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We establish theoretical bounds on qubit detuning for high fidelity controlled-NOT logic gate implementations with weakly coupled Josephson phase qubits. It is found that the value of qubit detuning during the entangling pulses must not exceed 2g for two-step, and g for single-step control sequences, where g is the relevant coupling constant.
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arxiv:0901.0001
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The EM algorithm is a widely used methodology for penalized likelihood estimation. Provable monotonicity and convergence are the hallmarks of the EM algorithm and these properties are well established for smooth likelihood and smooth penalty functions. However, many relaxed versions of variable selection penalties are not smooth. The goal of this paper is to introduce a new class of Space Alternating Penalized Kullback Proximal extensions of the EM algorithm for nonsmooth likelihood inference. We show that the cluster points of the new method are stationary points even when on the boundary of the parameter set. Special attention has been paid to the construction of component-wise version of the method in order to ease the implementation for complicated models. Illustration for the problems of model selection for finite mixtures of regression and to sparse image reconstruction is presented.
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arxiv:0901.0017
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As a generalization of Postnikov's construction (see arXiv: math/0609764), we define a map from the space of edge weights of a directed network in an annulus into a space of loops in the Grassmannian. We then show that universal Poisson brackets introduced for the space of edge weights in arXiv: 0805.3541 induce a family of Poisson structures on rational-valued matrix functions and on the space of loops in the Grassmannian. In the former case, this family includes, for a particular kind of networks, the Poisson bracket associated with the trigonometric R-matrix.
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arxiv:0901.0020
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We study the optic control for birefringence of a polarized light by an atomic ensemble with a tripod configuration, which is mediated by the electromagnetically induced transparency with a spatially inhomogeneous laser. The atom ensemble splits the linearly polarized light ray into two orthogonally-polarized components, whose polarizations depend on quantum superposition of the initial states of the atom ensemble. Accompanied with this splitting, the atom ensemble behaves as a birefringent lens, which allows one polarized light ray passing through straightly while focus another orthogonal to this polarization with finite aberration of focus.
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arxiv:0901.0078
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Two distinct types of magnetoresistance oscillations are observed in two electronic Fabry-Perot interferometers of different sizes in the integer quantum Hall regime. Measuring these oscillations as a function of magnetic field and gate voltages, we observe three signatures that distinguish the two types. The oscillations observed in a 2.0 square micron device are understood to arise from the Coulomb blockade mechanism, and those observed in an 18 square micron device from the Aharonov-Bohm mechanism. This work clarifies, provides ways to distinguish, and demonstrates control over, these distinct physical origins of resistance oscillations seen in electronic Fabry-Perot interferometers.
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arxiv:0901.0127
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The relationship between point vortex dynamics and the properties of polynomials with roots at the vortex positions is discussed. Classical polynomials, such as the Hermite polynomials, have roots that describe the equilibria of identical vortices on the line. Stationary and uniformly translating vortex configurations with vortices of the same strength but positive or negative orientation are given by the zeros of the Adler-Moser polynomials, which arise in the description of rational solutions of the Korteweg-de Vries equation. For quadupole background flow, vortex configurations are given by the zeros of polynomials expressed as wronskians of Hermite polynomials. Further new solutions are found in this case using the special polynomials arising the in the description of rational solutions of the fourth Painleve equation.
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arxiv:0901.0139
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Airy integrals are very classical but in recent years they have been generalized to higher dimensions and these generalizations have proved to be very useful in studying the topology of the moduli spaces of curves. We study a natural generalization of these integrals when the ground field is a non-archimedean local field such as the field of p-adic numbers. We prove that the p-adic Airy integrals are locally constant functions of moderate growth and present evidence that the Airy integrals associated to compact p-adic Lie groups also have these properties.
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arxiv:0901.0190
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Thermodynamic equivalence between classical many-body system and some auxiliary nonlinear auxiliary field is proved. Connection between Hamiltonians of the many-body system and the auxiliary field is derived.
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arxiv:0901.0191
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We propose an explanation of the peculiar linear temperature dependence of the uniform spin susceptibility $\chi(T)$ in ferropnictides. We argue that the linear in $T$ term appears due to non-analytic temperature dependence of $\chi(T)$ in a two-dimensional Fermi liquid. We show that the prefactor of the $T$ term is expressed via the square of the spin-density-wave (SDW) amplitude connecting nested hole and electron pockets. Due to an incipient SDW instability, this amplitude is large, which, along with a small value of the Fermi energy, makes the $T$ dependence of $\chi(T)$ strong. We demonstrate that this mechanism is in quantitative agreement with the experiment.
