@article{208, abstract = {For any ε > 0 and any diagonal quadratic form Q ∈ ℤ[x 1, x 2, x 3, x 4] with a square-free discriminant of modulus Δ Q ≠ 0, we establish the uniform estimate ≪ε B 3/2+ε + B 2+ε/Δ Q 1/6 for the number of rational points of height at most B lying in the projective surface Q = 0.}, author = {Timothy Browning}, journal = {Quarterly Journal of Mathematics}, number = {1}, pages = {11 -- 31}, publisher = {Oxford University Press}, title = {{Counting rational points on diagonal quadratic surfaces}}, doi = {10.1093/qjmath/54.1.11}, volume = {54}, year = {2003}, } @inproceedings{2337, author = {Lieb, Élliott H and Robert Seiringer}, editor = {Karpeshina, Yulia and Weikard, Rudi and Zeng, Yanni}, pages = {239 -- 250}, publisher = {American Mathematical Society}, title = {{Bose-Einstein condensation of dilute gases in traps }}, doi = {10.1090/conm/327/05818}, volume = {327}, year = {2003}, } @article{2354, abstract = {We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the Gross-Pitaevskii (GP) limit of a dilute gas. Analysing both the absolute and the bosonic ground states of the system, we show, in particular, their different behaviour for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.}, author = {Robert Seiringer}, journal = {Journal of Physics A: Mathematical and Theoretical}, number = {37}, pages = {9755 -- 9778}, publisher = {IOP Publishing Ltd.}, title = {{Ground state asymptotics of a dilute, rotating gas}}, doi = {10.1088/0305-4470/36/37/312}, volume = {36}, year = {2003}, } @article{2357, abstract = {The classic Poincaré inequality bounds the L q-norm of a function f in a bounded domain Ω ⊂ ℝ n in terms of some L p-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Τ from Ω and concentrate our attention on Λ = Ω \ Τ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it might have a very bad constant. This is so even if the volume of Τ is arbitrarily small. A Poincaré inequality does hold, however, if one makes the additional assumption that f has a finite L p gradient norm on the whole of Ω, not just on Λ. The important point is that the Poincaré inequality thus obtained bounds the L q-norm of f in terms of the L p gradient norm on Λ (not Ω) plus an additional term that goes to zero as the volume of Τ goes to zero. This error term depends on Τ only through its volume. Apart from this additive error term, the constant in the inequality remains that of the 'nice' domain Ω. In the second generalization we are given a vector field A and replace ∇ by ∇ + iA(x) (geometrically, a connection on a U(1) bundle). Unlike the A = 0 case, the infimum of ∥(∇ + iA)f∥ p over all f with a given ∥f∥ q is in general not zero. This permits an improvement of the inequality by the addition of a term whose sharp value we derive. We describe some open problems that arise from these generalizations.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Annals of Mathematics}, number = {3}, pages = {1067 -- 1080}, publisher = {Princeton University Press}, title = {{Poincaré inequalities in punctured domains}}, doi = {10.4007/annals.2003.158.1067 }, volume = {158}, year = {2003}, } @article{2358, abstract = {A study was conducted on the one-dimensional (1D) bosons in three-dimensional (3D) traps. A rigorous analysis was carried out on the parameter regions in which various types of 1D or 3D behavior occurred in the ground state. The four parameter regions include density, transverse, longitudinal dimensions and scattering length.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Physical Review Letters}, number = {15}, pages = {1504011 -- 1504014}, publisher = {American Physical Society}, title = {{One-dimensional Bosons in three-dimensional traps}}, doi = {10.1103/PhysRevLett.91.150401}, volume = {91}, year = {2003}, } @phdthesis{2414, author = {Uli Wagner}, publisher = {ETH Zurich}, title = {{On k-Sets and Their Applications}}, doi = {10.3929/ethz-a-004708408}, year = {2003}, } @inproceedings{2422, abstract = {We prove a lower bound of 0.3288(4 n) for the rectilinear crossing number cr̄(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadrilaterals in any set of n points in general position in the Euclidean plane. As we see it, the main contribution of this paper is not so much the concrete numerical improvement over earlier bounds, as the novel method of proof, which is not based on bounding cr̄(Kn) for some small n.}, author = {Uli Wagner}, pages = {583 -- 588}, publisher = {SIAM}, title = {{On the rectilinear crossing number of complete graphs}}, year = {2003}, } @inproceedings{2423, abstract = {A finite set N ⊃ Rd is a weak ε-net for an n-point set X ⊃ Rd (with respect to convex sets) if N intersects every convex set K with |K ∩ X| ≥ εn. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al. [7], that every point set X in Rd admits a weak ε-net of cardinality O(ε-d polylog(1/ε)). Moreover, for a number of special point sets (e.g., for points on the moment curve), our method gives substantially better bounds. The construction yields an algorithm to construct such weak ε-nets in time O(n ln(1/ε)). We also prove, by a different method, a near-linear upper bound for points uniformly distributed on the (d - 1)-dimensional sphere.