TY - JOUR AB - Systems of three interacting particles are notorious for their complex physical behaviour. A landmark theoretical result in few-body quantum physics is Efimov\'s prediction1,2 of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov\'s problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics3-8. However, the observation of Efimov quantum states has remained an elusive goal3,5. Here we report the observation of an Efimov resonance in an ultracold gas of caesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss9,10 when the strength of the two-body interaction is varied. We also detect a minimum 9,11,12 in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems7. While Feshbach resonances13,14 have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter15 to the world of few-body quantum phenomena. AU - Kraemer, Tobias AU - Mark, Michael AU - Waldburger, Philipp AU - Danzl, Johann G AU - Chin, Cheng AU - Engeser, Bastian AU - Lange, Adam AU - Pilch, Karl AU - Jaakkola, Antti AU - Nägerl, Hanns AU - Grimm, Rudolf ID - 1033 IS - 7082 JF - Nature TI - Evidence for Efimov quantum states in an ultracold gas of caesium atoms VL - 440 ER - TY - CONF AB - Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov\'s prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction [1, 2]. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov\'s scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms [3]. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems. AU - Nägerl, Hanns AU - Kraemer, Tobias AU - Mark, Michael AU - Waldburger, Philipp AU - Danzl, Johann G AU - Engeser, Bastian AU - Lange, Adam AU - Pilch, Karl AU - Jaakkola, Antti AU - Chin, Cheng AU - Grimm, Rudolf ID - 1034 TI - Experimental evidence for Efimov quantum states VL - 869 ER - TY - CHAP AU - Harris, J. Robin AU - Almouzni, Geneviève AU - Kirschner, Doris AU - Dimitrova, Daniela AU - Nickerson, Jeffrey A. AU - Underwood, Jean AU - Wagner, Stefan AU - Korbei, Barbara AU - Foisner, Roland AU - Walther, Tobias C. AU - HETZER, Martin W AU - Peters, Reiner AU - Walev, Ivan AU - de Kroon, Anton I. P. M. AU - Staffhorst, Rutger W. H. M. AU - de Kruijff, Ben AU - Burger, Koert N. J. AU - Netto, Luis Eduardo Soares AU - Bertrand, Eric AU - Alimonti, Judie B. AU - Greenberg, Arnold H. AU - Xiao, Jinnan AU - Pradhan, Anuradha AU - Liu, Yuechueng AU - Paiement, Jacques AU - Young, Robin AU - Goñi, Félix M. AU - Villar, Ana-Victoria AU - Contreras, F.-Xabier AU - Alonso, Alicia AU - Peter, Brian J. AU - Mills, Ian G. AU - Higgins, Matthew K. AU - Brown, William J. AU - Chambers, K. AU - Doody, A. AU - Cheng, C. Yan AU - Mruk, Dolores D. AU - Yang, Chunhong AU - Kirchhoff, Helmut AU - Haase, Winfried AU - Boggasch, Stephanie AU - Paulsen, Harald AU - Benesova, Julie AU - Liffers, Sven-T. AU - Rögner, Matthias AU - Gao, Ya-sheng AU - Sztul, Elizabeth AU - Thiemann, Meinolf AU - Fahimi, H. Dariush AU - Gniadecki, Robert AU - Gajkowska, Barbara AU - Bane, Susan L. AU - Hess, John F. AU - Voss, John C. AU - Fitzgerald, Paul G. AU - Hisanaga, Shin-ichi AU - Sasaki, Takahiro AU - Uéda, Kenji AU - Town, Terrence AU - Tan, Jun AU - Milton, Nathaniel G. N. AU - Chi, Richard AU - Keller, Thomas C. S. AU - Kriajevska, Marina AU - Bronstein, Igor AU - Lukanidin, Eugene AU - Holmes, David F. AU - Kadler, Karl E. ED - Harris, Robin ED - Graham, John ED - Rickwood, David ID - 11119 SN - 9780470847589 T2 - Cell Biology Protocols TI - In Vitro Techniques ER - TY - JOUR AB - Over the last years it has become evident that the nuclear envelope (NE) is more than a passive membrane barrier that separates the nucleus from the cytoplasm. The NE not only controls the trafficking of macromolecules between the nucleoplasm and the cytosol, but also provides anchoring sites for chromosomes and cytoskeleton to the nuclear periphery. Targeting of chromatin to the NE might actually be part of gene expression regulation in eukaryotes. Mutations in certain NE proteins are associated with a diversity of human diseases, including muscular dystrophy, neuropathy, lipodistrophy, torsion dystonia and the premature aging condition progeria. Despite the importance of the NE for cell division and differentiation, relatively little is known about its biogenesis and its role in human diseases. It is our goal to provide a comprehensive view of the NE and to discuss possible implications of NE-associated changes for gene expression, chromatin organization and signal transduction. AU - D’Angelo, M. A. AU - HETZER, Martin W ID - 11117 IS - 3 JF - Cellular and Molecular Life Sciences KW - Cell Biology KW - Cellular and Molecular Neuroscience KW - Pharmacology KW - Molecular Biology KW - Molecular Medicine SN - 1420-682X TI - The role of the nuclear envelope in cellular organization VL - 63 ER - TY - JOUR AB - Nuclear pore complexes are multiprotein channels that span the double lipid bilayer of the nuclear envelope. How new pores are inserted into the intact nuclear envelope of proliferating and differentiating eukaryotic cells is unknown. We found that the Nup107-160 complex was incorporated into assembly sites in the nuclear envelope from both the nucleoplasmic and the cytoplasmic sides. Nuclear pore insertion required the generation of Ran guanosine triphosphate in the nuclear and cytoplasmic compartments. Newly formed nuclear pore complexes did not contain structural components of preexisting pores, suggesting that they can form de novo. AU - D'Angelo, Maximiliano A. AU - Anderson, Daniel J. AU - Richard, Erin AU - HETZER, Martin W ID - 11118 IS - 5772 JF - Science KW - Multidisciplinary SN - 0036-8075 TI - Nuclear pores form de novo from both sides of the nuclear envelope VL - 312 ER - TY - CONF AB - Broder et al.'s [3] shingling algorithm and Charikar's [4] random projection based approach are considered "state-of-the-art" algorithms for finding near-duplicate web pages. Both algorithms were either developed at or used by popular