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Observations by the Large Area Telescope (LAT) on the \textit{Fermi} mission of diffuse $\gamma$-rays in a mid-latitude region in the third quadrant (Galactic longitude $l$ from $200\arcdeg$ to $260\arcdeg$ and latitude $| b |$ from $22\arcdeg$ to $60\arcdeg$) are reported. The region contains no known large molecular cloud and most of the atomic hydrogen is within 1 kpc of the solar system. The contributions of $\gamma$-ray point sources and inverse Compton scattering are estimated and subtracted. The residual $\gamma$-ray intensity exhibits a linear correlation with the atomic gas column density in energy from 100 MeV to 10 GeV. The measured integrated $\gamma$-ray emissivity is $(1.63 \pm 0.05) \times 10^{-26} {\rm photons s^{-1} sr^{-1} H\mathchar`-atom^{-1}}$ and $(0.66 \pm 0.02) \times 10^{-26} {\rm photons s^{-1} sr^{-1} H\mathchar`-atom^{-1}}$ above 100 MeV and above 300 MeV, respectively, with additional systematic error of $\sim 10%$. The differential emissivity in 100 MeV--10 GeV agrees with calculations based on cosmic ray spectra consistent with those directly measured, at the 10% level. The results obtained indicate that cosmic ray nuclei spectra within 1 kpc from the solar system in regions studied are close to the local interstellar spectra inferred from direct measurements at the Earth within $\sim 10%$.
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arxiv:0908.1171
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We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre functor of a finite dimensional triangular algebra A has always a lift, up to shift, to a product of suitably defined reflection functors in the category of perfect complexes over the trivial extension algebra of A.
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arxiv:0908.1218
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We consider data transmission through a time-selective, correlated (first-order Markov) Rayleigh fading channel subject to an average power constraint. The channel is estimated at the receiver with a pilot signal, and the estimate is fed back to the transmitter. The estimate is used for coherent demodulation, and to adapt the data and pilot powers. We explicitly determine the optimal pilot and data power control policies in a continuous-time limit where the channel state evolves as an Ornstein-Uhlenbeck diffusion process, and is estimated by a Kalman filter at the receiver. The optimal pilot policy switches between zero and the maximum (peak-constrained) value (``bang-bang'' control), and approximates the optimal discrete-time policy at low Signal-to-Noise Ratios (equivalently, large bandwidths). The switching boundary is defined in terms of the system state (estimated channel mean and associated error variance), and can be explicitly computed. Under the optimal policy, the transmitter conserves power by decreasing the training power when the channel is faded, thereby increasing the data rate. Numerical results show a significant increase in achievable rate due to the adaptive training scheme with feedback, relative to constant (non-adaptive) training, which does not require feedback. The gain is more pronounced at relatively low SNRs and with fast fading. Results are further verified through Monte Carlo simulations.
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arxiv:0908.1264
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We have investigated the initial growth of Fe on GaAs(110) by means of density functional theory. In contrast to the conventionally used (001)-surface the (110)-surface does not reconstruct. Therefore, a flat interface and small diffusion can be expected, which makes Fe/GaAs(110) a possible candidate for spintronic applications. Since experimentally, the actual quality of the interface seems to depend on the growth conditions, e.g., on the flux rate, we simulate the effect of different flux rates by different Fe coverages of the semiconductor surface. Systems with low coverages are highly diffusive. With increasing amount of Fe, i.e., higher flux rates, a flat interface becomes more stable. The magnetic structure strongly depends on the Fe coverage but no quenching of the magnetic moments is observed in our calculations.
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arxiv:0908.1282
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The application of photonics to astronomy offers major advantages in the area of highly-multiplexed spectroscopy, especially when applied to extremely large telescopes. These include the suppression of the near-infrared night-sky spectrum [J. Bland-Hawthorn et al, Opt. Express 12, 5902 (2004), S. G. Leon-Saval et al, Opt. Lett. 30, 2545 (2005)] and the miniaturisation of spectrographs so that they may integrated into the light-path of individual spatial samples [J. Bland-Hawthorn et al, Proc SPIE 6269, 62690N (2006)]. Efficient collection of light from the telescope requires multimode optical fibres and three-dimensional photonic devices. We propose ultrafast laser inscription (ULI) [R. R. Thomson et al, Opt. Express 15, 11691 (2007)] as the best technology to fabricate 3D photonic devices for astrophotonic applications.
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arxiv:0908.1325
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We compute the numbers g(n,2,2) of nilpotent groups of order n, of class at most 2 generated by at most 2 generators, by giving an explicit formula for the Dirichlet generating function \sum_{n=1}^\infty g(n,2,2)n^{-s}.
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arxiv:0908.1355
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In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact manifold with boundary and the case of a closed manifold pair. This approach also gives a possibility to construct the obstruction groups for natural maps of various structure sets and to investigate their properties.
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arxiv:0908.1372
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The determination of the stiffness center of a machine tool is a major element for knowing the dynamic behavior of this one. This stiffness center can be obtained from a static characterization of the machine tool. For an operation of turning, we present an experimental protocol to determine the stiffness matrix, then by inversion, the associated flexibility matrix. This step makes it possible to establish the privileged directions of the movement associated with the maximum and minimal stiffness as well as the stiffness center. Through this step, it is observed that, at the time of an operation of turning, the movement of the point of the tool is carried out according to an ellipse located in a tilted average plan compared to the machine spindle. This movement is linked with the self-excited vibrations. This analysis could be exploited and transposed in the case of the High Speed Machining. It will make it possible to predict various aspects of machining related to the behavior of the tool in the process of cut.
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arxiv:0908.1373
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We show that for any rational p \in [1,\infty) except p = 1, 2, unless P = NP, there is no polynomial-time algorithm for approximating the matrix p-norm to arbitrary relative precision. We also show that for any rational p\in [1,\infty) including p = 1, 2, unless P = NP, there is no polynomial-time algorithm approximates the \infty, p mixed norm to some fixed relative precision.
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arxiv:0908.1397
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On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that for the Schr\"odinger operator $\Delta +V$ with potential $V\in C^{1,\alpha}(M_0)$ for some $\alpha>0$, the Dirichlet-to-Neumann map $N|_{\Gamma}$ measured on an open set $\Gamma\subset \partial M_0$ determines uniquely the potential $V$. We also discuss briefly the corresponding consequences for potential scattering at 0 frequency on Riemann surfaces with asymptotically Euclidean or asymptotically hyperbolic ends.
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arxiv:0908.1417
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In this paper, by the method of moving planes, we prove the symmetry result which says that classical solutions of Monge-Ampere system in the whole plane are symmetric about some point. Our system under consideration comes from the differential geometry problem.
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arxiv:0908.1428
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We study the effects of clouds on the dynamical and chemical evolution of gas-rich dwarf galaxies, in particular focusing on two model galaxies similar to IZw18 and NGC1569. We consider both scenarios, clouds put at the beginning of the simulation and continuously created infalling ones. Due to dynamical processes and thermal evaporation, the clouds survive only a few tens of Myr, but during this time they act as an additional cooling agent and the internal energy of cloudy models is typically reduced by 20 - 40% in comparison with models without clouds. The clouds delay the development of large-scale outflows, therefore helping to retain a larger amount of gas inside the galaxy. However, especially in models with continuous creation of infalling clouds, their bullet effect can pierce the expanding supershell and create holes through which the superbubble can vent freshly produced metals. Moreover, assuming a pristine chemical composition for the clouds, their interaction with the superbubble dilutes the gas, reducing the metallicity (by up to ~ 0.4 dex) with respect to the one attained by diffuse models.
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arxiv:0908.1478
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The elastic properties of hcp $^4$He samples have been investigated using low frequency (20 Hz to 20 kHz) high sensitivity sound transducers. In agreement with the findings of other workers, most samples studied grew very significantly stiffer at low temperature; Poisson's ratio $\nu$ was observed to increase from 0.28 below 20 mK to $\sim 0.35$ at 0.7 K. The span of the variation of $\nu$ varies from sample to sample according to their thermal and mechanical history. Crystals carefully grown at the melting curve show a different behavior, the change in $\nu$ taking place at lower $T$ and being more abrupt.
