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We consider the question that the spectrum and arithmetic of locally symmetric spaces defined by congruent arithmetical lattices should mutually determine each other. We frame these questions in the context of automorphic representations.
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arxiv:1010.5411
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We show, conditional on a uniform version of the prime k-tuples conjecture, that there are x(log x)^{-1+o(1)} numbers not exceeding x common to the ranges of Euler's function phi(n) and the sum-of-divisors function sigma(m).
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arxiv:1010.5427
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We develop a general method to evaluate the Kondo temperature in a multilevel quantum dot that is weakly coupled to conducting leads. Our theory reveals that the Kondo temperature is strongly enhanced when the intradot energy-level spacing is comparable to or smaller than the charging energy. We propose an experiment to test our result, which consists of measuring the size-dependence of the Kondo temperature.
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arxiv:1010.5472
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The use of the absolute measure of local chirality is championed since it has a uniform distribution for randomly reshuffled chiral components so that any deviations from uniformity in the associated "X-distribution" are directly attributable to QCD-induced dynamics. We observe a transition in the qualitative behavior of this absolute X-distribution of low-lying eigenmodes which, we propose, defines a chiral polarization scale of the QCD vacuum.
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arxiv:1010.5474
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We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that appear in the closed neighborhood of u and v are distinct. Let $\chi_{lid}(G)$ be the minimum number of colors used in a locally identifying vertex-coloring of G. In this paper, we give several bounds on $\chi_{lid}$ for different families of graphs (planar graphs, some subclasses of perfect graphs, graphs with bounded maximum degree) and prove that deciding whether $\chi_{lid}(G)=3$ for a subcubic bipartite graph $G$ with large girth is an NP-complete problem.
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arxiv:1010.5624
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We present a detailed study of the heating effects in dielectric measurements carried out on a liquid. Such effects come from the dissipation of the electric power in the liquid and give a contribution to the nonlinear third harmonics susceptibility chi_3 which depends on the frequency and temperature. This study is used to evaluate a possible `spurious' contribution to the recently measured nonlinear susceptibility of an archetypical glassforming liquid (Glycerol). Those measurements have been shown to give a direct evaluation of the number of dynamically correlated molecules temperature dependence close to the glass transition temperature T_g~190K (Crauste-Thibierge et al., Phys. Rev. Lett 104,165703(2010)). We show that the heating contribution is totally negligible (i) below 204K at any frequency; (ii) for any temperature at the frequency where the third harmonics response chi_3 is maximum. Besides, this heating contribution does not scale as a function of f/f_{\alpha}, with f_{\alpha}(T) the relaxation frequency of the liquid. In the high frequency range, when f/f_{\alpha} >= 1, we find that the heating contribution is damped because the dipoles cannot follow instantaneously the temperature modulation due to the heating phenomenon. An estimate of the magnitude of this damping is given.
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arxiv:1010.5672
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There is evidence from radio-loud quasars to suggest that the distribution of the H$\beta$ broad emission line (BEL) gas is arranged in a predominantly planar orientation, and this result may well also apply to radio-quiet quasars. This would imply that the observed full width at half maximum (FWHM) of the H$\beta$ BELs is dependent on the orientation of the line of sight to the gas. If this view is correct then we propose that the FWHM can be used as a surrogate, in large samples, to determine the line of sight to the H$\beta$ BELs in broad absorption line quasars (BALQSOs).... It is determined that there is a statistically significant excess of narrow line profiles in the SDSS DR7 archival spectra of low ionization broad absorption line quasars (LoBALQSOs), indicating that BAL gas flowing close to the equatorial plane does not commonly occur in these sources. We also find that the data is not well represented by random lines of sight to the BAL gas. Our best fit indicates two classes of LoBALQSOs, the majority ($\approx 2/3$) are polar outflows, that are responsible for the enhanced frequency of narrow line profiles, and the remainder are equatorial outflows. We further motivated the line of sight explanation of the narrow line excess in LoBALQSOs by considering the notion that the skewed distribution of line profiles is driven by an elevated Eddington ratio in BALQSOs. We constructed a variety of control samples comprised of nonLoBALQSOs matched to a de-reddened LoBALQSO sample in redshift, luminosity, black hole mass and Eddington ratio. It is demonstrated that the excess of narrow profiles persists within the LoBALQSO sample relative to each of the control samples with no reduction of the statistical significance. Thus, we eliminate the possibility that the excess narrow lines seen in the LoBALQSOs arise from an enhanced Eddington ratio.
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arxiv:1010.5705
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This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the Brunn-Minkowski inequality and the statistical dependence between row and column sums.
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arxiv:1010.5706
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In this article I explain in detail a method for making small amounts of liquid oxygen in the classroom if there is no access to a cylinder of compressed oxygen gas. I also discuss two methods for identifying the fact that it is liquid oxygen as opposed to liquid nitrogen.
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arxiv:1010.5774
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An elementary presentation of the methods for the canonical quantization of constraint systems with Fermi variables is given. The emphasis is on the subtleties of the construction of an appropriate classical bracket that could be consistently replaced by commutators or anti--commutators of operators, as required by canonical quantization procedure for bosonic and fermionic degrees of freedom respectively. I present a consequent canonical quantization of the Dirac field, in which the role of Poincar\'e invariance is made marginal. This simple example provides an introduction to the Poincar\'e--free quantization of spinor electrodynamics in the second part of the paper.
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arxiv:1010.5797
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In the single degenerate (SD) scenario for Type Ia supernova (SN Ia) progenitors, an accreting white dwarf (WD) is expected to undergo a supersoft X-ray source (SSS) phase. Recently, Gilfanov & Bogdan (2010, hereafter GB10) claimed that observed X-ray fluxes of early type galaxies would be too low to be consistent with the prediction of the SD scenario based on rather simple assumptions. We present realistic evolutionary models of SD systems and calculate durations of SSS phases. In most cases, accreting WDs spend a large fraction of time in the optically thick wind phase and the recurrent nova phase rather than the SSS phase. Thus the SSS phase lasts only for a few hundred thousand years. This is by a factor of ~10 shorter than those adopted by GB10 where the SN~Ia progenitor WD was assumed to spend most of its life as a SSS. The theoretical X-ray luminosity of the SSS has a large uncertainty because of the uncertain atmospheric model of mass-accreting WDs and absorption of soft X-rays by the companion star's cool wind material. We thus adopt an average of the observed fluxes of existing symbiotic SSSs, i.e., ~0.4 x 10^{36} erg s^{-1} for 0.3--0.7 keV. Using these SSS duration and soft X-ray luminosity, we show that the observed X-ray flux obtained by GB10 is rather consistent with our estimated flux in early type galaxies based on the SD scenario. This is a strong support for the SD scenario as a main-contributor of SNe Ia in early type galaxies.
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arxiv:1010.5860
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We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this model, the usual quantum description arises as asymptotics of this process for large values of resistance of the medium per unit of mass of particle. It is shown that in this case the process passes several stages. During the first short stage, the wave function goes to one of "stationary" values. At the second long stage, the wave function varies in the subspace of "stationary" states according to the Schrodinger equation. Further, dissipation of the process leads to decoherence, and any superposition of states goes to one of eigenstates of the Hamilton operator. At the last stage, the mixed state of heat equilibrium (the Gibbs state) arises due to the heat influence of the medium and the random transitions among the eigenstates of the Hamilton operator. Besides that, it is shown that, on the contrary, if the resistance of the medium per unit of mass of particle is small, then in the considered model, the density of distribution of probability $\rho =|\phi |^2$ satisfies the standard Liouville equation, as in classical statistical mechanics.
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arxiv:1010.5898
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We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field correlation functions are examined, we establish their growth rates and scaling behavior. General assertions are illustrated by explicit solution of the model where the velocity field is short-correlated in time.
