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The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for effective decision procedures, called Satisfiability Modulo Theory solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we define a novel approach to interpolate combinations of theories, that applies to the Delayed Theory Combination approach. Efficiency is ensured by the fact that the proposed interpolation algorithms extend state of the art algorithms for Satisfiability Modulo Theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.
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arxiv:0906.4492
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We consider the Kaehler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kaehler manifold X. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in terms of cohomological data on X. We also give a sufficient condition for the singularity, if there is one, to be type-II.
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arxiv:0906.4496
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We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on the discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalizes our analysis to Hilbert spaces of prime dimensions d and their associated d*d phase spaces.
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arxiv:0906.4516
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We propose a scheme to implement high-fidelity conditional phase gates on pair of trapped ions immersed in a two-dimensional Coulomb crystal, using interaction mediated by all axial modes without side-band addressing. We show through numerical calculations that only local modes can be excited to achieve entangling gates through shaping the laser beams, so that the complexity of the quantum gate does not increase with the size of the system. These results suggest a promising approach for realization of large scale fault-tolerant quantum computation in two dimensional traps architecture.
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arxiv:0906.4598
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We experimentally investigated the excitation power dependence of a strongly coupled quantum dot (QD)-photonic crystal nanocavity system by photoluminescence (PL) measurements. At a low-excitation power regime, we observed vacuum Rabi doublet emission at QD-cavity resonance condition. With increasing excitation power, in addition to the doublet, a third emission peak appeared. This observed spectral change is unexpected from conventional atomic cavity quantum electrodynamics. The observations can be attributed to featured pumping processes in the semiconductor QD-cavity system.
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arxiv:0906.4622
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The work is inspired by thermo-and photoacoustic imaging, where recent efforts are devoted to take into account attenuation and varying wave speed parameters. In this paper we derive and analyze causal equations describing propagation of attenuated pressure waves. We also review standard models, like frequency power laws, and the thermo-viscous equation and show that they lack causality in the parameter range relevant for biological photoacoustic imaging. To discuss causality in mathematical rigor we use the results and concepts of linear system theory. We present some numerical experiments, which show the physically unmeaningful behavior of standard attenuation models, and the realistic behavior of the novel models.
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arxiv:0906.4678
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Every smooth manifold contains particles which propagate. These form objects and morphisms of a category equipped with a functor to the category of Abelian groups, turning this into a 0+1 topological field theory. We investigate the algebraic structure of this category, intimately related to the structure of Stasheff's polytops, introducing the notion of associahedral categories. An associahedral category is preadditive and close to being strict monoidal. Finally, we interpret Morse-Witten theory as a contravariant functor, the Morse functor, to the homotopy category of bounded chain complexes of particles.
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arxiv:0906.4712
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This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatise complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi and symmetric monoidal categories, our results provide a purely graphical formalisation of complementarity for quantum observables. Each individual observable, represented by a commutative special dagger Frobenius algebra, gives rise to an abelian group of phase shifts, which we call the phase group. We also identify a strong form of complementarity, satisfied by the Z and X spin observables, which yields a scaled variant of a bialgebra.
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arxiv:0906.4725
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We prove the existence of a Quillen Flat Model Structure in the category of unbounded complexes of h-unitary modules over a nonunital ring (or a $k$-algebra, with $k$ a field). This model structure provides a natural framework where a Morita-invariant homological algebra for these nonunital rings can be developed. And it is compatible with the usual tensor product of complexes. The Waldhausen category associated to its cofibrations allows to develop a Morita invariant excisive higher $K$-theory for nonunital algebras.
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arxiv:0906.4735
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We will discuss recent results for the spin structure functions, with an emphasis on g2 . High precision g2 data allows for tests of the Burkhardt-Cottingham sum rule, and is needed to consistently evaluate higher twist effects.
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arxiv:0906.4766
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We discuss the impact of adiabatic renormalization on the power spectrum of scalar and tensor perturbations from inflation. We show that adiabatic regularization is ambiguous as it leads to very different results, for different adiabatic subtraction schemes, both in the range $v\equiv k/(aH) \gsim 0.1$ and in the infrared regime. All these schemes agree in the far ultraviolet, $v\gg 1$. Therefore, we argue that in the far infrared regime, $v\ll 1$, the adiabatic expansion is no longer valid, and the unrenormalized spectra are the physical, measurable quantities. These findings cast some doubt on the validity of the adiabatic subtraction at horizon exit, $v=1$, to determine the perturbation spectra from inflation which has recently advocated in the literature.
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arxiv:0906.4772
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Let \Delta be a finite sequence of n vectors from a vector space over any field. We consider the subspace of \operatorname{Sym}(V) spanned by \prod_{v \in S} v, where S is a subsequence of \Delta. A result of Orlik and Terao provides a doubly indexed direct sum of this space. The main theorem is that the resulting Hilbert series is the Tutte polynomial evaluation T(\Delta;1+x,y). Results of Ardila and Postnikov, Orlik and Terao, Terao, and Wagner are obtained as corollaries.
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arxiv:0906.4774
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We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 560 femtoradians and the linear travel of a piezo actuator down to 20 femtometers.
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arxiv:0906.4828
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I construct a correspondence between the Schubert cycles on the variety of complete flags in C^n and some faces of the Gelfand-Zetlin polytope associated with the irreducible representation of SL_n(C) with a strictly dominant highest weight. The construction is based on a geometric presentation of Schubert cells by Bernstein-Gelfand-Gelfand using Demazure modules. The correspondence between the Schubert cycles and faces is then used to interpret the classical Chevalley formula in Schubert calculus in terms of the Gelfand-Zetlin polytopes. The whole picture resembles the picture for toric varieties and their polytopes.
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arxiv:0906.4866
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Let $\mathbf{x_1}, ..., \mathbf{x_t} \in \mathbb{R}^{n}$. A simultaneous integer relation (SIR) for $\mathbf{x_1}, ..., \mathbf{x_t}$ is a vector $\mathbf{m} \in \mathbb{Z}^{n}\setminus\{\textbf{0}\}$ such that $\mathbf{x_i}^T\mathbf{m} = 0$ for $i = 1, ..., t$. In this paper, we propose an algorithm SIRD to detect an SIR for real vectors, which constructs an SIR within $\mathcal {O}(n^4 + n^3 \log \lambda(X))$ arithmetic operations, where $\lambda(X)$ is the least Euclidean norm of SIRs for $\mathbf{x_1}, >..., \mathbf{x_t}$. One can easily generalize SIRD to complex number field. Experimental results show that SIRD is practical and better than another detecting algorithm in the literature. In its application, we present a new algorithm for finding the minimal polynomial of an arbitrary complex algebraic number from its an approximation, which is not based on LLL. We also provide a sufficient condition on the precision of the approximate value, which depends only on the height and the degree of the algebraic number.
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arxiv:0906.4917
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The origin and stability of a thin sheet of plasma in the magnetosphere of an accreting neutron star is investigated. First the radial extension of such a magnetospheric disc is explored. Then a mechanism for magnetospheric accretion is proposed, reconsidering the bending wave explored by Agapitou, Papaloizou & Terquem (1997), that was found to be stable in ideal MHD. We show that this warping becomes unstable and can reach high amplitudes, in a variant of Pringle's radiation-driven model for the warping of AGN accretion discs (Pringle (1996)). Finally we discuss how this mechanism might give a clue to explain the observed X-ray kHz QPO of neutron star binaries.
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arxiv:0906.4928
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Starbursts and substantial variations in the star formation histories are a common phenomenon in galaxies. We study the stability properties of isolated star-forming dwarf galaxies with the aim of identifying starburst modes. The impact of the stellar birth function, the initial mass function (IMF), the stellar feedback and the interstellar medium (ISM) model are investigated. We apply a one-zone model for a star-gas system coupled by mass and energy transfer. Additionally, we extend the network for active dynamical evolution. This allows for a coupling between the dynamical state of the galaxy and its internal properties. While the influence of the dynamics on the total star formation rate is strong, the coupling of the internal properties (gas temperature) on the dynamics is rather limited, because radiative cooling keeps the gas temperature well below the virial temperature. Because of short cooling and feedback timescales, the star formation rate is close to the equilibrium star formation rates. Quasi-periodic starbursts occur, because star formation follows the variations in the gas density induced by decaying virial oscillations. This behaviour is quite insensitive to the nature and the details of the stellar birth description, viz. whether spontaneous or induced star formation is considered or the IMF is varied. A second type of burst is found as an instability operating when the cooling may drop at very low densities with increasing temperature. Bursts of star formation occur during transitory phases, when dynamical equilibrium is established. Then they are quasi-periodic on the dynamical timescale. Because of short heating and cooling timescales, the star formation rate follows the equilibrium star formation rate corresponding to the actual gas density.