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arxiv:0901.0238
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In this paper, we discuss some subtle concepts, such as coordinate, measurement, simultaneity, Lorentz-FitzGerald contraction, singularity in fundamental physics. The explanations of these concepts in textbooks are usually incomplete and lead to puzzles. Some long-standing paradoxes such as the Ehrenfest one are caused by misinterpretation of these concepts. The analysis shows these concepts all have simple and naive meanings, and can be well understood using suitable logical procedure. The discussion may shed light on some famous paradoxes, and provide some new insights into the structure and features of a promising unified field theory.
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arxiv:0901.0309
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We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are related to cost-sensitive binary classification. As well as clarifying relationships between generative and discriminative views of learning, the new machinery leads to tight and more general surrogate loss bounds and generalised Pinsker inequalities relating f-divergences to variational divergence. The new viewpoint illuminates existing algorithms: it provides a new derivation of Support Vector Machines in terms of divergences and relates Maximum Mean Discrepancy to Fisher Linear Discriminants. It also suggests new techniques for estimating f-divergences.
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arxiv:0901.0356
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This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers acting on M${\rm \ddot{o}}$bius invariant spaces $Q_p$, which unify BMOA and Bloch space in the scale of $p$. The boundedness and compactness of these operators on $Q_p$ spaces are determined by means of an embedding theorem, i.e. $Q_p$ spaces boundedly embedded in the non-isotropic tent type spaces $T_q^\infty$.
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arxiv:0901.0366
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We investigate birationality of the anti-pluricanonical map $\phi_{-m}$, the rational map defined by the anti-pluricanonical system $|-mK|$, on $\mathbb{Q}$-Fano threefolds.
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arxiv:0901.0413
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Recently, charge radii and ground-state electromagnetic moments of Li and Be isotopes were measured precisely. We have performed large-scale ab initio no-core shell model calculations for these isotopes using high-precision nucleon-nucleon potentials. The isotopic trends of our computed charge radii and quadrupole and magnetic-dipole moments are in good agreement with experimental results with the exception of the 11Li charge radius. The magnetic moments are in particular well described, whereas the absolute magnitudes of the quadrupole moments are about 10% too small. The small magnitude of the 6Li quadrupole moment is reproduced, and with the CD-Bonn NN potential, also its correct sign.
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arxiv:0901.0453
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The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and reaches from the middle to the boundary. This transition is of the same type and has the same finite-size scaling properties as the corresponding transition for the Cayley tree. At the upper threshold, on the other hand, a single unbounded cluster forms which overwhelms all the others and occupies a finite fraction of the volume as well as of the boundary connections. The finite-size scaling properties for this upper threshold are different from those of the Cayley tree and two of the critical exponents are obtained. The results suggest that the percolation transition for the hyperbolic lattices forms a universality class of its own.
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arxiv:0901.0483
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A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN.
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arxiv:0901.0512
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We present a recent proposal of a simple prescription for including low-energy weak-interactions into the framework of holographic QCD, based on the standard AdS/CFT dictionary of double-trace deformations. This opens a new perspective on phenomenological applications of holographic QCD: calculating weak observables in the strongly coupled regime of QCD. The idea is general enough to be implemented in any holographic model. Its efficiency and usefulness are demonstrated by performing few exemplar calculations of weak reactions involving mesons and baryons, within the Sakai-Sugimoto and hard/soft wall holographic models.
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arxiv:0901.0563
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In this paper we prove that the Poincar\'e map associated to a Lorenz like flow has exponential decay of correlations with respect to Lipschitz observables. This implies that the hitting time associated to the flow satisfies a logarithm law. The hitting time $\tau_r(x,x_0)$ is the time needed for the orbit of a point $x$ to enter for the first time in a ball $B_r(x_0)$ centered at $x_0$, with small radius $r$. As the radius of the ball decreases to 0 its asymptotic behavior is a power law whose exponent is related to the local dimension of the SRB measure at $x_0$: for each $x_0$ such that the local dimension $d_{\mu}(x_0)$ exists, \lim_{r\to 0} \frac{\log \tau_r(x,x_0)}{-\log r} = d_{\mu}(x_0)-1 holds for $\mu$ almost each $x$. In a similar way it is possible to consider a quantitative recurrence indicator quantifying the speed of coming back of an orbit to its starting point. Similar results holds for this recurrence indicator.