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arxiv:1010.5904
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We consider the recursion relation for loop integrands in planar N = 4 SYM generated by an all-line shift of momentum twistors. We examine the behaviour of the rational loop integrands when the shift parameter becomes large, and find that a valid recursion relation may be obtained in all cases. The recursion relation is then formulated both in region momentum space and in momentum twistor space, and solved in detail for some one and two-loop examples. Finally, we show that the general iterative solution of the recursion relation generates the MHV vertex expansion for all loop integrands, providing a proof of the MHV diagram formalism for all loop amplitudes in planar N = 4 SYM.
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arxiv:1010.5921
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We present solutions of the Dirac equation with spin symmetry for vector and scalar modified P\"oschl-Teller potential within framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov-Uvarov method and the two-component spinor wavefunctions are obtain are in terms of the Jacobi polynomials. It is found that there exist only positive-energy states for bound states under spin symmetry, and the energy levels increase with the dimension and the potential range parameter $\alpha$.
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arxiv:1010.5981
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In this publication electroweak next-to-leading order corrections to semileptonic B-meson decays into (pseudo)scalar final states are presented. To this end, these corrections of O(alpha G_F) have been calculated in the QED-enhanced phenomenological model, incorporating the bound-state mesons as its degrees of freedom, and matched to a similar calculation on the level of constituent partons in the full Standard Model. Consequently, the effects arising due to corrections of the partial decay widths on the extraction of the CKM matrix elements |V_cb| and |V_ub| are detailed. Further, the results of two independent Monte-Carlo implementations are presented: One is the dedicated, strict fixed-order generator BLOR, and the other is embedded into the generic Yennie-Frautschi-Suura-type resummation of Photons++, which is part of the multi-purpose event generator Sherpa. The resulting distributions are compared against the standard tool used in many experimental analyses, PHOTOS, showing improvements on the shapes of kinematic distributions of both the lepton and the final state meson.
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arxiv:1010.5997
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The maximum mass of a neutron star (NS) is poorly defined. Theoretical attempts to define this mass have thus far been unsuccessful. Observational results currently provide the only means of narrowing this mass range down. Eclipsing X-ray binary (XRB) pulsar systems are the only interacting binaries in which the mass of the NS may be measured directly. Only 10 such systems are known to exist, 6 of which have yielded NS masses in the range 1.06 - 1.86 M$_{\odot}$.We present the first orbital solutions of two further eclipsing systems, OAO 1657-415 and EXO 1722-363, whose donor stars have only recently been identified. Using observations obtained using the VLT/ISAAC NIR spectrograph, our initial work was concerned with providing an accurate spectral classification of the two counterpart stars, leading to a consistent explanation of the mechanism for spin period evolution of OAO 1657-415. Calculating radial velocities allowed orbital solutions for both systems to be computed. These are the first accurate determinations of the NS and counterpart masses in XRB pulsar systems to be made employing NIR spectroscopy.
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arxiv:1010.6001
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In this paper, we first derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then we apply this estimate to study finite-time singularity behavior. We show that if the scalar curvature is uniformly bounded, then the Weyl tensor has to blow up, as a consequence, the corresponding singularity model must be Ricci flat with non-vanishing Weyl tensor.
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arxiv:1010.6064
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In the random case setting, scrambled polynomial lattice rules as discussed in \cite{BD10} enjoy more favourable strong tractablility properties than scrambled digital nets. This short note discusses the application of scrambled polynomial lattice rules to infinite-dimensional integration. In \cite{HMGNR10}, infinite-dimensional integration in the random case setting was examined in detail, and results based on scrambled digital nets were presented. Exploiting these improved strong tractability properties of scrambled polynomial lattice rules and making use of the analysis presented in \cite{HMGNR10}, we improve on the results that were achieved using scrambled digital nets.
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arxiv:1010.6122
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In this paper, we will show that the limit of some quasilocal mass integrals of the coordinate spheres in an asymptotically hyperbolic (AH) manifold is the mass integral of the AH manifold. This is the analogue of the well known result that the limit of the Brown-York mass of coordinate spheres is the ADM mass in an asymptotically flat manifold.
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arxiv:1010.6130
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We study the equivariant cobordism theory of schemes for torus actions. We give the explicit relation between the equivariant and the ordinary cobordism of schemes with torus action. We deduce analogous results for action of arbitrary connected linear algebraic groups. We prove some structure theorems for the equivariant and ordinary cobordism of schemes with torus action and derive important consequences. We establish the localization theorems in this setting. These are used to describe the structure of the ordinary cobordism ring of certain smooth projective varieties.
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arxiv:1010.6182
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From CCD observations of a fixed and large star field that contained the binary TNO Orcus, we have been able to derive high-precision relative astrometry and photometry of the Orcus system with respect to background stars. The RA residuals of an orbital fit to the astrometric data revealed a periodicity of 9.7+-0.3 days, which is what one would expect to be induced by the known Orcus companion. The residuals are also correlated with the theoretical positions of the satellite with regard to the primary. We therefore have revealed the presence of Orcus' satellite in our astrometric measurements. The photocenter motion is much larger than the motion of Orcus around the barycenter, and we show here that detecting some binaries through a carefully devised astrometric technique might be feasible with telescopes of moderate size. We also analyzed the system's mid-term photometry to determine whether the rotation could be tidally locked to the satellite's orbital period. We found that a photometric variability of 9.7+-0.3 days is clear in our data, and is nearly coincident with the orbital period of the satellite. We believe this variability might be induced by the satellite's rotation. There is also a slight hint for an additional small variability in the 10 hr range that was already reported in the literature. This short-term variability would indicate that the primary is not tidally locked and therefore the system would not have reached a double synchronous state. Implications for the basic physical properties of the primary and its satellite are discussed. From angular momentum considerations we suspect that the Orcus satellite might have formed from a rotational fission. This requires that the mass of the satellite would be around 0.09 times that of the primary, close to the value that one derives by using an albedo of 0.12 for the satellite and assuming equal densities for both objects.
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arxiv:1010.6187
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We derive an expression for the accuracy with which sources can be localized using a network of gravitational wave detectors. The result is obtained via triangulation, using timing accuracies at each detector and is applicable to a network with any number of detectors. We use this result to investigate the ability of advanced gravitational wave detector networks to accurately localize signals from compact binary coalescences. We demonstrate that additional detectors can significantly improve localization results and illustrate our findings with networks comprised of the advanced LIGO, advanced Virgo and LCGT. In addition, we evaluate the benefits of relocating one of the advanced LIGO detectors to Australia.
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arxiv:1010.6192
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Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization using first principle Monte Carlo simulations. We focus on studying the finite-size scaling of $\rho_{s1} L$ and $\rho_{s2} L$, where $L$ stands for the spatial box size used in the simulations and $\rho_{si}$ with $i \in \{1,2\}$ is the spin-stiffness in $i$-direction. From our Monte Carlo data, we find that $\rho_{s2} L$ suffers a much less severe correction compared to that of $\rho_{s1} L$. Therefore $\rho_{s2} L$ is a better quantity than $\rho_{s1} L$ for finite-size scaling analysis concerning the limitation of the availability of large volumes data in our study. Further, motivated by the so-called cubical regime in magnon chiral perturbation theory, we additionally perform a finite-size scaling analysis on our Monte Carlo data with the assumption that the ratio of spatial winding numbers squared is fixed through all simulations. As a result, the physical shape of the system remains fixed in our calculations. The validity of this new idea is confirmed by studying the phase transition driven by spatial anisotropy for the ladder anisotropic Heisenberg model. With this new strategy, even from $\rho_{s1} L$ which receives the most serious correction among the observables considered in this study, we arrive at a value for the critical exponent $\nu$ which is consistent with the expected $O(3)$ value by using only up to $L = 64$ data points.
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arxiv:1010.6267
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We present initial results from a long-baseline radial velocity survey for massive binaries in the cluster Westerlund 1. Four systems are examined: the dust-producing WC binary W239, the double-lined eclipsing binary W13, and the single-lined B0 supergiants W43a and W3003. Finally, the evolutionary implications for the population of massive stars in Westerlund 1 are discussed.