web search engines. We compare the two algorithms on a very large scale, namely on a set of 1.6B distinct web pages. The results show that neither of the algorithms works well for finding near-duplicate pairs on the same site, while both achieve high precision for near-duplicate pairs on different sites. Since Charikar's algorithm finds more near-duplicate pairs on different sites, it achieves a better precision overall, namely 0.50 versus 0.38 for Broder et al.'s algorithm. We present a combined algorithm which achieves precision 0.79 with 79% of the recall of the other algorithms. AU - Henzinger, Monika H ID - 11929 T2 - 29th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval TI - Finding near-duplicate web pages: A large-scale evaluation of algorithms ER - TY - JOUR AB - A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hubert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on ℂ2 (recovering results of Nakajima-Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced. AU - Tamas Hausel ID - 1462 IS - 16 JF - PNAS TI - Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform VL - 103 ER - TY - JOUR AB - This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial L 2 harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of L 2 harmonic forms on complete hyperkähler manifolds of linear growth. AU - Tamas Hausel AU - Swartz, Edward ID - 1461 IS - 8 JF - Proceedings of the American Mathematical Society TI - Intersection forms of toric hyperkähler varieties VL - 134 ER - TY - JOUR AB - Background: Cell-to-cell communication at the synapse involves synaptic transmission as well as signaling mediated by growth factors, which provide developmental and plasticity cues. There is evidence that a retrograde, presynaptic transforming growth factor-β (TGF-β) signaling event regulates synapse development and function in Drosophila. Results: Here we show that a postsynaptic TGF-β signaling event occurs during larval development. The type I receptor Thick veins (Tkv) and the R-Smad transcription factor Mothers-against-dpp (Mad) are localized postsynaptically in the muscle. Furthermore, Mad phosphorylation occurs in regions facing the presynaptic active zones of neurotransmitter release within the postsynaptic subsynaptic reticulum (SSR). In order to monitor in real time the levels of TGF-β signaling in the synapse during synaptic transmission, we have established a FRAP assay to measure Mad nuclear import/export in the muscle. We show that Mad nuclear trafficking depends on stimulation of the muscle. Conclusions: Our data suggest a mechanism linking synaptic transmission and postsynaptic TGF-β signaling that may coordinate nerve-muscle development and function. AU - Dudu, Veronika AU - Bittig, Thomas AU - Entchev, Eugeni AU - Kicheva, Anna AU - Julicher, Frank AU - González Gaitán, Marcos ID - 1715 IS - 7 JF - Current Biology TI - Postsynaptic mad signaling at the Drosophila neuromuscular junction VL - 16 ER - TY - JOUR AB - SiGe islands grown by deposition of 10 monolayers of Ge on Si(0 0 1) at 740 °C were investigated by using a combination of selective wet chemical etching and atomic force microscopy. The used etchant, a solution consisting of ammonium hydroxide and hydrogen peroxide, shows a high selectivity of Ge over SixGe1-x and is characterized by relatively slow etching rates for Si-rich alloys. By performing successive etching experiments on the same sample area, we are able to gain a deeper insight into the lateral displacement the islands undergo during post growth annealing. AU - Georgios Katsaros AU - Rastelli, Armando AU - Stoffel, Mathieu AU - Isella, Giovanni AU - Von Känel, Hans AU - Bittner, Alexander M AU - Tersoff, Jerry AU - Denker, Ulrich AU - Schmidt, Oliver G AU - Costantini, Giovanni AU - Kern, Klaus ID - 1745 IS - 12 JF - Surface Science TI - Investigating the lateral motion of SiGe islands by selective chemical etching VL - 600 ER - TY - JOUR AB - We report on recent advances in the understanding of surface processes occurring during growth and post-growth annealing of strained islands which may find application as self-assembled quantum dots. We investigate the model system SiGe/Si(0 0 1) by a new approach based on "reading the footprints" which islands leave on the substrate during their growth and evolution. Such footprints consist of trenches carved in the Si substrate. We distinguish between surface footprints and footprints buried below the islands. The former allow us to discriminate islands which are in the process of growing from those which are shrinking. Islands with steep morphologies grow at the expense of smaller and shallower islands, consistent with the kinetics of anomalous coarsening. While shrinking, islands change their shape according to thermodynamic predictions. Buried footprints are investigated by removing the SiGe epilayer by means of selective wet chemical etching. Their reading shows that: (i) during post-growth annealing islands move laterally because of surface-mediated Si-Ge intermixing; (ii) a tree-ring structure of trenches is created by dislocated islands during their "cyclic" growth. This allows us to distinguish coherent from dislocated islands and to establish whether the latter are the result of island coalescence. AU - Rastelli, Armando AU - Stoffel, Mathieu AU - Georgios Katsaros AU - Tersoff, Jerry AU - Denker, Ulrich AU - Merdzhanova, Tsvetelina AU - Kar, Gouranga S AU - Costantini, Giovanni AU - Kern, Klaus AU - Von Känel, Hans AU - Schmidt, Oliver G ID - 1747 IS - 12 JF - Microelectronics Journal TI - Reading the footprints of strained islands VL - 37 ER - TY - JOUR AB - A microscopic picture for the GaAs overgrowth of self-organized InAs/GaAs(001) quantum dots is developed. Scanning tunneling microscopy measurements reveal two capping regimes: the first being characterized by a dot shrinking and a backward pyramid-to-dome shape transition. This regime is governed by fast dynamics