[{"_id":"217","type":"journal_article","status":"public","date_updated":"2021-01-12T06:55:45Z","citation":{"chicago":"Browning, Timothy D. “The Density of Rational Points on a Certain Singular Cubic Surface.” Journal of Number Theory. Elsevier, 2005. https://doi.org/10.1016/j.jnt.2005.11.007.","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.” Journal of Number Theory, vol. 119, no. 2, Elsevier, 2005, pp. 242–83, doi:10.1016/j.jnt.2005.11.007.","short":"T.D. Browning, Journal of Number Theory 119 (2005) 242–283.","ieee":"T. D. Browning, “The density of rational points on a certain singular cubic surface,” Journal of Number Theory, vol. 119, no. 2. Elsevier, pp. 242–283, 2005.","apa":"Browning, T. D. (2005). The density of rational points on a certain singular cubic surface. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2005.11.007","ama":"Browning TD. The density of rational points on a certain singular cubic surface. Journal of Number Theory. 2005;119(2):242-283. doi:10.1016/j.jnt.2005.11.007"},"extern":1,"publist_id":"7695","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","last_name":"Browning"}],"title":"The density of rational points on a certain singular cubic surface","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","publisher":"Elsevier","quality_controlled":0,"month":"12","intvolume":" 119","publication_status":"published","year":"2005","day":"27","publication":"Journal of Number Theory","page":"242 - 283","date_published":"2005-12-27T00:00:00Z","volume":119,"issue":"2","doi":"10.1016/j.jnt.2005.11.007","date_created":"2018-12-11T11:45:16Z"},{"publist_id":"4619","author":[{"first_name":"Joel","last_name":"Schwartz","full_name":"Schwartz, Joel W"},{"last_name":"Novarino","orcid":"0000-0002-7673-7178","full_name":"Gaia Novarino","first_name":"Gaia","id":"3E57A680-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Piston","full_name":"Piston, David W","first_name":"David"},{"first_name":"Louis","last_name":"Defelice","full_name":"DeFelice, Louis J"}],"title":"Substrate binding stoichiometry and kinetics of the norepinephrine transporter","citation":{"chicago":"Schwartz, Joel, Gaia Novarino, David Piston, and Louis Defelice. “Substrate Binding Stoichiometry and Kinetics of the Norepinephrine Transporter.” Journal of Biological Chemistry. American Society for Biochemistry and Molecular Biology, 2005. https://doi.org/10.1074/jbc.M412923200.","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.” Journal of Biological Chemistry, vol. 280, no. 19, American Society for Biochemistry and Molecular Biology, 2005, pp. 19177–84, doi:10.1074/jbc.M412923200.","ama":"Schwartz J, Novarino G, Piston D, Defelice L. Substrate binding stoichiometry and kinetics of the norepinephrine transporter. Journal of Biological Chemistry. 2005;280(19):19177-19184. doi:10.1074/jbc.M412923200","apa":"Schwartz, J., Novarino, G., Piston, D., & Defelice, L. (2005). Substrate binding stoichiometry and kinetics of the norepinephrine transporter. Journal of Biological Chemistry. American Society for Biochemistry and Molecular Biology. https://doi.org/10.1074/jbc.M412923200","ieee":"J. Schwartz, G. Novarino, D. Piston, and L. Defelice, “Substrate binding stoichiometry and kinetics of the norepinephrine transporter,” Journal of Biological Chemistry, vol. 280, no. 19. American Society for Biochemistry and Molecular Biology, pp. 19177–19184, 2005.","short":"J. Schwartz, G. Novarino, D. Piston, L. Defelice, Journal of Biological Chemistry 280 (2005) 19177–19184."