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arxiv:1010.6270
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The process of $e^+e^-$ production in the superposition of a Coulomb and a strong laser field is considered. The pair production rate integrated over the momentum and summed over the spin projections of one of the particles is derived exactly in the parameters of the laser field and in the Born approximation with respect to the Coulomb field. The case of a monochromatic circularly polarized laser field is considered in detail. A very compact analytical expression of the pair production rate and its dependence on the polarization of one of the created particles is obtained in the quasiclassical approximation for the experimentally relevant case of an undercritical laser field. As a result, the polarization of the created electron (positron) is derived.
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arxiv:1010.6274
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We discuss results from simulations of black hole formation in failing core-collapse supernovae performed with the code GR1D, a new open-source Eulerian spherically-symmetric general-relativistic hydrodynamics code. GR1D includes rotation in an approximate way (1.5D), comes with multiple finite-temperature nuclear equations of state (EOS), and treats neutrinos in the post-core-bounce phase via a 3-flavor leakage scheme and a heating prescription. We chose the favored K_0=220 MeV-variant of the Lattimer & Swesty (1990) EOS and present collapse calculations using the progenitor models of Limongi & Chieffi (2006). We show that there is no direct (or ``prompt'') black hole formation in the collapse of ordinary massive stars (8 M_Sun ~< M_ZAMS ~< 100 M_Sun) and present first results from black hole formation simulations that include rotation.
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arxiv:1011.0005
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The implementation of an Fe buffer layer is a promising way to obtain epitaxial growth of Co-doped BaFe2As2 (Ba-122). However, the crystalline quality and the superconducting properties of Co-doped Ba-122 are influenced by the Fe buffer layer thickness, dFe. The well-textured growth of the Fe/Ba-122 bilayer with dFe = 15 nm results in a high Jc of 0.45 MAcm$^{-2}$ at 12 K in self-field, whereas a low Jc value of 61000 Acm$^{-2}$ is recorded for the bilayer with dFe = 4 nm at the corresponding reduced temperature due to the presence of grain boundaries.
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arxiv:1011.0035
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We give a self-contained exposition of the proof of faithfully flat descent for projectivity of modules. This fills a gap in the proof given in the literature.
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arxiv:1011.0038
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Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are the index-1 saddle points. Generalizations to high index saddle points are discussed. Both gradient and non-gradient systems are considered. Preliminary results on the nature of the dynamical behavior are presented.
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arxiv:1011.0042
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Chameleon scalar field is a new model, which introduced to provide a mechanism for exhibiting accelerating universe. Chameleon field has several interesting aspects, such as field dependence on the local matter density. For this model we introduce a new kind of potential which has run away form and satisfies chameleon constraints. The results are acceptable in comparison with the other potentials which studied up to now.
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arxiv:1011.0075
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Astronomically, there are viable mechanisms for distributing organic material throughout the Milky Way. Biologically, the destructive effects of ultraviolet light and cosmic rays means that the majority of organisms arrive broken and dead on a new world. The likelihood of conventional forms of panspermia must therefore be considered low. However, the information content of dam-aged biological molecules might serve to seed new life (necropanspermia).
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arxiv:1011.0101
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We study dynamics of the classicalization phenomenon suggested in arXiv:1010.1415, according to which a class of non-renormalizable theories self-unitarizes at high-energies via creation of classical configurations (classicalons). We study this phenomenon in an explicit model of derivatively-self-coupled scalar that serves as a prototype for a Nambu-Goldstone-St\"uckelberg field. We prepare the initial state in form of a collapsing wave-packet of a small occupation number but of very high energy, and observe that the classical configuration indeed develops. Our results confirm the previous estimates, showing that because of self-sourcing the wave-packet forms a classicalon configuration with radius that increases with center of mass energy. Thanks to self-sourcing by energy, unlike solitons, the production of classicalons dominates the high-energy scattering. In order to confront classicalizing and non-classicalizing theories, we use a language in which the scattering cross section can be universally understood as a geometric cross section set by a classical radius down to which waves can propagate freely. The difference is, that in non-classicalizing examples this radius shrinks with increasing energy, whereas in classicalizing theories expands and becomes macroscopic. We study analogous scattering in a Galileon system and discover that classicalization is less efficient there. We thus observe, that classicalization is source-sensitive and that Goldstones pass the first test.
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arxiv:1011.0114
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The history of how chiral symmetry has entered in nuclear physics, in which Gerry Brown and I have participated from 1970 up to today, is described from my personal viewpoint. The route of development we have traversed together goes from meson exchange currents, to "little chiral bag," to chiral effective field theory, to "Brown-Rho scaling" and then to dense matter and chiral phase transition. It has been a great fun and exciting, some right and some wrong in what we have done together, but none that can be dismissed as "not even wrong." We have found all along that whatever signal there may be for the manifestation of chiral symmetry in nuclear medium, be it at low density in meson exchange currents or at high density approaching the chiral phase transition, is very similar in its intricacy and subtlety.
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arxiv:1011.0135
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We fabricated high-mobility {\delta}-doped structures in SrTiO3 thin films in order to investigate the low temperature electronic transport properties of confined carriers in this system. An enhancement of the electron mobility above the bulk value was observed as the doped layer thickness decreased. High-field Hall measurements revealed that this mobility enhancement originates from higher-mobility electrons in the undoped clean regions, which have quantum-mechanically broadened from the doped layer. Because of the absence of apparent lattice misfit between the layers, this structure is highly suitable for investigating two-dimensional electron gases in SrTiO3.
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arxiv:1011.0159
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The impact of the Fermi Gamma-ray Space Telescope on blazar research is reviewed. This includes a brief description of the Fermi Large Area Telescope, a summary of the various classes of extragalactic sources found in the First Large Area Telescope AGN Catalog, and more detailed discussion of the flat spectrum radio quasar 3C454.3 and the BL Lac object PKS 2155-304. Some theoretical studies related to ongoing blazar research with Fermi are mentioned, including implications of gamma-ray observations of radio galaxies on blazar unification scenarios, variability in colliding shells, and whether blazars are sources of ultra-high energy cosmic rays.
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arxiv:1011.0169
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We discuss a Poincar\'e invariant coupled-channel formalism which is based on the point-form of relativistic quantum mechanics. Electromagnetic scattering of an electron by a 2-body bound state is treated as a 2-channel problem for a Bakamjian-Thomas-type mass operator. In this way retardation effects in the photon-exchange interaction are fully taken into account. The electromagnetic current of the 2-body bound state is then extracted from the one-photon-exchange optical potential. As an application we calculate electromagnetic pion and deuteron form factors. Wrong cluster properties, inherent in the Bakamjian-Thomas framework, are seen to cause spurious (unphysical) contributions in the current. These are separated and eliminated in an unambiguous way such that one is left with a current that has all the desired properties.
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arxiv:1011.0170
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We examine the evolution of the spatial counts-in-cells distribution of galaxies and show that the form of the galaxy distribution function does not change significantly as galaxies merge and evolve. In particular, bound merging pairs follow a similar distribution to that of individual galaxies. From the adiabatic expansion of the universe we show how clustering, expansion and galaxy mergers affect the clustering parameter b. We also predict the evolution of b with respect to redshift.
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arxiv:1011.0176
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We consider Higgs massive gravity [1,2] and investigate whether a nonlinear ghost in this theory can be avoided. We show that although the theory considered in [10,11] is ghost free in the decoupling limit, the ghost nevertheless reappears in the fourth order away from the decoupling limit. We also demonstrate that there is no direct relation between the value of the Vainshtein scale and the existence of nonlinear ghost. We discuss how massive gravity should be modified to avoid the appearance of the ghost.
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arxiv:1011.0183
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Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum.
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arxiv:1011.0202
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Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.
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arxiv:1011.0222
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We show that suitable convex energy functionals on a quadratic Wasserstein space satisfy a maximum principle on minimal networks. We explore consequences of this maximum principle for the structure of minimal networks.