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arxiv:0906.4929
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It is known that with restrictions on the type of the constitutive equations, Maxwell's equations in non-uniform media can sometimes be reduced to two 2nd order differential equations for 2 scalar quantities only. These results have previously been obtained in two quite different ways. Either by a ``scalarization of the sources'', where the relevant scalar quantities are essentially vector potential components and where the derivation was limited to isotropic media; or alternatively by using the ``scalar Hertz potentials'', and this method has been applied to more general media. In this paper it is shown that both methods are equivalent for gyrotropic media. We show that the scalarization can be obtained by a combination of transformations between electric and magnetic sources and gauge transformations. It is shown that the method based on the vector potential, which previously used a non-traditional definition of the vector potentials, can also be obtained using the traditional definition provided a proper gauge condition is applied and this method is then extended from isotropic to gyrotropic media. It is shown that the 2 basic scalar Hertz potentials occurring in the second method are invariant under the source scalarization transformations of the first method and therefore are the natural potentials for obtaining scalarization. Finally it is shown that both methods are also equivalent with a much older third method based on Hertz vectors.
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arxiv:0906.4965
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Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been eagerly adopted by practitioners in the service of network inference, they do not yet comprise a unified and coherent framework for the statistical analysis of large-scale network data. This paper serves as both an introduction to the topic and a first step toward formal inference procedures. We develop and illustrate our arguments using the example of hypothesis testing for network structure. We invoke a generalized likelihood ratio framework and use it to highlight the growing number of topics in this area that require strong contributions from statistical science. We frame our discussion in the context of previous work from across a variety of disciplines, and conclude by outlining fundamental statistical challenges whose solutions will in turn serve to advance the science of network inference.
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arxiv:0906.4980
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Selection systems and the corresponding replicator equations model the evolution of replicators with a high level of abstraction. In this paper we apply novel methods of analysis of selection systems to the replicator equations. To be suitable for the suggested algorithm the interaction matrix of the replicator equation should be transformed; in particular the standard singular value decomposition allows us to rewrite the replicator equation in a convenient form. The original $n$-dimensional problem is reduced to the analysis of asymptotic behavior of the solutions to the so-called escort system, which in some important cases can be of significantly smaller dimension than the original system. The Newton diagram methods are applied to study the asymptotic behavior of the solutions to the escort system, when interaction matrix has rank 1 or 2. A general replicator equation with the interaction matrix of rank 1 is fully analyzed; the conditions are provided when the asymptotic state is a polymorphic equilibrium. As an example of the system with the interaction matrix of rank 2 we consider the problem from [Adams, M.R. and Sornborger, A.T., J Math Biol, 54:357-384, 2007], for which we show, for arbitrary dimension of the system and under some suitable conditions, that generically one globally stable equilibrium exits on the 1-skeleton of the simplex.
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arxiv:0906.4986
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We consider a time-dependent bosonic string in graviton, dilaton and tachyon backgrounds, for which it was already shown that conformal invariance is respected to all orders in alpha' and in any space-time dimension. Assuming that the tachyon is off-shell, we show in this note that the specific time-homogeneity of the corresponding space time effective action leads to a power-law expanding Universe, that can be accelerating or decelerating, depending on the range of parameter space considered. We interpret this result as dark energy. We arrive at this result without requiring the knowledge of the structure of the string effective action, which is not known to all orders in alpha'. Moreover, in our approach, the background configurations are consistent in a four-dimensional space time, without any need for extra dimensions.
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arxiv:0906.4990
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In supersymmetric theories, the presence of axions usually implies the existence of a non-compact, (pseudo)moduli space. In gauge mediated models, the axion would seem a particularly promising dark matter candidate. The cosmology of the moduli then constrains the gravitino mass and the axion decay constant; the former can't be much below 10 MeV; the latter can't be much larger than 10^{13} GeV. Axinos, when identifiable, are typically heavy and do not play an important role in cosmology.
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arxiv:0906.5015
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We show that 4-dimensional conjugation manifolds are all obtained from branched 2-fold coverings of knotted surfaces in Z/2-homology 4-spheres.
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arxiv:0906.5057
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The phase shift a neutron interferometer caused by the gravitational field and the rotation of the earth is derived in a unified way from the standpoint of general relativity. General relativistic quantum interference effects in the slowly rotating braneworld as the Sagnac effect and phase shift effect of interfering particle in neutron interferometer are considered. It was found that in the case of the Sagnac effect the influence of brane parameter is becoming important due to the fact that the angular velocity of the locally non rotating observer must be larger than one in the Kerr space-time. In the case of neutron interferometry it is found that due to the presence of the parameter $Q^{*}$ an additional term in the phase shift of interfering particle emerges from the results of the recent experiments we have obtained upper limit for the tidal charge as $Q^{*}\lesssim 10^{7} \rm{cm}^{2}$. Finally, as an example, we apply the obtained results to the calculation of the (ultra-cold neutrons) energy level modification in the braneworld.
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arxiv:0906.5067
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The Elliott-Yafet mechanism is arguably the most promising candidate to explain the ultrafast demagnetization dynamics in ferromagnetic transition metals on timescales on the order of 100 femtoseconds. So far, only electron-phonon scattering has been analyzed as the scattering process needed to account for the demagnetization due to the Elliott-Yafet mechanism. We show for the first time that the electron-electron scattering contribution to the Elliott-Yafet mechanism has the potential to explain time-resolved magneto-optical Kerr effect measurements on thin magnetic cobalt and nickel films, without reference to a phononic "spin bath."
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arxiv:0906.5104
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We study the spin edge states in the quantum spin-Hall (QSH) effect on a single-atomic layer graphene ribbon system with both intrinsic and Rashba spin-orbit couplings. The Harper equation for solving the energies of the spin edge states is derived. The results show that in the QSH phase, there are always two pairs of gapless spin-filtered edge states in the bulk energy gap, corresponding to two pairs of zero points of the Bloch function on the complex-energy Riemann surface (RS). The topological aspect of the QSH phase can be distinguished by the difference of the winding numbers of the spin edge states with different polarized directions cross the holes of the RS, which is equivalent to the Z2 topological invariance proposed by Kane and Mele [Phys. Rev. Lett. 95, 146802 (2005)].
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arxiv:0906.5118
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Quantum fluctuations of electromagnetic vacuum are investigated in a half-space bounded by a perfectly reflecting plate by introducing a probe described by a charged wave-packet distribution in time-direction. The wave-packet distribution of the probe enables one to investigate the smearing effect upon the measured vacuum fluctuations caused by the quantum nature of the probe particle. It is shown that the wave-packet spread of the probe particle significantly influences the measured velocity dispersion of the probe. In particular, the asymptotic late-time behavior of its $z$-component, $ < \D v_{z}^{2}>$, for the wave-packet case is quite different from the test point-particle case ($z$ is the coordinate normal to the plate). The result for the wave-packet is $<\D v_{z}^{2} > \sim 1/\t^2$ in the late time ($\t$ is the measuring time), in stead of the reported late-time behavior $<\D v_{z}^{2} > \sim 1/z^2$ for a point-particle probe. This result can be quite significant for further investigations on the measurement of vacuum fluctuations.
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arxiv:0906.5142
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With the incorporation of high-J molecular lines, we aim to constrain the physical conditions of the dense gas in the central region of the Seyfert 2 galaxy NGC 1068 and to determine signatures of the AGN or the starburst contribution. We used the James Clerk Maxwell Telescope to observe the J=4-3 transition of HCN, HNC, and HCO+, as well as the CN N_J=2_{5/2}-1_{3/2} and N_J=3_{5/2}-2_{5/2}, in NGC 1068. We estimate the excitation conditions of HCN, HNC, and CN, based on the line intensity ratios and radiative transfer models. We find that the bulk emission of HCN, HNC, CN, and the high-J HCO+ emerge from dense gas n(H_2)>=10^5 cm^-3). However, the low-J HCO+ lines (dominating the HCO+ column density) trace less dense (n(H_2)<10^5 cm^-3) and colder (T_K<=20 K) gas, whereas the high-J HCO+ emerges from warmer (>30 K) gas than the other molecules. The HCO+ J=4-3 line intensity, compared with the lower transition lines and with the HCN J=4-3 line, support the influence of a local XDR environment. The estimated N(CN)/N(HCN)~1-4 column density ratios are indicative of an XDR/AGN environment with a possible contribution of grain-surface chemistry induced by X-rays or shocks.
