@article{228, abstract = {Let X be a projective non-singular quartic hypersurface of dimension 39 or more, which is defined over . We show that X() is non-empty provided that X() is non-empty and X has p-adic points for every prime p.}, author = {Timothy Browning and Heath-Brown, Roger}, journal = {Journal fur die Reine und Angewandte Mathematik}, number = {629}, pages = {37 -- 88}, publisher = {Walter de Gruyter}, title = {{Rational points on quartic hypersurfaces}}, doi = {10.1515/CRELLE.2009.026}, year = {2009}, } @article{229, abstract = {An upper bound of the expected order of magnitude is established for the number of ℚ-rational points of bounded height on Châtelet surfaces defined over ℚ.}, author = {Timothy Browning}, journal = {Mathematische Annalen}, number = {1}, pages = {41 -- 50}, publisher = {Springer Nature}, title = {{Linear growth for Châtelet surfaces}}, doi = {10.1007/s00208-009-0383-z}, volume = {346}, year = {2009}, } @article{230, abstract = {The Manin conjecture is established for a split singular cubic surface in ℙ 3, with singularity type D 5.}, author = {Timothy Browning and Derenthal, Ulrich}, journal = {International Mathematics Research Notices}, number = {14}, pages = {2620 -- 2647}, publisher = {Oxford University Press}, title = {{Manin's conjecture for a cubic surface with D 5 singularity}}, doi = {10.1093/imrn/rnp029}, volume = {2009}, year = {2009}, } @book{2326, abstract = {Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a complete, self-contained description of research on the stability of matter problem. It introduces the necessary quantum mechanics to mathematicians, and aspects of functional analysis to physicists. The topics covered include electrodynamics of classical and quantized fields, Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, gravitational stability of stars, basics of equilibrium statistical mechanics, and the existence of the thermodynamic limit. The book is an up-to-date account for researchers, and its pedagogical style makes it suitable for advanced undergraduate and graduate courses in mathematical physics.}, author = {Lieb, Élliott and Seiringer, Robert}, isbn = {978-0-521-19118-0 }, pages = {310}, publisher = {Cambridge University Press}, title = {{The Stability of Matter in Quantum Mechanics}}, year = {2009}, } @inproceedings{2330, author = {Hainzl, Christian and Robert Seiringer}, pages = {101 -- 104}, publisher = {American Mathematical Society}, title = {{A linear criterion for solutions of non-linear equations, with application to the BCS gap equation}}, doi = {10.1090/conm/500/09823}, volume = {500}, year = {2009}, } @article{2384, abstract = {We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.}, author = {Giuliani, Alessandro and Robert Seiringer}, journal = {Journal of Statistical Physics}, number = {5-6}, pages = {915 -- 934}, publisher = {Springer}, title = {{The ground state energy of the weakly interacting Bose gas at high density}}, doi = {10.1007/s10955-009-9718-0}, volume = {135}, year = {2009}, } @article{2385, abstract = {We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity, so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functional accurately describes the ground-state energy of the corresponding N -body Hamiltonian with contact interaction provided the total angular momentum L is much less than N2. While the Gross-Pitaevskii energy is always an obvious variational upper bound to the ground-state energy, a more refined analysis is needed to establish it as an exact lower bound. We also discuss the question of Bose-Einstein condensation in the parameter range considered. Coherent states together with inequalities in spaces of analytic functions are the main technical tools.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {6}, publisher = {American Physical Society}, title = {{Yrast line of a rapidly rotating Bose gas: Gross-Pitaevskii regime}}, doi = {10.1103/PhysRevA.79.063626}, volume = {79}, year = {2009}, } @article{2386, abstract = {We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a2 ρ is small and the temperature T satisfies T> 4πρ ln | ln (a2 ρ) |. Here, a is the scattering length of the repulsive interaction potential and ρ is the density. To the leading order in a2 ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when T- Tc (0) Tc (0) >5 a ρ1/3, where Tc (0) is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it gives a rigorous upper bound on the critical temperature for Bose-Einstein condensation.