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arxiv:1011.0236
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We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.
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arxiv:1011.0317
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Rotation measures of pulsars and extragalactic point sources have been known to reveal large-scale antisymmetries in the Faraday rotation sky with respect to the Galactic plane and halo that have been interpreted as signatures of the mean magnetic field in the Galactic halo. We describe Faraday rotation measurements of the diffuse Galactic polarized radio emission over a large region in the northern Galactic hemisphere. Through application of Rotation Measure Synthesis we achieve sensitive Faraday rotation maps with high angular resolution, capable of revealing fine-scale structures of about 1 deg in the Faraday rotation sky. Our analysis suggests that the observed antisymmetry in the Faraday rotation sky at b > 0 deg is dominated by the magnetic field around a local HI bubble at a distance of approx. 100 pc, and not by the magnetic field of the Galactic halo. We derive physical properties of the magnetic field of this shell, which we find to be 20 - 34 uG strong. It is clear that the diffuse polarized radio emission contains important information about the local magneto-ionic medium, which cannot yet be derived from Faraday rotation measures of extragalactic sources or pulsars alone.
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arxiv:1011.0341
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We investigate the corrections to scaling of the Renyi entropies of a region of size l at the end of a semi-infinite one-dimensional system described by a conformal field theory when the corrections come from irrelevant boundary operators. The corrections from irrelevant bulk operators with scaling dimension x have been studied by Cardy and Calabrese (2010), and they found not only the expected corrections of the form l^(4-2x) but also unusual corrections that could not have been anticipated by finite-size scaling arguments alone. However, for the case of perturbations from irrelevant boundary operators we find that the only corrections that can occur to leading order are of the form l^(2-2x_b) for boundary operators with scaling dimension x_b < 3/2, and l^(-1) when x_b > 3/2. When x_b=3/2 they are of the form l^(-1)log(l). A marginally irrelevant boundary perturbation will give leading corrections going as log(l)^(-3). No unusual corrections occur when perturbing with a boundary operator.
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arxiv:1011.0448
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We used the Submillimeter Array (SMA) to observe the thermal polarized dust emission from the protostellar source NGC 2024 FIR 5. The polarized emission outlines a partial hourglass morphology for the plane-of-sky component of the core magnetic field. Our data are consistent with previous BIMA maps, and the overall magnetic field geometries obtained with both instruments are similar. We resolve the main core into two components, FIR 5A and FIR 5B. A possible explanation for the asymmetrical field lies in depolarization effects due to the lack of internal heating from FIR 5B source, which may be in a prestellar evolutionary state. The field strength was estimated to be 2.2 mG, in agreement with previous BIMA data. We discuss the influence of a nearby H{\sc ii} region over the field lines at scales of $\sim 0.01$ pc. Although the hot component is probably compressing the molecular gas where the dust core is embedded, it is unlikely that the radiation pressure exceeds the magnetic tension. Finally, a complex outflow morphology is observed in CO (3 $\rightarrow$ 2) maps. Unlike previous maps, several features associated with dust condensations other than FIR 5 are detected.
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arxiv:1011.0475
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In this paper, we survey five different computational modeling methods. For comparison, we use the activation cycle of G-proteins that regulate cellular signaling events downstream of G-protein-coupled receptors (GPCRs) as a driving example. Starting from an existing Ordinary Differential Equations (ODEs) model, we implement the G-protein cycle in the stochastic Pi-calculus using SPiM, as Petri-nets using Cell Illustrator, in the Kappa Language using Cellucidate, and in Bio-PEPA using the Bio-PEPA eclipse plug in. We also provide a high-level notation to abstract away from communication primitives that may be unfamiliar to the average biologist, and we show how to translate high-level programs into stochastic Pi-calculus processes and chemical reactions.
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arxiv:1011.0490
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We introduce acyclic polygraphs, a notion of complete categorical cellular model for (small) categories, containing generators, relations and higher-dimensional globular syzygies. We give a rewriting method to construct explicit acyclic polygraphs from convergent presentations. For that, we introduce higher-dimensional normalisation strategies, defined as homotopically coherent ways to relate each cell of a polygraph to its normal form, then we prove that acyclicity is equivalent to the existence of a normalisation strategy. Using acyclic polygraphs, we define a higher-dimensional homotopical finiteness condition for higher categories which extends Squier's finite derivation type for monoids. We relate this homotopical property to a new homological finiteness condition that we introduce here.
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arxiv:1011.0558
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We study a uniform matrix product state as a variational state for classical and quantum spin chains in the thermodynamic limit. Under a careful treatment of the translational symmetry, eigen values of the transfer matrix defined in the calculation of expectation values can reflect the periodicity of the ground state and indicate optimum periodicity of the matrix product state. We discuss the relation between the periodicity and accuracy of magnetization curves. This approach is free from the error due to finite system size, which works well especially for the magnetic plateau problem.
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arxiv:1011.0576
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Motivated by fluorescence lifetime measurements this paper considers the problem of nonparametric density estimation in the pile-up model. Adaptive nonparametric estimators are proposed for the pile-up model in its simple form as well as in the case of additional measurement errors. Furthermore, oracle type risk bounds for the mean integrated squared error (MISE) are provided. Finally, the estimation methods are assessed by a simulation study and the application to real fluorescence lifetime data.
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arxiv:1011.0592
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New optical narrowband imaging observations of the fields of several ULXs are presented. Known supershell nebulae are associated with a number of these ULXs, which we detect in emission line filters such as [S II], He II, [O II] and [O III]. New nebulae are discovered, which are candidate ULX-powered supershells. The morphologies and emission line fluxes of these nebulae could then be used to infer the properties of the emitting gas, which gives clues to the energizing source (photoionization and/or shock-excitation, both possibly from the ULX). Studies of supershells powered by ULXs can help to constrain the nature of ULXs themselves, such as the isotropy of the X-ray emission and the strength of their outflows.
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arxiv:1011.0598
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Besides serving as prediction models, classification trees are useful for finding important predictor variables and identifying interesting subgroups in the data. These functions can be compromised by weak split selection algorithms that have variable selection biases or that fail to search beyond local main effects at each node of the tree. The resulting models may include many irrelevant variables or select too few of the important ones. Either eventuality can lead to erroneous conclusions. Four techniques to improve the precision of the models are proposed and their effectiveness compared with that of other algorithms, including tree ensembles, on real and simulated data sets.
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arxiv:1011.0608
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A relation between circular 1/2 BPS 't Hooft operators in 4d N=4 SYM and instantonic solutions in 2d Yang-Mills theory (YM_2) has recently been conjectured. Localization indeed predicts that those 't Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM_2, belonging to representations of the dual group ^LG. This conjecture has been tested in the case G=U(N)=^LG and for fundamental representations. In this paper we examine this conjecture in the case of the groups G=SU(N) and ^LG=SU(N)/Z_N and loops in different representations. Peculiarities when groups are not self-dual and representations not "minimal" are pointed out.
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arxiv:1011.0638
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A dual-Regge model with a nonlinear proton Regge trajectory in the missing mass channel, describing the experimental data on low-mass single diffraction dissociation, is constructed. Predictions for the LHC energies are given.
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arxiv:1011.0664
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Over the last years the Tevatron Run-II has extended several limits on Higgs boson masses and coupling which were pioneered during the LEP accelerator operation between 1989 and 2000. Higgs boson searches will also be at the forefront of research at the LHC. This review concisely discusses the experimental constraints set by the CDF and D0 collaborations in summer 2010 at the beginning of the LHC era. Model-independent and model-dependent limits on Higgs boson masses and couplings have been set and interpretations are discussed both in the Standard Model and in extended models. Recently, the Tevatron has extended the excluded SM Higgs boson mass range (158-175 GeV) beyond the LEP limit at 95% CL. The experimental sensitivities are estimated for the completion of the Tevatron programme.
