Justification of
    C-Number Substitutions in Bosonic Hamiltonians.” <i>Physical Review Letters</i>.
    American Physical Society, 2005. <a href="https://doi.org/10.1103/PhysRevLett.94.080401">https://doi.org/10.1103/PhysRevLett.94.080401</a>.
  ieee: É. Lieb, R. Seiringer, and J. Yngvason, “Justification of c-number substitutions
    in bosonic hamiltonians,” <i>Physical Review Letters</i>, vol. 94, no. 8. American
    Physical Society, 2005.
  ista: Lieb É, Seiringer R, Yngvason J. 2005. Justification of c-number substitutions
    in bosonic hamiltonians. Physical Review Letters. 94(8).
  mla: Lieb, Élliott, et al. “Justification of C-Number Substitutions in Bosonic Hamiltonians.”
    <i>Physical Review Letters</i>, vol. 94, no. 8, American Physical Society, 2005,
    doi:<a href="https://doi.org/10.1103/PhysRevLett.94.080401">10.1103/PhysRevLett.94.080401</a>.
  short: É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 94 (2005).
date_created: 2018-12-11T11:57:12Z
date_published: 2005-03-04T00:00:00Z
date_updated: 2021-01-12T06:57:00Z
day: '04'
doi: 10.1103/PhysRevLett.94.080401
extern: 1
intvolume: '        94'
issue: '8'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0412023
month: '03'
oa: 1
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4566'
quality_controlled: 0
status: public
title: Justification of c-number substitutions in bosonic hamiltonians
type: journal_article
volume: 94
year: '2005'
...
---
_id: '2361'
abstract:
- lang: eng
  text: The strong subadditivity of entropy plays a key role in several areas of physics
    and mathematics. It states that the entropy S[±]=- Tr(Ï±lnÏ±) of a density matrix
    Ï±123 on the product of three Hilbert spaces satisfies S[Ï±123]- S[Ï±12]≤S[Ï±23]-S[Ï±2].
    We strengthen this to S[Ï±123]-S[Ï±12] ≤αnα(S[Ï±23α]-S[Ï±2α]), where the nα are
    weights and the Ï±23α are partitions of Ï±23. Correspondingly, there is a strengthening
    of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove
    some monotonicity and convexity properties of the Wehrl coherent state entropy
    and entropy inequalities for quantum gases.
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. Stronger subadditivity of entropy. <i>Physical Review
    A - Atomic, Molecular, and Optical Physics</i>. 2005;71(6). doi:<a href="https://doi.org/10.1103/PhysRevA.71.062329">10.1103/PhysRevA.71.062329</a>
  apa: Lieb, É., &#38; Seiringer, R. (2005). Stronger subadditivity of entropy. <i>Physical
    Review A - Atomic, Molecular, and Optical Physics</i>. American Physical Society.
    <a href="https://doi.org/10.1103/PhysRevA.71.062329">https://doi.org/10.1103/PhysRevA.71.062329</a>
  chicago: Lieb, Élliott, and Robert Seiringer. “Stronger Subadditivity of Entropy.”
    <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>. American Physical
    Society, 2005. <a href="https://doi.org/10.1103/PhysRevA.71.062329">https://doi.org/10.1103/PhysRevA.71.062329</a>.
  ieee: É. Lieb and R. Seiringer, “Stronger subadditivity of entropy,” <i>Physical
    Review A - Atomic, Molecular, and Optical Physics</i>, vol. 71, no. 6. American
    Physical Society, 2005.
  ista: Lieb É, Seiringer R. 2005. Stronger subadditivity of entropy. Physical Review
    A - Atomic, Molecular, and Optical Physics. 71(6).
  mla: Lieb, Élliott, and Robert Seiringer. “Stronger Subadditivity of Entropy.” <i>Physical
    Review A - Atomic, Molecular, and Optical Physics</i>, vol. 71, no. 6, American
    Physical Society, 2005, doi:<a href="https://doi.org/10.1103/PhysRevA.71.062329">10.1103/PhysRevA.71.062329</a>.
  short: É. Lieb, R. Seiringer, Physical Review A - Atomic, Molecular, and Optical
    Physics 71 (2005).
date_created: 2018-12-11T11:57:13Z
date_published: 2005-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:01Z
day: '01'
doi: 10.1103/PhysRevA.71.062329
extern: 1
intvolume: '        71'
issue: '6'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0412009
month: '06'
oa: 1
publication: Physical Review A - Atomic, Molecular, and Optical Physics
publication_status: published
publisher: American Physical Society
publist_id: '4564'
quality_controlled: 0
status: public
title: Stronger subadditivity of entropy
type: journal_article
volume: 71
year: '2005'
...
---
_id: '2362'
abstract:
- lang: eng
  text: Recent developments in the physics of low-density trapped gases make it worthwhile
    to verify old, well-known results that, while plausible, were based on perturbation
    theory and assumptions about pseudopotentials. We use and extend recently developed
    techniques to give a rigorous derivation of the asymptotic formula for the ground-state
    energy of a dilute gas of N fermions interacting with a short-range, positive
    potential of scattering length a. For spin-12 fermions, this is E∼E0+(22m)2πNa,
    where E0 is the energy of the noninteracting system and is the density. A similar
    formula holds in two dimensions (2D), with a replaced by ln(a2). Obviously this
    2D energy is not the expectation value of a density-independent pseudopotential.
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: Jan
  full_name: Solovej, Jan P
  last_name: Solovej
citation:
  ama: Lieb É, Seiringer R, Solovej J. Ground state energy of the low density Fermi
    gas. <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>. 2005;71(5).
    doi:<a href="https://doi.org/10.1103/PhysRevA.71.053605">10.1103/PhysRevA.71.053605</a>
  apa: Lieb, É., Seiringer, R., &#38; Solovej, J. (2005). Ground state energy of the
    low density Fermi gas. <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>.
