@article{222, abstract = {Acknowledgements. The authors are grateful to Ulrich Derenthal and Brendan Hassett for several useful conversations relating to universal torsors for singular del Pezzo surfaces. Special thanks are due to Roger Heath–Brown whose ideas led us to the proof of Lemma 6. The paper was finalised while the first author was at the École Normale Supérieure, and the second author was at Oxford University supported by EPSRC grant number GR/R93155/01. The hospitality and financial support of these institutions is gratefully acknowledged. Finally, the authors would like to thank the anonymous referee for his careful reading of the manuscript and numerous useful suggestions.}, author = {de la Bretèche, Régis and Timothy Browning}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society}, number = {3}, pages = {579 -- 605}, publisher = {Unknown}, title = {{On Manin's conjecture for singular del Pezzo surfaces of degree four, II}}, doi = {10.1017/S0305004107000205}, volume = {143}, year = {2007}, } @article{223, abstract = {Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B → ∞. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.}, author = {Timothy Browning}, journal = {Monatshefte fur Mathematik}, number = {1}, pages = {13 -- 38}, publisher = {Springer}, title = {{Density of integer solutions to diagonal quadratic forms}}, doi = {10.1007/s00605-007-0457-5}, volume = {152}, year = {2007}, } @article{2367, abstract = {It was recently shown by Hansen that the Wigner-Yanase entropy is, for general states of quantum systems, not subadditive with respect to decomposition into two subsystems, although this property is known to hold for pure states. We investigate the question whether the weaker property of subadditivity for pure states with respect to decomposition into more than two subsystems holds. This property would have interesting applications in quantum chemistry. We show, however, that it does not hold in general, and provide a counterexample.}, author = {Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {3}, pages = {285 -- 288}, publisher = {Springer}, title = {{On the failure of subadditivity of the Wigner-Yanase entropy}}, doi = {10.1007/s11005-007-0159-x}, volume = {80}, year = {2007}, } @article{2370, abstract = {After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α0.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Reports on Mathematical Physics}, number = {3}, pages = {389 -- 399}, publisher = {Elsevier}, title = {{Bose-Einstein condensation and spontaneous symmetry breaking}}, doi = {10.1016/S0034-4877(07)80074-7}, volume = {59}, year = {2007}, } @article{2371, abstract = {We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zα = 2/π.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {479 -- 489}, publisher = {Springer}, title = {{Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value}}, doi = {10.1007/s00220-007-0307-2}, volume = {275}, year = {2007}, } @article{2372, abstract = {The increasing interest in the Müller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock (HF) functional, but with a modified exchange term in which the square of the density matrix γ(x, x′) is replaced by the square of γ1 2 (x, x′). After an extensive introductory discussion of density-matrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing γ 's have unique densities ρ(r), which is a physically desirable property often absent in HF theory. We show that minimizers exist if N≤Z, and derive various properties of the minimal energy and the corresponding minimizers. We also give a precise statement about the equation for the orbitals of γ, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer and Siedentop, Heinz K}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {5}, publisher = {American Physical Society}, title = {{Müller's exchange-correlation energy in density-matrix-functional theory}}, doi = {10.1103/PhysRevA.76.052517}, volume = {76}, year = {2007}, } @article{2373, abstract = {For the BCS equation with local two-body interaction λV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as γ"0. We derive necessary and sufficient conditions onV(x) for the existence of a nontrivial solution for all values of γ>0.