resulting in island morphologies close to thermodynamic equilibrium. The second regime is marked by a true overgrowth and is controlled by kinetically limited surface diffusion processes. A simple model is developed to describe the observed structural changes which are rationalized in terms of energetic minimization driven by lattice mismatch and alloying. AU - Costantini, Giovanni AU - Rastelli, Armando AU - Manzano, Carlos AU - Acosta-Diaz, P AU - Songmuang, Rudeeson AU - Georgios Katsaros AU - Schmidt, Oliver G AU - Kern, Klaus ID - 1746 IS - 22 JF - Physical Review Letters TI - Interplay between thermodynamics and kinetics in the capping of InAs/GaAs (001) quantum dots VL - 96 ER - TY - JOUR AB - The authors apply selective wet chemical etching and atomic force microscopy to reveal the three-dimensional shape of SiGeSi (001) islands after capping with Si. Although the "self-assembled quantum dots" remain practically unaffected by capping in the temperature range of 300-450 °C, significant morphological changes take place on the Si surface. At 450 °C, the morphology of the capping layer (Si matrix) evolves toward an intriguing semifacetted structure, which we call a "ziggurat," giving the misleading impression of a stepped SiGe island shape. AU - Georgios Katsaros AU - Rastelli, Armando AU - Stoffel, Mathieu AU - Costantini, Giovanni AU - Schmidt, Oliver G AU - Kern, Klaus AU - Tersoff, Jerry AU - Müller, Elisabeth AU - Von Känel, Hans ID - 1748 IS - 25 JF - Applied Physics Letters TI - Evolution of buried semiconductor nanostructures and origin of stepped surface mounds during capping VL - 89 ER - TY - JOUR AB - Drugs that block the entry of human immunodeficiency virus type 1 (HIV-1) into host cells abrogate the establishment of a productive infection and should ideally diminish the chances of HIV-1 developing resistance. This review will give an overview of the mechanism by which the envelope glycoprotein mediates HIV-1 entry and will summarize current drug developments. AU - Sandra Siegert AU - Schnierle, Peter AU - Schnierle, Barbara S ID - 1796 IS - 5 JF - Mini-Reviews in Medicinal Chemistry TI - Novel anti-viral therapy: Drugs that block HIV entry at different target sites VL - 6 ER - TY - JOUR AB - Respiratory complex I plays a central role in cellular energy production in bacteria and mitochondria. Its dysfunction is implicated in many human neurodegenerative diseases, as well as in aging. The crystal structure of the hydrophilic domain (peripheral arm) of complex I from Thermus thermophilus has been solved at 3.3 angstrom resolution. This subcomplex consists of eight subunits and contains all the redox centers of the enzyme, including nine iron-sulfur clusters. The primary electron acceptor, flavin-mononucleotide, is within electron transfer distance of cluster N3, leading to the main redox pathway, and of the distal cluster Nia, a possible antioxidant. The structure reveals new aspects of the mechanism and evolution of the enzyme. The terminal cluster N2 is coordinated, uniquely, by two consecutive cysteines. The novel subunit Nqo15 has a similar fold to the mitochondrial iron chaperone frataxin, and it may be involved in iron-sulfur cluster regeneration in the complex. AU - Leonid Sazanov AU - Hinchliffe, Philip ID - 1961 IS - 5766 JF - Science TI - Structure of the hydrophilic domain of respiratory complex I from Thermus thermophilus VL - 311 ER - TY - JOUR AB - The hydrophilic domain (peripheral arm) of the proton-translocating NADH:quinone oxidoreductase (complex I) from the thermophilic organism Thermus thermophilus HB8 has been purified and characterized. The subcomplex is stable in sodium dodecyl sulfate up to 80 °C. Of nine iron-sulfur clusters, four to five (one or two binuclear and three tetranuclear) could be detected by EPR in the NADH-reduced enzyme. The preparation consists of eight different polypeptides. Seven of them have been positively identified by peptide mass mapping and N-terminal sequencing as known hydrophilic subunits of T. thermophilus complex I. The eighth polypeptide copurified with the subcomplex at all stages, is strongly associated with the other subunits, and is present in crystals of the subcomplex, used for X-ray data collection. Therefore, it has been identified as a novel complex I subunit and named Nqo15. It is encoded in a locus separate from the nqo operon, containing the 14 other known complex I genes. ORFs encoding Nqo15 homologues are present in the genomes of the closest relatives of T. thermophilus. Our data show that, contrary to previous assumptions, bacterial complex I can contain proteins in addition to a "core" complement of 14 subunits. AU - Hinchliffe, Philip AU - Carroll, Joe D AU - Leonid Sazanov ID - 1966 IS - 14 JF - Biochemistry TI - Identification of a novel subunit of respiratory complex I from Thermus thermophilus VL - 45 ER - TY - JOUR AB - Although the X chromosome is usually similar to the autosomes in size and cytogenetic appearance, theoretical models predict that its hemizygosity in males may cause unusual patterns of evolution. The sequencing of several genomes has indeed revealed differences between the X chromosome and the autosomes in the rates of gene divergence, patterns of gene expression and rates of gene movement between chromosomes. A better understanding of these patterns should provide valuable information on the evolution of genes located on the X chromosome. It could also suggest solutions to more general problems in molecular evolution, such as detecting selection and estimating mutational effects on fitness AU - Beatriz Vicoso AU - Charlesworth, Brian ID - 2066 IS - 8 JF - Nature Reviews Genetics TI - Evolution on the X chromosome: Unusual patterns and processes VL - 7 ER - TY - CONF AB - We present an adaptive animation method for electrical discharges. Electrical discharges can be simulated using the dielectric breakdown model. Regular discretization of the