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arxiv:0901.0574
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We compute a twisted first cohomology group of the automorphism group of a free group with coefficients in the abelianization $V$ of the IA-automorphism group of a free group. In particular, we show that it is generated by two crossed homomorphisms constructed with the Magnus representation and the Magnus expansion due to Morita and Kawazumi respectively. As a corollary, we see that the first Johnson homomorphism does not extend to the automorphism group of a free group as a crossed homomorphism for the rank of the free group is greater than 4.
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arxiv:0901.0589
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The paper focuses on general properties of parametric minimum contrast estimators. The quality of estimation is measured in terms of the rate function related to the contrast, thus allowing to derive exponential risk bounds invariant with respect to the detailed probabilistic structure of the model. This approach works well for small or moderate samples and covers the case of a misspecified parametric model. Another important feature of the presented bounds is that they may be used in the case when the parametric set is unbounded and non-compact. These bounds do not rely on the entropy or covering numbers and can be easily computed. The most important statistical fact resulting from the exponential bonds is a concentration inequality which claims that minimum contrast estimators concentrate with a large probability on the level set of the rate function. In typical situations, every such set is a root-n neighborhood of the parameter of interest. We also show that the obtained bounds can help for bounding the estimation risk, constructing confidence sets for the underlying parameters. Our general results are illustrated for the case of an i.i.d. sample. We also consider several popular examples including least absolute deviation estimation and the problem of estimating the location of a change point. What we obtain in these examples slightly differs from the usual asymptotic results presented in statistical literature. This difference is due to the unboundness of the parameter set and a possible model misspecification.
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arxiv:0901.0655
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The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments focused on the notion of Measure Equivalence between groups, and Orbit Equivalence between group actions. We discuss known invariants and classification results (rigidity) in both areas.
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arxiv:0901.0678
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We study the spectrum of gravitational perturbations around a vacuum de Sitter brane in a 5D asymmetric braneworld model, with induced curvature on the brane. This generalises the stealth acceleration model proposed by Charmousis, Gregory and Padilla (CGP) which realises the Cardassian cosmology in which power law cosmic acceleration can be driven by ordinary matter. Whenever the bulk has infinite volume we find that there is always a perturbative ghost propagating on the de Sitter brane, in contrast to the Minkowski brane case analysed by CGP. We discuss the implication of this ghost for the stealth acceleration model, and identify a limiting case where the ghost decouples as the de Sitter curvature vanishes.
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arxiv:0901.0713
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We analyse new deep g and i-band imaging with the CFHT of 16 QSOs in the redshift range 0.9 to 1.3. The principal points of interest are the symmetry and signs of tidal effects in the QSO hosts and nearby (`companion') galaxies. The sample measures are compared with similar measures on randomly selected field galaxy samples. Asymmetry measures are made for all objects to g ~22, and magnitudes of all galaxies 2 magnitudes fainter. The QSOs are found in denser environments than the field, and are somewhat offset from the centroid of their surrounding galaxies. The QSO hosts appear more disturbed than other galaxies. While the QSO companions and field galaxies have the same average asymmetry, the distribution of asymmetry values is different. QSO companions within 15 arcsec are fainter than average field galaxies. We discuss scenarios that are consistent with these and other measured quantities.
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arxiv:0901.0723
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The silicon trackers of the ATLAS experiment at LHC (CERN) use optical links for data transmission. VCSEL arrays operating at 850 nm are used to transmit optical signals while PIN arrays are used to convert the optical signals into electrical signals. We investigate the feasibility of using the devices at the Super LHC (SLHC). We irradiated VCSEL and GaAs PIN arrays from three vendors and silicon PIN arrays from one vendor. All arrays can be operated up to the SLHC dosage except the GaAs PIN arrays which have very low responsivities after irradiation and hence are probably not suitable for the SLHC application.