}, author = {Frank, Rupert L and Hainzl, Christian and Naboko, Serguei N and Robert Seiringer}, journal = {Journal of Geometric Analysis}, number = {4}, pages = {559 -- 567}, publisher = {Springer}, title = {{The critical temperature for the BCS equation at weak coupling}}, doi = {10.1007/BF02937429}, volume = {17}, year = {2007}, } @article{2375, abstract = {We give a Cwikel-Lieb-Rozenblum type bound on the number of bound states of Schrödinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {2-3}, pages = {107 -- 116}, publisher = {Springer}, title = {{Number of bound states of Schrödinger operators with matrix-valued potentials}}, doi = {10.1007/s11005-007-0211-x}, volume = {82}, year = {2007}, } @article{2451, abstract = {Signal molecules known as phytohormones play a decisive role in processing signals coming to plants from the surrounding environment. They include auxin — a simple compound with a large range of effects. Auxin is irregularly deposited in plant tissues, it accumulates in certain cellules and through activation of a signal cascade it causes changes in the development programme of these cellules. This article forms a part of the series prepared in honour of the anniversary of the important plant physiologist — Bohumil Němec.}, author = {Friml, Jirí}, journal = {Živa}, publisher = {CSAV}, title = {{Auxin - Universal development signal in plant life}}, volume = {1}, year = {2007}, } @article{2462, author = {Michniewicz, Marta and Brewer, Philip B and Jirí Friml}, journal = {The Arabidopsis Book}, publisher = {The American Society of Plant Biologists}, title = {{Polar auxin transport and asymmetric auxin distribution}}, doi = {10.1199/tab.0108}, volume = {5}, year = {2007}, } @article{2495, abstract = {Metabotropic glutamate receptor 4 (mGluR4) is localized mainly to presynaptic membranes in the brain. Rat neostriatum has been reported to contain two types of mGluR4-immunoreactive axon varicosities: small, weakly immunoreactive varicosities that were distributed randomly (type 1) and large, intensely immunoreactive ones that were often aligned linearly (type 2). In the present study, most type 1 terminals formed asymmetric synapses on dendritic spines, whereas type 2 terminals made symmetric synapses on dendritic shafts, showing immunoreactivity for GABAergic markers. After depletion of neostriatal neurons, type 2 but not type 1 varicosities were largely decreased in the damaged region. When medium-sized spiny neurons (MSNs) were labeled with Sindbis virus expressing membrane-targeted green fluorescent protein, mGluR4 immunoreactivity was observed on some varicosities of their axon collaterals in immunofluorescence and immunoelectron microscopies. Furthermore, type 2 varicosities were often positive for substance P but mostly negative for striatal interneuron markers and preproenkephalin. Thus, striatonigral/striato- entopeduncular MSNs are likely to be the largest source of type 2 mGluR4-immunopositive axon terminals in the neostriatum. Next, in the double-immunofluorescence study, almost all choline acetyltransferase (ChAT)-immunopositive and 41% of NK1 receptor-positive dendrites were heavily associated with type 2 mGluR4-immunoreactive varicosities. Neuronal nitric oxide synthase (nNOS)-positive dendrites, in contrast, seemed associated with only a few type 2 varicosities. Conversely, almost all type 2 varicosities were closely apposed to NK1 receptor-positive dendrites that were known to be derived from cholinergic and nNOS-producing interneurons. These findings indicate that the mGluR4-positive terminals of MSN axon collaterals selectively form synapses with neostriatal cholinergic interneurons.}, author = {Kuramoto, Eriko and Fujiyama, Fumino and Unzai, Tomo and Nakamura, Kouichi and Hioki, Hiroyuki and Furuta, Takahiro and Ryuichi Shigemoto and Ferraguti, Francesco and Kaneko, Takeshi}, journal = {Journal of Comparative Neurology}, number = {5}, pages = {908 -- 922}, publisher = {Wiley-Blackwell}, title = {{Metabotropic glutamate receptor 4-immunopositive terminals of medium-sized spiny neurons selectively form synapses with cholinergic interneurons in the rat neostriatum}}, doi = {10.1002/cne.21216}, volume = {500}, year = {2007}, } @article{2496, abstract = {Glutamate is one candidate for the neurotransmitters and/or neuromodulators involved in taste signaling in taste buds. Group II metabotropic glutamate receptors (mGluRs: mGluR2 and mGluR3) are known to function as presynaptic receptors that regulate the release of glutamate and/or other neurotransmitters in the central nervous system. Group II mGluRs are negatively linked to