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arxiv:1011.0681
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In Little Higgs models a collective symmetry prevents the Higgs from acquiring a quadratically divergent mass at one loop. This collective symmetry is broken by weakly gauged interactions. Terms, like Yukawa couplings, that display collective symmetry in the bare Lagrangian are generically renormalized into a sum of terms that do not respect the collective symmetry except possibly at one renormalization point where the couplings are related so that the symmetry is restored. We study here the one loop renormalization of a prototypical example, the Littlest Higgs Model. Some features of the renormalization of this model are novel, unfamiliar form similar chiral Lagrangian studies.
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arxiv:1011.0682
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We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose a time delay and an action, and the action with the shorter delay is chosen. To prevent a player from winning by blocking time, we restrict each player to play strategies that ensure that the player cannot be responsible for causing a zeno run. First, we present an efficient reduction of these games to \emph{turn-based} (i.e., not concurrent) \emph{finite-state} (i.e., untimed) parity games. Our reduction improves the best known complexity for solving timed parity games. Moreover, the rich class of algorithms for classical parity games can now be applied to timed parity games. The states of the resulting game are based on clock regions of the original game, and the state space of the finite game is linear in the size of the region graph. Second, we consider two restricted classes of strategies for the player that represents the controller in a real-time synthesis problem, namely, \emph{limit-robust} and \emph{bounded-robust} winning strategies. Using a limit-robust winning strategy, the controller cannot choose an exact real-valued time delay but must allow for some nonzero jitter in each of its actions. If there is a given lower bound on the jitter, then the strategy is bounded-robust winning. We show that exact strategies are more powerful than limit-robust strategies, which are more powerful than bounded-robust winning strategies for any bound. For both kinds of robust strategies, we present efficient reductions to standard timed automaton games. These reductions provide algorithms for the synthesis of robust real-time controllers.
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arxiv:1011.0688
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A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of Hamiltonian systems defined on certain 3-dimensional (Riemannian) spaces. These two systems are shown to be either the Kepler or the oscillator potentials on the corresponding Bertrand spaces, and both of them are maximally superintegrable. Afterwards, the relationship between such Bertrand Hamiltonians and position-dependent mass systems is explicitly established. These results are illustrated through the example of a superintegrable (nonlinear) oscillator on a Bertrand-Darboux space, whose quantization and physical features are also briefly addressed.
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arxiv:1011.0708
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We study the Spectral Energy Distribution (SED) and the power spectrum of Galactic cirrus emission observed in the 14 deg^2 Science Demonstration Phase field of the Herschel-ATLAS using Herschel and IRAS data from 100 to 500 um. We compare the SPIRE 250, 350 and 500um maps with IRAS 100um emission, binned in 6' pixels. We assume a modified black-body SED with dust emissivity parameter beta (F ~ lambda^(-beta)) and a single dust temperature T_d, and find that the dust temperature and emissivity index varies over the science demonstration field as 10< T_rm < 25 K and 1 < beta< 4. The latter values are somewhat higher than the range of beta often quoted in the literature (1< beta< 2). We estimate the mean values of these parameters to be T_d=19.0 +/- 2.4 K and beta = 1.4 +/- 0.4. In regions of bright cirrus emission, we find that the dust has similar temperatures with T_d = 18.0 +/- 2.5 K, and similar values of beta, ranging from 1.4 +- 0.5 to 1.9+/- 0.5. We show that T_d and beta associated with diffuse cirrus emission are anti-correlated and can be described by the relationship: beta(T_d) = NT_d^alpha with [N=116+/-38, alpha=-1.4+/1 0.1]. The strong correlation found in this analysis is not just limited to high density clumps of cirrus emission as seen in previous studies, but is also seen in diffuse cirrus in low density regions. To provide an independent measure of $T_{\rm d}$ and $\beta$, we obtain the angular power spectrum of the cirrus emission in the {\it IRAS} and SPIRE maps, which is consistent with a power spectrum of the form P(k)=P_0(k/k_0)^gamma where gamma = \^a H R2.6+/-m 0.2 for scales of 50-200' in the SPIRE maps. The cirrus rms fluctuation amplitude at angular scales of 100' is consistent with a modified blackbody SED with T_d = 20.1+/- 0.9 K and beta = 1.3+/- 0.2, in agreement with the values obtained above.
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arxiv:1011.0725
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In this paper, we investigate three important issues: stability, ghost and strong coupling, in the Horava-Melby-Thompson setup of the Horava-Lifshitz theory with $\lambda \not= 1$, generalized recently by da Silva. We first develop the general linear scalar perturbations of the Friedmann-Robertson-Walker (FRW) universe with arbitrary spatial curvature, and find that an immediate by-product of the setup is that, in all the inflationary models described by a scalar field, the FRW universe is necessarily flat. Applying them to the case of the Minkowski background, we find that it is stable, and, similar to the case $\lambda = 1$, the spin-0 graviton is eliminated. The vector perturbations vanish identically in the Minkowski background. Thus, similar to general relativity, a free gravitational field in this setup is completely described by a spin-2 massless graviton even with $\lambda \not= 1$. We also study the ghost problem in the FRW background, and find explicitly the ghost-free conditions. To study the strong coupling problem, we consider two different kinds of spacetimes all with the presence of matter, one is cosmological and the one is static. We find that the coupling becomes strong for a process with energy higher than $M_{pl} |c_{\psi}|^{5/2}$ in the flat FRW background, and $M_{pl}|c_{\psi}|^{3}$ in a static weak gravitational field, where $|c_{\psi}| \equiv |(1-\lambda)/(3 \lambda -1)|^{1/2}$.
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arxiv:1011.0739
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We present results of high resolution (~ 55000) spectral observations of 830 photometrically pre-selected candidate red giants in the magnitude range of V = 9-12. We develop a pipeline for automated determination of the stellar atmospheric parameters from these spectra and estimate T_eff, logg, [Fe/H], microturbulence velocity, and projected rotational velocities, vsini, for the stars. The analysis confirms that the candidate selection procedure yielded red giants with very high success rate. We show that most of these stars are G and K giants with slightly subsolar metallicity ([Fe/H] ~ -0.3 dex) An analysis of Mg abundances in the sample results in consistency of the [Mg/Fe] vs [Fe/H] trend with published results.
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arxiv:1011.0744
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The effects of an intracavity photonic crystal in a multimode optical parametric oscillator are studied, with a special focus on quantum fluctuations. The capability to either stimulate or inhibit the spatial instability, lowering or increasing the parametric threshold, allows to control the intensity fluctuations and correlations. A significative quantum noise reduction and an increase of the range of squeezed quadratures are found above threshold where spatial Einstein-Podolsky-Rosen entanglement and inseparability are found.
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arxiv:1011.0844
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We have estimated the size of the light-shifts due to parity nonconservation (PNC) interactions in different isotopes of Ba+ and Ra+ ions based on the work of Fortson [Phys. Rev. Lett. 70, 2383 (1993)]. We have used the nuclear spin independent (NSI) amplitudes calculated earlier by us [Phys. Rev. Lett. 96, 163003 (2006); Phys. Rev. A 78, 050501(R) (2008)] and we have employed the third order many-body perturbation theory (MBPT(3)) in this work to estimate the nuclear spin dependent (NSD) amplitudes in these ions. Ra+ is found to be more favourable than Ba+ for measuring both the NSI and NSD PNC observables.
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arxiv:1011.0873
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We consider the asymptotic behaviour of finite energy solutions to the one-dimensional defocusing nonlinear wave equation $-u_{tt} + u_{xx} = |u|^{p-1} u$, where $p > 1$. Standard energy methods guarantee global existence, but do not directly say much about the behaviour of $u(t)$ as $t \to \infty$. Note that in contrast to higher-dimensional settings, solutions to the linear equation $-u_{tt} + u_{xx} = 0$ do not exhibit decay, thus apparently ruling out perturbative methods for understanding such solutions. Nevertheless, we will show that solutions for the nonlinear equation behave differently from the linear equation, and more specifically that we have the average $L^\infty$ decay $\lim_{T \to +\infty} \frac{1}{T} \int_0^T \|u(t)\|_{L^\infty_x(\R)}\ dt = 0$, in sharp contrast to the linear case. An unusual ingredient in our arguments is the classical Radamacher differentiation theorem that asserts that Lipschitz functions are almost everywhere differentiable.