},"date_updated":"2021-01-12T06:56:40Z","extern":1,"type":"journal_article","status":"public","_id":"2307","page":"19177 - 19184","issue":"19","date_published":"2005-05-13T00:00:00Z","doi":"10.1074/jbc.M412923200","volume":280,"date_created":"2018-12-11T11:56:54Z","year":"2005","publication_status":"published","day":"13","publication":"Journal of Biological Chemistry","quality_controlled":0,"publisher":"American Society for Biochemistry and Molecular Biology","month":"05","intvolume":" 280","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."}]},{"quality_controlled":"1","publisher":"Birkhäuser Verlag","oa":1,"page":"VIII, 203","date_published":"2005-01-01T00:00:00Z","doi":"10.1007/b137508","date_created":"2018-12-11T11:57:03Z","year":"2005","day":"01","author":[{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"},{"full_name":"Solovej, Jan","last_name":"Solovej","first_name":"Jan"},{"first_name":"Jakob","last_name":"Yngvason","full_name":"Yngvason, Jakob"}],"publist_id":"4591","article_processing_charge":"No","external_id":{"arxiv":["cond-mat/0610117"]},"title":"The Mathematics of the Bose gas and its Condensation","citation":{"chicago":"Lieb, Élliott, Robert Seiringer, Jan Solovej, and Jakob Yngvason. The Mathematics of the Bose Gas and Its Condensation. Vol. 34. Basel ; Berlin: Birkhäuser Verlag, 2005. https://doi.org/10.1007/b137508.","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. The Mathematics of the Bose Gas and Its Condensation. Vol. 34, Birkhäuser Verlag, 2005, doi:10.1007/b137508.","ieee":"É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, The Mathematics of the Bose gas and its Condensation, vol. 34. Basel ; Berlin: Birkhäuser Verlag, 2005.","short":"É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, The Mathematics of the Bose Gas and Its Condensation, Birkhäuser Verlag, Basel ; Berlin, 2005.","apa":"Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2005). The Mathematics of the Bose gas and its Condensation (Vol. 34). Basel ; Berlin: Birkhäuser Verlag. https://doi.org/10.1007/b137508","ama":"Lieb É, Seiringer R, Solovej J, Yngvason J. The Mathematics of the Bose Gas and Its Condensation. Vol 34. Basel ; Berlin: Birkhäuser Verlag; 2005. doi:10.1007/b137508"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","alternative_title":["Oberwolfach Seminars"],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/cond-mat/0610117"}],"month":"01","place":"Basel ; Berlin","intvolume":" 34","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","volume":34,"publication_identifier":{"isbn":["978-3-7643-7336-8"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"book","status":"public","_id":"2335","date_updated":"2021-12-22T08:04:00Z","extern":"1"},{"date_updated":"2021-01-12T06:56:52Z","citation":{"mla":"Lieb, Élliott, et al. “The Quantum-Mechanical Many-Body Problem: The Bose Gas.” Perspectives in Analysis, edited by Michael Benedicks et al., vol. 27, Springer, 2005, pp. 97–183, doi:10.1007/3-540-30434-7_9.","apa":"Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2005). The quantum-mechanical many-body problem: The Bose gas. In M. Benedicks, P. Jones, S. Smirnov, & B. Winckler (Eds.), Perspectives in Analysis (Vol. 27, pp. 97–183). Springer. https://doi.org/10.1007/3-540-30434-7_9","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. Perspectives in Analysis. Vol 27. Springer; 2005:97-183. doi:10.1007/3-540-30434-7_9","ieee":"É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “The quantum-mechanical many-body problem: The Bose gas,” in Perspectives in Analysis, vol. 27, M. Benedicks, P. Jones, S. Smirnov, and B. Winckler, Eds. Springer, 2005, pp. 97–183.","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.","chicago":"Lieb, Élliott, Robert Seiringer, Jan Solovej, and Jakob Yngvason. “The Quantum-Mechanical Many-Body Problem: The Bose Gas.” In Perspectives in Analysis, edited by Michael Benedicks, Peter Jones, Stanislav Smirnov, and Björn Winckler, 27:97–183. Springer, 2005. https://doi.org/10.1007/3-540-30434-7_9.","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."