adenylyl cyclase through Gαi subunits and thereby reduce the turnover of cAMP. In rat taste tissues, a subset of adenylyl-cyclase-8-expressing taste cells coexpress the Gαi subunits gustducin and Gαi2. However, the expression patterns of group II mGluRs in rat taste tissues have not yet been elucidated. We have therefore examined the expression patterns of mGluR2, mGluR3, and gustducin in rat gustatory tissues. Reverse transcription/polymerase chain reaction assays have revealed that mGluR2 and mGluR3 mRNAs are expressed in the circumvallate papillae. In situ hybridization analyses have detected positive signals for mGluR2 and mGluR3 mRNAs only in the circumvallate taste buds. Among the fungiform, foliate, and circumvallate papillae, an antibody against mGluR2/3 labels a subset of taste bud cells and nerve fibers immediately beneath the taste lingual epithelium. Double-labeling experiments have demonstrated that mGluR2/3-positive cells coexpress gustducin. These results indicate that mGluR2 and mGluR3 are coupled to Gαi subunits and play roles in glutamate-mediated signaling in taste transductions.}, author = {Toyono, Takashi and Kataoka, Shinji and Seta, Yuji and Ryuichi Shigemoto and Toyoshima, Kuniaki}, journal = {Cell and Tissue Research}, number = {1}, pages = {57 -- 63}, publisher = {Springer}, title = {{Expression of group II metabotropic glutamate receptors in rat gustatory papillae}}, doi = {10.1007/s00441-006-0351-9}, volume = {328}, year = {2007}, } @inbook{167, abstract = {This book contains research articles on Diophantine Geometry, written by participants of a research program held at the Ennio De Giorgi Mathematical Research Center in Pisa, Italy, during the period April – July 2005. The authors are eminent experts in the field. Several subfields of the main topic are presented; the volume thus is particularly useful to get a broad overview of recent research developments.}, author = {Browning, Timothy D and Heath Brown, Roger}, booktitle = {Diophantine Geometry}, editor = {Zannier, Umberto}, pages = {93 -- 100}, publisher = {Edizioni della Normale}, title = {{Simultaneous equal sums of three powers}}, volume = {4}, year = {2007}, } @article{1750, abstract = {The authors investigate the composition profile of SiGe islands after capping with Si to form quantum dots, using a two step etching procedure and atomic force microscopy. Initially, the Si capping layers are removed by etching selectively Si over Ge and then the composition of the disclosed islands is addressed by selectively etching Ge over Si. For samples grown at 580 °C the authors show that even when overgrowth leads to a flat Si surface and the islands undergo strong morphological changes, a Ge-rich core region is still preserved in the dot. At high growth and overgrowth temperatures (740 °C), the experiments show that the newly formed base of the buried islands is more Si rich than their top. Furthermore, the authors find that for the growth conditions used, no lateral motion takes place during capping.}, author = {Georgios Katsaros and Stoffel, Mathieu and Rastelli, Armando and Schmidt, Oliver G and Kern, Klaus and Tersoff, Jerry}, journal = {Applied Physics Letters}, number = {1}, publisher = {American Institute of Physics}, title = {{Three-dimensional isocompositional profiles of buried SiGeSi (001) islands}}, doi = {10.1063/1.2752730}, volume = {91}, year = {2007}, } @article{1762, abstract = {In quantum information science, the phase of a wave function plays an important role in encoding information. Although most experiments in this field rely on dynamic effects to manipulate this information, an alternative approach is to use geometric phase, which has been argued to have potential fault tolerance. We demonstrated the controlled accumulation of a geometric phase, Berry's phase, in a superconducting qubit; we manipulated the qubit geometrically by means of microwave radiation and observed the accumulated phase in an interference experiment. We found excellent agreement with Berry's predictions and also observed a geometry-dependent contribution to dephasing.