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arxiv:1011.0949
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An interpretation of the ridge phenomenon found in pp collisions at 7 TeV is given in terms of enhancement of soft partons due to energy loss of semihard jets. A description of ridge formation in nuclear collisions can directly be extended to pp collisions, since hydrodynamics is not used, and azimuthal anisotropy is generated by semihard scattering. Both the p_T and multiplicity dependencies are well reproduced. Some suggestions are made about other observables.
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arxiv:1011.0965
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We give a recursion for the multivariate Rogers-Szeg\"o polynomials, along with another recursive functional equation, and apply them to compute special values. We also consider the sum of all $q$-multinomial coefficients of some fixed degree and length, and give a recursion for this sum which follows from the recursion of the multivariate Rogers-Szeg\"o polynomials, and generalizes the recursion for the Galois numbers. The sum of all $q$-multinomial coefficients of degree $n$ and length $m$ is the number of flags of length $m-1$ of subspaces of an $n$-dimensional vector space over a field with $q$ elements. We give a combinatorial proof of the recursion for this sum of $q$-multinomial coefficients in terms of finite vector spaces.
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arxiv:1011.0984
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The alpha induced scintillation of the wavelength shifter 1,1,4,4-tetraphenyl-1,3-butadiene (TPB) was studied to improve the understanding of possible surface alpha backgrounds in the DEAP dark matter search experiment. We found that vacuum deposited thin TPB films emit 882 +/-210 photons per MeV under alpha particle excitation. The scintillation pulse shape consists of a double exponential decay with lifetimes of 11 +/-5 ns and 275 +/-10ns.
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arxiv:1011.1012
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It is shown that the IIB matrix model compactified on a six-dimensional torus with a nontrivial topology can provide chiral fermions and matter content close to the standard model on our four-dimensional spacetime. In particular, generation number three is given by the Dirac index on the torus.
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arxiv:1011.1015
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We show that a general estimate in the $\dib$-Neumann problem implies a upper bound on the order of contact of a complex curve with the boundary and a lower bound on the rate of the Levi form of a bounded family of weights.
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arxiv:1011.1046
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Using a discrete-lattice approach, we calculate the conductance spectra between a normal metal and an s-wave Larkin-Ovchinnikov (LO) superconductor, with the junction interface oriented {\em along} the direction of the order-parameter (OP) modulation. The OP sign reversal across one single nodal line can induce a sizable number of zero-energy Andreev bound states around the nodal line, and a hybridized midgap-states band is formed amid a momentum-dependent gap as a result of the periodic array of nodal lines in the LO state. This band-in-gap structure and its anisotropic properties give rise to distinctive features in both the point-contact and tunneling spectra as compared with the BCS and Fulde-Ferrell cases. These spectroscopic features can serve as distinguishing signatures of the LO state.
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arxiv:1011.1089
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I present some applications of geometric flows in string theory and gravity. In some circumstances time evolution in string theory can be approximately identified with Ricci-flow parametric evolution of spatial sections. In four dimensions, homogeneous, self-dual, gravitational instantons of general relativity evolve in time exactly as geometric flows of homogeneous three-manifolds. For non-relativistic versions of gravity, this property persists in any dimension, under the assumption of detailed-balance condition.
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arxiv:1011.1106
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The strong coupling treatment of the Fr\"ohlich-type polaronic system, based on a canonical transformation and a standard Landau-Pekar type variational wave function, is applied to the polaronic system consisting of an impurity in a condensate. Within this approach the Relaxed Excited States are retrieved as a typical polaronic feature in the energy spectrum. For these states we calculate the corresponding effective mass and the minimal coupling constant required for them to occur. The present approach allows to derive approximate expressions for the transition energies between different Relaxed Excited States in a much simpler way than with the full Mori-Zwanzig approach, and with a good accuracy, which improves with increasing coupling. The transition energies obtained here can be used as the spectroscopic fingerprint for the experimental observation of Relaxed Excited States of impurities in a condensate.
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arxiv:1011.1150
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Jim Hannan is a professor who has lived an interesting life and one whose fundamental research in repeated games was not fully appreciated until late in his career. During his service as a meteorologist in the Army in World War II, Jim played poker and made weather forecasts. It is curious that his later research included strategies for repeated play that apply to selecting the best forecaster. James Hannan was born in Holyoke, Massachusetts on September 14, 1922. He attended St. Jerome's High School and in January 1943 received the Ph.B. from St. Michael's College in Colchester, Vermont. Jim enlisted in the US Army Air Force to train and serve as a meteorologist. This took him to army airbases in China by the close of the war. Following discharge from the army, Jim studied mathematics at Harvard and graduated with the M.S. in June 1947. To prepare for doctoral work in statistics at the University of North Carolina that fall, Jim went to the University of Michigan in the summer of 1947. The routine admissions' physical revealed a spot on the lung and the possibility of tuberculosis. This caused Jim to stay at Ann Arbor through the fall of 1947 and then at a Veterans Administration Hospital in Framingham, Massachusetts to have his condition followed more closely. He was discharged from the hospital in the spring and started his study at Chapel Hill in the fall of 1948. There he began research in compound decision theory under Herbert Robbins. Feeling the need for teaching experience, Jim left Chapel Hill after two years and short of thesis to take a three year appointment as an instructor at Catholic University in Washington, DC. When told that renewal was not coming, Jim felt pressure to finish his degree.
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arxiv:1011.1160
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The Andromeda galaxy (M31) hosts a central super-massive black hole (SMBH), known as M31$^\ast$, which is remarkable for its mass ($\sim$$10^8{\rm~M_\odot}$) and extreme radiative quiescence. Over the past decade, the Chandra X-ray observatory has pointed to the center of M31 $\sim$100 times and accumulated a total exposure of $\sim$900 ks. Based on these observations, we present an X-ray study of a highly variable source that we associate with M31$^\ast$ based on positional coincidence. We find that M31$^\ast$ remained in a quiescent state from late 1999 to 2005, exhibiting an average 0.5-8 keV luminosity $\lesssim$$10^{36}{\rm~ergs~s^{-1}}$, or only $\sim$$10^{-10}$ of its Eddington luminosity. We report the discovery of an outburst that occurred on January 6, 2006, during which M31$^\ast$ radiated at $\sim$$4.3\times10^{37}{\rm~ergs~s^{-1}}$. After the outburst, M31$^\ast$ entered a more active state that apparently lasts to the present, which is characterized by frequent flux variability around an average luminosity of $\sim$$4.8\times10^{36}{\rm~ergs~s^{-1}}$. These flux variations are similar to the X-ray flares found in the SMBH of our Galaxy (Sgr A$^\ast$), making M31$^\ast$ the second SMBH known to exhibit recurrent flares. Future coordinated X-ray/radio observations will provide useful constraints on the physical origin of the flaring emission and help rule out a possible stellar origin of the X-ray source.
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arxiv:1011.1224
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There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized, naturally emerging without any overarching designs on topological structure yet enabling efficient interactions among nodes. Here we show that the number of nodes and the density of connections in such self-organized networks exhibit a power law relationship. We examined the size and connection density of 47 self-organizing networks of various biological, social, and technological origins, and found that the size-density relationship follows a fractal relationship spanning over 6 orders of magnitude. This finding indicates that there is an optimal connection density in self-organized networks following fractal scaling regardless of their sizes.