},"extern":1,"publist_id":"4590","author":[{"full_name":"Lieb, Élliott H","last_name":"Lieb","first_name":"Élliott"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan P"},{"first_name":"Jakob","last_name":"Yngvason","full_name":"Yngvason, Jakob"}],"title":"The quantum-mechanical many-body problem: The Bose gas","editor":[{"full_name":"Benedicks, Michael","last_name":"Benedicks","first_name":"Michael"},{"first_name":"Peter","full_name":"Jones, Peter W","last_name":"Jones"},{"last_name":"Smirnov","full_name":"Smirnov, Stanislav","first_name":"Stanislav"},{"last_name":"Winckler","full_name":"Winckler, Björn","first_name":"Björn"}],"_id":"2336","type":"book_chapter","status":"public","publication_status":"published","year":"2005","publication":"Perspectives in Analysis","day":"01","page":"97 - 183","date_created":"2018-12-11T11:57:04Z","volume":27,"date_published":"2005-01-01T00:00:00Z","doi":"10.1007/3-540-30434-7_9","abstract":[{"text":"\n\nNow 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.","lang":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0405004"}],"quality_controlled":0,"alternative_title":["Mathematical Physics Studies"],"publisher":"Springer","intvolume":" 27","month":"01"},{"publist_id":"4566","author":[{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"}],"title":"Justification of c-number substitutions in bosonic hamiltonians","citation":{"ama":"Lieb É, Seiringer R, Yngvason J. Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. 2005;94(8). doi:10.1103/PhysRevLett.94.080401","apa":"Lieb, É., Seiringer, R., & Yngvason, J. (2005). Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.94.080401","short":"É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 94 (2005).","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “Justification of c-number substitutions in bosonic hamiltonians,” Physical Review Letters, vol. 94, no. 8. American Physical Society, 2005.","mla":"Lieb, Élliott, et al. “Justification of C-Number Substitutions in Bosonic Hamiltonians.” Physical Review Letters, vol. 94, no. 8, American Physical Society, 2005, doi:10.1103/PhysRevLett.94.080401.","ista":"Lieb É, Seiringer R, Yngvason J. 2005. Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. 94(8).","chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Justification of C-Number Substitutions in Bosonic Hamiltonians.” Physical Review Letters. American Physical Society, 2005. https://doi.org/10.1103/PhysRevLett.94.080401."},"date_updated":"2021-01-12T06:57:00Z","extern":1,"type":"journal_article","status":"public","_id":"2359","date_created":"2018-12-11T11:57:12Z","issue":"8","volume":94,"date_published":"2005-03-04T00:00:00Z","doi":"10.1103/PhysRevLett.94.080401","publication_status":"published","year":"2005","publication":"Physical Review Letters","day":"04","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0412023"}],"oa":1,"publisher":"American Physical Society","quality_controlled":0,"intvolume":" 94","month":"03","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."}]},{"type":"journal_article","status":"public","_id":"2362","author":[{"last_name":"Lieb","full_name":"Lieb, Élliott H","first_name":"Élliott"},{"last_name":"Seiringer","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jan","full_name":"Solovej, Jan P","last_name":"Solovej"}],"publist_id":"4565","title":"Ground state energy of the low density Fermi gas","citation":{"chicago":"Lieb, Élliott, Robert Seiringer, and Jan Solovej. “Ground State Energy of the Low Density Fermi Gas.” Physical Review A - Atomic, Molecular, and Optical Physics. American Physical Society, 2005. https://doi.org/10.1103/PhysRevA.71.053605.","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.” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 71, no. 5, American Physical Society, 2005, doi:10.1103/PhysRevA.71.053605.","short":"É. Lieb, R. Seiringer, J. Solovej, Physical Review A - Atomic, Molecular, and Optical Physics 71 (2005).","ieee":"É. Lieb, R. Seiringer, and J. Solovej, “Ground state energy of the low density Fermi gas,” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 71, no. 5. American Physical Society, 2005.","apa":"Lieb, É., Seiringer, R., & Solovej, J. (2005). Ground state energy of the low density Fermi gas. Physical Review A - Atomic, Molecular, and Optical Physics. American Physical Society. https://doi.org/10.1103/PhysRevA.71.053605","ama":"Lieb É, Seiringer R, Solovej J. Ground state energy of the low density Fermi gas. Physical Review A - Atomic, Molecular, and Optical Physics. 2005;71(5). doi:10.1103/PhysRevA.71.053605"},"date_updated":"2021-01-12T06:57:01Z","extern":1,"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0412080","open_access":"1"}],"quality_controlled":0,"publisher":"American Physical Society","intvolume":" 71","month":"05","abstract":[{"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.","lang":"eng"}],"date_created":"2018-12-11T11:57:13Z","doi":"10.1103/PhysRevA.71.053605","issue":"5","date_published":"2005-05-01T00:00:00Z","volume":71,"year":"2005","publication_status":"published","publication":"Physical Review A - Atomic, Molecular, and Optical Physics","day":"01"},{"title":"Stronger subadditivity of entropy","author":[{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"publist_id":"4564","extern":1,"date_updated":"2021-01-12T06:57:01Z","citation":{"mla":"Lieb, Élliott, and Robert Seiringer. “Stronger Subadditivity of Entropy.” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 71, no. 6, American Physical Society, 2005, doi:10.1103/PhysRevA.71.062329.","short":"É. Lieb, R. Seiringer, Physical Review A - Atomic, Molecular, and Optical Physics 71 (2005).","ieee":"É. Lieb and R. Seiringer, “Stronger subadditivity of entropy,” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 71, no. 6. American Physical Society, 2005.","apa":"Lieb, É., & Seiringer, R. (2005). Stronger subadditivity of entropy. Physical Review A - Atomic, Molecular, and Optical Physics. American Physical Society. https://doi.org/10.1103/PhysRevA.71.062329","ama":"Lieb É, Seiringer R. Stronger subadditivity of entropy. Physical Review A - Atomic, Molecular, and Optical Physics. 2005;71(6). doi:10.1103/PhysRevA.71.062329","chicago":"Lieb, Élliott, and Robert Seiringer. “Stronger Subadditivity of Entropy.” Physical Review A - Atomic, Molecular, and Optical Physics. American Physical Society, 2005. https://doi.org/10.1103/PhysRevA.71.062329.","ista":"Lieb É, Seiringer R. 2005. Stronger subadditivity of entropy. Physical Review A - Atomic, Molecular, and Optical Physics. 71(6)."},"status":"public","type":"journal_article","_id":"2361","date_created":"2018-12-11T11:57:13Z","date_published":"2005-06-01T00:00:00Z","issue":"6","doi":"10.1103/PhysRevA.71.062329","volume":71,"publication":"Physical Review A - Atomic, Molecular, and Optical Physics","day":"01","year":"2005","publication_status":"published","intvolume":" 71","month":"06","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0412009","open_access":"1"}],"oa":1,"publisher":"American Physical Society","quality_controlled":0,"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(ϱlnϱ) of a density matrix ϱ123 on the product of three Hilbert spaces satisfies S[ϱ123]- S[ϱ12]≤S[ϱ23]-S[ϱ2]. We strengthen this to S[ϱ123]-S[ϱ12] ≤αnα(S[ϱ23α]-S[ϱ2α]), where the nα are weights and the ϱ23α are partitions of ϱ23. 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."