    American Physical Society. <a href="https://doi.org/10.1103/PhysRevA.71.053605">https://doi.org/10.1103/PhysRevA.71.053605</a>
  chicago: Lieb, Élliott, Robert Seiringer, and Jan Solovej. “Ground State Energy
    of the Low Density Fermi Gas.” <i>Physical Review A - Atomic, Molecular, and Optical
    Physics</i>. American Physical Society, 2005. <a href="https://doi.org/10.1103/PhysRevA.71.053605">https://doi.org/10.1103/PhysRevA.71.053605</a>.
  ieee: É. Lieb, R. Seiringer, and J. Solovej, “Ground state energy of the low density
    Fermi gas,” <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>,
    vol. 71, no. 5. American Physical Society, 2005.
  ista: Lieb É, Seiringer R, Solovej J. 2005. Ground state energy of the low density
    Fermi gas. Physical Review A - Atomic, Molecular, and Optical Physics. 71(5).
  mla: Lieb, Élliott, et al. “Ground State Energy of the Low Density Fermi Gas.” <i>Physical
    Review A - Atomic, Molecular, and Optical Physics</i>, vol. 71, no. 5, American
    Physical Society, 2005, doi:<a href="https://doi.org/10.1103/PhysRevA.71.053605">10.1103/PhysRevA.71.053605</a>.
  short: É. Lieb, R. Seiringer, J. Solovej, Physical Review A - Atomic, Molecular,
    and Optical Physics 71 (2005).
date_created: 2018-12-11T11:57:13Z
date_published: 2005-05-01T00:00:00Z
date_updated: 2021-01-12T06:57:01Z
day: '01'
doi: 10.1103/PhysRevA.71.053605
extern: 1
intvolume: '        71'
issue: '5'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0412080
month: '05'
oa: 1
publication: Physical Review A - Atomic, Molecular, and Optical Physics
publication_status: published
publisher: American Physical Society
publist_id: '4565'
quality_controlled: 0
status: public
title: Ground state energy of the low density Fermi gas
type: journal_article
volume: 71
year: '2005'
...
---
_id: '2427'
abstract:
- lang: eng
  text: Intersection graphs of disks and of line segments, respectively, have been
    well studied, because of both practical applications and theoretically interesting
    properties of these graphs. Despite partial results, the complexity status of
    the Clique problem for these two graph classes is still open. Here, we consider
    the Clique problem for intersection graphs of ellipses, which, in a sense, interpolate
    between disks and line segments, and show that the problem is APX-hard in that
    case. Moreover, this holds even if for all ellipses, the ratio of the larger over
    the smaller radius is some prescribed number. Furthermore, the reduction immediately
    carries over to intersection graphs of triangles. To our knowledge, this is the
    first hardness result for the Clique problem in intersection graphs of convex
    objects with finite description complexity. We also describe a simple approximation
    algorithm for the case of ellipses for which the ratio of radii is bounded.
author:
- first_name: Christoph
  full_name: Ambühl, Christoph
  last_name: Ambühl
- first_name: Uli
  full_name: Uli Wagner
  id: 36690CA2-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
  orcid: 0000-0002-1494-0568
citation:
  ama: Ambühl C, Wagner U. The Clique problem in intersection graphs of ellipses and
    triangles. <i>Theory of Computing Systems</i>. 2005;38(3):279-292. doi:<a href="https://doi.org/10.1007/s00224-005-1141-6">10.1007/s00224-005-1141-6</a>
  apa: Ambühl, C., &#38; Wagner, U. (2005). The Clique problem in intersection graphs
    of ellipses and triangles. <i>Theory of Computing Systems</i>. Springer. <a href="https://doi.org/10.1007/s00224-005-1141-6">https://doi.org/10.1007/s00224-005-1141-6</a>
  chicago: Ambühl, Christoph, and Uli Wagner. “The Clique Problem in Intersection
    Graphs of Ellipses and Triangles.” <i>Theory of Computing Systems</i>. Springer,
    2005. <a href="https://doi.org/10.1007/s00224-005-1141-6">https://doi.org/10.1007/s00224-005-1141-6</a>.
  ieee: C. Ambühl and U. Wagner, “The Clique problem in intersection graphs of ellipses
    and triangles,” <i>Theory of Computing Systems</i>, vol. 38, no. 3. Springer,
    pp. 279–292, 2005.
  ista: Ambühl C, Wagner U. 2005. The Clique problem in intersection graphs of ellipses
    and triangles. Theory of Computing Systems. 38(3), 279–292.
  mla: Ambühl, Christoph, and Uli Wagner. “The Clique Problem in Intersection Graphs
    of Ellipses and Triangles.” <i>Theory of Computing Systems</i>, vol. 38, no. 3,
    Springer, 2005, pp. 279–92, doi:<a href="https://doi.org/10.1007/s00224-005-1141-6">10.1007/s00224-005-1141-6</a>.
  short: C. Ambühl, U. Wagner, Theory of Computing Systems 38 (2005) 279–292.
date_created: 2018-12-11T11:57:36Z
date_published: 2005-05-01T00:00:00Z
date_updated: 2021-01-12T06:57:25Z
day: '01'
doi: 10.1007/s00224-005-1141-6
extern: 1
intvolume: '        38'
issue: '3'
month: '05'
page: 279 - 292
publication: Theory of Computing Systems
publication_status: published
publisher: Springer
publist_id: '4497'
quality_controlled: 0
status: public
title: The Clique problem in intersection graphs of ellipses and triangles
type: journal_article
volume: 38
year: '2005'
...
---
_id: '2428'
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 several
    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(√n) colors
    in the worst case. We then modify this approach, to obtain an efficient deterministic
    algorithm that uses a maximum of Θ(log 2 n) colors. Next, we present two randomized
    solutions. The first algorithm requires an expected number of at most O(log 2
    n) colors, and produces a coloring which is valid with high probability, and the
    second one, which is a variant of our efficient deterministic algorithm, requires
    an expected number of at most O(log n log log n) colors but always produces a
    valid coloring. 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. The average-case
    behavior for disks, and cases involving other planar ranges, are still open.
author:
- first_name: Amos
  full_name: Fiat, Amos
  last_name: Fiat
- 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: Pach, Elchanan M
  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: 'Fiat A, Levy M, Matoušek J, et al. Online conflict-free coloring for intervals.
    In: SIAM; 2005:545-554. doi:<a href="https://doi.org/10.1137/S0097539704446682">10.1137/S0097539704446682</a>'
  apa: 'Fiat, A., Levy, M., Matoušek, J., Pach, E., Sharir, M., Smorodinsky, S., …
    Welzl, E. (2005). Online conflict-free coloring for intervals (pp. 545–554). Presented
    at the SODA: Symposium on Discrete Algorithms, SIAM. <a href="https://doi.org/10.1137/S0097539704446682">https://doi.org/10.1137/S0097539704446682</a>'
  chicago: Fiat, Amos, Meital Levy, Jiří Matoušek, Elchanan Pach, Micha Sharir, Shakhar
    Smorodinsky, Uli Wagner, and Emo Welzl. “Online Conflict-Free Coloring for Intervals,”
    545–54. SIAM, 2005. <a href="https://doi.org/10.1137/S0097539704446682">https://doi.org/10.1137/S0097539704446682</a>.
  ieee: 'A. Fiat <i>et al.</i>, “Online conflict-free coloring for intervals,” presented
    at the SODA: Symposium on Discrete Algorithms, 2005, pp. 545–554.'
  ista: 'Fiat A, Levy M, Matoušek J, Pach E, Sharir M, Smorodinsky S, Wagner U, Welzl
    E. 2005. Online conflict-free coloring for intervals. SODA: Symposium on Discrete
    Algorithms, 545–554.'
  mla: Fiat, Amos, et al. <i>Online Conflict-Free Coloring for Intervals</i>. SIAM,
    2005, pp. 545–54, doi:<a href="https://doi.org/10.1137/S0097539704446682">10.1137/S0097539704446682</a>.
  short: A. Fiat, M. Levy, J. Matoušek, E. Pach, M. Sharir, S. Smorodinsky, U. Wagner,
    E. Welzl, in:, SIAM, 2005, pp. 545–554.
conference:
  name: 'SODA: Symposium on Discrete Algorithms'
date_created: 2018-12-11T11:57:36Z
date_published: 2005-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:25Z
day: '01'
doi: 10.1137/S0097539704446682
extern: 1
month: '01'
page: 545 - 554
publication_status: published
publisher: SIAM
publist_id: '4496'
quality_controlled: 0
status: public
title: Online conflict-free coloring for intervals
type: conference
year: '2005'
...