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arxiv:0906.5154
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We present an analysis of the mass of the X(3872) reconstructed via its decay to J/psi pi+ pi- using 2.4 fb^-1 of integrated luminosity from ppbar collisions at sqrt(s) = 1.96 TeV, collected with the CDF II detector at the Fermilab Tevatron. The possible existence of two nearby mass states is investigated. Within the limits of our experimental resolution the data are consistent with a single state, and having no evidence for two states we set upper limits on the mass difference between two hypothetical states for different assumed ratios of contributions to the observed peak. For equal contributions, the 95% confidence level upper limit on the mass difference is 3.6 MeV/c^2. Under the single-state model the X(3872) mass is measured to be 3871.61 +- 0.16 (stat) +- 0.19 (syst) MeV/c^2, which is the most precise determination to date.
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arxiv:0906.5218
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We outline our work (see [1,2,3,4]) on relaxation and 3d-2d passage with determinant type constraints. Some open questions are addressed. This outline-paper comes as a companion to [5].
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arxiv:0906.5262
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This paper reviews and develops the proposal, widely discussed but not examined in detail, to use stratospheric aerosols to increase the Earth's albedo to Solar radiation in order to control climate change. The potential of this method has been demonstrated by the "natural experiments" of volcanic injection of sulfate aerosols into the stratosphere that led to subsequent observed global cooling. I consider several hygroscopic oxides as possible aerosol materials in addition to oxides of sulfur. Aerosol chemistry, dispersion and transport have been the subject of little study and are not understood, representing a significant scientific risk. Even the optimal altitude of injection and aerosol size distribution are poorly known. Past attention focused on guns and airplanes as means of lofting aerosols or their chemical precursors, but large sounding rockets are cheap, energetically efficient, can be designed to inject aerosols at any required altitude, and involve little technical risk. Sophisticated, mass-optimized "engineered" particles have been proposed as possible aerosols, but the formidable problems of their production in quantity, lofting and dispersion have not been addressed.
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arxiv:0906.5307
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Weyl's law approximates the number of states in a quantum system by partitioning the energetically accessible phase-space volume into Planck cells. Here we show that typical resonances in generic open quantum systems follow a modified, fractal Weyl law, even though their classical dynamics is not globally chaotic but also contains domains of regular motion. Besides the obvious ramifications for quantum decay, this delivers detailed insight into quantum-to-classical correspondence, a phenomenon which is poorly understood for generic quantum-dynamical systems.
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arxiv:0906.5320
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The Palomar Transient Factory (PTF) is a fully-automated, wide-field survey aimed at a systematic exploration of the optical transient sky. The transient survey is performed using a new 8.1 square degree camera installed on the 48-inch Samuel Oschin telescope at Palomar Observatory; colors and light curves for detected transients are obtained with the automated Palomar 60-inch telescope. PTF uses eighty percent of the 1.2-m and fifty percent of the 1.5-m telescope time. With an exposure of 60-s the survey reaches a depth of approximately 21.3 in g' and 20.6 in R (5 sigma, median seeing). Four major experiments are planned for the five-year project: 1) a 5-day cadence supernova search; 2) a rapid transient search with cadences between 90 seconds and 1 day; 3) a search for eclipsing binaries and transiting planets in Orion; and 4) a 3-pi sr deep H-alpha survey. PTF provides automatic, realtime transient classification and follow up, as well as a database including every source detected in each frame. This paper summarizes the PTF project, including several months of on-sky performance tests of the new survey camera, the observing plans and the data reduction strategy. We conclude by detailing the first 51 PTF optical transient detections, found in commissioning data.
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arxiv:0906.5350
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Large extra dimensions have been proposed as a possible solution to the hierarchy problem in physics. One of the suggested models, the RS2 braneworld model, makes a prediction that black holes evaporate by Hawking radiation on a short timescale that depends on the black hole mass and on the asymptotic radius of curvature of the extra dimensions. Thus the size of the extra dimensions can be constrained by astrophysical observations. Here we point out that the black hole, recently discovered in a globular cluster in galaxy NGC 4472, places the strongest constraint on the maximum size of the extra dimensions, L < 0.003 mm. This black hole has the virtues of old age and relatively small mass. The derived upper limit is within an order of magnitude of the absolute limit afforded by astrophysical observations of black holes.
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arxiv:0906.5351
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We analyze the back-action influence of nuclear spins on the motion of the cantilever of a magnetic force resonance microscope. We calculate the contribution of nuclear spins to the damping and frequency shift of the cantilever. We show that, at the Rabi frequency, the energy exchange between the cantilever and the spin system cools or heats the cantilever depending on the sign of the high-frequency detuning. We also show that the spin noise leads to a significant damping of the cantilever motion.
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arxiv:0906.5420
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We present results for the first positive parity excited state of the nucleon, namely, the Roper resonance ($N^{{{1/2}}^{+}}$=1440 MeV) from a variational analysis technique. The analysis is performed for pion masses as low as 224 MeV in quenched QCD with the FLIC fermion action. A wide variety of smeared-smeared correlation functions are used to construct correlation matrices. This is done in order to find a suitable basis of operators for the variational analysis such that eigenstates of the QCD Hamiltonian may be isolated. A lower lying Roper state is observed that approaches the physical Roper state. To the best of our knowledge, the first time this state has been identified at light quark masses using a variational approach.
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arxiv:0906.5433
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The Sun's corona is millions of degrees hotter than its 5,000 K photosphere. This heating enigma is typically addressed by invoking the deposition at coronal heights of non-thermal energy generated by the interplay between convection and magnetic field near the photosphere. However, it remains unclear how and where coronal heating occurs and how the corona is filled with hot plasma. We show that energy deposition at coronal heights cannot be the only source of coronal heating, by revealing a significant coronal mass supply mechanism that is driven from below, in the chromosphere. We quantify the asymmetry of spectral lines observed with Hinode and SOHO and identify faint but ubiquitous upflows with velocities that are similar (50-100 km/s) across a wide range of magnetic field configurations and for temperatures from 100,000 to several million degrees. These upflows are spatio-temporally correlated with and have similar upward velocities as recently discovered, cool (10,000 K) chromospheric jets or (type II) spicules. We find these upflows to be pervasive and universal. Order of magnitude estimates constrained by conservation of mass and observed emission measures indicate that the mass supplied by these spicules can play a significant role in supplying the corona with hot plasma. The properties of these events are incompatible with coronal loop models that only include nanoflares at coronal heights. Our results suggest that a significant part of the heating and energizing of the corona occurs at chromospheric heights, in association with chromospheric jets.
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arxiv:0906.5434
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The closure of a discrete exponential family is described by a finite set of equations corresponding to the circuits of an underlying oriented matroid. These equations are similar to the equations used in algebraic statistics, although they need not be polynomial in the general case. This description allows for a combinatorial study of the possible support sets in the closure of an exponential family. If two exponential families induce the same oriented matroid, then their closures have the same support sets. Furthermore, the positive cocircuits give a parameterization of the closure of the exponential family.
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arxiv:0906.5462
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We consider the existence of simple closed geodesics or "geodesic knots" in finite volume orientable hyperbolic 3-manifolds. Previous results show that at least one geodesic knot always exists [Bull. London Math. Soc. 31(1) (1999) 81-86], and that certain arithmetic manifolds contain infinitely many geodesic knots [J. Diff. Geom. 38 (1993) 545-558], [Experimental Mathematics 10(3) (2001) 419-436]. In this paper we show that all cusped orientable finite volume hyperbolic 3-manifolds contain infinitely many geodesic knots. Our proof is constructive, and the infinite family of geodesic knots produced approach a limiting infinite simple geodesic in the manifold.
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arxiv:0906.5469
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According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Many programs, however, exhibit computational effects, and are not accounted for by the standard theory of relational parametricity. In this paper, we develop a foundational framework for extending the notion of relational parametricity to programming languages with effects.
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arxiv:0906.5488
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Time-dependent close-coupling calculations of the ionization and excitation cross section for antiproton collisions with molecular hydrogen ions are performed in an impact-energy range from 0.5 keV to 10 MeV. The Born-Oppenheimer and Franck-Condon approximations as well as the impact parameter method are applied in order to describe the target molecule and the collision process. It is shown that three perpendicular orientations of the molecular axis with respect to the trajectory are sufficient to accurately reproduce the ionization cross section calculated by [Sakimoto, Phys. Rev. A 71, 062704 (2005)] reducing the numerical effort drastically. The independent-event model is employed to approximate the cross section for double ionization and H+ production in antiproton collisions with H2.