governing Laplace equation leads to huge equation systems, and the computational cost of solving the equations quickly becomes prohibitive at high resolutions, especially for simulations in 3D. In contrast, our method discretizes the Laplace equation on an adaptive octree, reducing the size of the problem significantly, and making simulations of high resolution 3D datasets and even 3D animations feasible. In order to enhance realism for lightning animations, we propose a particle simulation that animates the residual positive charge. Thus, interaction of electrical discharges with their surroundings can be simulated. AU - Bernd Bickel AU - Wicke, Martin AU - Gross, Markus ID - 2077 TI - Adaptive simulation of electrical discharges ER - TY - JOUR AB - We have measured 3D face geometry, skin reflectance, and subsurface scattering using custom-built devices for 149 subjects of varying age, gender, and race. We developed a novel skin reflectance model whose parameters can be estimated from measurements. The model decomposes the large amount of measured skin data into a spatially-varying analytic BRDF, a diffuse albedo map, and diffuse subsurface scattering. Our model is intuitive, physically plausible, and - since we do not use the original measured data - easy to edit as well. High-quality renderings come close to reproducing real photographs. The analysis of the model parameters for our sample population reveals variations according to subject age, gender, skin type, and external factors (e.g., sweat, cold, or makeup). Using our statistics, a user can edit the overall appearance of a face (e.g., changing skin type and age) or change small-scale features using texture synthesis (e.g., adding moles and freckles). We are making the collected statistics publicly available to the research community for applications in face synthesis and analysis. AU - Weyrich, Tim AU - Matusik, Wojciech AU - Pfister, Hanspeter AU - Bernd Bickel AU - Donner, Craig AU - Tu, Chien AU - McAndless, Janet M AU - Lee, Jinho AU - Ngan, Addy AU - Jensen, Henrik W AU - Groß, Markus S ID - 2089 IS - 3 JF - ACM Transactions on Graphics TI - Analysis of human faces using a measurement-based skin reflectance model VL - 25 ER - TY - CONF AB - We have measured 3D face geometry, skin reflectance, and subsurface scattering using custom-built devices for 149 subjects of varying age, gender, and race. We developed a novel skin reflectance model whose parameters can be estimated from measurements. The model decomposes the large amount of measured skin data into a spatially-varying analytic BRDF, a diffuse albedo map, and diffuse subsurface scattering. Our model is intuitive, physically plausible, and - since we do not use the original measured data - easy to edit as well. High-quality renderings come close to reproducing real photographs. The analysis of the model parameters for our sample population reveals variations according to subject age, gender, skin type, and external factors (e.g., sweat, cold, or makeup). Using our statistics, a user can edit the overall appearance of a face (e.g., changing skin type and age) or change small-scale features using texture synthesis (e.g., adding moles and freckles). We are making the collected statistics publicly available to the research community for applications in face synthesis and analysis. AU - Weyrich, Tim AU - Matusik, Wojciech AU - Pfister, Hanspeter AU - Bernd Bickel AU - Donner, Craig AU - Tu, Chien AU - McAndless, Janet M AU - Lee, Jinho AU - Ngan, Addy AU - Jensen, Henrik W AU - Groß, Markus S ID - 2088 TI - Analysis of human faces using a measurement-based skin reflectance model ER - TY - CONF AU - Bernd Bickel AU - Weyrich, Tim AU - Matusik, Wojciech AU - Pfister, Hanspeter AU - Donner, Craig AU - Tu, Chien AU - McAndless, Janet M AU - Lee, Jinho AU - Ngan, Addy AU - Jensen, Henrik W AU - Groß, Markus S ID - 2090 TI - Processing and editing of faces using a measurement-based skin reflectance model ER - TY - JOUR AB - Predissociation of the N+2 C 2Σ+u(v') vibrational levels with v' ≥ 3 was observed via dispersed C 2Σ+u → X 2Σ+g fluorescence in the spectral range of 165–208 nm after resonant 1s−1π*(vr) excitation of N2 and its subsequent autoionization into the N+2 C state. This range is dominated by lines in atomic nitrogen, by overlapped C 2Σ+u(v') → X 2Σ+g(v'') vibrational band sequences with Δv = const and broad unresolved band systems (D, (2))2Πg(v') → A2Πu(v'') in the N+2 molecular ion. With very high fluorescence resolution of about 0.1 nm FWHM individual C 2Σ+u(v') → X 2Σ+g(v'') vibrational bands have been resolved. Calculation of the observed fluorescence spectra by taking into account predissociation and molecular rotation describes well the shape of both individual vibrational bands C 2Σ+u(v') → X 2Σ+g(v'') and the whole band system. AU - Ehresmann, Arno AU - Werner, Lutz AU - Klumpp, Stefan AU - Demekhin, Ph V AU - Mikhail Lemeshko AU - Sukhorukov, V. L AU - Schartner, Karl H AU - Schmoranzer, Hans P ID - 2134 IS - 6 JF - Journal of Physics B: Atomic, Molecular and Optical Physics TI - Predissociation of the N+2(C 2Σ+u) state observed via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule VL - 39 ER - TY - JOUR AB - For any integers d,n ≥2, let X ⊂ Pn be a non‐singular hypersurface of degree d that is defined over the rational numbers. The main result in this paper is a proof that the number of rational points on X which have height at most B is O(Bn − 1 + ɛ), for any ɛ > 0. The implied constant in this estimate depends at most upon d, ɛ and n. 2000 Mathematics Subject Classification 11D45 (primary), 11G35, 14G05 (secondary). AU - Timothy Browning AU - Heath-Brown, Roger AU - Starr, Jason M ID - 213 IS - 2 JF - Proceedings of the London Mathematical Society TI - The density of rational points on non-singular hypersurfaces, II VL - 93 ER - TY - JOUR AB - Temperature dependent preedge and extended x-ray absorption fine structure