}, author = {Leek, Peter J and Johannes Fink and Blais, Alexandre and Bianchetti, R and Göppl, M and Gambetta, Jay M and Schuster, David I and Frunzio, Luigi and Schoelkopf, Robert J and Wallraff, Andreas}, journal = {Science}, number = {5858}, pages = {1889 -- 1892}, publisher = {American Association for the Advancement of Science}, title = {{Observation of Berry's phase in a solid-state qubit}}, doi = {10.1126/science.1149858}, volume = {318}, year = {2007}, } @article{17714, abstract = {We investigate the effect of planetary rotation on the transit spectrum of an extrasolar giant planet. During ingress and egress, absorption features arising from the planet's atmosphere are Doppler shifted by of order the planet's rotational velocity (~1-2 km/s) relative to where they would be if the planet were not rotating. We focus in particular on the case of HD209458b, which ought to be at least as good a target as any other known transiting planet. For HD209458b, this shift should give rise to a small net centroid shift of ~60 cm/s on the stellar absorption lines. Using a detailed model of the transmission spectrum due to a rotating star transited by a rotating planet with an isothermal atmosphere, we simulate the effect of the planet's rotation on the shape of the spectral lines, and in particular on the magnitude of their width and centroid shift. We then use this simulation to determine the expected signal-to-noise ratio for distinguishing a rotating from a non-rotating planet, and assess how this S/N scales with various parameters of HD209458b. We find that with a 6 m telescope, an equatorial rotational velocity of ~2 km/s could be detected with a S/N~5 by accumulating the signal over many transits over the course of several years. With a 30 m telescope, the time required to make such a detection reduces to less than 2 months.}, author = {Spiegel, David S. and Haiman, Zoltán and Gaudi, B. Scott}, issn = {0004-637X}, journal = {The Astrophysical Journal}, number = {2}, pages = {1324--1335}, publisher = {American Astronomical Society}, title = {{On constraining a transiting exoplanet’s rotation rate with its transit spectrum}}, doi = {10.1086/521921}, volume = {669}, year = {2007}, } @article{17716, abstract = {Recent observations imply that the observed number counts of Lyα emitters (LAEs) evolved significantly between z= 5.7 and 6.5. It has been suggested that this was due to a rapid evolution in the ionization state, and hence transmission of the intergalactic medium (IGM) which caused Lyα flux from z= 6.5 galaxies to be more strongly suppressed. In this paper, we consider the joint evolution of the Lyα and the ultraviolet luminosity functions (LFs) and show that the IGM transmission evolved between z= 6.5 and 5.7 by a factor 1.1 < R < 1.8 (95 per cent confidence level). This result is insensitive to the underlying model of the Lyα LF (as well as cosmic variance). Using a model for IGM transmission, we find that the evolution of the mean IGM density through cosmic expansion alone may result in a value for the ratio of transmissions as high as R= 1.3. Thus, the existing LFs do not provide evidence for overlap. Furthermore, the constraint R < 1.8 suggests that the Universe at z= 6.5 was more than half-ionized by volume, that is, xi,V > 0.5.}, author = {Dijkstra, M. and Wyithe, J. S. B. and Haiman, Zoltán}, issn = {0035-8711}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {1}, pages = {253--259}, publisher = {Oxford University Press}, title = {{Luminosity functions of Lyα emitting galaxies and cosmic reionization of hydrogen}}, doi = {10.1111/j.1365-2966.2007.11936.x}, volume = {379}, year = {2007}, } @article{17724, abstract = {The continuous improvement in localization errors (sky position and distance) in real time as LISA observes the gradual inspiral of a supermassive black hole (SMBH) binary can be of great help in identifying any prompt electromagnetic counterpart associated with the merger. We develop a new method, based on a Fourier decomposition of the time-dependent, LISA-modulated gravitational-wave signal, to study this intricate problem. The method is faster than standard Monte Carlo simulations by orders of magnitude. By surveying the parameter space of potential LISA sources, we find that counterparts to SMBH binary mergers with total mass M~10^5-10^7 M_Sun and redshifts z<~3 can be localized to within the field of view of astronomical instruments (~deg^2) typically hours to weeks prior to coalescence. This will allow targeted searches for variable electromagnetic counterparts as the merger proceeds, as well as monitoring of the most energetic coalescence phase. A rich set of astrophysical and cosmological applications would emerge from the identification of electromagnetic counterparts to these gravitational-wave standard sirens.