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arxiv:0906.5500
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In this paper, we give some convergence results of Lagrangian mean curvature flow under some stability conditions in a general K\"ahler-Einstein manifold. In particular, we prove that the flow will converge if the initial data is some small perturbation of stable minimal Lagrangian submanifold in a K\"ahler-Einstein manifold.
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arxiv:0906.5527
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We explore the connection between quantum brachistochrone (time-optimal) evolution of a three-qubit system and its residual entanglement called three-tangle. The result shows that the entanglement between two qubits is not required for some brachistochrone evolutions of a three-qubit system. However, the evolution between two distinct states cannot be implemented without its three-tangle, except for the trivial cases in which less than three qubits attend evolution. Although both the probability density function of the time-averaged three-tangle and that of the time-averaged squared concurrence between two subsystems become more and more uniform with the decrease in angles of separation between an initial state and a final state, the features of their most probable values exhibit a different trend.
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arxiv:0907.0052
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The Grothendieck construction is a process to form a single category from a diagram of small categories. In this paper, we extend the definition of the Grothendieck construction to diagrams of small categories enriched over a symmetric monoidal category satisfying certain conditions. Symmetric monoidal categories satisfying the conditions in this paper include the category of $k$-modules over a commutative ring $k$, the category of chain complexes, the category of simplicial sets, the category of topological spaces, and the category of modern spectra. In particular, we obtain a generalization of the orbit category construction in [math/0312214]. We also extend the notion of graded categories and show that the Grothendieck construction takes values in the category of graded categories. Our definition of graded category does not require any coproduct decompositions and generalizes $k$-linear graded categories indexed by small categories defined by Lowen. There are two popular ways to construct functors from the category of graded categories to the category of oplax functors. One of them is the smash product construction defined and studied in [math/0312214,0807.4706,0905.3884] for $k$-linear categories and the other one is the fiber functor. We construct extensions of these functors for enriched categories and show that they are ``right adjoint'' to the Grothendieck construction in suitable senses. As a byproduct, we obtain a new short description of small enriched categories.
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arxiv:0907.0061
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We examine the stability of the valence bond solid (VBS) phase against the Dzyaloshinskii-Moriya (DM) interaction in the bipartite lattice. Despite the VBS is vulnerable against the antiferromagnetic interaction, for example in the Q-J model proposed by Sandvik, where the quantum phase transition occurs at $J^*/Q = 0.04$, we found that on the contrary the VBS is very stable against the DM interaction. The quantum phase transition does not occur until D/Q goes to infinity, where D is the strength of the DM interaction. The VBS in the ALKT model and the Haldane gap system also exhibit the same property.
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arxiv:0907.0080
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The synchrotron self-Compton (SSC) models and External Compton (EC) models of AGN jets with continually longitudinal and transverse bulk velocity structures are constructed. The observed spectra show complex and interesting patterns in different velocity structures and viewing angles. These models are used to calculate the synchrotron and inverse Compton spectra of two typical BL Lac objects (BLO) (Mrk 421 and 0716+714) and one Flat Spectrum Radio Quasars (FSRQs) (3c 279), and to discuss the implications of jet bulk velocity structures in unification of the BLO and FR I radio galaxies (FRI). By calculating the synchrotron spectra and SSC spectra of BL Lac object jets with continually bulk velocity structures, we find that the spectra are much different from ones in jets with uniform velocity structure under the increase of viewing angles. The unification of BLO and FRI is less constrained by viewing angles and would be imprinted by velocity structures intrinsic to the jet themselves. By considering the jets with bulk velocity structures constrained by apparent speed, we discuss the velocity structures imprinted on the observed spectra for different viewing angles. We find that the spectra are greatly impacted by longitudinal velocity structures, becasue the volume elements are compressed or expanded. Finally, we present the EC spectra of FSRQs and FR II radio galaxies (FRII) and find that they are weakly affected by velocity structures compared to synchrotron and SSC spectra.
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arxiv:0907.0094
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We report on Landauer-B\"uttiker studies of anomalous Hall transport in a two-dimensional electron gas with Rashba spin-orbit coupling and a magnetization provided by localized magnetic moments. Our system is described by a discretized tight-binding model in a four-terminal geometry. We consider both the case of magnetically disordered systems as well as ballistic transport in disorder-free systems with spatially homoge- neous magnetization. In the latter case we investigate both out-of-plane and in-plane magnetizations. We numerically establish a close connection between singularities in the density of states and peaks in the Hall conductance close to the lower band edge. Consistent with previous theoretical studies based on diagrammatic perturbation expansions, these peaks occur at Fermi energies where only the lower dispersion branch is occupied. Moreover, for large magnetization the Hall conductance is, along with the density of states, sup- pressed. This numerical finding can be understood from analytical properties of the underlying model in the limit of an infinite system.
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arxiv:0907.0110
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The first and second Born approximation are studied with the path integral representation for $ {\cal T} $ matrix. The $ {\cal T}$ matrix is calculated for Woods-Saxon potential scattering. To make corresponding integrals solvable analytically, an approximate function for the Woods-Saxon potential is used. Finally it shown that the Born series is converge at high energies and orders higher than two in Born approximation series can be neglected.
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arxiv:0907.0115
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We describe the structure of the Lie groups endowed with a left-invariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This description is particularly nice if the group is Hamiltonian, that is, if the left canonical action of the group on itself is Hamiltonian. The principal tool used for our description is a canonical affine structure associated with the symplectic form. We also characterize the Hamiltonian symplectic Lie groups among the connected symplectic Lie groups. We specialize our principal results to the cases of simply connected Hamiltonian symplectic nilpotent Lie groups or Frobenius symplectic Lie groups. Finally we pursue the study of the classical affine Lie group as a symplectic Lie group. MSC Classes 53D20,70G65 Key words:Symplectic Lie groups,Hamiltonian Lie groups, Symplectic reduction,Symplectic double extension.
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arxiv:0907.0124
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The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is supposed to exist, nothing can discriminate two apparently identical states even if they give a different result. In this paper we try to put the basis for a more fundamental theory that (approximately) coincides with quantum mechanics when comparing statistics, but it is more fundamental, since it mathematically describes measurement processes giving an explicit time evolution of the wave function during the collapse. The theory is deterministic even if the Heisenberg uncertainty principle is still valid. The theory distinguishes physical states that collapse and physical states that do not collapse. The theory can be made compatible with all experiments done in the past, but new phenomena such as violations of the Born law or the superposition principle could transpire. However, even if we have probably shown that it is possible to build ad hoc a theory that can describe both the wave function collapse and the Schroedinger linear evolution, a simple and unified construction is still missing.
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arxiv:0907.0125
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In this paper we consider the problem of finding a vector that can be written as a nonnegative integer linear combination of given 0-1 vectors, the generators, such that the l_1-distance between this vector and a given target vector is minimized. We prove that this closest vector problem is NP-hard to approximate within a O(d) additive error, where d is the dimension of the ambient vector space. We show that the problem can be approximated within a O(d^{3/2}) additive error in polynomial time, by rounding an optimal solution of a natural LP relaxation for the problem. We also observe that in the particular case where the target vector is integer and the generators form a totally unimodular matrix, the problem can be solved in polynomial time. The closest vector problem arises in the elaboration of radiation therapy plans. In this context, the target is a nonnegative integer matrix and the generators are certain 0-1 matrices whose rows satisfy the consecutive ones property. Here we mainly consider the version of the problem in which the set of generators comprises all those matrices that have on each nonzero row a number of ones that is at least a certain constant. This set of generators encodes the so-called minimum separation constraint.