measurements at the Zr K edge for the perovskite-type zirconates Pb Zr0.515 Ti0.485 O3 (PZT), PbZr O3 (PZ), and BaZr O3 are performed. To carry out a more accurate study of the weak reconstruction of the local atomic structure we employed a combination of two techniques: (i) analysis of the preedge fine structure, and (ii) analysis of the Fourier transform of the difference between χ (k) functions obtained at different temperatures. A detailed investigation of local atomic structure in the cubic phase for all the crystals is also performed. It is shown that neither the displacive nor the order-disorder model can describe correctly the changes of local atomic structure during phase transitions in PZ and PZT. A spherical model describing the local atomic structure of perovskite-type crystals suffering structural phase transitions is proposed. AU - Vedrinskiǐ, Rostislav V AU - Nazarenko, Elena S AU - Mikhail Lemeshko AU - Nassif, Vivian M AU - Proux, Olivier AU - Novakovich, Alexander A AU - Joly, Yves ID - 2144 IS - 13 JF - Physical Review B - Condensed Matter and Materials Physics TI - Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates VL - 73 ER - TY - JOUR AB - Fluorescence from fragments formed after the de-excitation of the N*2(1s−1π*) resonance has been measured in the spectral range of 135–190 nm. This range is dominated by lines in atomic nitrogen and lines formed by overlapping C2Σ+u(v') → X2Σ+g(v'') bands with Δv = const in the N+2 molecular ion which result from the spectator Auger decays of the N*2(1s−1π*(vr)) resonances. Ab initio calculations of the corresponding potential curves and transition probabilities showed that the observed irregular intensity dependence of the C2Σ+u(v') → X2Σ+g(v'')(Δv = const) fluorescence lines on the vibrational quantum number vr is due to transitions between vibrational levels during the reaction N2(v0 = 0)→ N*2(1s−1π*(vr)) Longrightarrow C2Σ+u(v') → X2Σ+g(v''). AU - Ehresmann, Arno AU - Werner, Lutz AU - Klumpp, Stefan AU - Lucht, S AU - Schmoranzer, Hans P AU - Mickat, Sascha AU - Schill, Rüdiger H AU - Schartner, Karl H AU - Demekhin, Philipp AU - Mikhail Lemeshko AU - Sukhorukov, Victor L ID - 2142 IS - 2 JF - Journal of Physics B: Atomic, Molecular and Optical Physics TI - Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance VL - 39 ER - TY - JOUR AB - For any n≥3, let F ∈ Z[X0,...,Xn ] be a form of degree d *≥5 that defines a non-singular hypersurface X ⊂ Pn . The main result in this paper is a proof of the fact that the number N (F ; B) of Q-rational points on X which have height at most B satisfiesN (F ; B) = Od,ε,n (Bn −1+ε ), for any ε > 0. The implied constant in this estimate depends at most upon d, ε and n. New estimates are also obtained for the number of representations of a positive integer as the sum of three dth powers, and for the paucity of integer solutions to equal sums of like polynomials.* AU - Timothy Browning AU - Heath-Brown, Roger ID - 215 IS - 3 JF - Bulletin of the London Mathematical Society TI - The density of rational points on non-singular hypersurfaces, I VL - 38 ER - TY - JOUR AB - For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is concerned with the number Nz(B) of ℚ-rational points on Z which have height at most B. For any ε > 0, we establish the estimate NZ(B) = O d,ε,N(Bdim Z+ε), provided that d ≥ 6. As indicated, the implied constant depends at most on d, ε, and N. AU - Timothy Browning AU - Heath-Brown, Roger AU - Salberger, Per ID - 216 IS - 3 JF - Duke Mathematical Journal TI - Counting rational points on algebraic varieties VL - 132 ER - TY - JOUR AB - This paper is concerned with the average order of certain arithmetic functions, as they range over the values taken by binary forms. AU - de la Bretèche, Régis AU - Timothy Browning ID - 218 IS - 3 JF - Acta Arithmetica TI - Sums of arithmetic functions over values of binary forms VL - 125 ER - TY - CONF AU - Lieb, Élliott H AU - Robert Seiringer AU - Solovej, Jan P ID - 2333 TI - Ground-state energy of a dilute Fermi gas VL - 412 ER - TY - CONF AU - Robert Seiringer AU - Lieb, Élliott H AU - Yngvason, Jakob ED - Zambrini, Jean-Claude ID - 2334 TI - One-dimensional behavior of dilute, trapped Bose gases in traps ER - TY - GEN AB - We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state. AU - Lieb, Élliott H AU - Robert Seiringer ID - 2363 IS - 2 T2 - Communications in Mathematical Physics TI - Derivation of the Gross-Pitaevskii equation for rotating Bose gases VL - 264 ER - TY - JOUR AB - We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation. AU - Robert Seiringer ID - 2364 IS - 3 JF - Reviews in Mathematical Physics TI - A correlation estimate for quantum many-body systems at positive temperature VL - 18 ER - TY - JOUR AB - We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller. AU - Robert Seiringer ID - 2365 IS - 3 JF - Communications in Mathematical Physics TI - The thermodynamic pressure of a dilute fermi gas VL - 261 ER - TY - JOUR AB - Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential. AU - Frank, Rupert L AU - Laptev, Ari AU - Lieb, Élliott H AU - Robert Seiringer ID - 2366 IS - 3 JF - Letters in Mathematical Physics TI - Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials VL - 77 ER - TY - CHAP AB - The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases. AU - Robert Seiringer ED - Dereziński, Jan ED - Siedentop, Heinz ID - 2368 T2 - Large Coulomb Systems TI - Dilute, trapped Bose gases and Bose-Einstein condensation VL - 695 ER - TY - CHAP AB - One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results. AU - Aizenman, Michael AU - Lieb, Élliott H AU - Robert Seiringer AU - Solovej, Jan P AU - Yngvason, Jakob ED - Asch, Joachim ED - Joye, Alain ID - 2369 T2 - Mathematical Physics of Quantum Mechanics TI - Bose-Einstein condensation as a quantum phase transition in an optical lattice VL - 690 ER - TY - CHAP AU - Bang-Jensen, Jørgen AU - Reed, Bruce AU - Schacht, Bruce AU - Šámal, Robert AU - Toft, Bjarne AU - Uli Wagner ID - 2416 T2 - Topics in Discrete Mathematics TI - On six problems posed by Jarik Nešetřil VL - 26 ER - TY - JOUR AB - We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I. We present deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of inserted points. We first show that a natural and simple (deterministic) approach may perform rather poorly, requiring Ω(√̃) colors in the worst case. We then derive two efficient variants of this simple algorithm. The first is deterministic and uses O(log 2 n) colors, and the second is randomized and uses O(log n) colors with high probability. We also show that the O(log 2 n) bound on the number of colors used by our deterministic algorithm is tight on the worst case. We also analyze the performance of the simplest proposed algorithm when the points are inserted in a random order and present an incomplete analysis that indicates that, with high probability, it uses only O(log n) colors. Finally, we show that in the extension of this problem to two dimensions, where the relevant ranges are disks, n colors may be required in the worst case. AU - Chent, Ke AU - Fiat, Amos AU - Kaplan, Haim AU - Levy, Meital B AU - Matoušek, Jiří AU - Mossel, Elchanan AU - Pach, János AU - Sharir, Micha AU - Smorodinsky, Shakhar AU - Uli Wagner AU - Welzl, Emo ID - 2430 IS - 5 JF - SIAM Journal on Computing TI - Online conflict-free coloring for intervals VL - 36 ER - TY - CONF AB - We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most t in an arrangement of n halfspaces in R , for arbitrary n and d (in particular, the dimension d is not considered constant). This partially settles a conjecture of Eckhoff, Linhart, and Welzl. Up to the factor of 2, the result generalizes McMullen's Upper Bound Theorem for convex polytopes (the case ℓ = O) and extends a theorem of Linhart for the case d ≤ 4. Moreover, the bound sharpens asymptotic estimates obtained by Clarkson and Shor. The proof is based on the h-matrix of the arrangement (a generalization, introduced by Mulmuley, of the h-vector of a convex polytope). We show that bounding appropriate sums of entries of this matrix reduces to a lemma about quadrupels of sets with certain intersection properties, and we prove this lemma, up to a factor of 2, using tools from multilinear algebra. This extends an approach of Alon and Kalai, who used linear algebra methods for an alternative proof of the classical Upper Bound Theorem. The bounds for the entries of the h-matrix also imply bounds for the number of i-dimensional faces, i > 0, at level at most ℓ. Furthermore, we discuss a connection with crossing numbers of graphs that was one of the main motivations for investigating exact bounds that are valid for arbitrary dimensions. AU - Uli Wagner ID - 2431 TI - On a geometric generalization of the Upper Bound Theorem ER - TY - JOUR AB - We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane. AU - Matoušek, Jiří AU - Sharir, Micha AU - Smorodinsky, Shakhar AU - Uli Wagner ID - 2429 IS - 2 JF - Discrete & Computational Geometry TI - K-sets in four dimensions VL - 35 ER - TY - JOUR AB - Transmembrane AMPA receptor regulatory proteins (TARPs), including stargazin/γ-2, are associated with AMPA receptors and participate in their surface delivery and anchoring at the postsynaptic membrane. TARPs may also act as a positive modulator of the AMPA receptor ion channel function; however, little is known about other TARP members except for stargazin/γ-2. We examined the synaptic localization of stargazin/γ-2 and γ-8 by immunoelectron microscopy and biochemical analysis. The analysis of sodium dodecyl sulfate-digested freeze-fracture replica labeling revealed that stargazin/γ-2 was concentrated in the postsynaptic area, whereas γ-8 was distributed both in synaptic and extra-synaptic plasma membranes of the hippocampal neuron. When a synaptic plasma membrane-enriched brain fraction was treated with Triton X-100 and separated by sucrose density gradient ultracentrifugation, a large proportion of NMDA receptor and stargazin/γ-2 was accumulated in raft-enriched fractions, whereas AMPA receptor and γ-8 were distributed in both the raft-enriched fractions and other Triton-insoluble fractions. Phosphorylation of stargazin/γ-2 and γ-8 was regulated by different sets of kinases and phosphatases in cultured cortical neurons. These results suggested that stargazin/γ-2 and γ-8 have distinct roles in postsynaptic membranes under the regulation of different intracellular signaling pathways. AU - Inamura, Mihoko AU - Itakura, Makoto AU - Okamoto, Hirotsugu AU - Hoka, Sumio AU - Mizoguchi, Akira AU - Fukazawa, Yugo AU - Ryuichi Shigemoto AU - Yamamori, Saori AU - Takahashi, Masami ID - 2659 IS - 1 JF - Neuroscience Research TI - Differential localization and regulation of stargazin-like protein, γ-8 and stargazin in the plasma membrane of hippocampal and cortical neurons VL - 55 ER - TY - JOUR AB - The highest densities of the two metabotropic GABA subunits, GABA B1 and GABAB2, have been reported as occurring around the glutamatergic synapses between Purkinje cell spines and parallel fibre varicosities. In order to determine how this distribution is achieved during development, we investigated the expression pattern and the cellular and subcellular localization of the GABAB1 and GABAB2 subunits in the rat cerebellum during postnatal development. At the light microscopic level, immunoreactivity for the GABAB1 and GABAB2 subunits was very prominent in the developing molecular layer, especially in Purkinje cells. Using double immunofluorescence, we demonstrated that GABAB1 was transiently expressed in glial cells. At the electron microscopic level, immunoreactivity for GABAB receptors was always detected both pre- and postsynaptically. Presynaptically, GABAB1 and GABAB2 were localized in the extrasynaptic membrane of parallel fibres at all ages, and only