}, author = {Kocsis, Bence and Haiman, Zoltán and Menou, Kristen and Frei, Zsolt}, issn = {1550-7998}, journal = {Physical Review D}, number = {2}, publisher = {American Physical Society}, title = {{Premerger localization of gravitational-wave standard sirens with LISA: Harmonic mode decomposition}}, doi = {10.1103/physrevd.76.022003}, volume = {76}, year = {2007}, } @article{17729, abstract = {We make use of hydrodynamical simulations of the intergalactic medium (IGM) to create model quasar absorption spectra. We compare these model spectra with the observed Keck spectra of three z>6.2 quasars with full Gunn-Peterson troughs: SDSS J1148+5251 (z=6.42), SDSS J1030+0524 (z=6.28), and SDSS J1623+3112 (z=6.22). We fit the probability density distributions (PDFs) of the observed Ly alpha optical depths with those generated from the simulation, by exploring a range of values for the size of the quasar's surrounding HII region, R_S, the volume-weighted mean neutral hydrogen fraction in the ambient IGM, x_H, and the quasar's ionizing photon emissivity, N_Q. In order to avoid averaging over possibly large sightline-to-sightline fluctuations in IGM properties, we analyze each observed quasar independently. We find the following results for J1148+5251, J1030+0524, and J1623+3112: The best-fit sizes R_S are 40, 41, and 29 (comoving) Mpc, respectively. These constraints are tight, with only ~ 10% uncertainties, comparable to those caused by redshift--determination errors. The best-fit values of N_Q are 2.1, 1.3, and 0.9 x 10^{57} s^{-1}, respectively, with a factor of ~ 2 uncertainty in each case. Finally, the best--fit values of x_H are 0.16, 1.0, and 1.0, respectively. The uncertainty in the case of J1148+5251 is large, and x_H is not well constrained. However, for both J1030+0524 and J1623+3112, we find a significant lower limit of x_H >~ 0.033. Our method is different from previous analyses of the GP absorption spectra of these quasars, and our results strengthen the evidence that the rapid end--stage of reionization is occurring near z ~ 6.}, author = {Mesinger, Andrei and Haiman, Zoltán}, issn = {0004-637X}, journal = {The Astrophysical Journal}, number = {2}, pages = {923--932}, publisher = {American Astronomical Society}, title = {{Constraints on reionization and Source Properties from the Absorption Spectra of z > 6.2 quasars}}, doi = {10.1086/513688}, volume = {660}, year = {2007}, } @article{17732, abstract = {Energetic feedback processes during the formation of galaxy clusters may have heated and ionized a large fraction of the intergalactic gas in proto-cluster regions. When such a highly ionized hot ``super-bubble'' falls along the sightline to a background quasar, it would be seen as a large void, with little or no absorption, in the Lyman alpha forest. We examine the spectra of 137 quasars in the Sloan Digital Sky Survey, to search for such voids, and find no clear evidence of their existence. The size distribution of voids in the range 5-70 Angstrom (corresponding to physical sizes of approximately 3-35 comoving Mpc/h) is consistent with the standard model for the Lyman alpha forest without additional hot bubbles. We adapt a physical model for HII bubble growth during cosmological reionization (Furlanetto, Zaldarriaga and Hernquist 2004), to describe the expected size-distribution of hot super-bubbles at redshift around z = 3. This model incorporates the conjoining of bubbles around individual neighboring galaxies. Using the non-detection of voids, we find that models in which the volume filling factor of hot bubbles exceeds approximately 20 percent at z=3 can be ruled out, primarily because they overproduce the number of large (40-50 Angstrom) voids. We conclude that any pre-heating mechanism that explains galaxy cluster observations must avoid heating the low-density gas in the proto-cluster regions, either by operating relatively recently (z<3) or by depositing entropy in the high-density regions.}, author = {Shang, Cien and Crotts, Arlin and Haiman, Zoltán}, issn = {0004-637X}, journal = {The Astrophysical Journal}, number = {1}, pages = {136--145}, publisher = {American Astronomical Society}, title = {{Constraints on the abundance of highly ionized protocluster regions from the absence of large voids in the Lyα forest}}, doi = {10.1086/522331}, volume = {671}, year = {2007}, }