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arxiv:0908.1480
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We introduce a fundamental concept -- closed sets of correlations -- for studying non-local correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum non-locality is limited, and for finding constraints on physical theories beyond quantum mechanics.
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arxiv:0908.1496
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In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators $m-(m^{2/\alpha}-\Delta)^{\alpha/2}$] in $C^{1,1}$ open sets. Here $m>0$ and $\alpha\in(0,2)$. The estimates are uniform in $m\in(0,M]$ for each fixed $M>0$. Letting $m\downarrow0$, we recover the Dirichlet heat kernel estimates for $\Delta^{\alpha/2}:=-(-\Delta)^{\alpha/2}$ in $C^{1,1}$ open sets obtained in [14]. Sharp two-sided estimates are also obtained for Green functions of relativistic stable processes in bounded $C^{1,1}$ open sets.
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arxiv:0908.1509
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Using numerical simulations we examine the velocity fluctuations of a probe particle driven with constant force through a two-dimensional disordered assembly of disks which has a well-defined jamming point J at a density of \phi_J=0.843. As \phi increases toward \phi_J, the average velocity of the probe particle decreases and the velocity fluctuations show an increasingly intermittent or avalanchelike behavior. When the system is within a few percent of the jamming density, the velocity distributions are exponential, while when the system is less than a percent away from jamming, the velocity distributions have a non-exponential or power law character. The velocity power spectra exhibit a crossover from a Lorentzian form to a 1/f shape near jamming. We extract a correlation exponent \nu which is in good agreement with recent shear simulations. For \phi > \phi_J, there is a critical threshold force F_c that must be applied for the probe particle to move through the sample which increases with increasing \phi. The onset of the probe motion above \phi_J occurs via a local yielding of the particles around the probe particle which we term a local shear banding effect.
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arxiv:0908.1592
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Motivated by recent experiments\cite{BA}\cite{BB}, we study quasi 2D ferromagnetic condensates with various aspect ratios. We find that in zero magnetic field, dipolar energy generates a local energy minimum with all the spins lie in the 2D plane forming a row of {\em circular} spin textures with {\em alternating} orientation, corresponding to a packing of vortices of {\em identical} vorticity in different spin components. In a large magnetic field, the system can fall into a long lived dynamical state consisting of an array of elliptic and hyperbolic Mermin-Ho spin textures, while the true equilibrium is an uniaxial spin density wave with a single wave-vector along the magnetic field, and a wavelength similar to the characteristic length of the long lived vortex array state.
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arxiv:0908.1593
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An emergent Fermi surface in a Mott insulator, an exotic quantum spin liquid state, was suggested by Anderson in 1987. After a quick support for its existence in spin-half Heisenberg model in a square lattice in a RVB mean field theory, pseudo Fermi surface was found only recently in an exactly solvable spin-3/2 model by Yao, Zhang and Kivelson. We show that a minimal spin-half Kitaev model on a decorated square lattice exhibits a Fermi surface. Volume and shape of the Fermi surface change with exchange couplings or on addition of a 3 spin interaction terms.
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arxiv:0908.1614
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We study limit shapes for dimer models on domains of the hexagonal lattice with free boundary conditions. This is equivalent to the large deviation phenomenon for a random stepped surface over domains fixed only at part of the boundary.
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arxiv:0908.1630
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We present a reformulation of the inverse problem of the calculus of variations for time dependent systems of second order ordinary differential equations using the Fr\"olicher-Nijenhuis theory on the first jet bundle, $J^1\pi$. We prove that a system of time dependent SODE, identified with a semispray $S$, is Lagrangian if and only if a special class, $\Lambda^1_S(J^1\pi)$, of semi-basic 1-forms is not empty. We provide global Helmholtz conditions to characterize the class $\Lambda^1_S(J^1\pi)$ of semi-basic 1-forms. Each such class contains the Poincar\'e-Cartan 1-form of some Lagrangian function. We prove that if there exists a semi-basic 1-form in $\Lambda^1_S(J^1\pi)$, which is not a Poincar\'e-Cartan 1-form, then it determines a dual symmetry and a first integral of the given system of SODE.
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arxiv:0908.1631
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Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s > 0.07. For 0.02 < s < 0.07, we find that increasing the polydispersity at a given concentration slows down crystal nucleation. The main effect here is that polydispersity reduces the supersaturation since it tends to stabilise the fluid but to destabilise the crystal. At a given polydispersity (< 0.07) we find three regimes of nucleation: standard nucleation and growth at concentrations in and slightly above the coexistence region; "spinodal nucleation", where the free energy barrier to nucleation appears to be negligible, at intermediate concentrations; and, at the highest concentrations, a new mechanism, still to be fully understood, which only requires small re-arrangement of the particle positions. The cross-over between the second and third regimes occurs at a concentration, around 58% by volume, where the colloid experiments show a marked change in the nature of the crystals formed and the particle dynamics indicate an "ideal" glass transition.
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arxiv:0908.1663
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In this paper the linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 less than or equal to nu which is less than or equal to 1 . At the lower end, nu = 0, the equation represents an un-damped oscillator and at the upper end, nu = 1, the ordinary linearly damped oscillator equation is recovered. A solution is found analytically and a comparison with the ordinary linearly damped oscillator is made. It is found that there are nine distinct cases as opposed to the usual three for the ordinary equation (damped, over-damped, and critically damped). For three of these cases it is shown that the frequency of oscillation actually increases with increasing damping order before eventually falling to the limiting value given by the ordinary damped oscillator equation. For the other six cases the behavior is as expected, the frequency of oscillation decreases with increasing order of the derivative (damping term).
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arxiv:0908.1683
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We consider the motion of a collection of fluid loaded elastic plates, situated horizontally in an infinitely long channel. We use a new, unified approach to boundary value problems, introduced by A.S. Fokas in the late 1990s, and show the problem is equivalent to a system of 1-parameter integral equations. We give a detailed study of the linear problem, providing explicit solutions and well-posedness results in terms of standard Sobolev spaces. We show that the associated Cauchy problem is completely determined by a matrix, which depends solely on the mean separation of the plates and the horizontal velocity of each of the driving fluids. This matrix corresponds to the infinitesimal generator of the semigroup for the evolution equations in Fourier space. By analysing the properties of this matrix, we classify necessary and sufficient conditions for which the problem is asymptotically stable.
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arxiv:0908.1691
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An admissible estimator of the eigenvalues of the variance-covariance matrix is given for multivariate normal distributions with respect to the scale-invariant squared error loss.
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arxiv:0908.1701
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We investigated the bound state problem of the S wave charged $D_1 \bar{D}^*$ ($D_1' \bar{D}^*$) system in a chiral quark model by solving the resonating group method equation. Our preliminary study does not favor the molecular assumption of $Z^+(4430)$. On the contrary, if $Z^+(4430)$ is really a molecule, its partner with opposite $G$-parity should also exist and probably may be found in the $\pi^+\eta_c(2S)$, $J/\psi \pi^+\pi^0$, or $\psi'\pi^+\pi^0$ channel. For the bottom systems, we found the existence of both $I^G$=$1^+$ and $I^G$=$1^-$ $B_1 \bar{B}^*$ ($B_1' \bar{B}^*$) molecules is possible.
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arxiv:0908.1734
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We present arguments that show what the running of the cosmological constant means when quantum general relativity is formulated following the prescription developed by Feynman.
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arxiv:0908.1764
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If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy (TIRM), with femto-Newton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.
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arxiv:0908.1795
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Molecular electronics is a new, exciting and interdisciplinary field of research. The main concern of the subject is to exploit the organic materials in electronic and optoelectronic devices. On the other hand Langmuir-Blodgett (LB) film deposition technique is one of the best among few methods used to manipulate materials in molecular level. In this article LB film preparation technique has been discussed briefly with an emphasize of its application towards molecular electronics.
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arxiv:0908.1814
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We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper investigates the transition between the compressible and incompressible regions. To capture this transition, we study a one-dimensional Riemann problem and introduce a perturbation problem which regularizes the compressible-incompressible transition. Specific difficulties related to the non-conservativity of the problem are discussed.
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arxiv:0908.1817
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We construct stable configurations of n overlapping discs of radius r in a unit square, with r = O(1/n). By a result of Diaconis, Lebeau, and Michel, this result is best possible, up to a constant factor. A consequence is that the Metropolis algorithm, a well-studied Markov chain on the hardcore model, is not irreducible in this range of parameters.