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arxiv:0901.0727
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We investigate the early phase of the first state change during the 2008 September-November outburst of H1743-322, first detected by the INTEGRAL satellite. We analyse INTEGRAL, RXTE, Swift, and XMM/Newton observations, which provide coverage of the quiescence to outburst evolution in the 3-200 keV range every few days. The energy spectra are well fitted by a phenomenological model consisting of an exponentially cut-off power law plus a disc component. A more physical model of thermal Comptonisation (and a disc) represents the spectra equally well. In a first phase (up to MJD 54760), the photon index and temperature of the disc do not vary significantly, and have values reminiscent of the Hard State (HS). The timing analysis is also consistent with that of a HS, and shows in particular a rather high degree of variability (~30%), and a strong ~0.5-1 Hz QPO with its first harmonic. The timing and spectral characteristics of H1743-322 are similar to those of the first HS during its 2003 outburst. After MJD 54760, a change to softer spectra and a ~5-6 Hz QPO indicate that the source underwent a state transition into a Hard-Intermediate State (HIMS). We observe in both states a correlation between the QPO frequency and the photon index, which indicates a strong link between the accretion disc, generally understood to determine the QPO frequency, and the corona, which determines the QPO power. The gradual disappearance of the QPO harmonic, and the slowly decreasing hard X-ray flux, imply that the accretion disc gradually moved inwards during the HS.
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arxiv:0901.0731
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We show that certain classes of contact 3-manifolds do not admit non-separating contact type embeddings into any closed symplectic 4-manifolds, e.g. this is the case for all contact manifolds that are (partially) planar or have Giroux torsion. The latter implies that manifolds with Giroux torsion do not admit contact type embeddings into any closed symplectic 4-manifolds. Similarly, there are symplectic 4-manifolds that can admit smoothly embedded non-separating hypersurfaces, but not of contact type: we observe that this is the case for all symplectic ruled surfaces.
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arxiv:0901.0854
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We compute the gravitational waveform produced by cosmic superstring reconnections. This is done by first constructing the superstring reconnection trajectory, which closely resembles that of classical, instantaneous reconnection but with the singularities smoothed out due to the string path integral. We then evaluate the graviton vertex operator in this background to obtain the burst amplitude. The result is compared to the detection threshold for current and future gravitational wave detectors, finding that neither bursts nor the stochastic background would be detectable by Advanced LIGO. This disappointing but anticipated conclusion holds even for the most optimistic values of the reconnection probability and loop sizes.
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arxiv:0901.0867
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Recent numerical and analytical work has shown that for the square-lattice Heisenberg model the boundary can induce Dimer correlations near the edge which are absent in spin-wave theories and non-linear sigma model approaches. Here, we calculate the nearest-neighbor spin correlations parallel and perpendicular to the boundary in a semi-infinite system for two different square-lattice Heisenberg models: (i) A frustrated $J_1-J_2$ model with nearest and second neighbor couplings and (ii) a spatially anisotropic Heisenberg model, with nearest-neighbor couplings $J$ perpendicular to the boundary and $J^\prime$ parallel to the boundary. We find that in the latter model, as $J^\prime/J$ is reduced from unity the Dimer correlations near the edge become longer ranged. In contrast, in the frustrated model, with increasing $J_2$, dimer correlations are strengthened near the boundary but they decrease rapidly with distance. These results imply that deep inside the N\'{e}el phase of the $J_1-J_2$ Heisenberg model, dimer correlations remain short-ranged. Hence, if there is a direct transition between the two it is either first order or there is a very narrow critical region.
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arxiv:0901.0894
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The Casimir force between two parallel uncharged closely spaced metallic plates is evaluated in ways alternatives to those usually considered in the literature. In a first approximation we take in account the suppressed quantum numbers of a cubic box, representing a cavity which was cut in a metallic block. We combine these ideas with those of the MIT bag model of hadrons, but adapted to non-relativistic particles. In a second approximation we consider the particles occupying the energy levels of the Bohr atom, so that the Casimir force depends explicitly on the fine structure constant alpha. In both treatments, the mean energies which have explicit dependence on the particle mass and on the maximum occupied quantum number (related to the Fermi level of the system) at the beginning of the calculations, have these dependences mutually canceled at the end of them. Finally by comparing the averaged energies computed in both approximations, we are able to make an estimate of the value of the fine structure constant alpha.