rarely in GABAergic axons. Postsynaptically, GABAB receptors were localized to the extrasynaptic and perisynaptic plasma membrane of Purkinje cell dendrites and spines throughout development. Quantitative analysis and three-dimensional reconstructions further revealed a progressive developmental movement of the GABAB1 subunit on the surface of Purkinje cells from dendritic shafts to its final destination, the dendritic spines. Together, these results indicate that GABAB receptors undergo dynamic regulation during cerebellar development in association with the establishment and maturation of glutamatergic synapses to Purkinje cells. AU - Luján, Rafael AU - Ryuichi Shigemoto ID - 2657 IS - 6 JF - European Journal of Neuroscience TI - Localization of metabotropic GABA receptor subunits GABAB1 and GABAB2 relative to synaptic sites in the rat developing cerebellum VL - 23 ER - TY - JOUR AB - The rocker mice are hereditary ataxic mutants that carry a point mutation in the gene encoding the CaV2.1 (P/Q-type) Ca2+ channel α1 subunit, and show the mildest symptoms among the reported CaV2.1 mutant mice. We studied the basic characteristics of the rocker mutant Ca2+ channel and their impacts on excitatory synaptic transmission in cerebellar Purkinje cells (PCs). In acutely dissociated PC somas, the rocker mutant channel showed a moderate reduction in Ca2+ channel current density, whereas its kinetics and voltage dependency of gating remained nearly normal. Despite the small changes in channel function, synaptic transmission in the parallel fiber (PF)-PC synapses was severely impaired. The climbing fiber inputs onto PCs showed a moderate impairment but could elicit normal complex spikes. Presynaptic function of the PF-PC synapses, however, was unexpectedly almost normal in terms of paired-pulse facilitation, sensitivity to extracellular Ca2+ concentration and glutamate concentration in synaptic clefts. Electron microscopic analyses including freeze-fracture replica labeling revealed that both the number and density of postsynaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors substantially decreased without gross structural changes of the PF-PC synapses. We also observed an abnormal arborization of PC dendrites in young adult rocker mice (∼ 1 month old). These lines of evidence suggest that even a moderate dysfunction of CaV2.1 Ca2+ channel can cause substantial changes in postsynaptic molecular composition of the PF-PC synapses and dendritic structure of PCs. AU - Kodama, Takashi AU - Itsukaichi-Nishida, Yuko AU - Fukazawa, Yugo AU - Wakamori, Minoru AU - Miyata, Mariko AU - Molnár, Elek AU - Mori, Yasuo AU - Ryuichi Shigemoto AU - Imoto, Keiji ID - 2663 IS - 11 JF - European Journal of Neuroscience TI - A CaV2.1 calcium channel mutation rocker reduces the number of postsynaptic AMPA receptors in parallel fiber-Purkinje cell synapses VL - 24 ER - TY - JOUR AB - GABAB receptors are the G protein-coupled receptors for the main inhibitory neurotransmitter in the brain, γ-aminobutyric acid (GABA). Molecular diversity in the GABAB system arises from the GABAB1a and GABAB1b subunit isoforms that solely differ in their ectodomains by a pair of sushi repeats that is unique to GABAB1a. Using a combined genetic, physiological, and morphological approach, we now demonstrate that GABAB1 isoforms localize to distinct synaptic sites and convey separate functions in vivo. At hippocampal CA3-to-CA1 synapses, GABAB1a assembles heteroreceptors inhibiting glutamate release, while predominantly GABAB1b mediates postsynaptic inhibition. Electron microscopy reveals a synaptic distribution of GABAB1 isoforms that agrees with the observed functional differences. Transfected CA3 neurons selectively express GABAB1a in distal axons, suggesting that the sushi repeats, a conserved protein interaction motif, specify heteroreceptor localization. The constitutive absence of GABAB1a but not GABAB1b results in impaired synaptic plasticity and hippocampus-dependent memory, emphasizing molecular differences in synaptic GABAB functions. AU - Vigot, Réjan AU - Barbieri, Samuel AU - Bräuner-Osborne, Hans AU - Tureček, Rostislav AU - Ryuichi Shigemoto AU - Zhang, Yan Ping AU - Luján, Rafael AU - Jacobson, Laura H AU - Biermann, Barbara AU - Fritschy, Jean-Marc AU - Vacher, Claire-Marie AU - Müller, Matthias P AU - Sansig, Gilles AU - Guetg, Nicole AU - Cryan, John F AU - Kaupmann, Klemens AU - Gassmann, Martin AU - Oertner, Thomas G AU - Bettler, Bernhard ID - 2661 IS - 4 JF - Neuron TI - Differential Compartmentalization and Distinct Functions of GABAB Receptor Variants VL - 50 ER - TY - JOUR AB - G-protein-coupled inwardly rectifying K+ channels (Kir3 channels) coupled to metabotropic GABAB receptors are essential for the control of neuronal excitation. To determine the distribution of Kir3 channels and their spatial relationship to GABAB receptors on hippocampal pyramidal cells, we used a high-resolution immunocytochemical approach. Immunoreactivity for the Kir3.2 subunit was most abundant postsynaptically and localized to the extrasynaptic plasma membrane of dendritic shafts and spines of principal cells. Quantitative analysis of immunogold particles for Kir3.2 revealed an enrichment of the protein around putative glutamatergic synapses on dendritic spines, similar to that of GABA B1. Consistent with this observation, a high degree of coclustering of Kir3.2 and GABAB1 was revealed around excitatory synapses by the highly sensitive SDS-digested freeze-fracture replica immunolabeling. In contrast, in dendritic shafts receptors and channels were found to be mainly segregated. These results suggest that Kir3.2-containing K+ channels on dendritic spines preferentially mediate the effect of GABA, whereas channels on dendritic shafts are likely to be activated by other neurotransmitters as well. Thus, Kir3 channels, localized to different subcellular compartments of hippocampal principal cells, appear