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arxiv:0908.1830
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We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are $n^{1/\alpha}$-consistent and converge in distribution to the maximizer of a random function. The form of this limiting distribution is intractable, but the shape of the distribution for these estimators can be examined using the bootstrap procedure. The bootstrap is asymptotically valid under general conditions. The estimators for the parameters of the stable noise distribution have the traditional $n^{1/2}$ rate of convergence and are asymptotically normal. The behavior of the estimators for finite samples is studied via simulation, and we use maximum likelihood estimation to fit a noncausal autoregressive model to the natural logarithms of volumes of Wal-Mart stock traded daily on the New York Stock Exchange.
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arxiv:0908.1895
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We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the Curie-Weiss models. Under appropriate assumptions there exists a real number $\alpha$, a positive real number $\mu$, and a positive integer $k$ such that $(S_n- n \alpha)/n^{1 - 1/2k}$ converges weakly to a random variable with density proportional to $\exp(-\mu |x|^{2k} /(2k)!)$. We develop Stein's method for exchangeable pairs for a rich class of distributional approximations including the Gaussian distributions as well as the non-Gaussian limit distributions with density proportional to $\exp(-\mu |x|^{2k} /(2k)!)$. Our results include the optimal Berry-Esseen rate in the Central Limit Theorem for the total magnetization in the classical Curie-Weiss model, for high temperatures as well as at the critical temperature $\beta_c=1$, where the Central Limit Theorem fails. Moreover, we analyze Berry-Esseen bounds as the temperature $1/ \beta_n$ converges to one and obtain a threshold for the speed of this convergence. Single spin distributions satisfying the Griffiths-Hurst-Sherman (GHS) inequality like models of liquid helium or continuous Curie-Weiss models are considered.
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arxiv:0908.1909
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Obtaining the rest mass of leptons with electric charge minus 1 is pursued by considering the existence of a medium made up of sub-quantum particles, called etherons, having a rest energy at the lowest limit which is possible in the Universe. This medium is assumed to have a periodic structure, that generates zones of allowed and forbidden energy. The basic assumption consists in considering the photon interaction with this hypothetical medium to be similar with the interaction of the electrons with the particles of a crystalline lattice. It is further assumed that an inverse particle-antiparticle annihilation process in the presence of the periodical sub-quantum field generates the particles of the Universe. The quantization of the photons in this sub-quantum lattice is achieved with the help of the operator of the square of the energy and a well-known formula of F. Bloch has been further used to empirically fix the lattice parameters. The rest energy of fundamental particles would correspond to zones of allowed energy.
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arxiv:0908.1945
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We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization (in the sense of Schofield) of R at a set of finitely presented modules of projective dimension one. We then investigate tilting modules arising from universal localization. Furthermore, we discuss the relationship between universal localization and the localization given by a perfect Gabriel topology. Finally, we give some applications to Artin algebras and to Pruefer domains.
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arxiv:0908.1985
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We study connections between recollements of the derived category D(Mod-R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature. Secondly, we show how to construct a recollement from a tilting module of projective dimension one. Our results will be employed in a forthcoming paper in order to investigate stratifications of D(Mod-R).
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arxiv:0908.1988
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Using the semi-classical method of Nikishov-Ritus (NR), the derivation of the transition rate of the beamstrahlung process is reviewed. This method uses the Bound Interaction Picture and the exact solutions of the Dirac equation in the external field potential. For future linear colliders, the nominal machine parameters are such that this external field can be considered to be a constant crossed electromagnetic field. The Dirac equation solutions can be Fourier transformed such that they are functions of Dirac gamma matrices, Airy functions and the usual non-external field solution. The resultant analytic form for the transition rate is the same as that obtained by the Quasiclassical Operator (QO) method of Baier-Katkov which sets a limit of ultra-relativistic electron and vanishingly small radiation angle. The NR calculation however also exhibits a pole in the radiation angle for back-radiated photons. The removal of this pole requires a further study of IR divergences within the Bound Interaction Picture.
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arxiv:0908.2075
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In this work we present scanning Fabry-Perot H$\alpha$ observations of the isolated interacting galaxy pair NGC 5278/79 obtained with the PUMA Fabry-Perot interferometer. We derived velocity fields, various kinematic parameters and rotation curves for both galaxies. Our kinematical results together with the fact that dust lanes have been detected in both galaxies, as well as the analysis of surface brightness profiles along the minor axis, allowed us to determine that both components of the interacting pair are trailing spirals.
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arxiv:0908.2109
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We present high resolution spectroscopy in the [\ion{O}{3}]$\lambda$5007 and H$\alpha$ lines of bright planetary nebulae in the Milky Way bulge and the dwarf galaxies M32, Fornax, Sagittarius, and NGC 6822 obtained at the Observatorio Astronomico Nacional in the Sierra San Pedro Martir using the Manchester Echelle Spectrograph. We use the high signal-to-noise (S/N) observations of Milky Way bulge planetary nebulae to explore what kinematic information can be determined reliably when observing extragalactic planetary nebulae in the [\ion{O}{3}]$\lambda$5007 line at modest S/N. We find that the intrinsic line widths measured in [\ion{O}{3}]$\lambda$5007 and H$\alpha$ are very similar. Over the range of S/N available in this sample, the line width we measure is independent of the S/N. Finally, deviations from a Gaussian line shape are small. Thus, the line width of the [\ion{O}{3}]$\lambda$5007 line in bright extragalactic planetary nebulae should reflect the kinematics of most of the mass in the ionized nebular shell.
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arxiv:0908.2111
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Here we show that Iapetus can serve to discriminate between satellite formation models. Its accretion history can be understood in terms of a two-component gaseous subnebula, with a relatively dense inner region, and an extended tail out to the location of the irregular satellites, as in the SEMM model of Mosqueira and Estrada (2003a,b). Following giant planet formation, planetesimals in the feeding zone of Jupiter and Saturn become dynamically excited, and undergo a collisional cascade. Ablation and capture of planetesimal fragments crossing the gaseous circumplanetary disks delivers enough collisional rubble to account for the mass budgets of the regular satellites of Jupiter and Saturn. This process can result in rock/ice fractionation provided the make up of the population of disk crossers is non-homogeneous, thus offering a natural explanation for the marked compositional differences between outer solar nebula objects and those that accreted in the subnebulae of the giant planets. Consequently, our model leads to an enhancement of the ice content of Iapetus, and to a lesser degree those of Ganymede, Titan and Callisto, and accounts for the (non-stochastic) compositions of these large, low-porosity outer regular satellites of Jupiter and Saturn. (abridged)
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arxiv:0908.2112
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Motivated by the result that an `approximate' evaluation of the Jones polynomial of a braid at a $5^{th}$ root of unity can be used to simulate the quantum part of any algorithm in the quantum complexity class BQP, and results relating BQP to the counting class GapP, we introduce a form of additive approximation which can be used to simulate a function in BQP. We show that all functions in the classes #P and GapP have such an approximation scheme under certain natural normalisations. However we are unable to determine whether the particular functions we are motivated by, such as the above evaluation of the Jones polynomial, can be approximated in this way. We close with some open problems motivated by this work.
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arxiv:0908.2122
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We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV equation in the presence of weak dissipative disorder in the linear growth/damping term. With the weak disorder in the system, the amplitude of solitary wave randomly fluctuates during evolution. We demonstrate numerically that the probability density function of a solitary wave parameter $\kappa$ which characterizes the soliton amplitude exhibits loglognormal divergence near the maximum possible $\kappa$ value.
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arxiv:0908.2152
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We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate the Whitehead groups of the Iwasawa algebra and its canonical Ore localisation by using Oliver-Taylor's theory upon integral logarithms. This calculation reduces the existence of the non-commutative p-adic zeta function to certain congruence conditions among abelian p-adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne-Ribet's theory and certain inductive technique. As an application we shall prove a special case of (the p-part of) the non-commutative equivariant Tamagawa number conjecture for critical Tate motives. The main results of this paper give generalisation of those of the preceding paper of the author.