---
_id: '4560'
abstract:
- lang: eng
  text: |
    We define and study a quantitative generalization of the traditional boolean framework of model-based specification and verification. In our setting, propositions have integer values at states, and properties have integer values on traces. For example, the value of a quantitative proposition at a state may represent power consumed at the state, and the value of a quantitative property on a trace may represent energy used along the trace. The value of a quantitative property at a state, then, is the maximum (or minimum) value achievable over all possible traces from the state. In this framework, model checking can be used to compute, for example, the minimum battery capacity necessary for achieving a given objective, or the maximal achievable lifetime of a system with a given initial battery capacity. In the case of open systems, these problems require the solution of games with integer values.
    Quantitative model checking and game solving is undecidable, except if bounds on the computation can be found. Indeed, many interesting quantitative properties, like minimal necessary battery capacity and maximal achievable lifetime, can be naturally specified by quantitative-bound automata, which are finite automata with integer registers whose analysis is constrained by a bound function f that maps each system K to an integer f(K). Along with the linear-time, automaton-based view of quantitative verification, we present a corresponding branching-time view based on a quantitative-bound μ-calculus, and we study the relationship, expressive power, and complexity of both views.
alternative_title:
- LNCS
author:
- first_name: Arindam
  full_name: Chakrabarti, Arindam
  last_name: Chakrabarti
- first_name: Krishnendu
  full_name: Krishnendu Chatterjee
  id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
  last_name: Chatterjee
  orcid: 0000-0002-4561-241X
- first_name: Thomas A
  full_name: Thomas Henzinger
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
- first_name: Orna
  full_name: Kupferman, Orna
  last_name: Kupferman
- first_name: Ritankar
  full_name: Majumdar, Ritankar S
  last_name: Majumdar
citation:
  ama: 'Chakrabarti A, Chatterjee K, Henzinger TA, Kupferman O, Majumdar R. Verifying
    quantitative properties using bound functions. In: Vol 3725. Springer; 2005:50-64.
    doi:<a href="https://doi.org/10.1007/11560548_7">10.1007/11560548_7</a>'
  apa: 'Chakrabarti, A., Chatterjee, K., Henzinger, T. A., Kupferman, O., &#38; Majumdar,
    R. (2005). Verifying quantitative properties using bound functions (Vol. 3725,
    pp. 50–64). Presented at the CHARME: Correct Hardware Design and Verification
    Methods, Springer. <a href="https://doi.org/10.1007/11560548_7">https://doi.org/10.1007/11560548_7</a>'
  chicago: Chakrabarti, Arindam, Krishnendu Chatterjee, Thomas A Henzinger, Orna Kupferman,
    and Ritankar Majumdar. “Verifying Quantitative Properties Using Bound Functions,”
    3725:50–64. Springer, 2005. <a href="https://doi.org/10.1007/11560548_7">https://doi.org/10.1007/11560548_7</a>.
  ieee: 'A. Chakrabarti, K. Chatterjee, T. A. Henzinger, O. Kupferman, and R. Majumdar,
    “Verifying quantitative properties using bound functions,” presented at the CHARME:
    Correct Hardware Design and Verification Methods, 2005, vol. 3725, pp. 50–64.'
  ista: 'Chakrabarti A, Chatterjee K, Henzinger TA, Kupferman O, Majumdar R. 2005.
    Verifying quantitative properties using bound functions. CHARME: Correct Hardware
    Design and Verification Methods, LNCS, vol. 3725, 50–64.'
  mla: Chakrabarti, Arindam, et al. <i>Verifying Quantitative Properties Using Bound
    Functions</i>. Vol. 3725, Springer, 2005, pp. 50–64, doi:<a href="https://doi.org/10.1007/11560548_7">10.1007/11560548_7</a>.
  short: A. Chakrabarti, K. Chatterjee, T.A. Henzinger, O. Kupferman, R. Majumdar,
    in:, Springer, 2005, pp. 50–64.
conference:
  name: 'CHARME: Correct Hardware Design and Verification Methods'
date_created: 2018-12-11T12:09:29Z
date_published: 2005-09-19T00:00:00Z
date_updated: 2021-01-12T07:59:42Z
day: '19'
doi: 10.1007/11560548_7
extern: 1
intvolume: '      3725'
month: '09'
page: 50 - 64
publication_status: published
publisher: Springer
publist_id: '149'
quality_controlled: 0
status: public
title: Verifying quantitative properties using bound functions
type: conference
volume: 3725
year: '2005'
...
---
_id: '4576'
abstract:
- lang: eng
  text: We present a language for specifying web service interfaces. A web service
    interface puts three kinds of constraints on the users of the service. First,
    the interface specifies the methods that can be called by a client, together with
    types of input and output parameters; these are called signature constraints.
    Second, the interface may specify propositional constraints on method calls and
    output values that may oc- cur in a web service conversation; these are called
    consis- tency constraints. Third, the interface may specify temporal constraints
    on the ordering of method calls; these are called protocol constraints. The interfaces
    can be used to check, first, if two or more web services are compatible, and second,
    if a web service A can be safely substituted for a web ser- vice B. The algorithm
    for compatibility checking verifies that two or more interfaces fulfill each others’
    constraints. The algorithm for substitutivity checking verifies that service A
    demands fewer and fulfills more constraints than service B.
acknowledgement: This research was supported in part by the ONR grant N00014-02-1-0671
  and by the NSF grants CCR-0234690 and CCR-0225610.
author:
- first_name: Dirk
  full_name: Beyer, Dirk
  last_name: Beyer
- first_name: Arindam
  full_name: Chakrabarti, Arindam
  last_name: Chakrabarti
- first_name: Thomas A
  full_name: Thomas Henzinger
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
citation:
  ama: 'Beyer D, Chakrabarti A, Henzinger TA. Web service interfaces. In: ACM; 2005:148-159.