}, author = {Matoušek, Jiří and Uli Wagner}, pages = {129 -- 135}, publisher = {ACM}, title = {{New constructions of weak epsilon-nets}}, doi = {10.1145/777792.777813}, year = {2003}, } @inproceedings{2424, abstract = {We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some (potentially very high-dimensional) Euclidean space ℝd. We assume that M is known to us only through a finite sample P ⊂ M, as it is often the case in applications. The adaptive neighborhood graph is a geometric graph on P. Its complexity is at most min{2O(k)(n, n2}, where n = |P| and k = dim M, as opposed to the n⌈d/2⌉ complexity of the Delaunay triangulation, which is often used to model manifolds. We show that we can provably correctly infer the connectivity of M and the dimension of M from the adaptive neighborhood graph provided a certain standard sampling condition is fulfilled. The running time of the dimension detection algorithm is d2O(k7 log k) for each connected component of M. If the dimension is considered constant, this is a constant-time operation, and the adaptive neighborhood graph is of linear size. Moreover, the exponential dependence of the constants is only on the intrinsic dimension k, not on the ambient dimension d. This is of particular interest if the co-dimension is high, i.e., if k is much smaller than d, as is the case in many applications. The adaptive neighborhood graph also allows us to approximate the geodesic distances between the points in P.}, author = {Giesen, Joachim and Uli Wagner}, pages = {329 -- 337}, publisher = {ACM}, title = {{Shape dimension and intrinsic metric from samples of manifolds with high co-dimension}}, doi = {10.1145/777792.777841}, year = {2003}, } @inproceedings{4561, abstract = {We present a formalism for specifying component interfaces that expose component requirements on limited resources. The formalism permits an algorithmic check if two or more components, when put together, exceed the available resources. Moreover, the formalism can be used to compute the quantity of resources necessary for satisfying the requirements of a collection of components. The formalism can be instantiated in several ways. For example, several components may draw power from the same source. Then, the formalism supports compatibility checks such as: can two components, when put together, achieve their tasks without ever exceeding the available amount of peak power? or, can they achieve their tasks by using no more than the initially available amount of energy (i.e., power accumulated over time)? The corresponding quantitative questions that our algorithms answer are the following: what is the amount of peak power needed for two components to be put together? what is the corresponding amount of initial energy? To solve these questions, we model interfaces with resource requirements as games with quantitative objectives. The games are played on state spaces where each state is labeled by a number (representing, e.g., power consumption), and a play produces an infinite path of labels. The objective may be, for example, to minimize the largest label that occurs during a play. We illustrate our approach by modeling compatibility questions for the components of robot control software, and of wireless sensor networks.}, author = {Chakrabarti, Arindam and De Alfaro, Luca and Henzinger, Thomas A and Stoelinga, Mariëlle}, booktitle = {Third International Conference on Embedded Software}, isbn = {9783540202233}, location = {Philadelphia, PA, USA}, pages = {117 -- 133}, publisher = {ACM}, title = {{Resource interfaces}}, doi = {10.1007/978-3-540-45212-6_9}, volume = {2855}, year = {2003}, } @inproceedings{4628, abstract = {Discounting the future means that the value, today, of a unit payoffis 1 if the payoffo ccurs today, a if it occurs tomorrow, a 2 if it occurs the day after tomorrow, and so on, for some real-valued discount factor 0 < a < 1. Discounting (or inflation) is a key paradigm in economics and has been studied in Markov decision processes as well as game theory. We submit that discounting also has a natural place in systems engineering: for nonterminating systems, a potential bug in the far-away future is less troubling than a potential bug today. We therefore develop a systems theory with discounting. Our theory includes several basic elements: discounted versions of system properties that correspond to the ω-regular properties, fixpoint-based algorithms for checking discounted properties, and a quantitative notion of bisimilarity for capturing the difference between two states with respect to discounted properties. We present the theory in a general form that applies to probabilistic systems as well as multicomponent systems (games), but it readily specializes to classical transition systems. We show that discounting, besides its natural practical appeal, has also several mathematical benefits. First, the resulting theory is robust, in that small perturbations of a system can cause only small changes in the properties of the system. Second, the theory is computational, in that the values of discounted properties, as well as the discounted bisimilarity distance between states, can be computed to any desired degree of precision.