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arxiv:0908.2178
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Effective field theory (EFT) has been recently used for the calculation of neutron-deuteron radiative capture at very low energies.We present here the use of EFT to calculate the two-body photodisintegration of the triton, considering the three-body force. The calculated cross section shows sharp rising from threshold to maximum about 0.88 mb at 13 MeV and decreasing slightly to about 0.81 mb at 19 MeV, in agreement with the experimental data. Our results are in good agreement with the experimental data and the other calculations using modern realistic two- and three-nucleon forces, like AV18/UrbanaIX potential.
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arxiv:0908.2220
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We explore short-distance static correlation functions in the infinite XXZ chain using previously derived formulae which represent the correlation functions in factorized form. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field in the massive regime $\Delta>1$, extending our previous results to the full parameter plane of the antiferromagnetic chain ($\Delta > -1$ and arbitrary field $h$). The factorized formulae are numerically efficient and allow for taking the isotropic limit ($\Delta = 1$) and the Ising limit ($\Delta = \infty$). At the critical field separating the fully polarized phase from the N\'eel phase, the Ising chain possesses exponentially many ground states. The residual entropy is lifted by quantum fluctuations for large but finite $\Delta$ inducing unexpected crossover phenomena in the correlations.
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arxiv:0908.2232
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Consider a fully connected network where up to $t$ processes may crash, and all processes start in an arbitrary memory state. The self-stabilizing firing squad problem consists of eventually guaranteeing simultaneous response to an external input. This is modeled by requiring that the non-crashed processes "fire" simultaneously if some correct process received an external "GO" input, and that they only fire as a response to some process receiving such an input. This paper presents FireAlg, the first self-stabilizing firing squad algorithm. The FireAlg algorithm is optimal in two respects: (a) Once the algorithm is in a safe state, it fires in response to a GO input as fast as any other algorithm does, and (b) Starting from an arbitrary state, it converges to a safe state as fast as any other algorithm does.
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arxiv:0908.2295
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Generic model predictions for the early neutrino signal of a core-collapse supernova (SN) imply that IceCube can reconstruct the bounce to within about +/- 3.5 ms at 95% CL (assumed SN distance 10 kpc), relevant for coincidence with gravitational-wave detectors. The timing uncertainty scales approximately with distance-squared. The offset between true and reconstructed bounce time of up to several ms depends on the neutrino flavor oscillation scenario. Our work extends the recent study of Pagliaroli et al. [PRL 103, 031102 (2009)] and demonstrates IceCube's superb timing capabilities for neutrinos from the next nearby SN.
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arxiv:0908.2317
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Inspired by our earlier work on Automatic Repeat reQuest (ARQ) secrecy, we propose a simple, yet efficient, security overlay protocol to existing 802.11 networks. Our work targets networks secured by the Wired Equivalent Privacy (WEP) protocol because of its widespread use and vulnerability to a multitude of security threats. By exploiting the existing ARQ protocol in the 802.11 standard, our proposed opportunistic secrecy scheme is shown to defend against all known passive WEP attacks. Moreover, our implementation on the madwifi-ng driver is used to establish the achievability of a vanishing secrecy outage probability in several realistic scenarios.
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arxiv:0908.2328
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The GOES X1.5 class flare that occurred on August 30,2002 at 1327:30 UT is one of the few events detected so far at submillimeter wavelengths. We present a detailed analysis of this flare combining radio observations from 1.5 to 212 GHz (an upper limit of the flux is also provided at 405 GHz) and X-ray. Although the observations of radio emission up to 212 GHz indicates that relativistic electrons with energies of a few MeV were accelerated, no significant hard X-ray emission was detected by RHESSI above ~ 250 keV. Images at 12--20 and 50--100 keV reveal a very compact, but resolved, source of about ~ 10" x 10". EUV TRACE images show a multi-kernel structure suggesting a complex (multipolar) magnetic topology. During the peak time the radio spectrum shows an extended flatness from ~ 7 to 35 GHz. Modeling the optically thin part of the radio spectrum as gyrosynchrotron emission we obtained the electron spectrum (spectral index delta, instantaneous number of emitting electrons). It is shown that in order to keep the expected X-ray emission from the same emitting electrons below the RHESSI background at 250 keV, a magnetic field above 500 G is necessary. On the other hand, the electron spectrum deduced from radio observations >= 50 GHz is harder than that deduced from ~ 70 - 250 keV X-ray data, meaning that there must exist a breaking energy around a few hundred keV. During the decay of the impulsive phase, a hardening of the X-ray spectrum is observed which is interpreted as a hardening of the electron distribution spectrum produced by the diffusion due to Coulomb collisions of the trapped electrons in a medium with an electron density of n_e ~ 3E10 - 5E10 cm-3.
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arxiv:0908.2339
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In order to understand the source and extent of the greater-than-classical information processing power of quantum systems, one wants to characterize both classical and quantum mechanics as points in a broader space of possible theories. One approach to doing this, pioneered by Abramsky and Coecke, is to abstract the essential categorical features of classical and quantum mechanics that support various information-theoretic constraints and possibilities, e.g., the impossibility of cloning in the latter, and the possibility of teleportation in both. Another approach, pursued by the authors and various collaborators, is to begin with a very conservative, and in a sense very concrete, generalization of classical probability theory--which is still sufficient to encompass quantum theory--and to ask which "quantum" informational phenomena can be reproduced in this much looser setting. In this paper, we review the progress to date in this second programme, and offer some suggestions as to how to link it with the categorical semantics for quantum processes developed by Abramsky and Coecke.
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arxiv:0908.2352
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We present simultaneous operation of ten single-electron turnstiles leading to one order of magnitude increase in current level up to 100 pA. Our analysis of device uniformity and background charge stability implies that the parallelization can be made without compromising the strict requirements of accuracy and current level set by quantum metrology. In addition, we discuss how offset charge instability limits the integration scale of single-electron turnstiles.
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arxiv:0908.2357
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Surprising enhancement of the magnetic moments recently observed in dilute Co-Mn alloy clusters is explained using ab initio electronic structure calculations. The calculated magnetic moments generally agree with the reported experimental data. An equation for calculating the magnetic moments of the Co-Mn alloy clusters has been derived to correct the deviations predicted by the rigid-band model and the virtual bound states approximation. A strategy is proposed to obtain the ground-state structures of the Co-Mn clusters and it was also put to the test of the experiment.
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arxiv:0908.2358
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Arguably the best hope of understanding the tail end of the reionization of the intergalactic medium (IGM) at redshift z > 6 is through the detection and characterization of the Gunn-Peterson (GP) damping wing absorption of the IGM in bright quasar spectra. However, the use of quasar spectra to measure the IGM damping wing requires a model of the quasar's intrinsic Lyman-alpha emission line. Here we quantify the uncertainties in the intrinsic line shapes, and how those uncertainties affect the determination of the IGM neutral fraction. We have assembled a catalog of high-resolution HST spectra of the emission lines of unobscured low-redshift quasars, and have characterized the variance in the shapes of their lines. We then add simulated absorption from the high-redshift IGM to these quasar spectra in order to determine the corresponding uncertainties in reionization constraints using current and future samples of z > 6 quasar spectra. We find that, if the redshift of the Lyman-alpha emission line is presumed to coincide with the systemic redshift determined from metal lines, the inferred IGM neutral fraction is systematically biased to low values due to a systematic blueshift of the Lyman-alpha line relative to the metal lines. If a similar blueshift persists in quasars at z > 6, this bias strengthens previous claims of a significant neutral hydrogen fraction at z ~ 6. This technique is capable of making a robust distinction between a highly ionized (x_IGM ~ 10^-3) and a neutral (x_IGM = 1) IGM with even a few bright quasars.
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arxiv:0908.2374
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Multiple hard interactions of partons in the same p+p(\bar p) collision are a useful concept in the description of these collisions at collider energies. In particular, they play a crucial role for the understanding of the background (the so-called underlying event) in the reconstruction of jets. In nucleus-nucleus collisions multiple hard parton interactions and the corresponding production of mini-jets are expected to contribute significantly to the total particle multiplicity. In this article a brief overview of results on particle production at high-pT in proton-proton and nucleus-nucleus at RHIC will be given. Moreover, the observed centrality dependence of the charged particle multiplicity in Au+Au collisions will be discussed in light of multiple partonic interactions.