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arxiv:0907.0138
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In contrast to the static operations of conventional semiconductor devices, the dynamic conformational freedom in molecular devices opens up the possibility of using molecules as new types of devices such as a molecular conformational switch or for molecular data storage. Bistable molecules, with e.g. two stable cis and trans isomeric configurations, could provide, once clamped between two electrodes, a switching phenomenon in the nonequilibrium current response. Here, we model molecular switch junctions formed at silicon contacts and demonstrate the potential of tunable molecular switches in electrode/molecule/electrode configurations. Using the non equilibrium Green function approach implemented with the density-functional-based tight-binding theory, a series of properties such as electron transmissions, I-V characteristics in the different isomer-conformations, and potential energy surfaces as a function of the reaction coordinates along the trans to cis transition were calculated. Furthermore, in order to investigate stability of molecular switches in ambient conditions, molecular dynamics (MD) simulations at room temperature were performed and time- dependent fluctuations of the conductance along the MD pathways were calculated. Our numerical results show that the transmission spectra of the cis isomers are more conductive than trans counterparts inside the bias window for all two model molecules. The current-voltage characteristics consequently show the same trends. Additionally, the calculations of time-dependent transmission fluctuations along the MD pathways have shown that the transmission in cis isomers is always significantly larger than that of trans counterparts showing that molecular switches can be expected to work as robust molecular switching components.
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arxiv:0907.0155
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New technologies and equipment allow for mass treatment of samples and research teams share acquired data on an always larger scale. In this context scientists are facing a major data exploitation problem. More precisely, using these data sets through data mining tools or introducing them in a classical experimental approach require a preliminary understanding of the information space, in order to direct the process. But acquiring this grasp on the data is a complex activity, which is seldom supported by current software tools. The goal of this paper is to introduce a solution to this scientific data grasp problem. Illustrated in the Tissue MicroArrays application domain, the proposal is based on the synthesis notion, which is inspired by Information Retrieval paradigms. The envisioned synthesis model gives a central role to the study the researcher wants to conduct, through the task notion. It allows for the implementation of a task-oriented Information Retrieval prototype system. Cases studies and user studies were used to validate this prototype system. It opens interesting prospects for the extension of the model or extensions towards other application domains.
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arxiv:0907.0164
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We consider a finite dimensional damped second order system and obtain spectral inclusion theorems for the related quadratic eigenvalue problem. The inclusion sets are the 'quasi Cassini ovals' which may greatly outperform standard Gershgorin circles. As the unperturbed system we take a modally damped part of the system; this includes the known proportionally damped models, but may give much sharper estimates. These inclusions are then applied to derive some easily calculable sufficient conditions for the overdampedness of a given damped system.
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arxiv:0907.0167
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We study the properties of low-column density gas clumps in the halo of the Milky Way based on high-resolution 21-cm observations. Using interferometric data from the WSRT and the VLA we study HI emission at low-, intermediate- and high radial velocities along four lines of sight towards quasars. Along these sightlines we previously detected weak CaII and NaI absorbers in their optical spectra. The analysis of the high-resolution HI data reveals the presence of several compact and cold clumps of neutral gas at velocities similar to the optical absorption. The clumps have narrow HI line widths in the range of 1.8 to 13 km/s, yielding upper limits for the kinetic temperature of the gas of 70 to 3700 K. The neutral gas has low HI column densities in the range of 5E18 to 3E19 1/cm^2. All clumps have angular sizes of only a few arcminutes. Our high-resolution 21-cm observations indicate that many of the CaII and NaI absorbers seen in our optical quasar spectra are associated with low-column density HI clumps at small angular scales. This suggests that next to the massive, high-column density neutral gas clouds in the halo (the common 21-cm LVCs, IVCs, and HVCs) there exists a population of low-mass, neutral gas structures in the halo that remain mostly unseen in the existing 21-cm all-sky surveys of IVCs and HVCs. The estimated thermal gas pressures of the detected HI clumps are consistent with what is expected from theoretical models of gas in the inner and outer Milky Way halo.
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arxiv:0907.0171
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We study the evolution of a cosmological baryon asymmetry produced via leptogenesis by means of the full classical Boltzmann equations, without the assumption of kinetic equilibrium and including all quantum statistical factors. Beginning with the full mode equations we derive the usual equations of motion for the right-handed neutrino number density and integrated lepton asymmetry, and show explicitly the impact of each assumption on these quantities. For the first time, we investigate also the effects of scattering of the right-handed neutrino with the top quark to leading order in the Yukawa couplings by means of the full Boltzmann equations. We find that in our full Boltzmann treatment the final lepton asymmetry can be suppressed by as much as a factor of 1.5 in the weak wash-out regime (K<1), compared to the usual integrated approach which assumes kinetic equilibrium and neglects quantum statistics. This suppression is in contrast with the enhancement seen in some previous studies that considered only decay and inverse decay of the right-handed neutrino. However, this suppression quickly decreases as we increase K. In the strong wash-out regime (K>1), the full Boltzmann treatment and the integrated approach give nearly identical final lepton asymmetries (within 10 % of each other at K>3). Finally, we show that the opposing effects of quantum statistics on decays/inverse decays and the scattering processes tend to reduce the net importance of scattering on leptogenesis in the full treatment compared to the integrated approach.
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arxiv:0907.0205
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Oxypnictide superconductor NdFeAsO0.85 sample was irradiated with 2 GeV Ta ions at a fluence of 5x10^10 ions/cm2. High resolution transmission electron microscopy study revealed that the irradiation produced columnar-like defects. The effect of these defects on the irreversible magnetisation in polycrystalline randomly oriented fragments was studied as a function of field angle and field sweep rate. We find that the critical current density is enhanced at fields below the matching field (~1 Tesla) but only marginally. The pinning enhancement is anisotropic and maximum along the defect direction at high temperatures but the pinning then becomes more isotropic at low temperatures. The creep rate is suppressed at high temperatures and at fields below the matching field, indicating the columnar defects are efficient pinning sites at these H and T conditions.
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arxiv:0907.0217
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We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means to handle the otherwise uncontrolled exceptional set.
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arxiv:0907.0245
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For a braided vector space $(V,\sigma)$ with braiding $\sigma$ of Hecke type, we introduce three associative algebra structures on the space $\oplus_{p=0}^{M}\mathrm{End}S_\sigma^p(V)$ of graded endomorphisms of the quantum symmetric algebra $S_\sigma(V)$. We use the second product to construct a new trace. This trace is an algebra morphism with respect to the third product. In particular, when $V$ is the fundamental representation of $\mathcal{U}_{q}\mathfrak{sl}_{N+1}$ and $\sigma$ is the action of the $R$-matrix, this trace is a scalar multiple of the quantum trace of type $A$.
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arxiv:0907.0257
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This paper is devoted to the study of the stochastic fixed-point equation X \stackrel{d}{=} \inf_{i \geq 1: T_i > 0} X_i/T_i and the connection with its additive counterpart $X \stackrel{d}{=} \sum_{i\ge 1}T_{i}X_{i}$ associated with the smoothing transformation. Here $\stackrel{d}{=}$ means equality in distribution, $T := (T_i)_{i \geq 1}$ is a given sequence of nonnegative random variables and $X, X_1, ...$ is a sequence of nonnegative i.i.d. random variables independent of $T$. We draw attention to the question of the existence of nontrivial solutions and, in particular, of special solutions named $\alpha$-regular solutions $(\alpha>0)$. We give a complete answer to the question of when $\alpha$-regular solutions exist and prove that they are always mixtures of Weibull distributions or certain periodic variants. We also give a complete characterization of all fixed points of this kind. A disintegration method which leads to the study of certain multiplicative martingales and a pathwise renewal equation after a suitable transform are the key tools for our analysis. Finally, we provide corresponding results for the fixed points of the related additive equation mentioned above. To some extent, these results have been obtained earlier by Iksanov.
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arxiv:0907.0300
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We prove that a composition operator is bounded on the Hardy space $H^2$ of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative $\lambda$ there. In this case the norm, essential norm, and spectral radius of the operator are all equal to $\sqrt{\lambda}$.
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arxiv:0907.0350
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Madam is a CMB map-making code, designed to make temperature and polarization maps of time-ordered data of total power experiments like Planck. The algorithm is based on the destriping technique, but it also makes use of known noise properties in the form of a noise prior. The method in its early form was presented in an earlier work by Keihanen et al. (2005). In this paper we present an update of the method, extended to non-averaged data, and include polarization. In this method the baseline length is a freely adjustable parameter, and destriping can be performed at a different map resolution than that of the final maps. We show results obtained with simulated data. This study is related to Planck LFI activities.
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arxiv:0907.0367
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It is shown that $u_k \cdot v_k$ converges weakly to $u\cdot v$ if $u_k\weakto u$ weakly in $L^p$ and $v_k\weakly v$ weakly in $L^q$ with $p, q\in (1,\infty)$, $1/p+1/q=1$, under the additional assumptions that the sequences $\Div u_k$ and $\curl v_k$ are compact in the dual space of $W^{1,\infty}_0$ and that $u_k\cdot v_k$ is equi-integrable. The main point is that we only require equi-integrability of the scalar product $u_k\cdot v_k$ and not of the individual sequences.