to be differentially involved in synaptic integration in pyramidal cell dendrites. AU - Kulik, Ákos AU - Vida, Imre AU - Fukazawa, Yugo AU - Guetg, Nicole AU - Kasugai, Yu AU - Marker, Cheryl L AU - Rigato, Franck AU - Bettler, Bernhard AU - Wickman, Kevin D AU - Frotscher, Michael AU - Ryuichi Shigemoto ID - 2662 IS - 16 JF - Journal of Neuroscience TI - Compartment-dependent colocalization of Kir3.2-containing K+ channels and GABAB receptors in hippocampal pyramidal cells VL - 26 ER - TY - JOUR AB - Pavlovian fear conditioning, a simple form of associative learning, is thought to involve the induction of associative, NMDA receptor-dependent long-term potentiation (LTP) in the lateral amygdala. Using a combined genetic and electrophysiological approach, we show here that lack of a specific GABAB receptor subtype, GABAB(1a,2), unmasks a nonassociative, NMDA receptor-independent form of presynaptic LTP at cortico-amygdala afferents. Moreover, the level of presynaptic GABA B(1a,2) receptor activation, and hence the balance between associative and nonassociative forms of LTP, can be dynamically modulated by local inhibitory activity. At the behavioral level, genetic loss of GABA B(1a) results in a generalization of conditioned fear to nonconditioned stimuli. Our findings indicate that presynaptic inhibition through GABAB(1a,2) receptors serves as an activity-dependent constraint on the induction of homosynaptic plasticity, which may be important to prevent the generalization of conditioned fear. AU - Shaban, Hamdy AU - Humeau, Yann AU - Herry, Cyril AU - Cassasus, Guillaume AU - Ryuichi Shigemoto AU - Ciocchi, Stéphane AU - Barbieri, Samuel AU - Van Der Putten, Herman V AU - Kaupmann, Klemens AU - Bettler, Bernhard AU - Lüthi, Andreas ID - 2660 IS - 8 JF - Nature Neuroscience TI - Generalization of amygdala LTP and conditioned fear in the absence of presynaptic inhibition VL - 9 ER - TY - GEN AB - Metabotropic glutamate receptors (mGlus) are a family of G-protein-coupled receptors activated by the neurotransmitter glutamate. Molecular cloning has revealed eight different subtypes (mGlu1-8) with distinct molecular and pharmacological properties. Multiplicity in this receptor family is further generated through alternative splicing. mGlus activate a multitude of signalling pathways important for modulating neuronal excitability, synaptic plasticity and feedback regulation of neurotransmitter release. In this review, we summarize anatomical findings (from our work and that of other laboratories) describing their distribution in the central nervous system. Recent evidence regarding the localization of these receptors in peripheral tissues will also be examined. The distinct regional, cellular and subcellular distribution of mGlus in the brain will be discussed in view of their relationship to neurotransmitter release sites and of possible functional implications. AU - Ferraguti, Francesco AU - Ryuichi Shigemoto ID - 2664 IS - 2 T2 - Cell and Tissue Research TI - Metabotropic glutamate receptors VL - 326 ER - TY - JOUR AB - Consider a system of N bosons on the three-dimensional unit torus interacting via a pair potential N 2V(N(x i - x j)) where x = (x i, . . ., x N) denotes the positions of the particles. Suppose that the initial data ψ N,0 satisfies the condition 〈ψ N,0, H 2 Nψ N,0) ≤ C N 2 where H N is the Hamiltonian of the Bose system. This condition is satisfied if ψ N,0 = W Nφ N,t where W N is an approximate ground state to H N and φ N,0 is regular. Let ψ N,t denote the solution to the Schrödinger equation with Hamiltonian H N. Gross and Pitaevskii proposed to model the dynamics of such a system by a nonlinear Schrödinger equation, the Gross-Pitaevskii (GP) equation. The GP hierarchy is an infinite BBGKY hierarchy of equations so that if u t solves the GP equation, then the family of k-particle density matrices ⊗ k |u t?〉 〈 t | solves the GP hierarchy. We prove that as N → ∞ the limit points of the k-particle density matrices of ψ N,t are solutions of the GP hierarchy. Our analysis requires that the N-boson dynamics be described by a modified Hamiltonian that cuts off the pair interactions whenever at least three particles come into a region with diameter much smaller than the typical interparticle distance. Our proof can be extended to a modified Hamiltonian that only forbids at least n particles from coming close together for any fixed n. AU - László Erdös AU - Schlein, Benjamin AU - Yau, Horng-Tzer ID - 2747 IS - 12 JF - Communications on Pure and Applied Mathematics TI - Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate VL - 59 ER - TY - JOUR AB - We consider the dynamics of N boson systems interacting through a pair potential N -1 V a (x i -x j ) where V a (x)=a -3 V(x/a). We denote the solution to the N-particle Schrödinger equation by Ψ N, t . Recall that the Gross-Pitaevskii (GP) equation is a nonlinear Schrödinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if u t solves the GP equation, then the family of k-particle density matrices [InlineMediaObject not available: see fulltext.] solves the GP hierarchy. Under the assumption that a = Nε for 0 < ε < 3/5, we prove that as N→∞ the limit points of the k-particle density matrices of Ψ N, t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by ∫ V (x)dx. The uniqueness of the solutions of this hierarchy remains an open question. AU - Elgart, Alexander AU - László Erdös AU - Schlein, Benjamin AU - Yau, Horng-Tzer ID - 2745 IS - 2 JF - Archive for Rational Mechanics and Analysis TI - Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons VL - 179 ER - TY - CONF AB - We consider random Schrödinger equations on Rd or Zd for d ≥ 3 with uncorrelated, identically distributed random potential. Denote by λ the coupling constant and ψt the solution with initial data ψ0. AU - László Erdös AU - Salmhofer, Manfred AU - Yau, Horng-Tzer ID - 2746 TI - Towards the quantum Brownian motion VL - 690 ER -