}]},{"day":"01","year":"2005","publication_status":"published","date_created":"2018-12-11T11:57:36Z","date_published":"2005-01-01T00:00:00Z","doi":"10.1137/S0097539704446682","page":"545 - 554","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."}],"month":"01","publisher":"SIAM","quality_controlled":0,"extern":1,"citation":{"short":"A. Fiat, M. Levy, J. Matoušek, E. Pach, M. Sharir, S. Smorodinsky, U. Wagner, E. Welzl, in:, SIAM, 2005, pp. 545–554.","ieee":"A. Fiat et al., “Online conflict-free coloring for intervals,” presented at the SODA: Symposium on Discrete Algorithms, 2005, pp. 545–554.","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. https://doi.org/10.1137/S0097539704446682","ama":"Fiat A, Levy M, Matoušek J, et al. Online conflict-free coloring for intervals. In: SIAM; 2005:545-554. doi:10.1137/S0097539704446682","mla":"Fiat, Amos, et al. Online Conflict-Free Coloring for Intervals. SIAM, 2005, pp. 545–54, doi:10.1137/S0097539704446682.","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.","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. https://doi.org/10.1137/S0097539704446682."},"date_updated":"2021-01-12T06:57:25Z","title":"Online conflict-free coloring for intervals","publist_id":"4496","author":[{"first_name":"Amos","last_name":"Fiat","full_name":"Fiat, Amos"},{"first_name":"Meital","full_name":"Levy, Meital B","last_name":"Levy"},{"full_name":"Matoušek, Jiří","last_name":"Matoušek","first_name":"Jiří"},{"full_name":"Pach, Elchanan M","last_name":"Pach","first_name":"Elchanan"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"},{"first_name":"Shakhar","full_name":"Smorodinsky, Shakhar","last_name":"Smorodinsky"},{"full_name":"Uli Wagner","orcid":"0000-0002-1494-0568","last_name":"Wagner","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Emo","last_name":"Welzl","full_name":"Welzl, Emo"}],"_id":"2428","status":"public","conference":{"name":"SODA: Symposium on Discrete Algorithms"},"type":"conference"},{"type":"journal_article","status":"public","_id":"2427","author":[{"first_name":"Christoph","last_name":"Ambühl","full_name":"Ambühl, Christoph"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","orcid":"0000-0002-1494-0568","full_name":"Uli Wagner","last_name":"Wagner"}],"publist_id":"4497","title":"The Clique problem in intersection graphs of ellipses and triangles","citation":{"chicago":"Ambühl, Christoph, and Uli Wagner. “The Clique Problem in Intersection Graphs of Ellipses and Triangles.” Theory of Computing Systems. Springer, 2005. https://doi.org/10.1007/s00224-005-1141-6.","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.” Theory of Computing Systems, vol. 38, no. 3, Springer, 2005, pp. 279–92, doi:10.1007/s00224-005-1141-6.","ieee":"C. Ambühl and U. Wagner, “The Clique problem in intersection graphs of ellipses and triangles,” Theory of Computing Systems, vol. 38, no. 3. Springer, pp. 279–292, 2005.","short":"C. Ambühl, U. Wagner, Theory of Computing Systems 38 (2005) 279–292.","apa":"Ambühl, C., & Wagner, U. (2005). The Clique problem in intersection graphs of ellipses and triangles. Theory of Computing Systems. Springer. https://doi.org/10.1007/s00224-005-1141-6","ama":"Ambühl C, Wagner U. The Clique problem in intersection graphs of ellipses and triangles. Theory of Computing Systems. 2005;38(3):279-292. doi:10.1007/s00224-005-1141-6"},"date_updated":"2021-01-12T06:57:25Z","extern":1,"publisher":"Springer","quality_controlled":0,"month":"05","intvolume":" 38","abstract":[{"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.","lang":"eng"}],"page":"279 - 292","issue":"3","doi":"10.1007/s00224-005-1141-6","date_published":"2005-05-01T00:00:00Z","volume":38,"date_created":"2018-12-11T11:57:36Z","publication_status":"published","year":"2005","day":"01","publication":"Theory of Computing