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arxiv:0907.0397
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The motion of sufficiently small body in general relativity should be accurately described by a geodesic. However, there should be ``gravitational self-force'' corrections to geodesic motion, analogous to the ``radiation reaction forces'' that occur in electrodynamics. It is of considerable importance to be able to calculate these self-force corrections in order to be able to determine such effects as inspiral motion in the extreme mass ratio limit. However, severe difficulties arise if one attempts to consider point particles in the context of general relativity. This article describes these difficulties and how they have been dealt with.
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arxiv:0907.0412
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We consider a quantum model of a nanomechanical flexing beam resonator interacting with a bath comprising a few damped tunneling two level systems (TLS's). In contrast with a resonator interacting bilinearly with an ohmic free oscillator bath (modeling clamping loss, for example), the mechanical resonator damping is amplitude dependent, while the decoherence of quantum superpositions of mechanical position states depends only weakly on their spatial separation.
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arxiv:0907.0431
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We have fabricated hybrid magnetic complexes from V atoms and tetracyanoethylene (TCNE) ligands via atomic manipulation with a cryogenic scanning tunneling microscope. Using tunneling spectroscopy we observe spin-polarized molecular orbitals as well as Kondo behavior. For complexes having two V atoms, the Kondo behavior can be quenched for different molecular arrangements, even as the spin-polarized orbitals remain unchanged. This is explained by variable spin-spin (i.e., V-V) ferromagnetic coupling through a single TCNE molecule, as supported by density functional calculations.
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arxiv:0907.0490
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The Littlest Higgs Model with T-parity is one of the attractive candidates of physics beyond the Standard Model. One of the important predictions of the model is the existence of new heavy gauge bosons, where they acquire mass terms through the breaking of global symmetry necessarily imposed on the model. The determination of the masses are, hence, quite important to test the model. In this paper, the measurement accuracy of the heavy gauge bosons at ILC is eported.
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arxiv:0907.0525
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Starting from the full--shift on a finite alphabet $A$, mingling some symbols of $A$, we obtain a new full shift on a smaller alphabet $B$. This amalgamation defines a factor map from $(A^{\mathbb N},T_A)$ to $(B^{\mathbb N},T_B)$, where $T_A$ and $T_B$ are the respective shift maps. According to the thermodynamic formalism, to each regular function (`potential') $\psi:A^{\mathbb N}\to{\mathbb R}$, we can associate a unique Gibbs measure $\mu_\psi$. In this article, we prove that, for a large class of potentials, the pushforward measure $\mu_\psi\circ\pi^{-1}$ is still Gibbsian for a potential $\phi:B^{\mathbb N}\to{\mathbb R}$ having a `bit less' regularity than $\psi$. In the special case where $\psi$ is a `2--symbol' potential, the Gibbs measure $\mu_\psi$ is nothing but a Markov measure and the amalgamation $\pi$ defines a hidden Markov chain. In this particular case, our theorem can be recast by saying that a hidden Markov chain is a Gibbs measure (for a H\"older potential).
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arxiv:0907.0528
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We study the one-neutron removal strength of the 7He ground state, which provides us with the 6He-n component in 7He. The He isotopes are described on the basis of the 4He+Xn cluster model (X=1,2,3). The complex scaling method is applied to describe not only the Gamow resonances but also the nonresonant continuum states of valence neutrons, with the correct boundary condition of particle decays. The one-neutron removal strength of 7He into the unbound states of 6He is calculated using the complex-scaled Green's function, in which a complex-scaled complete set of 4He+n+n states is adopted. Using this framework, we investigate resonant and nonresonant contributions of the strength, which individually produce specific structures in the distributions. In addition, we propose a method to obtain the real-value strength using the complex values of spectroscopic factors of Gamow states. As a result, the 6He(2+) resonance is found to give the largest contribution.
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arxiv:0907.0531
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The Large Area Telescope (LAT) instrument on board the Fermi satellite consists of a multi-layer silicon-strip tracker interleaved with tungsten converters (TKR), followed by a CsI crystal hodoscopic calorimeter (CAL). Sixteen TKR and CAL modules are assembled in a 4$\times$4 array. A segmented anticoincidence plastic scintillator (ACD) surrounds the TKRs. The primary cosmic-ray electron/positron energy spectrum has been measured from 20 GeV to 1 TeV using a dedicated event analysis that ensures efficient electron detection and reduced hadron contamination. Results from detailed Monte Carlo simulations have been used to reconstruct the observed energy spectrum to the primary cosmic ray spectrum. We present here details of the analysis procedure and the energy spectrum reconstruction.
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arxiv:0907.0638
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The challenge of designing an efficient Medium Access Control (MAC) protocol and analyzing it has been an important research topic for over 30 years. This paper focuses on the performance analysis (through simulation) and modification of a well known MAC protocol CSMA/CD. The existing protocol does not consider the wastage of bandwidth due to unutilized periods of the channel. By considering this fact, performance of MAC protocol can be enhanced. The purpose of this work is to modify the existing protocol by enabling it to adapt according to state of the network. The modified protocol takes appropriate action whenever unutilized periods detected. In this way, to increase the effective bandwidth utilization and determine how it behaves under increasing load, and varying packet sizes. It will also include effects of attacks i.e. Denial of service attacks, Replay Attack, Continuous Channel Access or Exhaustion attack, Flooding attack, Jamming (Radio interference) attack, Selective forwarding attack which degrade performance of MAC protocol. In Continuous Channel Access or Exhaustion attack, a malicious node disrupts the MAC protocol, by continuously requesting or transmitting over the channel. This eventually leads a starvation for other nodes in the network w.r.t channel access. remedy may be the network ignores excessive requests without sending expensive radio transmissions. This limit however cannot drop below the expected maximum data rate the network has to support. This limit is usually coded into the protocol during the design phase and requires additional logic also. Repeated application of these exhaustion or collision based MAC layer attacks can lead into unfairness.
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arxiv:0907.0678
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Using an integrable discrete Dirac operator, we construct a discrete version of the Weierstrass representation of time-like surfaces parametrized along isotropic directions in $R^{2,1}$, $R^{3,1}$ and $R^{2,2}$. The corresponding discrete surfaces have isotropic edges. We show that any discrete surface satisfying a general monotonicity condition and having isotropic edges admits such a representation.
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arxiv:0907.0688
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We present an alternative technique for measuring the precursor masses of transient events in stars undergoing late stage stellar evolution. We use the well-established techniques of stellar population modeling to age-date the stars surrounding the site of the recent transient event in NGC 300 (NGC 300 OT2008-1). The surrounding stars must share a common turnoff mass with the transient, since almost all stars form in stellar clusters that remain physically associated for periods longer than the lifetime of the most massive stars. We find that the precursor of NGC 300 OT2008-1 is surrounded by stars that formed in a single burst between 8-13 Myr ago, with 70% confidence. The transient was therefore likely to be due to a progenitor whose mass falls between the main sequence turnoff mass (12 Msun) and the maximum stellar mass (25 Msun) found for isochrones bounding this age range. We characterize the general applicability of this technique in identifying precursor masses of historic and future transients and supernovae (SNe), noting that it requires neither precursor imaging nor sub-arcsecond accuracy in the position of the transient. It is also based on the well-understood physics of the main sequence, and thus may be a more reliable source of precursor masses than fitting evolutionary tracks to precursor magnitudes. We speculate that if the progenitor mass is close to 17 Msun, there may be a connection between optical transients such as NGC 300 OT2008-1 and the missing type II-P SNe, known as the "red supergiant problem."
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arxiv:0907.0710
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It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we compute the corresponding sequences of Poisson-commuting functions when the contact manifold is the unit cotangent bundle of a Riemannian manifold.
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arxiv:0907.0789
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We present a document compression system that uses a hierarchical noisy-channel model of text production. Our compression system first automatically derives the syntactic structure of each sentence and the overall discourse structure of the text given as input. The system then uses a statistical hierarchical model of text production in order to drop non-important syntactic and discourse constituents so as to generate coherent, grammatical document compressions of arbitrary length. The system outperforms both a baseline and a sentence-based compression system that operates by simplifying sequentially all sentences in a text. Our results support the claim that discourse knowledge plays an important role in document summarization.