    doi:<a href="https://doi.org/10.1145/1060745.1060770">10.1145/1060745.1060770</a>'
  apa: 'Beyer, D., Chakrabarti, A., &#38; Henzinger, T. A. (2005). Web service interfaces
    (pp. 148–159). Presented at the WWW: World Wide Web Conference, ACM. <a href="https://doi.org/10.1145/1060745.1060770">https://doi.org/10.1145/1060745.1060770</a>'
  chicago: Beyer, Dirk, Arindam Chakrabarti, and Thomas A Henzinger. “Web Service
    Interfaces,” 148–59. ACM, 2005. <a href="https://doi.org/10.1145/1060745.1060770">https://doi.org/10.1145/1060745.1060770</a>.
  ieee: 'D. Beyer, A. Chakrabarti, and T. A. Henzinger, “Web service interfaces,”
    presented at the WWW: World Wide Web Conference, 2005, pp. 148–159.'
  ista: 'Beyer D, Chakrabarti A, Henzinger TA. 2005. Web service interfaces. WWW:
    World Wide Web Conference, 148–159.'
  mla: Beyer, Dirk, et al. <i>Web Service Interfaces</i>. ACM, 2005, pp. 148–59, doi:<a
    href="https://doi.org/10.1145/1060745.1060770">10.1145/1060745.1060770</a>.
  short: D. Beyer, A. Chakrabarti, T.A. Henzinger, in:, ACM, 2005, pp. 148–159.
conference:
  name: 'WWW: World Wide Web Conference'
date_created: 2018-12-11T12:09:33Z
date_published: 2005-05-01T00:00:00Z
date_updated: 2021-01-12T07:59:50Z
day: '01'
doi: 10.1145/1060745.1060770
extern: 1
month: '05'
page: 148 - 159
publication_status: published
publisher: ACM
publist_id: '132'
quality_controlled: 0
status: public
title: Web service interfaces
type: conference
year: '2005'
...
---
_id: '4579'
abstract:
- lang: eng
  text: BLAST is an automatic verification tool for checking temporal safety properties
    of C programs. Given a C program and a temporal safety property, BLAST statically
    proves that either the program satisfies the safety property or the program has
    an execution trace that exhibits a violation of the property. BLAST constructs,
    explores, and refines abstractions of the program state space based on lazy predicate
    abstraction and interpolation-based predicate discovery. We show how BLAST can
    be used to statically prove memory safety for C programs. We take a two-step approach.
    First, we use Ccured, a type-based memory safety analyzer, to annotate with run-time
    checks all program points that cannot be proved memory safe by the type system.
    Second, we use BLAST to remove as many of the run-time checks as possible (by
    proving that these checks never fail), and to generate for the remaining run-time
    checks execution traces that witness them fail. Our experience shows that BLAST
    can remove many of the run-time checks added by Ccured and provide useful information
    to the programmer about many of the remaining checks.
acknowledgement: This research was supported in part by the NSF grants CCR-0234690,
  CCR-0225610, and ITR-0326577.
alternative_title:
- LNCS
author:
- first_name: Dirk
  full_name: Beyer, Dirk
  last_name: Beyer
- first_name: Thomas A
  full_name: Thomas Henzinger
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
- first_name: Ranjit
  full_name: Jhala, Ranjit
  last_name: Jhala
- first_name: Ritankar
  full_name: Majumdar, Ritankar S
  last_name: Majumdar
citation:
  ama: 'Beyer D, Henzinger TA, Jhala R, Majumdar R. Checking memory safety with BLAST.
    In: Vol 3442. Springer; 2005:2-18. doi:<a href="https://doi.org/10.1007/978-3-540-31984-9_2">10.1007/978-3-540-31984-9_2</a>'
  apa: 'Beyer, D., Henzinger, T. A., Jhala, R., &#38; Majumdar, R. (2005). Checking
    memory safety with BLAST (Vol. 3442, pp. 2–18). Presented at the FASE: Fundamental
    Approaches To Software Engineering, Springer. <a href="https://doi.org/10.1007/978-3-540-31984-9_2">https://doi.org/10.1007/978-3-540-31984-9_2</a>'
  chicago: Beyer, Dirk, Thomas A Henzinger, Ranjit Jhala, and Ritankar Majumdar. “Checking
    Memory Safety with BLAST,” 3442:2–18. Springer, 2005. <a href="https://doi.org/10.1007/978-3-540-31984-9_2">https://doi.org/10.1007/978-3-540-31984-9_2</a>.
  ieee: 'D. Beyer, T. A. Henzinger, R. Jhala, and R. Majumdar, “Checking memory safety
    with BLAST,” presented at the FASE: Fundamental Approaches To Software Engineering,
    2005, vol. 3442, pp. 2–18.'
  ista: 'Beyer D, Henzinger TA, Jhala R, Majumdar R. 2005. Checking memory safety
    with BLAST. FASE: Fundamental Approaches To Software Engineering, LNCS, vol. 3442,
    2–18.'
  mla: Beyer, Dirk, et al. <i>Checking Memory Safety with BLAST</i>. Vol. 3442, Springer,
    2005, pp. 2–18, doi:<a href="https://doi.org/10.1007/978-3-540-31984-9_2">10.1007/978-3-540-31984-9_2</a>.
  short: D. Beyer, T.A. Henzinger, R. Jhala, R. Majumdar, in:, Springer, 2005, pp.
    2–18.
conference:
  name: 'FASE: Fundamental Approaches To Software Engineering'
date_created: 2018-12-11T12:09:34Z
date_published: 2005-03-24T00:00:00Z
date_updated: 2021-01-12T07:59:51Z
day: '24'
doi: 10.1007/978-3-540-31984-9_2
extern: 1
intvolume: '      3442'
month: '03'
page: 2 - 18
publication_status: published
publisher: Springer
publist_id: '131'
quality_controlled: 0
status: public
title: Checking memory safety with BLAST
type: conference
volume: 3442
year: '2005'
...
---
_id: '4624'
abstract:
- lang: eng
  text: Surveying results from [5] and [6], we motivate and introduce the theory behind
    formalizing rich interfaces for software and hardware components. Rich interfaces
    specify the protocol aspects of component interaction. Their formalization, called
    interface automata, permits a compiler to check the compatibility of component
    interaction protocols. Interface automata support incremental design and independent
    implementability. Incremental design means that the compatibility checking of
    interfaces can proceed for partial system descriptions, without knowing the interfaces
    of all components. Independent implementability means that compatible interfaces
    can be refined separately, while still maintaining compatibility.
alternative_title:
- 'NATO Science Series: Mathematics, Physics, and Chemistry'
author:
- first_name: Luca
  full_name: de Alfaro, Luca
  last_name: De Alfaro
- first_name: Thomas A
  full_name: Thomas Henzinger
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
citation:
  ama: 'De Alfaro L, Henzinger TA. Interface-based design. In: Vol 195. Springer;
    2005:83-104. doi:<a href="https://doi.org/10.1007/1-4020-3532-2_3">10.1007/1-4020-3532-2_3</a>'
  apa: De Alfaro, L., &#38; Henzinger, T. A. (2005). Interface-based design (Vol.