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arxiv:0901.0908
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A detailed analysis of gravitational slip, a new post-general relativity cosmological parameter characterizing the degree of departure of the laws of gravitation from general relativity on cosmological scales, is presented. This phenomenological approach assumes that cosmic acceleration is due to new gravitational effects; the amount of spacetime curvature produced per unit mass is changed in such a way that a universe containing only matter and radiation begins to accelerate as if under the influence of a cosmological constant. Changes in the law of gravitation are further manifest in the behavior of the inhomogeneous gravitational field, as reflected in the cosmic microwave background, weak lensing, and evolution of large-scale structure. The new parameter, $\varpi_0$, is naively expected to be of order unity. However, a multiparameter analysis, allowing for variation of all the standard cosmological parameters, finds that $\varpi_0 = 0.09^{+0.74}_{-0.59} (2\sigma)$ where $\varpi_0=0$ corresponds to a $\Lambda$CDM universe under general relativity. Future probes of the cosmic microwave background (Planck) and large-scale structure (Euclid) may improve the limits by a factor of four.
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arxiv:0901.0919
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Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment densities. An example is given and consequences discussed.
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arxiv:0901.0942
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The consequence of energy conservation in the flat Friedmannn-Robertson-Walker (FRW) cosmology is a strictly positive accelerating expansion. A mechanism is proposed for this expansion due to the effect of the attractive (negative) gravitational potential of matter as it is being included within the expanding horizon, and the offsetting work of metric expansion, which takes place at sub-luminal speed. In our semi-classical treatment, we deal with a quintic as the equation for the scale parameter. Implications for modeling the earliest parts of the primordial expansion are discussed.
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arxiv:0901.0945
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The main task of an introductory laboratory course is to foster students' manual, conceptual and statistical ability to investigate physical phenomena. Needing very simple apparatus, pendulum experiments are an ideal starting point in our first-year laboratory course because they are rich in both physical content and data processing. These experiments allow many variations, e.g. pendulum bobs can have different shapes, threads can be tied to a hook at their edge or pass through their centre of mass, they can be hanged as simple or bifilar pendulums. In these many variations, they emphasize the difference between theory and practice in the passage from an idealized scheme to a real experimental asset, which becomes evident, for example, when the pendulum bob cannot be considered an idealized point mass. Moreover, they require careful observation of details such as the type of thread used and its rigidity or the bob initial slant, which leads to different behaviors. Their mathematical models require a wide range of fundamental topics in experimental data analysis: arithmetic and weighted mean, standard deviation, central limit theorem application, data distribution, and the significant difference between theory and practice. Setting the mass-spring experiment immediately after the pendulum highlights the question of resonance, revises the gap between theory and practice in another context, and provides another occasion to practice further techniques in data analysis.
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arxiv:0901.0994
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A search for pair production of the lightest supersymmetric partner of the top quark is performed in the lepton+jets channel using 0.9 fb-1 of data collected by the D0 experiment. Kinematic differences between scalar top quark pair production and the dominant top quark pair production background are used to separate the two processes. First limits from Run II of the Fermilab Tevatron Collider for the scalar top quark decaying to a chargino and a b quark are obtained for scalar top quark masses of 130-190 GeV and chargino masses of 90-150 GeV.
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arxiv:0901.1063
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The main result of the paper is a new representation for the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show that this gives the Weyl Lagrangian up to a nonlinear change of dynamical variable. The advantage of our approach is that it does not require the use of spinors, Pauli matrices or covariant differentiation. The only geometric concepts we use are those of a metric, differential form, wedge product and exterior derivative. Our result assigns a variational meaning to the tetrad representation of the Weyl equation suggested by J. B. Griffiths and R. A. Newing.
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arxiv:0901.1070
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[abridged] It has been widely claimed that several lines of observational evidence point towards a "downsizing" (DS) of the process of galaxy formation over cosmic time. This behavior is sometimes termed "anti-hierarchical", and contrasted with the "bottom-up" assembly of the dark matter structures in Cold Dark Matter models. In this paper we address three different kinds of observational evidence that have been described as DS: the stellar mass assembly, star formation rate and the ages of the stellar populations in local galaxies. We compare a broad compilation of available data-sets with the predictions of three different semi-analytic models of galaxy formation within the Lambda-CDM framework. In the data, we see only weak evidence at best of DS in stellar mass and in star formation rate. We find that, when observational errors on stellar mass and SFR are taken into account, the models acceptably reproduce the evolution of massive galaxies, over the entire redshift range that we consider. However, lower mass galaxies are formed too early in the models and are too passive at late times. Thus, the models do not correctly reproduce the DS trend in stellar mass or the archaeological DS, while they qualitatively reproduce the mass-dependent evolution of the SFR. We demonstrate that these discrepancies are not solely due to a poor treatment of satellite galaxies but are mainly connected to the excessively efficient formation of central galaxies in high-redshift haloes with circular velocities ~100-200 km/s. [abridged]
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arxiv:0901.1130
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We investigate the performance of superconducting nanowire photon detectors fabricated from ultra-thin Nb. A direct comparison is made between these detectors and similar nanowire detectors fabricated from NbN. We find that Nb detectors are significantly more susceptible than NbN to thermal instability (latching) at high bias. We show that the devices can be stabilized by reducing the input resistance of the readout. Nb detectors optimized in this way are shown to have approximately 2/3 the reset time of similar large-active-area NbN detectors of the same geometry, with approximately 6% detection efficiency for single photons at 470 nm.