}, author = {Robert Seiringer and Ueltschi, Daniel}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {1}, publisher = {American Physical Society}, title = {{Rigorous upper bound on the critical temperature of dilute Bose gases}}, doi = {10.1103/PhysRevB.80.014502}, volume = {80}, year = {2009}, } @article{2387, abstract = {We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.}, author = {Lewin, Mathieu and Robert Seiringer}, journal = {Journal of Statistical Physics}, number = {5}, pages = {1040 -- 1062}, publisher = {Springer}, title = {{Strongly correlated phases in rapidly rotating Bose gases}}, doi = {10.1007/s10955-009-9833-y}, volume = {137}, year = {2009}, } @article{2388, abstract = {This paper provides self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifies the connection of coherence and proper scoring rules to Bregman divergence.}, author = {Predd, Joel B and Robert Seiringer and Lieb, Élliott H and Osherson, Daniel N and Poor, Harold V and Kulkarni, Sanjeev R}, journal = {IEEE Transactions on Information Theory}, number = {10}, pages = {4786 -- 4792}, publisher = {IEEE}, title = {{Probabilistic coherence and proper scoring rules}}, doi = {10.1109/TIT.2009.2027573}, volume = {55}, year = {2009}, } @inproceedings{2433, abstract = {Let EMBEDk→d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k, does there exist a (piecewise linear) embedding of K into ℝd? Known results easily imply polynomiality of EMBEDk→2 (k = 1, 2; the case k = 1, d = 2 is graph planarity) and of EMBEDk→2k for all k ≥ 3 (even if k is not considered fixed). We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that EMBED d→d and EMBED(d-1)→d are undecidable for each d ≥ 5. Our main result is NP-hardness of EMBED2→4 and, more generally, of EMBEDk→d for all k, d with d ≥ 4 and d ≥ k ≥ (2d - 2)/3.}, author = {Matoušek, Jiří and Martin Tancer and Uli Wagner}, pages = {855 -- 864}, publisher = {SIAM}, title = {{Hardness of embedding simplicial complexes in ℝd}}, year = {2009}, } @article{2434, abstract = {For a planar point set we consider the graph whose vertices are the crossing-free straight-line spanning trees of the point set, and two such spanning trees are adjacent if their union is crossing-free. An upper bound on the diameter of this graph implies an upper bound on the diameter of the flip graph of pseudo-triangulations of the underlying point set. We prove a lower bound of Ω(logn/loglogn) for the diameter of the transformation graph of spanning trees on a set of n points in the plane. This nearly matches the known upper bound of O(logn). If we measure the diameter in terms of the number of convex layers k of the point set, our lower bound construction is tight, i.e., the diameter is in Ω(logk) which matches the known upper bound of O(logk). So far only constant lower bounds were known.}, author = {Buchin, Kevin and Razen, Andreas and Uno, Takeaki and Uli Wagner}, journal = {Computational Geometry: Theory and Applications}, number = {8}, pages = {724 -- 730}, publisher = {Elsevier}, title = {{Transforming spanning trees: A lower bound}}, doi = {10.1016/j.comgeo.2008.03.005}, volume = {42}, year = {2009}, } @article{2498, abstract = {Activation of G protein-gated inwardly-rectifying K+ (GIRK or Kir3) channels by metabotropic gamma-aminobutyric acid (B) (GABAB) receptors is an essential signalling pathway controlling neuronal excitability and synaptic transmission in the brain. To investigate the relationship between GIRK channel subunits and GABAB receptors in cerebellar Purkinje cells at post- and pre-synaptic sites, we used biochemical, functional and immunohistochemical techniques. Co-immunoprecipitation analysis demonstrated that GIRK subunits are co-assembled with GABAB receptors in the cerebellum. Immunoelectron microscopy showed that the subunit composition of GIRK channels in Purkinje cell spines is compartment-dependent. Thus, at extrasynaptic sites GIRK channels are formed by GIRK1/GIRK2/GIRK3, post-synaptic densities contain GIRK2/GIRK3 and dendritic shafts contain GIRK1/GIRK3. The post-synaptic association of GIRK subunits with GABAB receptors in Purkinje cells is supported by the subcellular regulation of the ion channel and the receptor in mutant mice. At pre-synaptic sites, GIRK channels localized to parallel fibre terminals are formed by GIRK1/GIRK2/GIRK3 and co-localize with GABAB receptors. Consistent with this morphological evidence we demonstrate their functional interaction at axon terminals in the cerebellum by showing that GIRK channels play a role in the inhibition of glutamate release by GABAB receptors. The association of GIRK channels and GABA B receptors with excitatory synapses at both post- and pre-synaptic sites indicates their intimate involvement in the modulation of glutamatergic neurotransmission in the cerebellum.