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arxiv:0908.2377
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Let $\mathbb{F}_q$ be a finite field with $q$ elements, where $q$ is the power of an odd prime, and let $\mathrm{GSp}(2n, \mathbb{F}_q)$ and $\mathrm{GO}^{\pm}(2n, \mathbb{F}_q)$ denote the symplectic and orthogonal groups of similitudes over $\mathbb{F}_q$, respectively. We prove that every real-valued irreducible character of $\mathrm{GSp}(2n, \mathbb{F}_q)$ or $\mathrm{GO}^{\pm}(2n, \mathbb{F}_q)$ is the character of a real representation, and we find the sum of the dimensions of the real representations of each of these groups. We also show that if $\boldsymbol{G}$ is a classical connected group defined over $\mathbb{F}_q$ with connected center, with dimension $d$ and rank $r$, then the sum of the degrees of the irreducible characters of $\boldsymbol{G}(\mathbb{F}_q)$ is bounded above by $(q+1)^{(d+r)/2}$. Finally, we show that if $\boldsymbol{G}$ is any connected reductive group defined over $\mathbb{F}_q$, for any $q$, the sum of the degrees of the irreducible characters of $\boldsymbol{G}(\FF_q)$ is bounded below by $q^{(d-r)/2}(q-1)^r$. We conjecture that this sum can always be bounded above by $q^{(d-r)/2}(q+1)^r$.
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arxiv:0908.2398
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We explore the relation between colour and specific star formation rate (derived from optical spectra obtained by SDSS DR4) of over 6,000 galaxies (M_r<=-20.5) in and around low redshift (z<0.12) clusters. Even though most red galaxies have little or no ongoing star formation, and most blue galaxies are currently forming stars, there are significant populations of red star-forming (SF) and blue passive galaxies. This paper examines various properties of galaxies belonging to the latter two categories. These properties include morphological parameters, internal extinction, spectral features such as EW(H_delta) and the 4000 ang break, and metallicity. Our analysis shows that the blue passive galaxies have properties very similar to their SF counterparts, except that their large range in EW(H_delta) indicates recent truncation of star formation. The red SF galaxies fall into two broad categories, one of them being massive galaxies in cluster cores dominated by an old stellar population, but with evidence of current star formation in the core. For the remaining red SF galaxies it is evident from various metallicity measures and mean stellar ages, that their colours result from the predominance of a metal-rich stellar population. The implication of the properties of these SF galaxies on environmental studies, like that of the Butcher-Oemler effect, is discussed.
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arxiv:0908.2434
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We consider parton showers based on radiation from QCD dipoles or `antennae'. These showers are built from 2->3 parton splitting processes. The question then arises of what functions replace the Altarelli-Parisi splitting functions in this approach. We give a detailed answer to this question, applicable to antenna showers in which partons carry definite helicity, and to both initial- and final-state emissions.
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arxiv:0908.2450
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We provide a new algorithm for the treatment of the noisy inversion of the Radon transform using an appropriate thresholding technique adapted to a well-chosen new localized basis. We establish minimax results and prove their optimality. In particular, we prove that the procedures provided here are able to attain minimax bounds for any $\mathbb {L}_p$ loss. It s important to notice that most of the minimax bounds obtained here are new to our knowledge. It is also important to emphasize the adaptation properties of our procedures with respect to the regularity (sparsity) of the object to recover and to inhomogeneous smoothness. We perform a numerical study that is of importance since we especially have to discuss the cubature problems and propose an averaging procedure that is mostly in the spirit of the cycle spinning performed for periodic signals.
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arxiv:0908.2514
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The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or shape complexity (i.e., the disequilibrium times the Shannon entropic power) of hydrogenic stationary states are investigated in both position and momentum spaces. First, it is shown that not only the Fisher information and the variance (then, the Cramer-Rao measure) but also the disequilibrium associated to the quantum-mechanical probability density can be explicitly expressed in terms of the three quantum numbers (n, l, m) of the corresponding state. Second, the three composite measures mentioned above are analytically, numerically and physically discussed for both ground and excited states. It is observed, in particular, that these configuration complexities do not depend on the nuclear charge Z. Moreover, the Fisher-Shannon measure is shown to quadratically depend on the principal quantum number n. Finally, sharp upper bounds to the Fisher-Shannon measure and the shape complexity of a general hydrogenic orbital are given in terms of the quantum numbers.
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arxiv:0908.2545
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A dual conformal symmetry, analogous to the dual conformal symmetry observed for the scattering amplitudes of N=4 Super Yang-Mills theory, is identified in the Regge limit of QCD. Combined with the original two-dimensional conformal symmetry of the theory, this dual symmetry can potentially explain the integrability of the BFKL Hamiltonian. We also give evidence that the symmetry survives when a subset of unitarity corrections are taken into account by studying briefly the non-planar 2 to m reggeon transition vertices.
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arxiv:0908.2568
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In the framework of the littlest Higgs model with T-parity (LHT), we study the contributions of the T-even and T-odd particles to the branching ratio R_b. We find that the precision data of R_b can give strong constraints on the masses of T-odd fermions.
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arxiv:0908.2572
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We examine the correlation function \xi of the Sloan Digital Sky Survey (SDSS) Luminous Red Galaxy sample (LRG) at large scales (60<s<400 Mpc/h) using the final data release (DR7; 105,831 LRGs between 0.16<z<0.47). Using mock catalogs, we demonstrate that the observed baryonic acoustic peak and larger scale signal are consistent with LCDM at the 1.5\sigma level. The signal at 155<s<200 Mpc/h tends to be high relative to theoretical expectations; this slight deviation can be attributed to a bright subsample of the LRGs. Fitting data to a non-linear, redshift-space, template based-model, we constrain the peak position at s_p=103.6+3.6-2.4 Mpc/h when fitting the range 60<s<150 Mpc/h (1\sigma uncertainties measured from the mocks. This redshift-space distance s_p is related to the comoving sound horizon scale r_s after taking into account matter clustering non-linearities, redshift distortions and galaxy clustering bias. Mock catalogs show that the probability that a DR7-sized sample would not have an identifiable peak is at least 10%. As a consistency check of a fiducial cosmology, we use the observed s_p to obtain the distance D_V=[(1+z)^2D_A^2cz/H(z)]^(1/3) relative to the acoustic scale. We find r_s/D_V(z=0.278)=0.1394+-0.0049. This result is in excellent agreement with Percival et. al (2009), who examine roughly the same data set, but using the power spectrum. Comparison with other determinations in the literature are also in very good agreement. We have tested our results against a battery of possible systematic effects, finding all effects are smaller than our estimated sample variance.
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arxiv:0908.2598
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We study the potential to observe CP-violating effects in SUSY cascade decay chains at the LHC. We consider squark and gluino production followed by subsequent decays into neutralinos with a three-body leptonic decay in the final step. Asymmetries composed by triple products of momenta of the final state particles are sensitive to CP-violating effects. Due to large boosts these asymmetries can be difficult to observe at a hadron collider. We show that using all available kinematic information one can reconstruct the decay chains on an event-by-event basis even in the case of 3-body decays, neutrinos and LSPs in the final state. We also discuss the most important experimental effects like major backgrounds and momentum smearing due to finite detector resolution. We show that with 300 fb$^{-1}$ of collected data, CP violation may be discovered at the LHC for a wide range of the phase of the bino mass parameter $M_1$.
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arxiv:0908.2631
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We prove that the mixing time of the Glauber dynamics for random k-colorings of the complete tree with branching factor b undergoes a phase transition at $k=b(1+o_b(1))/\ln{b}$. Our main result shows nearly sharp bounds on the mixing time of the dynamics on the complete tree with n vertices for $k=Cb/\ln{b}$ colors with constant C. For $C\geq1$ we prove the mixing time is $O(n^{1+o_b(1)}\ln{n})$. On the other side, for $C<1$ the mixing time experiences a slowing down; in particular, we prove it is $O(n^{1/C+o_b(1)}\ln{n})$ and $\Omega(n^{1/C-o_b(1)})$. The critical point C=1 is interesting since it coincides (at least up to first order) with the so-called reconstruction threshold which was recently established by Sly. The reconstruction threshold has been of considerable interest recently since it appears to have close connections to the efficiency of certain local algorithms, and this work was inspired by our attempt to understand these connections in this particular setting.