}, author = {De Alfaro, Luca and Henzinger, Thomas A and Majumdar, Ritankar}, booktitle = {Proceedings of the 30th International Colloquium on Automata, Languages and Programming}, isbn = {9783540404934}, location = {Eindhoven, The Netherlands}, pages = {1022 -- 1037}, publisher = {Springer}, title = {{Discounting the future in systems theory}}, doi = {10.1007/3-540-45061-0_79}, volume = {2719}, year = {2003}, } @inproceedings{4630, abstract = {We consider concurrent two-person games played in real time, in which the players decide both which action to play, and when to play it. Such timed games differ from untimed games in two essential ways. First, players can take each other by surprise, because actions are played with delays that cannot be anticipated by the opponent. Second, a player should not be able to win the game by preventing time from diverging. We present a model of timed games that preserves the element of surprise and accounts for time divergence in a way that treats both players symmetrically and applies to all ω-regular winning conditions. We prove that the ability to take each other by surprise adds extra power to the players. For the case that the games are specified in the style of timed automata, we provide symbolic algorithms for their solution with respect to all ω-regular winning conditions. We also show that for these timed games, memory strategies are more powerful than memoryless strategies already in the case of reachability objectives.}, author = {De Alfaro, Luca and Faella, Marco and Henzinger, Thomas A and Majumdar, Ritankar and Stoelinga, Mariëlle}, booktitle = {Proceedings of the 14th International Conference on Concurrency Theory}, isbn = {9783540407539}, location = {Marseille, France}, pages = {144 -- 158}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The element of surprise in timed games}}, doi = {10.1007/978-3-540-45187-7_9}, volume = {2761}, year = {2003}, } @article{576, abstract = {We study the free expansion of a pancake-shaped Bose-condensed gas, which is initially trapped under harmonic confinement and containing a vortex at its centre. In the case of a radial expansion holding the axial confinement fixed we consider various models for the interactions, depending on the thickness of the condensate relative to the value of the scattering length. We are thus able to evaluate different scattering regimes ranging from quasi-three-dimensional (Q3D) to strictly two-dimensional (2D). We find that as the system goes from Q3D to 2D the expansion rate of the condensate increases whereas that of the vortex core decreases. In the Q3D scattering regime we also examine a fully free expansion in 3D and find oscillatory behaviour for the vortex core radius: an initial fast expansion of the vortex core is followed by a slowing down. Such a nonuniform expansion rate of the vortex core implies that the timing of its observation should be chosen appropriately.}, author = {Onur Hosten and Vignolo, Patrizia and Minguzzi, Anna and Tanatar, Bilal and Tosi, Mario P}, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, number = {12}, pages = {2455 -- 2463}, publisher = {IOP Publishing Ltd.}, title = {{Free expansion of two-dimensional condensates with a vortex}}, doi = {10.1088/0953-4075/36/12/306}, volume = {36}, year = {2003}, } @article{6156, abstract = {Social and solitary feeding in natural Caenorhabditis elegans isolates are associated with two alleles of the orphan G-protein-coupled receptor (GPCR) NPR-1: social feeders contain NPR-1 215F, whereas solitary feeders contain NPR-1 215V. Here we identify FMRFamide-related neuropeptides (FaRPs) encoded by the flp-18 and flp-21 genes as NPR-1 ligands and show that these peptides can differentially activate the NPR-1 215F and NPR-1 215V receptors. Multicopy overexpression of flp-21 transformed wild social animals into solitary feeders. Conversely, a flp-21 deletion partially phenocopied the npr-1(null) phenotype, which is consistent with NPR-1 activation by FLP-21 in vivo but also implicates other ligands for NPR-1. Phylogenetic studies indicate that the dominant npr-1 215V allele likely arose from an ancestral npr-1 215F gene in C. elegans. Our data suggest a model in which solitary feeding evolved in an ancestral social strain of C. elegans by a gain-of-function mutation that modified the response of NPR-1 to FLP-18 and FLP-21 ligands.