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arxiv:0901.1146
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Using a representative sample of 911 central galaxies (CENs) from the SDSS DR4 group catalogue, we study how the structure of the most massive members in groups and clusters depend on (1) galaxy stellar mass (Mstar), (2) dark matter halo mass of the host group (Mhalo), and (3) their halo-centric position. We establish and thoroughly test a GALFIT-based pipeline to fit 2D Sersic models to SDSS data. We find that the fitting results are most sensitive to the background sky level determination and strongly recommend using the SDSS global value. We find that uncertainties in the background translate into a strong covariance between the total magnitude, half-light size (r50), and Sersic index (n), especially for bright/massive galaxies. We find that n depends strongly on Mstar for CENs, but only weakly or not at all on Mhalo. Less (more) massive CENs tend to be disk (spheroid)-like over the full Mhalo range. Likewise, there is a clear r50-Mstar relation for CENs, with separate slopes for disks and spheroids. When comparing CENs with satellite galaxies (SATs), we find that low mass (<10e10.75 Msun/h^2) SATs have larger median n than CENs of similar Mstar. Low mass, late-type SATs have moderately smaller r50 than late-type CENs of the same Mstar. However, we find no size differences between spheroid-like CENs and SATs, and no structural differences between CENs and SATs matched in both mass and colour. The similarity of massive SATs and CENs shows that this distinction has no significant impact on the structure of spheroids. We conclude that Mstar is the most fundamental property determining the basic structure of a galaxy. The lack of a clear n-Mhalo relation rules out a distinct group mass for producing spheroids, and the responsible morphological transformation processes must occur at the centres of groups spanning a wide range of masses. (abridged)
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arxiv:0901.1150
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We consider the linear Schr\"odinger equation and its discretization by split-step methods where the part corresponding to the Laplace operator is approximated by the midpoint rule. We show that the numerical solution coincides with the exact solution of a modified partial differential equation at each time step. This shows the existence of a modified energy preserved by the numerical scheme. This energy is close to the exact energy if the numerical solution is smooth. As a consequence, we give uniform regularity estimates for the numerical solution over arbitrary long time
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arxiv:0901.1190
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The so-called Vegetation Red-Edge (VRE), a sharp increase in the reflectance around $700 nm$, is a characteristic of vegetation spectra, and can therefore be used as a biomarker if it can be detected in an unresolved extrasolar Earth-like planet integrated reflectance spectrum. Here we investigate the potential for detection of vegetation spectra during the last Quaternary climatic extrema, the Last Glacial Maximum (LGM) and the Holocene optimum, for which past climatic simulations have been made. By testing the VRE detectability during these extrema when Earth's climate and biomes maps were different from today, we are able to test the vegetation detectability on a terrestrial planet different from our modern Earth. Data from the Biome3.5 model have been associated to visible GOME spectra for each biome and cloud cover to derive Earth's integrated spectra for given Earth phases and observer positions. The VRE is then measured. Results show that the vegetation remains detectable during the last climatic extrema. Compared to current Earth, the Holocene optimum with a greener Sahara slightly increases the mean VRE on one hand, while on the other hand, the large ice cap over the northern Hemisphere during the LGM decreases vegetation detectability. We finally discuss the detectability of the VRE in the context of recently proposed space missions.
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arxiv:0901.1214
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A complete list of homogeneous operators in the Cowen-Douglas class $B_n(D)$ is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.