Systems"},{"type":"journal_article","status":"public","_id":"2455","publist_id":"4448","author":[{"last_name":"Billou","full_name":"Billou, Ikram","first_name":"Ikram"},{"first_name":"Jian","last_name":"Xu","full_name":"Xu, Jian"},{"last_name":"Wildwater","full_name":"Wildwater, Marjolein","first_name":"Marjolein"},{"first_name":"Viola","last_name":"Willemsen","full_name":"Willemsen, Viola"},{"first_name":"Ivan","last_name":"Paponov","full_name":"Paponov, Ivan A"},{"last_name":"Friml","orcid":"0000-0002-8302-7596","full_name":"Jirí Friml","first_name":"Jirí","id":"4159519E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Heldstra, Renze","last_name":"Heldstra","first_name":"Renze"},{"full_name":"Aida, Mitsuhiro","last_name":"Aida","first_name":"Mitsuhiro"},{"last_name":"Palme","full_name":"Palme, Klaus J","first_name":"Klaus"},{"full_name":"Scheres, Ben","last_name":"Scheres","first_name":"Ben"}],"title":"The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots","date_updated":"2021-01-12T06:57:35Z","citation":{"ama":"Billou I, Xu J, Wildwater M, et al. The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots. Nature. 2005;433(7021):39-44. doi:10.1038/nature03184","apa":"Billou, I., Xu, J., Wildwater, M., Willemsen, V., Paponov, I., Friml, J., … Scheres, B. (2005). The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots. Nature. Nature Publishing Group. https://doi.org/10.1038/nature03184","ieee":"I. Billou et al., “The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots,” Nature, vol. 433, no. 7021. Nature Publishing Group, pp. 39–44, 2005.","short":"I. Billou, J. Xu, M. Wildwater, V. Willemsen, I. Paponov, J. Friml, R. Heldstra, M. Aida, K. Palme, B. Scheres, Nature 433 (2005) 39–44.","mla":"Billou, Ikram, et al. “The PIN Auxin Efflux Facilitator Network Controls Growth and Patterning in Arabidopsis Roots.” Nature, vol. 433, no. 7021, Nature Publishing Group, 2005, pp. 39–44, doi:10.1038/nature03184.","ista":"Billou I, Xu J, Wildwater M, Willemsen V, Paponov I, Friml J, Heldstra R, Aida M, Palme K, Scheres B. 2005. The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots. Nature. 433(7021), 39–44.","chicago":"Billou, Ikram, Jian Xu, Marjolein Wildwater, Viola Willemsen, Ivan Paponov, Jiří Friml, Renze Heldstra, Mitsuhiro Aida, Klaus Palme, and Ben Scheres. “The PIN Auxin Efflux Facilitator Network Controls Growth and Patterning in Arabidopsis Roots.” Nature. Nature Publishing Group, 2005. https://doi.org/10.1038/nature03184."},"extern":1,"publisher":"Nature Publishing Group","quality_controlled":0,"intvolume":" 433","month":"01","abstract":[{"text":"Local accumulation of the plant growth regulator auxin mediates pattern formation in Arabidopsis roots and influences outgrowth and development of lateral root- and shoot-derived primordia. However, it has remained unclear how auxin can simultaneously regulate patterning and organ outgrowth and how its distribution is stabilized in a primordium-specif ic manner. Here we show that five PIN genes collectively control auxin distribution to regulate cell division and cell expansion in the primary root. Furthermore, the joint action of these genes has an important role in pattern formation by focusing the auxin maximum and restricting the expression domain of PLETHORA (PLT) genes, major determinants for root stem cell specification. In turn, PLT genes are required for PIN gene transcription to stabilize the auxin maximum at the distal root tip. Our data reveal an interaction network of auxin transport facilitators and root fate determinants that control patterning and growth of the root primordium.","lang":"eng"}],"page":"39 - 44","date_created":"2018-12-11T11:57:46Z","doi":"10.1038/nature03184","volume":433,"issue":"7021","date_published":"2005-01-01T00:00:00Z","year":"2005","publication_status":"published","publication":"Nature","day":"01"}]