    195, pp. 83–104). Presented at the Engineering Theories of Software Intensive
    Systems, Springer. <a href="https://doi.org/10.1007/1-4020-3532-2_3">https://doi.org/10.1007/1-4020-3532-2_3</a>
  chicago: De Alfaro, Luca, and Thomas A Henzinger. “Interface-Based Design,” 195:83–104.
    Springer, 2005. <a href="https://doi.org/10.1007/1-4020-3532-2_3">https://doi.org/10.1007/1-4020-3532-2_3</a>.
  ieee: L. De Alfaro and T. A. Henzinger, “Interface-based design,” presented at the
    Engineering Theories of Software Intensive Systems, 2005, vol. 195, pp. 83–104.
  ista: 'De Alfaro L, Henzinger TA. 2005. Interface-based design. Engineering Theories
    of Software Intensive Systems, NATO Science Series: Mathematics, Physics, and
    Chemistry, vol. 195, 83–104.'
  mla: De Alfaro, Luca, and Thomas A. Henzinger. <i>Interface-Based Design</i>. Vol.
    195, Springer, 2005, pp. 83–104, doi:<a href="https://doi.org/10.1007/1-4020-3532-2_3">10.1007/1-4020-3532-2_3</a>.
  short: L. De Alfaro, T.A. Henzinger, in:, Springer, 2005, pp. 83–104.
conference:
  name: Engineering Theories of Software Intensive Systems
date_created: 2018-12-11T12:09:49Z
date_published: 2005-07-15T00:00:00Z
date_updated: 2021-01-12T08:00:36Z
day: '15'
doi: 10.1007/1-4020-3532-2_3
extern: 1
intvolume: '       195'
month: '07'
page: 83 - 104
publication_status: published
publisher: Springer
publist_id: '85'
quality_controlled: 0
status: public
title: Interface-based design
type: conference
volume: 195
year: '2005'
...
---
_id: '4625'
abstract:
- lang: eng
  text: |-
    Temporal logic is two-valued: formulas are interpreted as either true or false. When applied to the analysis of stochastic systems, or systems with imprecise formal models, temporal logic is therefore fragile: even small changes in the model can lead to opposite truth values for a specification. We present a generalization of the branching-time logic CTL which achieves robustness with respect to model perturbations by giving a quantitative interpretation to predicates and logical operators, and by discounting the importance of events according to how late they occur. In every state, the value of a formula is a real number in the interval [0,1], where 1 corresponds to truth and 0 to falsehood. The boolean operators and and or are replaced by min and max, the path quantifiers ∃ and ∀ determine sup and inf over all paths from a given state, and the temporal operators ⋄ and □ specify sup and inf over a given path; a new operator averages all values along a path. Furthermore, all path operators are discounted by a parameter that can be chosen to give more weight to states that are closer to the beginning of the path.

    We interpret the resulting logic DCTL over transition systems, Markov chains, and Markov decision processes. We present two semantics for DCTL: a path semantics, inspired by the standard interpretation of state and path formulas in CTL, and a fixpoint semantics, inspired by the μ-calculus evaluation of CTL formulas. We show that, while these semantics coincide for CTL, they differ for DCTL, and we provide model-checking algorithms for both semantics.
author:
- first_name: Luca
  full_name: de Alfaro, Luca
  last_name: De Alfaro
- first_name: Marco
  full_name: Faella, Marco
  last_name: Faella
- first_name: Thomas A
  full_name: Thomas Henzinger
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
- first_name: Ritankar
  full_name: Majumdar, Ritankar S
  last_name: Majumdar
- first_name: Mariëlle
  full_name: Stoelinga, Mariëlle
  last_name: Stoelinga
citation:
  ama: De Alfaro L, Faella M, Henzinger TA, Majumdar R, Stoelinga M. Model checking
    discounted temporal properties. <i>Theoretical Computer Science</i>. 2005;345(1):139-170.
    doi:<a href="https://doi.org/10.1016/j.tcs.2005.07.033">10.1016/j.tcs.2005.07.033</a>
  apa: De Alfaro, L., Faella, M., Henzinger, T. A., Majumdar, R., &#38; Stoelinga,
    M. (2005). Model checking discounted temporal properties. <i>Theoretical Computer
    Science</i>. Elsevier. <a href="https://doi.org/10.1016/j.tcs.2005.07.033">https://doi.org/10.1016/j.tcs.2005.07.033</a>
  chicago: De Alfaro, Luca, Marco Faella, Thomas A Henzinger, Ritankar Majumdar, and
    Mariëlle Stoelinga. “Model Checking Discounted Temporal Properties.” <i>Theoretical
    Computer Science</i>. Elsevier, 2005. <a href="https://doi.org/10.1016/j.tcs.2005.07.033">https://doi.org/10.1016/j.tcs.2005.07.033</a>.
  ieee: L. De Alfaro, M. Faella, T. A. Henzinger, R. Majumdar, and M. Stoelinga, “Model
    checking discounted temporal properties,” <i>Theoretical Computer Science</i>,
    vol. 345, no. 1. Elsevier, pp. 139–170, 2005.
  ista: De Alfaro L, Faella M, Henzinger TA, Majumdar R, Stoelinga M. 2005. Model
    checking discounted temporal properties. Theoretical Computer Science. 345(1),
    139–170.
  mla: De Alfaro, Luca, et al. “Model Checking Discounted Temporal Properties.” <i>Theoretical
    Computer Science</i>, vol. 345, no. 1, Elsevier, 2005, pp. 139–70, doi:<a href="https://doi.org/10.1016/j.tcs.2005.07.033">10.1016/j.tcs.2005.07.033</a>.
  short: L. De Alfaro, M. Faella, T.A. Henzinger, R. Majumdar, M. Stoelinga, Theoretical
    Computer Science 345 (2005) 139–170.
date_created: 2018-12-11T12:09:49Z
date_published: 2005-11-21T00:00:00Z
date_updated: 2021-01-12T08:00:37Z
day: '21'
doi: 10.1016/j.tcs.2005.07.033
extern: 1
intvolume: '       345'
issue: '1'
month: '11'
page: 139 - 170
publication: Theoretical Computer Science
publication_status: published
publisher: Elsevier
publist_id: '80'
quality_controlled: 0
status: public
title: Model checking discounted temporal properties
type: journal_article
volume: 345
year: '2005'
...