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arxiv:0908.2665
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The main purpose of the paper is the analysis of seismic site effects in various alluvial basins. The analysis is performed considering a numerical approach (Boundary Element Method). Two main cases are considered : a shallow deposit in the centre of Nice (France) [1] and a deep irregular basin in Caracas (Venezuela) [2]. The amplification of seismic motion is analysed in terms of level, occuring frequency and location. For both sites, the amplification factor is found to reach maximum values of 20 (weak motion). Site effects nevertheless have very different features concerning the frequency dependence and the location of maximum amplification. For the shallow deposit in Nice, the amplification factor is very small for low frequencies and fastly increases above 1.0 Hz. The irregular Caracas basin gives a much different frequency dependence with many different peaks at various frequencies. The model for Caracas deep alluvial basin also includes a part of the local topography such as the nearest mountain. One can estimate seismic site effects due to both velocity contrast (between the basin and the bedrock) and local topography of the site. Furthermore, the maximum amplification is located on the surface for Nice, whereas some strong amplification areas also appear inside the basin itself in the case of Caracas. One investigates the influence of this focusing effect on the motion vs depth dependence. This is of great interest for the analysis of seismic response of underground structures. The form and the depth of alluvial deposits are then found to have a great influence on the location of maximum amplification on the surface but also inside the deposit for deep irregular basins. It is essential for the analysis of the seismic response of both surface and underground structures.
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arxiv:0908.2712
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We review the experimental results obtained by the NA49 collaboration in the context of its beam energy scan programme. The data on particle yields and spectral distributions suggest that the deconfinement phase transition is first reached in central collisions of heavy nuclei at about 30A GeV beam energy. Hadron-string transport models as well as the hadron gas model fail to describe the observed energy dependences unless additional parameters or unmeasured states are included.
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arxiv:0908.2720
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The integrated spectro-photometric properties of star clusters are subject to large cluster-to-cluster variations. They are distributed in non trivial ways around the average properties predicted by standard population synthesis models. This results from the stochastic mass distribution of the finite (small) number of luminous stars in each cluster, stars which may be either particularly blue or particularly red. The color distributions are broad and usually far from Gaussian, especially for young and intermediate age clusters, as found in interacting galaxies. When photometric measurements of clusters are used to estimate ages and masses in conjunction with standard models, biases are to be expected. We present a Bayesian approach that explicitly accounts for stochasticity when estimating ages and masses of star clusters that cannot be resolved into stars. Based on Monte-Carlo simulations, we are starting to explore the probability distributions of star cluster properties obtained given a set of multi-wavelength photometric data.
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arxiv:0908.2742
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The mass function of super-massive black holes in our cosmic neighborhood is required to understand the statistics of their activity and consequently the origin of the ultra high energy particles. We determine a mass function of black hole candidates from the entire sky except for the Galactic plane. Using the 2MASS catalogue as a starting point, and the well established correlation between black hole mass and the bulge of old population of stars, we derive a list of nearby black hole candidates within the redshift range z < 0.025, then do a further selection based on the Hubble-type, and give this as a catalogue elsewhere. The final list of black hole candidates above a mass of M_BH > 3*10^{6} M_sol has 5,829 entries; moreover doing a further Hubble type correction to account for the selection effects cuts down the number to 2,919 black hole candidates. We also correct for volume, so that this mass function is a volume limited distribution to redshift 0.025 The differential mass function of nearby black hole candidates is a curved function, with a straight simple power-law of index -3 above 10^{8} M_sol, growing progressively flatter towards lower masses, turning off towards a gap below 3*10^{6} M_sol, and then extending into the range where nuclear star clusters replace black holes. The shape of this mass function can be explained in a simple merger picture. Integrating this mass function over the redshift range, from which it has been derived, gives a total number of black holes with z < 0.025, and M_BH > 10^{7} M_sol of about 2.4*10^{4}, or, if we just average uniformly, 0.6 for every square degree on the sky. In different models many of these are candidates for ultra high energy particles sources. If a very small fraction of the super-massive black holes produces ultra high energy cosmic rays, this should be enough to observe the highly inhomogeneous distribution of the galaxies.
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arxiv:0908.2764
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We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence assumption between the two continuous variables with the space of permutation equipped with the uniform distribution and we show the exact distribution of the statistic. We calculate the distribution for several sample sizes. Through a simulation study we estimate the power of our test for diverse alternative hypothesis under the null hypothesis of independence.
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arxiv:0908.2794
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The method of generalized Hamilton-Jacobi-Bellman equations (GHJB) is a powerful way of creating near-optimal controllers by learning. It is based on the fact that if we have a feedback controller, and we learn to compute the gradient grad-J of its cost-to-go function, then we can use that gradient to define a better controller. We can then use the new controller's grad-J to define a still-better controller, and so on. Here I point out that GHJB works indirectly in the sense that it doesn't learn the best approximation to grad-J but instead learns the time derivative dJ/dt, and infers grad-J from that. I show that we can get simpler and lower-cost controllers by learning grad-J directly. To do this, we need teaching signals that report grad-J(x) for a varied set of states x. I show how to obtain these signals, using the GHJB equation to calculate one component of grad-J(x) -- the one parallel with dx/dt -- and computing all the other components by backward-in-time integration, using a formula similar to the Euler-Lagrange equation. I then compare this direct algorithm with GHJB on 2 test problems.
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arxiv:0908.2859
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We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Here we determine and solve the basic CCM equations by using the localised approximation scheme commonly referred to as the `LSUB$m$' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetisation and the local (sublattice) magnetisations as a function of the magnetic field strength. Our results for the lattice magnetisation of the square-lattice case compare well to those results of QMC for all values of the applied external magnetic field. We find a value for magnetic susceptibility of $\chi=0.070$ for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., $\chi=0.0669$ via QMC). Our estimate for the range of the extent of the ($M/M_s=$)$\frac 13$ magnetisation plateau for the triangular-lattice antiferromagnet is $1.37< \lambda < 2.15$, which is in good agreement with results of spin-wave theory ($1.248 < \lambda < 2.145$) and exact diagonalisations ($1.38 < \lambda < 2.16$). The CCM value for the in-plane magnetic susceptibility per site is $\chi=0.065$, which is below the result of the spin-wave theory (evaluated to order 1/S) of $\chi_{SWT}=0.0794$.
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arxiv:0908.2881
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It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply classical concepts and introduce probabilities in a manner inconsistent with the Hilbert space structure of standard quantum mechanics. Instead, Einstein locality is a valid quantum principle: objective properties of individual quantum systems do not change when something is done to another noninteracting system. There is no reason to suspect any conflict between quantum theory and special relativity.
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arxiv:0908.2914
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A strong direct product theorem states that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then the overall success probability will be exponentially small in $k$. We establish such a theorem for the randomized communication complexity of the Disjointness problem, i.e., with communication $const\cdot kn$ the success probability of solving $k$ instances of size $n$ can only be exponentially small in $k$. We show that this bound even holds for $AM$ communication protocols with limited ambiguity. This also implies a new lower bound for Disjointness in a restricted 3-player NOF protocol, and optimal communication-space tradeoffs for Boolean matrix product. Our main result follows from a solution to the dual of a linear programming problem, whose feasibility comes from a so-called Intersection Sampling Lemma that generalizes a result by Razborov.
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arxiv:0908.2940
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It was recently pointed out that mono-energetic neutrino lines from the 2-body decay of tritium (tau ~ 18-y) can be emitted, a significant fraction, with natural line width (~10-24 eV) for hypersharp resonance transitions 3H--> <--3He. The very long lifetime typical of a neutrino transition, encountered for the first time in resonance, is the key to this surprising effect which is not intuitive from perspectives of line broadening in resonances of short lived (tau ~ microsec) states.
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arxiv:0908.2980
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The recent availability of wideband receivers and high sensitivity instruments in the mm and submm wavelengths has opened the possibility of studying in detail the chemistry of the interstellar medium in extragalactic objects. Within the central few hundred parsec of galaxies, we find enormous amounts of molecular material fueling a wide variety of highly energetic events observed in starbursts (galaxies undergoing an intense burst of star formation) and active galactic nuclei (AGN, where activity is driven by the accretion of material onto the nuclear black hole). Here it is presented a brief summary of both the history and the latest results in observational chemistry in distant galaxies. It will be shown how the molecular emission, is a powerful tool to explore the physics of the dust-enshrouded, buried nuclei of distant ultraluminous galaxies, which are heavily obscured at other wavelengths. Special attention will be given to the possibilities offered by next generationinstruments such as ALMA (Atacama Large Millimeter Array), expected to have a vast impact on the field of Extragalactic Chemistry. Molecular studies in the early Universe will become available at unprecedented sensitivity and resolution.