}, author = {Fernández-Alacid, Laura and Aguado, Carolina and Ciruela, Francisco and Martín, Ricardo J and Colón, José and Cabañero, María José and Gassmann, Martin and Watanabe, Masahiko and Ryuichi Shigemoto and Wickman, Kevin D and Bettler, Bernhard and Sánchez-Prieto, José and Luján, Rafael}, journal = {Journal of Neurochemistry}, number = {4}, pages = {1363 -- 1376}, publisher = {Wiley-Blackwell}, title = {{ Subcellular compartment-specific molecular diversity of pre- and post-synaptic GABAB-activated GIRK channels in Purkinje cells}}, doi = {10.1111/j.1471-4159.2009.06229.x}, volume = {110}, year = {2009}, } @article{2499, abstract = {G protein-coupled receptors (GPCRs) have critical functions in intercellular communication. Although a wide range of different receptors have been identified in the same cells, the mechanism by which signals are integrated remains elusive. The ability of GPCRs to form dimers or larger hetero-oligomers is thought to generate such signal integration. We examined the molecular mechanisms responsible for the GABAB receptor-mediated potentiation of the mGlu receptor signalling reported in Purkinje neurons. We showed that this effect does not require a physical interaction between both receptors. Instead, it is the result of a more general mechanism in which the βγ subunits produced by the Gi-coupled GABAB receptor enhance the mGlu-mediated Gq response. Most importantly, this mechanism could be generally applied to other pairs of Gi- and Gq-coupled receptors and the signal integration varied depending on the time delay between activation of each receptor. Such a mechanism helps explain specific properties of cells expressing two different Gi- and Gq-coupled receptors activated by a single transmitter, or properties of GPCRs naturally coupled to both types of the G protein.}, author = {Rives, Marie L and Vol, Claire and Fukazawa, Yugo and Tinel, Norbert and Trinquet, Eric and Ayoub, Mohammed A and Ryuichi Shigemoto and Pin, Jean-Philippe and Prezèau, Laurent}, journal = {EMBO Journal}, number = {15}, pages = {2195 -- 2208}, publisher = {Wiley-Blackwell}, title = {{Crosstalk between GABAB and mGlu1a receptors reveals new insight into GPCR signal integration}}, doi = {10.1038/emboj.2009.177}, volume = {28}, year = {2009}, } @article{2500, abstract = {To examine the intrasynaptic arrangement of postsynaptic receptors in relation to the functional role of the synapse,we quantitatively analyzed the two-dimensional distribution of AMPA and NMDA receptors (AMPARs and NMDARs, respectively) using SDS-digested freeze-fracture replica labeling (SDS-FRL) and assessed the implication of distribution differences on the postsynaptic responses by simulation. In the dorsal lateral geniculate nucleus, corticogeniculate (CG) synapses were twice as large as retinogeniculate (RG) synapses but expressed similar numbers of AMPARs. Two-dimensional views of replicas revealed that AMPARs form microclusters in both synapses to a similar extent, resulting in larger AMPAR-lacking areas in the CG synapses. Despite the broad difference in the AMPAR distribution within a synapse, our simulations based on the actual receptor distributions suggested that the AMPAR quantal response at individual RG synapses is only slightly larger in amplitude, less variable, and faster in kinetics than that at CG synapses having a similar number of the receptors. NMDARs at the CG synapses were expressed twice as many as those in the RG synapses. Electrophysiological recordings confirmed a larger contribution of NMDAR relative to AMPAR-mediated responses in CG synapses. We conclude that synapse size and the density and distribution of receptors have minor influences on quantal responses and that the number of receptors acts as a predominant postsynaptic determinant of the synaptic strength mediated by both the AMPARs and NMDARs. }, author = {Tarusawa, Etsuko and Matsui, Ko and Budisantoso, Timotheus and Molnár, Elek and Watanabe, Masahiko and Matsui, Minoru and Fukazawa, Yugo and Ryuichi Shigemoto}, journal = {Journal of Neuroscience}, number = {41}, pages = {12896 -- 12908}, publisher = {Society for Neuroscience}, title = {{Input-specific intrasynaptic arrangements of ionotropic glutamate receptors and their impact on postsynaptic responses}}, doi = {10.1523/JNEUROSCI.6160-08.2009}, volume = {29}, year = {2009}, } @article{2501, abstract = {The brain-specific immediate early gene Arc/Arg3.1 is induced in response to a variety of stimuli, including sensory and behavior-linked neural activity. Here we report the generation