---
_id: '575'
abstract:
- lang: eng
  text: We present the first demonstration of Jozsa's &quot;counterfactual computation&quot;,
    using an optical Grover's search algorithm. We put the algorithm in a superposition
    of 'running' and 'not-running', obtaining information even though the algorithm
    does not run.
alternative_title:
- QELS
author:
- first_name: Onur
  full_name: Onur Hosten
  id: 4C02D85E-F248-11E8-B48F-1D18A9856A87
  last_name: Hosten
  orcid: 0000-0002-2031-204X
- first_name: Matthew
  full_name: Rakher, Matthew T
  last_name: Rakher
- first_name: Julio
  full_name: Barreiro, Julio T
  last_name: Barreiro
- first_name: Nicholas
  full_name: Peters, Nicholas A
  last_name: Peters
- first_name: Paul
  full_name: Kwiat, Paul G
  last_name: Kwiat
citation:
  ama: 'Hosten O, Rakher M, Barreiro J, Peters N, Kwiat P. Counterfactual quantum
    computation. In: Vol 1. IEEE; 2005:365-367. doi:<a href="https://doi.org/ 10.1109/QELS.2005.1548783">
    10.1109/QELS.2005.1548783</a>'
  apa: 'Hosten, O., Rakher, M., Barreiro, J., Peters, N., &#38; Kwiat, P. (2005).
    Counterfactual quantum computation (Vol. 1, pp. 365–367). Presented at the QELS:
    Quantum Electronics and Laser Science, IEEE. <a href="https://doi.org/ 10.1109/QELS.2005.1548783">https://doi.org/
    10.1109/QELS.2005.1548783</a>'
  chicago: Hosten, Onur, Matthew Rakher, Julio Barreiro, Nicholas Peters, and Paul
    Kwiat. “Counterfactual Quantum Computation,” 1:365–67. IEEE, 2005. <a href="https://doi.org/
    10.1109/QELS.2005.1548783">https://doi.org/ 10.1109/QELS.2005.1548783</a>.
  ieee: 'O. Hosten, M. Rakher, J. Barreiro, N. Peters, and P. Kwiat, “Counterfactual
    quantum computation,” presented at the QELS: Quantum Electronics and Laser Science,
    2005, vol. 1, pp. 365–367.'
  ista: 'Hosten O, Rakher M, Barreiro J, Peters N, Kwiat P. 2005. Counterfactual quantum
    computation. QELS: Quantum Electronics and Laser Science, QELS, vol. 1, 365–367.'
  mla: Hosten, Onur, et al. <i>Counterfactual Quantum Computation</i>. Vol. 1, IEEE,
    2005, pp. 365–67, doi:<a href="https://doi.org/ 10.1109/QELS.2005.1548783"> 10.1109/QELS.2005.1548783</a>.
  short: O. Hosten, M. Rakher, J. Barreiro, N. Peters, P. Kwiat, in:, IEEE, 2005,
    pp. 365–367.
conference:
  name: 'QELS: Quantum Electronics and Laser Science'
date_created: 2018-12-11T11:47:16Z
date_published: 2005-01-01T00:00:00Z
date_updated: 2021-01-12T08:03:18Z
day: '01'
doi: ' 10.1109/QELS.2005.1548783'
extern: 1
intvolume: '         1'
month: '01'
page: 365 - 367
publication_status: published
publisher: IEEE
publist_id: '7237'
quality_controlled: 0
status: public
title: Counterfactual quantum computation
type: conference
volume: 1
year: '2005'
...
---
_id: '6153'
abstract:
- lang: eng
  text: A current challenge in neuroscience is to bridge the gaps between genes, proteins,
    neurons, neural circuits, and behavior in a single animal model. The nematode
    Caenorhabditis elegans has unique features that facilitate this synthesis. Its
    nervous system includes exactly 302 neurons, and their pattern of synaptic connectivity
    is known. With only five olfactory neurons, C. elegans can dynamically respond
    to dozens of attractive and repellant odors. Thermosensory neurons enable the
    nematode to remember its cultivation temperature and to track narrow isotherms.
    Polymodal sensory neurons detect a wide range of nociceptive cues and signal robust
    escape responses. Pairing of sensory stimuli leads to long-lived changes in behavior
    consistent with associative learning. Worms exhibit social behaviors and complex
    ultradian rhythms driven by Ca2+ oscillators with clock-like properties. Genetic
    analysis has identified gene products required for nervous system function and
    elucidated the molecular and neural bases of behaviors.
article_processing_charge: No
article_type: original
author:
- first_name: Mario
  full_name: de Bono, Mario
  id: 4E3FF80E-F248-11E8-B48F-1D18A9856A87
  last_name: de Bono
  orcid: 0000-0001-8347-0443
- first_name: Andres
  full_name: Villu Maricq, Andres
  last_name: Villu Maricq
citation:
  ama: de Bono M, Villu Maricq A. Neuronal substrates of complex behaviors in C. elegans.
    <i>Annual Review of Neuroscience</i>. 2005;28:451-501. doi:<a href="https://doi.org/10.1146/annurev.neuro.27.070203.144259">10.1146/annurev.neuro.27.070203.144259</a>
  apa: de Bono, M., &#38; Villu Maricq, A. (2005). Neuronal substrates of complex
    behaviors in C. elegans. <i>Annual Review of Neuroscience</i>. Annual Reviews.
    <a href="https://doi.org/10.1146/annurev.neuro.27.070203.144259">https://doi.org/10.1146/annurev.neuro.27.070203.144259</a>
  chicago: Bono, Mario de, and Andres Villu Maricq. “Neuronal Substrates of Complex
    Behaviors in C. Elegans.” <i>Annual Review of Neuroscience</i>. Annual Reviews,
    2005. <a href="https://doi.org/10.1146/annurev.neuro.27.070203.144259">https://doi.org/10.1146/annurev.neuro.27.070203.144259</a>.
  ieee: M. de Bono and A. Villu Maricq, “Neuronal substrates of complex behaviors
    in C. elegans,” <i>Annual Review of Neuroscience</i>, vol. 28. Annual Reviews,
    pp. 451–501, 2005.
  ista: de Bono M, Villu Maricq A. 2005. Neuronal substrates of complex behaviors
    in C. elegans. Annual Review of Neuroscience. 28, 451–501.
  mla: de Bono, Mario, and Andres Villu Maricq. “Neuronal Substrates of Complex Behaviors
    in C. Elegans.” <i>Annual Review of Neuroscience</i>, vol. 28, Annual Reviews,
    2005, pp. 451–501, doi:<a href="https://doi.org/10.1146/annurev.neuro.27.070203.144259">10.1146/annurev.neuro.27.070203.144259</a>.
  short: M. de Bono, A. Villu Maricq, Annual Review of Neuroscience 28 (2005) 451–501.
date_created: 2019-03-21T09:31:29Z
date_published: 2005-07-21T00:00:00Z
date_updated: 2021-01-12T08:06:24Z
day: '21'
doi: 10.1146/annurev.neuro.27.070203.144259
extern: '1'
external_id:
  pmid:
  - '16022603'
intvolume: '        28'
language:
- iso: eng
month: '07'
oa_version: None
page: 451-501
pmid: 1
publication: Annual Review of Neuroscience
publication_identifier:
  issn:
  - 0147-006X
  - 1545-4126
publication_status: published
publisher: Annual Reviews
quality_controlled: '1'
status: public
title: Neuronal substrates of complex behaviors in C. elegans
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 28
year: '2005'
...