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arxiv:0908.3016
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Recently we have evaluated the matrix elements $<Or^{p}>$,$ where $O$ $={1,\beta, i\mathbf{\alpha n}\beta} $ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions $_{3}F_{2}(1) $ for all suitable powers and established two sets of Pasternack-type matrix identities for these integrals. The corresponding Kramers--Pasternack three-term vector recurrence relations are derived here.
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arxiv:0908.3021
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The mathematical functions log(x), exp(x), root[n]x, sin(x), cos(x), tan(x), arcsin(x), arctan(x), x^y, sinh(x), cosh(x), tanh(x) and Gamma(x) have been implemented for arguments x in the real domain in a native Java library on top of the multi-precision BigDecimal representation of floating point numbers. This supports scientific applications where more than the double precision accuracy of the library of the Standard Edition is desired. The full source code is made available under the LGPL v3.0.
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arxiv:0908.3030
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By making use of the approximation method, we obtain the existence and regularity of the viscosity solutions for the generalized mean curvature flow. The asymptotic behavior of the flow is also considered. In particular, the Dirichlet problem of the degenerate elliptic equation $$ -|\nabla v|(\mathrm{div}(\frac{\nabla v}{|\nabla v|})+\nu)=0 $$ is solvable in viscosity sense.
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arxiv:0908.3057
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We analyze the quark spectral function above and below the critical temperature for deconfinement and at finite momentum in quenched lattice QCD. It is found that the temporal quark correlation function in the deconfined phase near the critical temperature is well reproduced by a two-pole ansatz for the spectral function. The bare quark mass and momentum dependences of the spectral function are analyzed with this ansatz. In the chiral limit we find that even near the critical temperature the quark spectral function has two collective modes corresponding to the normal and plasmino excitations in the high temperature (T) limit. The pole mass of these modes at zero momentum, which should be identified to be the thermal mass of the quark, is approximately proportional to T in a rather wide range of T in the deconfined phase.
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arxiv:0908.3079
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In this article we extend the validity Suslin's Local-Global Principle for the elementary transvection subgroup of the general linear group, the symplectic group, and the orthogonal group, where n > 2, to a Local-Global Principle for the elementary transvection subgroup of the automorphism group Aut(P) of either a projective module P of global rank > 0 and constant local rank > 2, or of a nonsingular symplectic or orthogonal module P of global hyperbolic rank > 0 and constant local hyperbolic rank > 2. In Suslin's results, the local and global ranks are the same, because he is concerned only with free modules. Our assumption that the global (hyperbolic) rank > 0 is used to define the elementary transvection subgroups. We show further that the elementary transvection subgroup ET(P) is normal in Aut(P), that ET(P) = T(P) where the latter denotes the full transvection subgroup of Aut(P), and that the unstable K_1-group K_1(Aut(P)) = Aut(P)/ET(P) = Aut(P)/T(P) is nilpotent by abelian, provided R has finite stable dimension. The last result extends previous ones of Bak and Hazrat for the above mentioned classical groups. An important application to the results in the current paper can be found in the work of last two named authors where they have studied the decrease in the injective stabilization of classical modules over a non-singular affine algebra over perfect C_1-fields. We refer the reader to that article for more details.
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arxiv:0908.3094
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We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.
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arxiv:0908.3095
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In this paper, we study how the interaction of the axigluon with quarks is modified when we introduce new color-octet spin-one fields in a chiral color model. We show that in this case the strength of this interaction is not completely determined by the gauge symmetry any more and can be significantly weaker than the one predicted in the original chiral color model. In this way, we reinterpret the non-observability of the axigluon at the Tevatron, not as a limit on the axigluon mass, but as a limit on the strength of the axigluon coupling to quarks.
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arxiv:0908.3116
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In this paper, we give an algebra-combinatorics formula of the M\"obius transform for an abstract simplicial complex $K$ on $[m]=\{1, ..., m\}$ in terms of the Betti numbers of the Stanley-Reisner face ring of $K$. Furthermore, we employ a way of compressing $K$ to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex $\mathcal{Z}_K$ (resp. real moment-angle complex ${\Bbb R}\mathcal{Z}_K$) of $K$, we show that the Halperin-Carlsson conjecture holds for $\mathcal{Z}_K$ (resp. ${\Bbb R}\mathcal{Z}_K$) under the restriction of the natural $T^m$-action on $\mathcal{Z}_K$ (resp. $({\Bbb Z}_2)^m$-action on ${\Bbb R}\mathcal{Z}_K$).
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arxiv:0908.3174
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Many studies and simulations suggest gas-rich mergers do not contribute significantly to the overall star-formation rate and total mass function of galaxies. The velocity dispersions (sigma) of Luminous & Ultraluminous Infrared Galaxies measured using the 1.62 or 2.29 micron CO bandheads imply they will form m < m* ellipticals. Yet, sigma's obtained with the Calcium II triplet (CaT) at 0.85 micron suggest all types of mergers will form m > m* ellipticals. Presented here are recent results, based on high-resolution imaging and multi-wavelength spectroscopy, which demonstrate the dominance of a nuclear disk of Red Supergiants (RSG) or Asymptotic Giant Branch (AGB) stars in the near-infrared bands, where dust obscuration does not sufficiently block their signatures. The presence of these stars severely biases the dynamical mass. At I-band, where dust can sufficiently block RSG or AGB stars, LIRGs populate the Fundamental Plane over a large dynamic range and are virtually indistinguishable from elliptical galaxies.
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arxiv:0908.3175
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We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function [n(k)] and the density-density structure factor [N(k)], respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of N(k) for fermions is very similar to the one of hardcore bosons, the behavior of n(k) is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of n(k) in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.
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arxiv:0908.3188
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Cosmological observations are normally fit under the assumption that the dark sector can be decomposed into dark matter and dark energy components. However, as long as the probes remain purely gravitational, there is no unique decomposition and observations can only constrain a single dark fluid; this is known as the dark degeneracy. We use observations to directly constrain this dark fluid in a model-independent way, demonstrating in particular that the data cannot be fit by a dark fluid with a single constant equation of state. Parameterizing the dark fluid equation of state by a variety of polynomials in the scale factor $a$, we use current kinematical data to constrain the parameters. While the simplest interpretation of the dark fluid remains that it is comprised of separate dark matter and cosmological constant contributions, our results cover other model types including unified dark energy/matter scenarios.
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arxiv:0908.3197
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In this note we will adapt Topping's $\mathcal{L}$-optimal transportation theory for Ricci flow to a more general situation, i.e. to a closed manifold $(M,g_{ij}(t))$ evolving by $\partial_tg_{ij}=-2S_{ij}$, where $S_{ij}$ is a symmetric tensor field of (2,0)-type on $M$. We extend some recent results of Topping, Lott and Brendle, generalize the monotonicity of List's (and hence also of Perelman's) $\mathcal{W}$-entropy, and recover the monotonicity of M$\ddot{u}$ller's (and hence also of Perelman's) reduced volume.
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arxiv:0908.3293
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We report the discovery by the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope of high-energy gamma-ray emission from the peculiar quasar PMN J0948+0022 (z=0.585+/-0.001). Contrary to the expectations, the optical spectrum of this quasar shows only narrow lines [FWHM(Hbeta) ~ 1500 km/s] and the typical characteristics of narrow-line Seyfert 1 type galaxies. However, the strong radio emission and the flat spectrum suggest the presence of a relativistic jet, which can now be confirmed by the detection of MeV-GeV photons. PMN J0948+0022 is therefore the first radio-loud narrow-line Seyfert 1 quasar to be detected at gamma-rays and the third type of gamma-ray emitting AGN, after blazars and radiogalaxies.