of transgenic mice, termed TgArc/Arg3.1-d4EGFP, expressing a 4-h half-life form of enhanced green fluorescent protein (d4EGFP) under the control of the Arc/Arg3.1 promoter. We show that d4EGFP-mediated fluorescence faithfully reports Arc/Arg3.1 induction in response to physiological, pathological and pharmacological stimuli, and that this fluorescence permits electrical recording from activated neurons in the live mouse. Moreover, the fluorescent Arc/Arg3.1 indicator revealed activity changes in circumscribed brain areas in distinct modes of stress and in a mouse model of Alzheimer's disease. These findings identify the TgArc/Arg3.1-d4EGFP mouse as a versatile tool to monitor Arc/Arg3.1 induction in neural circuits, both in vitro and in vivo.}, author = {Grinevich, Valery V and Kolleker, Alexander and Eliava, Marina I and Takada, Naoki and Takuma, Hiroshi and Fukazawa, Yugo and Ryuichi Shigemoto and Kuhl, Dietmar and Waters, Jack and Seeburg, Peter H and Osten, Pavel}, journal = {Journal of Neuroscience Methods}, number = {1}, pages = {25 -- 36}, publisher = {Elsevier}, title = {{Fluorescent Arc/Arg3.1 indicator mice: A versatile tool to study brain activity changes in vitro and in vivo}}, doi = {10.1016/j.jneumeth.2009.07.015}, volume = {184}, year = {2009}, } @article{2502, abstract = {In order to acquire phase-contrast images with adequate contrast, conventional TEM requires large amount of defocus. Increasing the defocus improves the low-frequency components but attenuates the high-frequency ones. On the other hand, Zernike phase-contrast TEM (ZPC-TEM) can recover low-frequency components without losing the high-frequency ones under in-focus conditions. ZPC-TEM however, has another problem, especially in imaging of complex biological specimens such as cells and tissues; strong halos appear around specimen structures, and these halos hinder the interpretation of images. Due to this problem, the application of ZPC-TEM has been restricted to imaging of smaller particles. In order to improve the halo appearance, we fabricated a new quarter-wave thin film phase-plate with a smaller central hole and tested it on vitreous biological specimens. ZPC-TEM with the new plate could successfully visualize, in in-focus images, the intracellular fine features of cultured cells and brain tissues. This result indicates that reduction of the central hole diameter makes ZPC-TEM applicable on size scales ranging from protein particles to tissue sections. The application of ZPC-TEM to vitreous biological specimens will be a powerful method to advance the new field of imaging science for ultrastructures in close-to-physiological state.}, author = {Fukuda, Yoshiyuki and Fukazawa, Yugo and Danev, Radostin S and Ryuichi Shigemoto and Nagayama, Kuniaki}, journal = {Journal of Structural Biology}, number = {3}, pages = {476 -- 484}, publisher = {Academic Press}, title = {{Tuning of the Zernike phase-plate for visualization of detailed ultrastructure in complex biological specimens}}, doi = {10.1016/j.jsb.2009.08.011}, volume = {168}, year = {2009}, } @inbook{164, abstract = {Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension <n-10. The proof is based on the Hardy-Littlewood circle method.}, author = {Browning, Timothy D and Heath Brown, Roger}, booktitle = {Analytic Number Theory: Essays in honour of Klaus Roth}, pages = {75 -- 90}, publisher = {Cambridge University Press}, title = {{Integral points on cubic hypersurfaces}}, year = {2009}, } @inproceedings{165, abstract = {We survey the state of affairs for the distribution of ℚ-rational points on non-singular del Pezzo surfaces of low degree, highlighting the recent resolution of Manin's conjecture for a non-singular del Pezzo surface of degree 4 by la Bretèche and Browning.}, author = {Timothy Browning}, editor = {Aoki, Takashi and Kanemitsu, Shigeru and Liu, Jianya}, pages = {1 -- 18}, publisher = {World Scientific Publishing}, title = {{Resent progress on the quantitative arithmetic of del Pezzo surfaces}}, doi = {https://doi.org/10.1142/9789814289924_0001}, volume = {6}, year = {2009}, } @inbook{168, abstract = {The arithmetic of ternary diagonal equation is considered for degree d >1, with the outcome that the set of coefficients for which the equation admits a non-zero integer solution is shown to have density zero.}, author = {Timothy Browning and Dietmann, Rainer}, booktitle = {Quadratic Forms - algebra, arithmetic and geometry}, pages = {99 -- 106}, publisher = {American Mathematical Society}, title = {{Solubility of Fermat equations}}, doi = {http://dx.doi.org/10.1090/conm/493}, volume = {493}, year = {2009}, }