---
_id: '6154'
author:
- first_name: Benny H.H.
  full_name: Cheung, Benny H.H.
  last_name: Cheung
- first_name: Merav
  full_name: Cohen, Merav
  last_name: Cohen
- first_name: Candida
  full_name: Rogers, Candida
  last_name: Rogers
- first_name: Onder
  full_name: Albayram, Onder
  last_name: Albayram
- first_name: Mario
  full_name: de Bono, Mario
  id: 4E3FF80E-F248-11E8-B48F-1D18A9856A87
  last_name: de Bono
  orcid: 0000-0001-8347-0443
citation:
  ama: Cheung BHH, Cohen M, Rogers C, Albayram O, de Bono M. Experience-dependent
    modulation of C. elegans behavior by ambient oxygen. <i>Current Biology</i>. 2005;15(10):905-917.
    doi:<a href="https://doi.org/10.1016/j.cub.2005.04.017">10.1016/j.cub.2005.04.017</a>
  apa: Cheung, B. H. H., Cohen, M., Rogers, C., Albayram, O., &#38; de Bono, M. (2005).
    Experience-dependent modulation of C. elegans behavior by ambient oxygen. <i>Current
    Biology</i>. Elsevier. <a href="https://doi.org/10.1016/j.cub.2005.04.017">https://doi.org/10.1016/j.cub.2005.04.017</a>
  chicago: Cheung, Benny H.H., Merav Cohen, Candida Rogers, Onder Albayram, and Mario
    de Bono. “Experience-Dependent Modulation of C. Elegans Behavior by Ambient Oxygen.”
    <i>Current Biology</i>. Elsevier, 2005. <a href="https://doi.org/10.1016/j.cub.2005.04.017">https://doi.org/10.1016/j.cub.2005.04.017</a>.
  ieee: B. H. H. Cheung, M. Cohen, C. Rogers, O. Albayram, and M. de Bono, “Experience-dependent
    modulation of C. elegans behavior by ambient oxygen,” <i>Current Biology</i>,
    vol. 15, no. 10. Elsevier, pp. 905–917, 2005.
  ista: Cheung BHH, Cohen M, Rogers C, Albayram O, de Bono M. 2005. Experience-dependent
    modulation of C. elegans behavior by ambient oxygen. Current Biology. 15(10),
    905–917.
  mla: Cheung, Benny H. H., et al. “Experience-Dependent Modulation of C. Elegans
    Behavior by Ambient Oxygen.” <i>Current Biology</i>, vol. 15, no. 10, Elsevier,
    2005, pp. 905–17, doi:<a href="https://doi.org/10.1016/j.cub.2005.04.017">10.1016/j.cub.2005.04.017</a>.
  short: B.H.H. Cheung, M. Cohen, C. Rogers, O. Albayram, M. de Bono, Current Biology
    15 (2005) 905–917.
date_created: 2019-03-21T09:37:48Z
date_published: 2005-05-24T00:00:00Z
date_updated: 2021-01-12T08:06:24Z
day: '24'
doi: 10.1016/j.cub.2005.04.017
extern: '1'
external_id:
  pmid:
  - '15916947'
intvolume: '        15'
issue: '10'
language:
- iso: eng
month: '05'
oa_version: None
page: 905-917
pmid: 1
publication: Current Biology
publication_identifier:
  issn:
  - 0960-9822
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Experience-dependent modulation of C. elegans behavior by ambient oxygen
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2005'
...
---
_id: '1444'
abstract:
- lang: eng
  text: The paper surveys the mirror symmetry conjectures of Hausel-Thaddeus and Hausel-Rodriguez-Villegas
    concerning the equality of certain Hodge numbers of SL(n, ℂ) vs. PGL(n, ℂ) flat
    connections and character varieties for curves, respectively. Several new results
    and conjectures and their relations to works of Hitchin, Gothen, Garsia-Haiman
    and Earl-Kirwan are explained. These use the representation theory of finite groups
    of Lie-type via the arithmetic of character varieties and lead to an unexpected
    conjecture for a Hard Lefschetz theorem for their cohomology.
alternative_title:
- Progress in Mathematics
author:
- first_name: Tamas
  full_name: Tamas Hausel
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
citation:
  ama: 'Hausel T. Mirror symmetry and Langlands duality in the non-Abelian Hodge theory
    of a curve. In: <i>Geometric Methods in Algebra and Number Theory</i>. Vol 235.
    Springer; 2005:193-217. doi:<a href="https://doi.org/10.1007/0-8176-4417-2_9">10.1007/0-8176-4417-2_9</a>'
  apa: Hausel, T. (2005). Mirror symmetry and Langlands duality in the non-Abelian
    Hodge theory of a curve. In <i>Geometric Methods in Algebra and Number Theory</i>
    (Vol. 235, pp. 193–217). Springer. <a href="https://doi.org/10.1007/0-8176-4417-2_9">https://doi.org/10.1007/0-8176-4417-2_9</a>
  chicago: Hausel, Tamás. “Mirror Symmetry and Langlands Duality in the Non-Abelian
    Hodge Theory of a Curve.” In <i>Geometric Methods in Algebra and Number Theory</i>,
    235:193–217. Springer, 2005. <a href="https://doi.org/10.1007/0-8176-4417-2_9">https://doi.org/10.1007/0-8176-4417-2_9</a>.
  ieee: T. Hausel, “Mirror symmetry and Langlands duality in the non-Abelian Hodge
    theory of a curve,” in <i>Geometric Methods in Algebra and Number Theory</i>,
    vol. 235, Springer, 2005, pp. 193–217.
  ista: 'Hausel T. 2005.Mirror symmetry and Langlands duality in the non-Abelian Hodge
    theory of a curve. In: Geometric Methods in Algebra and Number Theory. Progress
    in Mathematics, vol. 235, 193–217.'
  mla: Hausel, Tamás. “Mirror Symmetry and Langlands Duality in the Non-Abelian Hodge
    Theory of a Curve.” <i>Geometric Methods in Algebra and Number Theory</i>, vol.