}, author = {Rogers, Candida and Reale, Vincenzina and Kim, Kyuhyung and Chatwin, Heather and Li, Chris and Evans, Peter and de Bono, Mario}, issn = {1097-6256}, journal = {Nature Neuroscience}, number = {11}, pages = {1178--1185}, publisher = {Springer Nature}, title = {{Inhibition of Caenorhabditis elegans social feeding by FMRFamide-related peptide activation of NPR-1}}, doi = {10.1038/nn1140}, volume = {6}, year = {2003}, } @article{6157, abstract = {In many animal species individuals aggregate to live in groups. A range of experimental approaches in different animals, including studies of social feeding in nematodes, maternal behavior in rats and sheep, and pair-bonding in voles, are providing insights into the neural bases for these behaviors. These studies are delineating multiple neural circuits and gene networks in the brain that interact in ways that are as yet poorly understood to coordinate social behavior.}, author = {de Bono, Mario}, issn = {0022-3034}, journal = {Journal of Neurobiology}, number = {1}, pages = {78--92}, publisher = {Wiley}, title = {{Molecular approaches to aggregation behavior and social attachment}}, doi = {10.1002/neu.10162}, volume = {54}, year = {2003}, } @article{1457, abstract = {Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Stromdnger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equal. This provides significant evidence in support of SYZ. Moreover, the examples are of great interest in their own right: they are spaces of flat SLr-connections on a smooth curve. The mirror is the corresponding space for the Langlands dual group PGLr. These examples therefore throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.}, author = {Tamas Hausel and Thaddeus, Michael}, journal = {Inventiones Mathematicae}, number = {1}, pages = {197 -- 229}, publisher = {Springer}, title = {{Mirror symmetry, langlands duality, and the Hitchin system}}, doi = {10.1007/s00222-003-0286-7}, volume = {153}, year = {2003}, } @article{1458, abstract = {The moduli space of stable bundles of rank $2$ and degree $1$ on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the noncompact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance.}, author = {Tamas Hausel and Thaddeus, Michael}, journal = {Journal of the American Mathematical Society}, number = {2}, pages = {303 -- 329}, publisher = {American Mathematical Society}, title = {{Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles}}, doi = {10.1090/S0894-0347-02-00417-4}, volume = {16}, year = {2003}, } @article{1459, abstract = {In this paper we explicitly calculate the analogue of the 't Hooft SU (2) Yang-Mills instantons on Gibbons-Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi-Hanson, or Ak ALE gravitational instantons and the multi-Taub-NUT spaces, or Ak ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU (2) magnetic monopole solutions of the Bogomolny equations on flat ℝ3.}, author = {Etesi, Gábor and Tamas Hausel}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {275 -- 288}, publisher = {Springer}, title = {{On Yang-Mills instantons over multi-centered gravitational instantons}}, doi = {10.1007/s00220-003-0806-8}, volume = {235}, year = {2003}, } @article{13436, abstract = {Cross-metathesis reactions of α,β-unsaturated sulfones and sulfoxides in the presence of molybdenum and ruthenium pre-catalysts were tested. A selective metahesis reaction was achieved between functionalized terminal olefins and vinyl sulfones by using the ‘second generation’ ruthenium catalysts 1c–h while the highly active Schrock catalyst 1b was found to be functional group incompatible with vinyl sulfones. The cross-metathesis products were isolated in good yields with an excellent (E)-selectivity. Both the molybdenum and ruthenium-based complexes were, however, incompatible with α,β- and β,γ-unsaturated sulfoxides.}, author = {Michrowska, Anna and Bieniek, Michał and Kim, Mikhail and Klajn, Rafal and Grela, Karol}, issn = {1464-5416}, journal = {Tetrahedron}, keywords = {Organic Chemistry, Drug Discovery, Biochemistry}, number = {25}, pages = {4525--4531}, publisher = {Elsevier}, title = {{Cross-metathesis reaction of vinyl sulfones and sulfoxides}}, doi = {10.1016/s0040-4020(03)00682-3}, volume = {59}, year = {2003}, } @article{9455, abstract = {Proteins of the ARGONAUTE family are important in diverse posttranscriptional RNA-mediated gene-silencing systems as well as in transcriptional gene silencing in Drosophila and fission yeast and in programmed DNA elimination in Tetrahymena. We cloned ARGONAUTE4 (AGO4) from a screen for mutants that suppress silencing of the Arabidopsis SUPERMAN(SUP) gene. The ago4-1 mutant reactivated silentSUP alleles and decreased CpNpG and asymmetric DNA methylation as well as histone H3 lysine-9 methylation. In addition,ago4-1 blocked histone and DNA methylation and the accumulation of 25-nucleotide small interfering RNAs (siRNAs) that correspond to the retroelement AtSN1. These results suggest that AGO4 and long siRNAs direct chromatin modifications, including histone methylation and non-CpG DNA methylation.}, author = {Zilberman, Daniel and Cao, Xiaofeng and Jacobsen, Steven E.}, issn = {1095-9203}, journal = {Science}, keywords = {Multidisciplinary}, number = {5607}, pages = {716--719}, publisher = {American Association for the Advancement of Science}, title = {{ARGONAUTE4 control of locus-specific siRNA accumulation and DNA and histone methylation}}, doi = {10.1126/science.1079695}, volume = {299}, year = {2003}, }