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arxiv:1011.1228
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We construct four-dimensional covariant non-linear theories of massive gravity which are ghost-free in the decoupling limit to all orders. These theories resum explicitly all the nonlinear terms of an effective field theory of massive gravity. We show that away from the decoupling limit the Hamiltonian constraint is maintained at least up to and including quartic order in non-linearities, hence, excluding the possibility of the Boulware-Deser ghost up to this order. We also show that the same remains true to all orders in a similar toy-model.
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arxiv:1011.1232
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Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov-Smirnov and Cramer-von-Mises tests do not scale well as the dimensionality increases and provides no easy way to characterize the difference should it exist. In this work, we propose a theoretical framework for inference that addresses these challenges in the form of a prior for Bayesian nonparametric analysis. The new prior is constructed based on a random-partition-and-assignment procedure similar to the one that defines the standard optional P\'olya tree distribution, but has the ability to generate multiple random distributions jointly. These random probability distributions are allowed to "couple", that is to have the same conditional distribution, on subsets of the sample space. We show that this "coupling optional P\'olya tree" prior provides a convenient and effective way for both the testing of two sample difference and the learning of the underlying structure of the difference. In addition, we discuss some practical issues in the computational implementation of this prior and provide several numerical examples to demonstrate its work.
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arxiv:1011.1253
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We report the first measurement of the differential cross section on $\phi$-meson photoproduction from deuterium near the production threshold for a proton using the CLAS detector and a tagged-photon beam in Hall B at Jefferson Lab. The measurement was carried out by a triple coincidence detection of a proton, $K^+$ and $K^-$ near the theoretical production threshold of 1.57 GeV. The extracted differential cross sections $\frac{d\sigma}{dt}$ for the initial photon energy from 1.65-1.75 GeV are consistent with predictions based on a quasifree mechanism. This experiment establishes a baseline for a future experimental search for an exotic $\phi$-N bound state from heavier nuclear targets utilizing subthreshold/near-threshold production of $\phi$ mesons.
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arxiv:1011.1305
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In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where the current operator is also orthogonal to the set of conserved quantities associated with integrability but becomes itself conserved in the thermodynamic limit.
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arxiv:1011.1354
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The Interstellar Medium has a fractal structure, in the sense that gas and dust distribute in a hierarchical and self-similar manner. Stars in new-born cluster probably follow the same fractal patterns of their parent molecular clouds. Moreover, it seems that older clusters tend to distribute their stars with radial density profiles. Thus, it is expected that clusters form with an initial fractal distribution of stars that eventually evolves toward centrally concentrated distributions. Is this really the case? This simple picture on to the origin and early evolution of star clusters and associations is very far from being clearly understood. There can be both young clusters exhibiting radial patterns and evolved clusters showing fractal structure. Additionally, the fractal structure of some open clusters is very different from that of the Interstellar Medium in the Milky Way. Here we summarize and discuss observational and numerical evidences concerning this subject.
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arxiv:1011.1374
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We study a new family of "classical" orthogonal polynomials, here called big -1 Jacobi polynomials, which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with differential operators of Dunkl-type. These polynomials can be obtained from the big $q$-Jacobi polynomials in the limit $q \to -1$. An explicit expression of these polynomials in terms of Gauss' hypergeometric functions is found. The big -1 Jacobi polynomials are orthogonal on the union of two symmetric intervals of the real axis. We show that the big -1 Jacobi polynomials can be obtained from the Bannai-Ito polynomials when the orthogonality support is extended to an infinite number of points. We further indicate that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for $q \to -1$.
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arxiv:1011.1429
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We have studied the interactions of the scalar resonances f_0(980) and a_0(980) with the vector resonance \phi(1020) and with the lightest pseudoscalars \pi, K, \eta and \eta'. We first obtain the interaction kernels without including any new free parameter. Afterwards, the interaction kernels are unitarized and the final S-wave amplitudes result. We find that these interactions are very rich and generate a large amount of pseudoscalar resonances including the K(1460), \pi(1300), \pi(1800), \eta(1475) and X(1835) resonances. The f_0(980)\phi(1020) self-interactions give rise to the \phi(2170) resonance. For realistic choices of the parameters we also obtain an isovector companion in the same mass region from the a_0(980) \phi(1020) interactions.
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arxiv:1011.1448
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We analyze the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-Sivashinsky (KS) equation in a regime close to the instability onset. We show that when the noise is highly degenerate, in the sense that it acts only on the first stable mode, the solution of the KS equation undergoes several transitions between different states, including a critical on-off intermittent state that is eventually stabilized as the noise strength is increased. Such noise-induced transitions can be completely characterized through critical exponents, obtaining that both the KS and the noisy Burgers equation belong to the same universality class. The results of our numerical investigations are explained rigorously using multiscale techniques.
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arxiv:1011.1481
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The confined, quasi-two-dimensional guiding center plasma and a system of interacting line vortices in an ideal fluid are examples of Hamiltonian systems with infinite interaction distances. The existence of metastable states with negative specific is investigated by standard entropy maximization of the thermodynamic limit of vortices as they become infinitesimal and form a continuous field. We find metastable states and suggest that these imply a runaway reaction leading to a rapid expansion of a confined plasma or fluid similar to the rapid collapse of globular clusters in astrophysics.
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arxiv:1011.1535
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Random linear systems over the Galois Field modulo 2 have an interest in connection with problems ranging from computational optimization to complex networks. They are often approached using random matrices with Poisson-distributed or finite column/row-sums. This technical note considers the typical rank of random matrices belonging to a specific ensemble wich has genuinely power-law distributed column-sums. For this ensemble, we find a formula for calculating the typical rank in the limit of large matrices as a function of the power-law exponent and the shape of the matrix, and characterize its behavior through "phase diagrams" with varying model parameters.
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arxiv:1011.1563
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Much effort is spent everyday by programmers in trying to reduce long, failing execution traces to the cause of the error. We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem (MAX-SAT), which asks what is the maximum number of clauses of a Boolean formula that can be simultaneously satisfied by an assignment. At an intuitive level, our algorithm takes as input a program and a failing test, and comprises the following three steps. First, using symbolic execution, we encode a trace of a program as a Boolean trace formula which is satisfiable iff the trace is feasible. Second, for a failing program execution (e.g., one that violates an assertion or a post-condition), we construct an unsatisfiable formula by taking the trace formula and additionally asserting that the input is the failing test and that the assertion condition does hold at the end. Third, using MAX-SAT, we find a maximal set of clauses in this formula that can be satisfied together, and output the complement set as a potential cause of the error. We have implemented our algorithm in a tool called bug-assist for C programs. We demonstrate the surprising effectiveness of the tool on a set of benchmark examples with injected faults, and show that in most cases, bug-assist can quickly and precisely isolate the exact few lines of code whose change eliminates the error. We also demonstrate how our algorithm can be modified to automatically suggest fixes for common classes of errors such as off-by-one.
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arxiv:1011.1589
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Comment on "Event Excess in the MiniBooNE Search for $\bar \nu_{\mu}\rightarrow \bar \nu_e$ Oscillations"
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arxiv:1011.1600
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Based on analysis of the annual averaged relative sunspot number (ASN) during 1700 -- 2009, 3 kinds of solar cycles are confirmed: the well-known 11-yr cycle (Schwabe cycle), 103-yr secular cycle (numbered as G1, G2, G3, and G4, respectively since 1700); and 51.5-yr Cycle. From similarities, an extrapolation of forthcoming solar cycles is made, and found that the solar cycle 24 will be a relative long and weak Schwabe cycle, which may reach to its apex around 2012-2014 in the vale between G3 and G4. Additionally, most Schwabe cycles are asymmetric with rapidly rising-phases and slowly decay-phases. The comparisons between ASN and the annual flare numbers with different GOES classes (C-class, M-class, X-class, and super-flare, here super-flare is defined as $\geq$ X10.0) and the annal averaged radio flux at frequency of 2.84 GHz indicate that solar flares have a tendency: the more powerful of the flare, the later it takes place after the onset of the Schwabe cycle, and most powerful flares take place in the decay phase of Schwabe cycle. Some discussions on the origin of solar cycles are presented.