    235, Springer, 2005, pp. 193–217, doi:<a href="https://doi.org/10.1007/0-8176-4417-2_9">10.1007/0-8176-4417-2_9</a>.
  short: T. Hausel, in:, Geometric Methods in Algebra and Number Theory, Springer,
    2005, pp. 193–217.
date_created: 2018-12-11T11:52:03Z
date_published: 2005-01-01T00:00:00Z
date_updated: 2021-01-12T06:50:47Z
day: '01'
doi: 10.1007/0-8176-4417-2_9
extern: 1
intvolume: '       235'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math/0406380
month: '01'
oa: 1
page: 193 - 217
publication: Geometric Methods in Algebra and Number Theory
publication_status: published
publisher: Springer
publist_id: '5752'
quality_controlled: 0
status: public
title: Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a
  curve
type: book_chapter
volume: 235
year: '2005'
...
---
_id: '1447'
abstract:
- lang: eng
  text: Building on a recent paper [8], here we argue that the combinatorics of matroids
    are intimately related to the geometry and topology of toric hyperkähler varieties.
    We show that just like toric varieties occupy a central role in Stanley’s proof
    for the necessity of McMullen’s conjecture (or g-inequalities) about the classification
    of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties
    leads to new restrictions on face vectors of matroid complexes. Namely in this
    paper we will give two proofs that the injectivity part of the Hard Lefschetz
    theorem survives for toric hyperkähler varieties. We explain how this implies
    the g-inequalities for rationally representable matroids. We show how the geometrical
    intuition in the first proof, coupled with results of Chari [3], leads to a proof
    of the g-inequalities for general matroid complexes, which is a recent result
    of Swartz [20]. The geometrical idea in the second proof will show that a pure
    O-sequence should satisfy the g-inequalities, thus showing that our result is
    in fact a consequence of a long-standing conjecture of Stanley.
acknowledgement: Financial support wa s provided by a Miller Research Fellowship at
  the University of California at Berkeley , and by NSF grants DMS- 0072675 and DMS-0305505.
author:
- first_name: Tamas
  full_name: Tamas Hausel
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
citation:
  ama: Hausel T. Quaternionic geometry of matroids. <i>Open Mathematics</i>. 2005;3(1):26-38.
    doi:<a href="https://doi.org/10.2478/BF02475653">10.2478/BF02475653</a>
  apa: Hausel, T. (2005). Quaternionic geometry of matroids. <i>Open Mathematics</i>.
    Central European Science Journals. <a href="https://doi.org/10.2478/BF02475653">https://doi.org/10.2478/BF02475653</a>
  chicago: Hausel, Tamás. “Quaternionic Geometry of Matroids.” <i>Open Mathematics</i>.
    Central European Science Journals, 2005. <a href="https://doi.org/10.2478/BF02475653">https://doi.org/10.2478/BF02475653</a>.
  ieee: T. Hausel, “Quaternionic geometry of matroids,” <i>Open Mathematics</i>, vol.
    3, no. 1. Central European Science Journals, pp. 26–38, 2005.
  ista: Hausel T. 2005. Quaternionic geometry of matroids. Open Mathematics. 3(1),
    26–38.
  mla: Hausel, Tamás. “Quaternionic Geometry of Matroids.” <i>Open Mathematics</i>,
    vol. 3, no. 1, Central European Science Journals, 2005, pp. 26–38, doi:<a href="https://doi.org/10.2478/BF02475653">10.2478/BF02475653</a>.
  short: T. Hausel, Open Mathematics 3 (2005) 26–38.
date_created: 2018-12-11T11:52:05Z
date_published: 2005-03-01T00:00:00Z
date_updated: 2021-01-12T06:50:49Z
day: '01'
doi: 10.2478/BF02475653
extern: 1
intvolume: '         3'
issue: '1'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math/0308146
month: '03'
oa: 1
page: 26 - 38
publication: Open Mathematics
publication_status: published
publisher: Central European Science Journals
publist_id: '5749'
quality_controlled: 0
status: public
title: Quaternionic geometry of matroids
type: journal_article
volume: 3
year: '2005'
...
---
_id: '1463'
abstract:
- lang: eng
  text: We study an integration theory in circle equivariant cohomology in order to
    prove a theorem relating the cohomology ring of a hyperkähler quotient to the
    cohomology ring of the quotient by a maximal abelian subgroup, analogous to a
    theorem of Martin for symplectic quotients. We discuss applications of this theorem
    to quiver varieties, and compute as an example the ordinary and equivariant cohomology
    rings of a hyperpolygon space.
acknowledgement: ' Financial support was provided in part by NSF Grants DMS-0072675
  and DMS-0305505.'
author:
- first_name: Tamas
  full_name: Tamas Hausel
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
- first_name: Nicholas
  full_name: Proudfoot, Nicholas J
  last_name: Proudfoot
citation:
  ama: Hausel T, Proudfoot N. Abelianization for hyperkähler quotients. <i>Topology</i>.
    2005;44(1):231-248. doi:<a href="https://doi.org/10.1016/j.top.2004.04.002">10.1016/j.top.2004.04.002</a>
  apa: Hausel, T., &#38; Proudfoot, N. (2005). Abelianization for hyperkähler quotients.
    <i>Topology</i>. Elsevier. <a href="https://doi.org/10.1016/j.top.2004.04.002">https://doi.org/10.1016/j.top.2004.04.002</a>
  chicago: Hausel, Tamás, and Nicholas Proudfoot. “Abelianization for Hyperkähler
    Quotients.” <i>Topology</i>. Elsevier, 2005. <a href="https://doi.org/10.1016/j.top.2004.04.002">https://doi.org/10.1016/j.top.2004.04.002</a>.
  ieee: T. Hausel and N. Proudfoot, “Abelianization for hyperkähler quotients,” <i>Topology</i>,
    vol. 44, no. 1. Elsevier, pp. 231–248, 2005.
  ista: Hausel T, Proudfoot N. 2005. Abelianization for hyperkähler quotients. Topology.
    44(1), 231–248.
  mla: Hausel, Tamás, and Nicholas Proudfoot. “Abelianization for Hyperkähler Quotients.”
    <i>Topology</i>, vol. 44, no. 1, Elsevier, 2005, pp. 231–48, doi:<a href="https://doi.org/10.1016/j.top.2004.04.002">10.1016/j.top.2004.04.002</a>.
  short: T. Hausel, N. Proudfoot, Topology 44 (2005) 231–248.
date_created: 2018-12-11T11:52:10Z
date_published: 2005-01-01T00:00:00Z
date_updated: 2021-01-12T06:50:55Z
day: '01'
doi: 10.1016/j.top.2004.04.002
extern: 1
intvolume: '        44'
issue: '1'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math/0310141
month: '01'
oa: 1
page: 231 - 248
publication: Topology
publication_status: published
publisher: Elsevier
publist_id: '5735'
quality_controlled: 0
status: public
title: Abelianization for hyperkähler quotients
type: journal_article
volume: 44
year: '2005'
...