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arxiv:0908.3313
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We report significant enhancement in superconducting properties of yttrium substituted Ce1-xYxOFFeAs superconductors. The polycrystalline samples were prepared by two step solid state reaction technique. X-ray diffraction confirmed tetragonal ZrCuSiAs structure with decrease in both a and c lattice parameters on increasing yttrium substitution (with fixed F content). With smaller ion Y in place of Ce, the transition temperature increased by 6 K. Yttrium doping also lead to higher critical fields as well as stronger inter and intra-granular current density. The magnetization critical current density increased by an order of magnitude at 30 K and 1 T magnetic field.
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arxiv:0908.3372
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In most sociophysical simulations on public opinion, only two opinions are allowed: Pro and Contra. However, in all political elections many people do not vote. Here we analyse two models of dynamics of public opinion, taking into account Indifferent voters: {\it i)} the Sznajd model with symmetry Pro-Contra, {\it ii)} the outflow one move voter model, where Contra's are converted to Indifferent by their Pro neighbours. Our results on the Sznajd model are in an overall agreement with the results of the mean field approach and with those known from the initial model formulation. The simulation on the voter model shows that an amount of Contra's who remain after convertion depends on the network topology.
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arxiv:0908.3387
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We explore the possibility to trap polynitrogen clusters inside C60 fullerene cage, opening a new direction of developing nitrogen-rich high energy materials. We found that a maximum of 13 nitrogen atoms can be encapsulated in a C60 cage. The nitrogen clusters in confinement exhibit unique stable structures in polymeric form which possess a large component of (~ 70-80%) single bond character. The Nn@C60 molecules retain their structure at 300K for n<12. The Mulliken charge analysis shows very small charge transfer in N@C60, consistent with the quartet spin state of N. However, for 2<n<10, charge transfer take place from cage surface to Nn compounds and inverse polarization thereafter. These nitrogen clusters when allowed to relax to N2 molecules which are triply bonded are capable of releasing a large amount of energy.
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arxiv:0908.3412
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We report the discovery of supersonic downflows in a sunspot light bridge using measurements taken with the spectropolarimeter on board the Hinode satellite. The downflows occur in small patches close to regions where the vector magnetic field changes orientation rapidly, and are associated with anomalous circular polarization profiles. An inversion of the observed Stokes spectra reveals velocities of up to 10 km/s, making them the strongest photospheric flows ever measured in light bridges. Some (but not all) of the downflowing patches are cospatial and cotemporal with brightness enhancements in chromospheric Ca II H filtergrams. We suggest that these flows are due to magnetic reconnection in the upper photosphere/lower chromosphere, although other mechanisms cannot be ruled out.
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arxiv:0908.3465
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We show in some lower-dimensional supergravity models that the holographic counterterms which are needed in the AdS/CFT correspondence to make the theory finite, coincide with the counterterms that are needed to make the action supersymmetric without imposing any boundary conditions on the fields.
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arxiv:0908.3486
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What kind of New Physics, if any, we expect to discover at the LHC? I will try to address this formidable question by re-formulating it as follows: is the breaking of the electroweak symmetry strong or weak ?
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arxiv:0908.3578
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Using the basic Lie symmetry method, we find the most general Lie point symmetries group of the $\nabla u=f(u)$ Poisson's equation, which has a subalgebra isomorphic to the $3-$dimensional special Euclidean group ${\rm SE}(3)$ or group of rigid motions of ${\Bbb R}^3$. Looking the adjoint representation of ${\rm SE}(3)$ on its Lie algebra $\goth{se}(3)$, we will find the complete optimal system of its subalgebras. This latter provides some properties of solutions for the Poisson's equation.
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arxiv:0908.3619
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Motivated by the recent detection of a large number of embedded young stellar objects (YSOs) with mass accretion rates that are inconsistent with the predictions of the standard model of inside-out collapse (Shu 1977), we perform a series on numerical hydrodynamic simulations of the gravitational collapse of molecular cloud cores with various initial masses, rotation rates, and sizes. We focus on the early Class I stage of stellar evolution when circumstellar disks are exposed to high rates of mass deposition from infalling envelopes. Our numerical modeling reproduces the large observed spread in accretion rates inferred for embedded YSOs in Perseus, Serpens, and Ophiuchus star forming regions by Enoch et al. (2009), yielding 37%--75% of objects with "sub-Shu" accretion rates \dot{M} \la 10^{-6} Msun/yr and 1%--2% of objects with "super-Shu" accretion rates \dot{M}>10^{-5} Msun/yr. Mass accretion rates in the Class I stage have a log-normal distribution, with its shape controlled by disk viscosity and disk temperature. The spread in $\dot{M}$ is greater in models with lower viscosity and smaller in models with higher viscosity and higher disk temperature, suggesting that gravitational instability may be a dominant cause of the observed diversity in $\dot{M}$ in embedded YSOs. Our modeling predicts a weak dependence between the mean mass accretion rates and stellar masses in the Class I stage, in sharp contrast to the corresponding steep dependence for evolved T Tauri stars and brown dwarfs.
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arxiv:0908.3645
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We use smoothed particle hydrodynamics (SPH) models to study the large-scale morphology and dynamical evolution of the intergalactic gas in Stephan's Quintet, and compare to multiwavelength observations. Specifically, we model the formation of the hot X-ray gas, the large-scale shock, and emission line gas as the result of NGC 7318b colliding with the group. We also reproduce the N-body model of Renaud and Appleton for the tidal structures in the group.
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arxiv:0908.3659
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We partially generalize the results of Kudla and Rallis on the poles of degenerate, Siegel-parabolic Eisenstein series to residual-data Eisenstein series. In particular, for $a,b$ integers greater than 1, we show that poles of the Eisenstein series induced from the Speh representation $\Delta(\tau,b)$ on the Levi $\mathrm{GL}_{ab}$ of $\mathrm{Sp}_{2ab}$ are located in the "segment" of half integers $X_{b}$ between a "right endpoint" and its negative, inclusive of endpoints. The right endpoint is $\pm b/2$, or $(b-1)/2$, depending on the analytic properties of the automorphic $L$-functions attached to $\tau$. We study the automorphic forms $\Phi_{i}^{(b)}$ obtained as residues at the points $s_i^{(b)}$ (defined precisely in the paper) by calculating their cuspidal exponents in certain cases. In the case of the "endpoint" $s_0^{(b)}$ and `first interior point' $s_1^{(b)}$ in the segment of singularity points, we are able to determine a set containing \textit{all possible} cuspidal exponents of $\Phi_0^{(b)}$ and $\Phi_1^{(b)}$ precisely for all $a$ and $b$. In these cases, we use the result of the calculation to deduce that the residual automorphic forms lie in $L^2(G(k)\backslash G(\mathbf{A}))$. In a more precise sense, our result establishes a relationship between, on the one hand, the actually occurring cuspidal exponents of $\Phi_i^{(b)}$, residues at interior points which lie to the right of the origin, and, on the other hand, the "analytic properties" of the original residual-data Eisenstein series at the origin. This preprint is a longer version of the paper "Analytic Properties of Residual Eisenstein Series, I", with the details of some proofs added and some additional examples adduced in support of the main conjecture.
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arxiv:0908.3667
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We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss entanglement conditions and entanglement witnesses for states with a positive partial transpose.
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arxiv:0908.3679
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For a large class of Schrodinger operators, we introduce the hyperbolic quadratic pencils by making the coupling constant dependent on the energy in the very special way. For these pencils, many problems of scattering theory are easier to study. Then, we give some applications to the original Schrodinger operators.
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arxiv:0908.3682
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Since the first experimental realization of Bose-Einstein condensation in cold atomic gases in 1995 there has been a surge of activity in this field. Ingenious experiments have allowed us to probe matter close to zero temperature and reveal some of the fascinating effects quantum mechanics has bestowed on nature. It is a challenge for mathematical physicists to understand these various phenomena from first principles, that is, starting from the underlying many-body Schr\"odinger equation. Recent progress in this direction concerns mainly equilibrium properties of dilute, cold quantum gases. We shall explain some of the results in this article, and describe the mathematics involved in understanding these phenomena. Topics include the ground state energy and the free energy at positive temperature, the effect of interparticle interaction on the critical temperature for Bose-Einstein condensation, as well as the occurrence of superfluidity and quantized vortices in rapidly rotating gases.
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arxiv:0908.3686
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