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arxiv:1011.1613
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We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein--Yang-Mills--Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordstrom solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. In addition a solution in closed form describing an extremal black hole with non-Abelian hair is found for a special value of the Chern-Simons coupling constant.
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arxiv:1011.1624
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We discuss various sources of azimuthal correlations in relativistic heavy-ion collisions. The integral measure Phi is applied to quantify the correlations. We first consider separately the correlations caused by the elliptic flow, resonance decays, jets and transverse momentum conservation. An effect of randomly lost particles is also discussed. Using the PYTHIA and HIJING event generators we produce a sample of events which mimic experimental data. By means of kinematic cuts and particle's selection criteria, the data are analyzed to identify a dominant source of correlations.
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arxiv:1011.1631
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We represent and analyze the general solution of the sixth Painleve transcendent in the Picard-Hitchin-Okamoto class in the Painleve form as the logarithmic derivative of the ratio of certain $\tau$-functions. These functions are expressible explicitly in terms of the elliptic Legendre integrals and Jacobi $\theta$-functions, for which we write the general differentiation rules. We also establish a relation between the P6-equation and the uniformization of algebraic curves and present examples.
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arxiv:1011.1641
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We study the effect of a potential fourth quark generation on the upper and lower Higgs boson mass bounds. This investigation is based on the numerical evaluation of a chirally invariant lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model. In particular, the considered model obeys a Ginsparg-Wilson version of the underlying ${SU}(2)_L\times {U}(1)_Y$ symmetry, being a global symmetry here due to the neglection of gauge fields in this model. We present our results on the modification of the upper and lower Higgs boson mass bounds induced by the presence of a hypothetical very heavy fourth quark doublet. Finally, we compare these findings to the standard scenario of three fermion generations.
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arxiv:1011.1648
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In this paper, the author discusses the eigenvalues and entropies under the harmonic-Ricci flow, which is the Ricci flow coupled with the harmonic map flow. We give an alternative proof of results for compact steady and expanding harmonic-Ricci breathers. In the second part, we derive some monotonicity formulas for eigenvalues of Laplacian under the harmonic-Ricci flow. Finally, we obtain the first variation of the shrinker and expanding entropies of the harmonic-Ricci flow.
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arxiv:1011.1697
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Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being a special case of limited dependent data, the models also apply to variables that are a fraction or a proportion. It is shown how to fit these models and they are applied to a Loss Given Default dataset from insurance to which they provide a good fit.
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arxiv:1011.1796
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We calculate the asymmetries in parity nonconserving deuteron photodisintegration due to circularly polarized photons gamma+d to n+p with the photon laboratory energy ranging from the threshold up to 10 MeV and the radiative capture of thermal polarized neutrons by protons n+p to gamma+d. We use the leading order electromagnetic Hamiltonian neglecting the smaller nuclear exchange currents. Comparative calculations are done by using the Reid93 and Argonne v18 potentials for the strong interaction and the DDH and FCDH "best" values for the weak couplings in a weak one-meson exchange potential. A weak NDelta transition potential is used to incorporate also the Delta(1232)-isobar excitation in the coupled-channels formalism.
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arxiv:1011.1807
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We investigate the conditions on the Higgs sector that allow supersymmetric SO(10) grand unified theories (GUT) to break spontaneously to the standard electroweak model (SM) at the renormalizable level. If one considers Higgs representations of dimension up to the adjoint, a supersymmetric standard model vacuum requires in most cases the presence of non-renormalizable (NR) operators. The active role of Planck induced NR operators in the breaking of the gauge symmetry introduces a hierarchy in the mass spectrum at the GUT scale that may be an issue for gauge unification and proton decay. We show that the minimal Higgs scenario that allows for a renormalizable breaking to the SM is obtained by considering flipped $SO(10) \otimes U(1)$ with one adjoint ($45_H$) and two pairs of $16_H \oplus \bar{16}_H$ Higgs representations. We consider a non-anomalous matter content and discuss the embedding of the model in an $E_6$ grand unified scenario just above the flipped SO(10) scale.
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arxiv:1011.1821
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The transition quadrupole moments, $Q_{\rm t}$, of four weakly populated collective bands up to spin $\sim$ $65\hbar$ in $^{157,158}$Er have been measured to be ${\sim}11 {\rm eb}$ demonstrating that these sequences are associated with large deformations. However, the data are inconsistent with calculated values from cranked Nilsson-Strutinsky calculations that predict the lowest energy triaxial shape to be associated with rotation about the short principal axis. The data appear to favor either a stable triaxial shape rotating about the intermediate axis or, alternatively, a triaxial shape with larger deformation rotating about the short axis. These new results challenge the present understanding of triaxiality in nuclei.
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arxiv:1011.1836
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We report evidence of a fully established galaxy cluster at z=2.07, consisting of a ~20sigma overdensity of red, compact spheroidal galaxies spatially coinciding with extended X-ray emission detected with XMM-Newton. We use VLT VIMOS and FORS2 spectra and deep Subaru, VLT and Spitzer imaging to estimate the redshift of the structure from a prominent z=2.07 spectroscopic redshift spike of emission-line galaxies, concordant with the accurate 12-band photometric redshifts of the red galaxies. Using NICMOS and Keck AO observations, we find that the red galaxies have elliptical morphologies and compact cores. While they do not form a tight red sequence, their colours are consistent with that of a >1.3$~Gyr population observed at z~2.1. From an X-ray luminosity of .2*10^43 erg s^-1 and the stellar mass content of the red galaxy population, we estimate a halo mass of 5.3-8*10^13 Msun, comparable to the nearby Virgo cluster. These properties imply that this structure could be the most distant, mature cluster known to date and that X-ray luminous, elliptical-dominated clusters are already forming at substantially earlier epochs than previously known.
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arxiv:1011.1837
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Air pollution is a great concern because of its impact on human health and on the environment. Statistical models play an important role in improving knowledge of this complex spatio-temporal phenomenon and in supporting public agencies and policy makers. We focus on the class of hierarchical models that provides a flexible framework for incorporating spatio-temporal interactions at different hierarchical levels. The challenge is to choose a model that is satisfactory in terms of goodness of fit, interpretability, parsimoniousness, prediction capability and computational costs. In order to support this choice, we propose a comparison approach based on a set of criteria summarized in a table that can be easily communicated to non-statisticians. Our proposal - simple in principle but articulated in practice - holds true for many environmental phenomena where a hierarchical structure is suitable, a large-scale trend is included and a spatio-temporal covariance function has to be chosen. We illustrate the details of our proposal through a case study concerning particulate matter concentrations in Piemonte region (Italy) during the cold season October 2005-March 2006. From the evaluation of the proposed criteria for our case study we draw some conclusions. First, a model with a complex hierarchical structure is globally preferable to one with a complex spatio-temporal covariance function. Moreover, in the absence of suitable computational resources, a model simple in structure and with a simple covariance function can be chosen, since it shows good prediction performance at reasonable computational costs.
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arxiv:1011.1845
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Quasars that allow the study of IGM He II are very rare, since they must be at high redshift along sightlines free of substantial hydrogen absorption, but recent work has dramatically expanded the number of such quasars known. We analyze two dozen higher-redshift (z=3.1-3.9) low-resolution He II quasar spectra from HST and find that their He II Gunn-Peterson troughs suggest exclusion of very early and very late reionization models, favoring a reionization redshift of z~3. Although the data quality is not sufficient to reveal details such as the expected redshift evolution of helium opacity, we obtain the first ensemble measure of helium opacity at high redshift averaged over many sightlines: tau=4.90 at z~3.3. We also find that it would be very difficult to observe the IGM red wing of absorption from the beginning of He II reionization, but depending on the redshift of reionization and the size of ionization zones, it might be possible to do so in some objects with the current generation of UV spectrographs.
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arxiv:1011.1946
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