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arxiv:0907.0806
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We search for persistent and quasi-periodic release events of streamer blobs during 2007 with the Large Angle Spectrometric Coronagraph on the \textit{Solar and Heliospheric Observatory} and assess the velocity of the slow solar wind along the plasma sheet above the corresponding streamer by measuring the dynamic parameters of blobs. We find 10 quasi-periodic release events of streamer blobs lasting for three to four days. In each day of these events, we observe three-five blobs. The results are in line with previous studies using data observed near the last solar minimum. Using the measured blob velocity as a proxy for that of the mean flow, we suggest that the velocity of the background slow solar wind near the Sun can vary significantly within a few hours. This provides an observational manifestation of the large velocity variability of the slow solar wind near the Sun.
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arxiv:0907.0819
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We argue with claims of the paper [Agostini F., Caprara S. and Ciccotti G., Europhys. Lett. EPL, 78 (2007) Art. 30001, 6] that the quantum-classic bracket introduced in [arXiv:quant-ph/0506122] produces "artificial coupling" and has "genuinely classical nature". Keywords: p-mechanics, quantum, classic, commutator, Poisson bracket, mixing, coupling, semi-classical
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arxiv:0907.0855
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This research report presents an extension of Cumulative of Choco constraint solver, which is useful to encode over-constrained cumulative problems. This new global constraint uses sweep and task interval violation-based algorithms.
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arxiv:0907.0939
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In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward--backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the differentiability of a FBSDE with respect to the initial value of its forward component. This enables us to obtain the main result of this article, namely a representation formula for the control component of its solution. The latter is relevant in the context of securitization of random liabilities arising from exogenous risk, which are optimally hedged by investment in a given financial market with respect to exponential preferences. In a purely stochastic formulation, the control process of the backward component of the FBSDE steers the system into the random liability and describes its optimal derivative hedge by investment in the capital market, the dynamics of which is given by the forward component.
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arxiv:0907.0941
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It has been conjectured that the algebraic crossing number of a link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links. The Morton-Franks-Williams inequality gives a lower bound for braid index. And sharpness of the inequality on a knot type implies the truth of the conjecture for the knot type. We prove that there are infinitely many examples of knots and links for which the inequality is not sharp but the conjecture is still true. We also show that if the conjecture is true for K and L, then it is also true for the (p,q)-cable of K and for the connect sum of K and L.
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arxiv:0907.1019
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The exclusive reaction $\gamma p \to p \pi^+ \pi^-$ was studied in the photon energy range 3.0 - 3.8 GeV and momentum transfer range $0.4<-t<1.0$ GeV$^2$. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. In this kinematic range the integrated luminosity was about 20 pb$^{-1}$. The reaction was isolated by detecting the $\pi^+$ and proton in CLAS, and reconstructing the $\pi^-$ via the missing-mass technique. Moments of the di-pion decay angular distributions were derived from the experimental data. Differential cross sections for the $S$, $P$, and $D$-waves in the $M_{\pi^+\pi^-}$ mass range $0.4-1.4$ GeV were derived performing a partial wave expansion of the extracted moments. Besides the dominant contribution of the $\rho(770)$ meson in the $P$-wave, evidence for the $f_0(980)$ and the $f_2(1270)$ mesons was found in the $S$ and $D$-waves, respectively. The differential production cross sections $d\sigma/dt$ for individual waves in the mass range of the above-mentioned mesons were extracted. This is the first time the $f_0(980)$ has been measured in a photoproduction experiment.
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arxiv:0907.1021
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We review the foundations and the applications of the statistical and the quark recombination model as hadronization models.
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arxiv:0907.1031
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The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hormander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime.
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arxiv:0907.1034
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The flat-spectrum radio-quasar 3C279 (z=0.536) is the most distant object detected at very high energy (VHE) gamma-rays. It is thus an important beacon for the study of the interaction of the VHE gamma-rays with the Extra-galactic Background Light (EBL). Previous observations by EGRET showed a highly variable flux that can differ up to a factor of 100. In this paper results from an observation campaign with the MAGIC telescope during an optical flare in January 2007 will be presented and previous MAGIC results from 2006 will be summarized.
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arxiv:0907.1046
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We extend earlier work by studying in the quiet Sun the line profiles of the hydrogen Lyman-alpha and Lyman-beta lines, which were obtained quasi-simultaneously in a raster scan near disk center. The self-reversal depths of the Ly-a and Ly-b profiles are quantified by measuring the maximum spectral radiances of the two horns and the minimum spectral radiance of the central reversal. The information on the asymmetries of the Ly-a and Ly-b profiles is obtained through the calculation of the 1st and 3rd-order moments of the line profiles. We find that the emissions of the Lyman lines tend to be more strongly absorbed in the internetwork, as compared to those in the network region. Almost all of the Ly-a profiles are self-reversed, whilst about 17% of the Ly-b profiles are not reversed. The ratio of Ly-a and Ly-b intensities seems to be independent of the magnetic field strength. Most Ly-a profiles are stronger in the blue horn, while most Ly-b profiles are stronger in the red horn. However, the opposite asymmetries of Ly-a and Ly-b are not pixel-to-pixel correlated. We also confirm that when larger transition-region downflows are present, the Ly-a and Ly-b profiles are more enhanced in the blue and red horns, respectively. The first-order moment of Ly-b, which reflects the combined effects of the profile asymmetry and motion of the emitting material, strongly correlates with the Doppler shifts of the Si iii and O vi lines, whilst for Ly-a this correlation is much weaker. Our analysis shows that both Ly-a and Ly-b might be more redshifted if larger transition-region downflows are present. We also find that the observed average Ly-b profile is redshifted with respect to its rest position.
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arxiv:0907.1069
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The rank problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form rank(k) = Sum_{i=1}^k A[i]. The problem has been intensely studied, and features as a subroutine in a majority of succinct data structures. We show that in the cell probe model with w-bit cells, if rank takes t time, the space of the data structure must be at least n + n/w^{O(t)} bits. This redundancy/query trade-off is essentially optimal, matching our upper bound from [FOCS'08].
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arxiv:0907.1103
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The possible quantum Hall ferromagnet at a filling factor $\nu =0$ is investigated for the zero-energy (N=0) Landau level of the two dimensional massless Dirac fermions in $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure with tilted cones and a twofold valley degeneracy resulting from time-reversal symmetry. In the case of the Dirac cones without tilting, the long-range Coulomb interaction in the N=0 Landau level exhibits the SU(2) valley-pseudo-spin symmetry even to the order $O(a/l_{\rm H})$, in contrast to $N \ne 0$ Landau levels, where $a$ and $l_{\rm H}$ represent the lattice constant and the magnetic length, respectively. Such a characteristic comes from a fact that zero-energy states in a particular valley are restricted to only one of the spinor components, whereas the other spinor component is necessarily zero. In the case of the tilted Dirac cones as found in $\alpha$-(BEDT-TTF)$_2$I$_3$, one obtains a non-zero value of the second component and then the ackscattering processes between valleys becomes non-zero. It is shown that this fact can lead to easy-plane pseudospin ferromagnetism (XY-type). In this case, the phase fluctuations of the order parameters can be described by the XY model leading to Kosterlitz-Thouless transition at lower temperature. In view of these theoretical results, experimental findings in resistivity of $\alpha$-(BEDT-TTF)$_2$I$_3$ are discussed.
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arxiv:0907.1160
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This work focuses on the fabrication and use of a Biological Micro-ElectroMechanical System (BioMEMS) for TeraHertz (THz) detection and characterization of enzymatic catalysis reactions. The fluidic microdevice was fabricated using traditional lithographic techniques. It was then functionalized by reactive amine functions using plasma polymerized allylamine (pp-allylamine), followed by enzyme immobilization inside the microchannels. The enzymatic reaction was controlled by fluorescent microscopy before being analysed by sub-THz spectroscopy in the frequency range 0.06--0.11 THz. The preliminary results show the feasibility of terahertz monitoring of the biocatalysis reaction.
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arxiv:0907.1162
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The thermodynamics of the lattice model of intercalation of ions in crystals is considered in the mean field approximation. Pseudospin formalism is used for the description of interaction of electrons with ions and the possibility of hopping of intercalated ions between different positions is taken into account. Phase diagrams are built. It is shown that the effective interaction between intercalated ions can lead to phase separation or to appearance of modulated phase (it depends on filling of the electron energy band). At high values of the parameter of ion transfer the ionic subsystem can pass to the superfluid-like state.
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arxiv:0907.1181
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The CoRoT satellite has provided high-quality light curves of several solar-like stars. Analysis of the light curves provides oscillation frequencies that make it possible to probe the interior of the stars. However, additional constraints on the fundamental parameters of the stars are important for the theoretical modelling to be successful. We will estimate the fundamental parameters (mass, radius and luminosity) of the first four solar-like targets to be observed in the asteroseismic field. In addition, we will determine their effective temperature, metallicity and detailed abundance pattern. To constrain the stellar mass, radius and age we use the SHOTGUN software which compares the location of the stars in the Hertzsprung-Russell diagram with theoretical evolution models. This method takes into account the uncertainties of the observed parameters including the large separation determined from the solar-like oscillations. We determine the effective temperatures and abundance patterns in the stars from the analysis of high-resolution spectra. We have determined the mass, radius and luminosity of the four CoRoT targets to within 5-10 percent, 2-4 percent and 5-13 percent, respectively. The quality of the stellar spectra determines how well we can constrain the effective temperature. For the two best spectra we get 1-sigma uncertainties below 60 K and for the other two 100-150 K. The uncertainty on the surface gravity is less than 0.08 dex for three stars while for HD 181906 it is 0.15 dex. The reason for the larger uncertainty is that the spectrum has two components with a luminosity ratio of Lp/Ls = 0.50+-0.15. While Hipparcos astrometric data strongly suggest it is a binary star we find evidence that the fainter star may be a background star, since it is less luminous but hotter.
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arxiv:0907.1198
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We present a rigorous derivation of classical molecular dynamics (MD) from quantum molecular dynamics (QMD) that applies to the standard Hamiltonians of molecular physics with Coulomb interactions. The derivation is valid away from possible electronic eigenvalue crossings.
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arxiv:0907.1205
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We test the ability of semiclassical theory to describe quantitatively the revival of quantum wavepackets --a long time phenomena-- in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wavefunction up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times.
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arxiv:0907.1220
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In this paper, we propose an HB-like protocol for privacy-preserving authentication of RFID tags, whereby a tag can remain anonymous and untraceable to an adversary during the authentication process. Previous proposals of such protocols were based on PRF computations. Our protocol can instead be used on low-cost tags that may be incapable of computing standard PRFs. Moreover, since the underlying computations in HB protocols are very efficient, our protocol also reduces reader load compared to PRF-based protocols. We suggest a tree-based approach that replaces the PRF-based authentication from prior work with a procedure such as HB+ or HB#. We optimize the tree- traversal stage through usage of a "light version" of the underlying protocol and shared random challenges across all levels of the tree. This provides significant reduction of the communication resources, resulting in a privacy-preserving protocol almost as efficient as the underlying HB+ or HB#
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arxiv:0907.1227
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The possibility of the decomposition of the three dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schr\"{o}dinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, solutions of the 3D controlled GPE can be constructed from the solutions of a 2D linear Schr\"{o}dinger equation (transverse component of the GPE) coupled with a 1D nonlinear Schr\"{o}dinger equation (longitudinal component of the GPE). Such a decomposition, called the 'controlling potential method' (CPM), allows one to cast the above solutions in the form of the product of the solutions of the transverse and the longitudinal components of the GPE. The coupling between these two equations is the functional of both the transverse and the longitudinal profiles. The analysis shows that the CPM is based on the variational principle that sets up a condition on the controlling potential well, and whose physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control operation.
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arxiv:0907.1240
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We study the influence of mutual interaction on the conformation of flexible poly(propyleneamine) dendrimers of fourth generation in concentrated solution. Mixtures of dendrimers with protonated and deuterated end groups are investigated by small-angle neutron scattering up to volume fractions of 0.23. This value is in the range of the overlap concentration of the dendrimers. The contrast between the solute and the solvent was varied by using mixtures of protonated and deuterated solvents. This allows us to investigate the partial structure factors of the deuterated dendrimers in detail. An analysis of the measured scattering intensities reveals that the shape of the flexible dendrimers is practically independent of the concentration in contrast to the pronounced conformational changes of flexible linear polymers.
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arxiv:0907.1241
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The availability of Bose-Einstein condensates as mesoscopic or macroscopic quantum objects has aroused new interest in the possiblity of making and detecting coherent superpositions involving many atoms. In this article we show that it may be possible to generate such a superposition state in a reasonably short time using Feshbach resonances to tune the inter-atomic interactions in a double-well condensate. We also consider the important problem of distinguishing whether a coherent superposition or a statistical mixture is generated by a given experimental procedure. We find that unambiguously distinguishing even a perfect `NOON' state from a statistical mixture using standard detection methods will present experimental difficulties.
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arxiv:0907.1333
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We report on the analysis of the low-energy electron-recoil spectrum from the CDMS II experiment using data with an exposure of 443.2 kg-days. The analysis provides details on the observed counting rate and possible background sources in the energy range of 2 - 8.5 keV. We find no significant excess in the counting rate above background, and compare this observation to the recent DAMA results. In the framework of a conversion of a dark matter particle into electromagnetic energy, our 90% confidence level upper limit of 0.246 events/kg/day at 3.15 keV is lower than the total rate above background observed by DAMA by 8.9$\sigma$. In absence of any specific particle physics model to provide the scaling in cross section between NaI and Ge, we assume a Z^2 scaling. With this assumption the observed rate in DAMA differs from the upper limit in CDMS by 6.8$\sigma$. Under the conservative assumption that the modulation amplitude is 6% of the total rate we obtain upper limits on the modulation amplitude a factor of ~2 less than observed by DAMA, constraining some possible interpretations of this modulation.
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arxiv:0907.1438
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We compare the detection abilities for the relic gravitational waves by two kinds of forthcoming cosmic microwave background radiation (CMB) experiments, space-based Planck satellite and the various ground-based experiments. Comparing with the ground-based experiments, Planck satellite can observe all the CMB power spectra in all the multipole range, but having much larger instrumental noises. We find that, for the uncertainty of the tensor-to-scalar ratio $\Delta r$, PolarBear (II) as a typical ground-based experiment can give much smaller value than Planck satellite. However, for the uncertainty of the spectral index $\Delta n_t$, Planck can give the similar result with PolarBear (II). If combining these two experiments, the value of $\Delta n_t$ can be reduced by a factor 2. For the model with $r=0.1$, the constraint $\Delta n_t=0.10$ is expected to be achieved, which provides an excellent opportunity to study the physics in the very early universe. We also find the observation in the largest scale ($\ell<20$) is very important for constraining the spectral index $n_t$. So it is necessary to combine the observations of the future space-based and ground-based CMB experiments to determine the relic gravitational waves.
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arxiv:0907.1453
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We investigate the prospects for indirect detection of right-handed sneutrino dark matter at the IceCube neutrino telescope in a $U(1)_{B-L}$ extension of the MSSM. The capture and annihilation of sneutrinos inside the Sun reach equilibrium, and the flux of produced neutrinos is governed by the sneutrino-proton elastic scattering cross section, which has an upper bound of $8 \times 10^{-9}$ pb from the $Z^{\prime}$ mass limits in the $B-L$ model. Despite the absence of any spin-dependent contribution, the muon event rates predicted by this model can be detected at IceCube since sneutrinos mainly annihilate into leptonic final states by virtue of the fermion $B-L$ charges. These subsequently decay to neutrinos with 100% efficiency. The Earth muon event rates are too small to be detected for the standard halo model irrespective of an enhanced sneutrino annihilation cross section that can explain the recent PAMELA data. For modified velocity distributions, the Earth muon events increase substantially and can be greater than the IceCube detection threshold of 12 events $\mathrm{km}^{-2}$ $\mathrm{yr}^{-1}$. However, this only leads to a mild increase of about 30% for the Sun muon events. The number of muon events from the Sun can be as large as roughly 100 events $\mathrm{km}^{-2}$ $\mathrm{yr}^{-1}$ for this model.
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arxiv:0907.1486
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Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the lossy bosonic channel, but extension to other capacities and other Gaussian channels seems feasible. Solutions for both memoryless and memory channels are presented. It is first dealt with single use (single-mode) channel where the capacity dependence from channel's parameters is analyzed providing a full classification of the possible cases. Then it is dealt with multiple uses (multi-mode) channel where the capacity dependence from the (multi-mode) environment state is analyzed when both total environment energy and environment purity are fixed. This allows a fair comparison among different environments, thus understanding the role of memory (inter-mode correlations) and phenomenon like superadditivity of the capacity. The developed methods are also used for deriving transmission rates with heterodyne and homodyne measurements at the channel output. Classical capacity and transmission rates are presented within a unique framework where the rates can be treated as logarithmic approximations of the capacity.
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arxiv:0907.1532
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