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arxiv:0901.1233
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The electromagnetic transition between the almost degenerate 5/2+ and 3/2+ states in Th229 is deemed to be very sensitive to potential changes in the fine structure constant alpha. State of the art Hartree-Fock and Hartree-Fock-Bogoliubov calculations are performed to compute the difference in Coulomb energies of the two states which determines the amplification of variations in alpha into variations of the transition frequency. The kinetic energies are also calculated which reflect a possible variation in the nucleon or quark masses. A generalized Hellmann-Feynman theorem is proved including the use of density-matrix functionals. As the two states differ mainly in the orbit occupied by the last unpaired neutron the Coulomb energy difference results from a change in the nuclear polarization of the proton distribution. This effect turns out to be rather small and to depend on the nuclear model, the amplification varies between about -4 x 10^4 and +4 x 10^4. Therefore much more effort must be put into the improvement of the nuclear models before one can draw conclusions from a measured drift in the transition frequency on a temporal drift of fundamental constants. All calculations published so far do not reach the necessary fidelity. PACS 06.20.Jr,21.60.Jz,27.90.+b
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arxiv:0901.1240
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We introduce a functor which associates to every measure preserving system (X,B,\mu,T) a topological system (C_2(\mu),\tilde{T}) defined on the space of 2-fold couplings of \mu, called the topological lens of T. We show that often the topological lens "magnifies" the basic measure dynamical properties of T in terms of the corresponding topological properties of \tilde{T}. Some of our main results are as follows: (i) T is weakly mixing iff \tilde{T} is topologically transitive (iff it is topologically weakly mixing). (ii) T has zero entropy iff \tilde{T} has zero topological entropy, and T has positive entropy iff \tilde{T} has infinite topological entropy. (iii) For T a K-system, the topological lens is a P-system (i.e. it is topologically transitive and the set of periodic points is dense; such systems are also called chaotic in the sense of Devaney).
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arxiv:0901.1247
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The ferromagnetic nano-structures are recently of great interest for modern investigations. A comparison of the experimental data and theoretical results shows that the use of the standard molecular field approximation is insufficient for the description of nano-structure properties. Therefore, we use the effective field approach in order to show the usefulness of the Valenta model generalized in this way. The agreement between experiment and theory is then excellent. The magnetization profiles and the calculated Curie temperatures are presented for the systems consisting of Ni and Co layers with different configuration of the surfaces and interfaces including terraces and wires. We have shown that the position in the system as well as the kind of neighbouring layers and their mutual interactions can determine the shape of magnetization profiles. The use of the Valenta model allows us to present all dependences in the layer resolved mode.
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arxiv:0901.1253
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In this talk we discuss enveloping algebra based noncommutative gauge field theory, constructed at the first order in noncommutative parameter theta, as an effective, anomaly free theory, with one-loop renormalizable gauge sector. Limits on the scale of noncommutativity parameter Lambda_NC, via related phenomenology and associated experiments, are analyzed and a firm bound to the scale of the noncommutativity is set around few TeV's.
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arxiv:0901.1265
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One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar "conventional" probability calculus and always retains the latter as a special case when all matrices are diagonal. We motivate both the conventional and the generalized Bayes rule with a minimum relative entropy principle, where the Kullbach-Leibler version gives the conventional Bayes rule and Umegaki's quantum relative entropy the new Bayes rule for density matrices. Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data likelihood, the generalization maintains uncertainty about which unit direction has the largest variance. Surprisingly the bounds also generalize: as in the conventional setting we upper bound the negative log likelihood of the data by the negative log likelihood of the MAP estimator.
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arxiv:0901.1273
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We review the current status of small x resummation of evolution of parton distributions and of deep-inelastic coefficient functions. We show that the resummed perturbative expansion is stable, robust upon different treatments of subleading terms, and that it matches smoothly to the unresummed perturbative expansions, with corrections which are of the same order as the typical NNLO ones in the HERA kinematic region. We discuss different approaches to small x resummation: we show that the ambiguities in the resummation procedure are small, provided all parametrically enhanced terms are included in the resummation and properly matched.
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arxiv:0901.1294
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We report the first photoemission study of Fe1+xTe - the host compound of the newly discovered iron-chalcogenide superconductors. Our results reveal a pair of nearly electron- hole compensated Fermi pockets, strong Fermi velocity renormalization and an absence of a spin-density-wave gap. A shadow hole pocket is observed at the "X"-point of the Brillouin zone which is consistent with a long-range ordered magneto-structural groundstate. No signature of Fermi surface nesting instability associated with Q= pi(1/2, 1/2) is observed. Our results collectively reveal that the Fe1+xTe series is dramatically different from the undoped phases of the high Tc pnictides and likely harbor unusual mechanism for superconductivity and quantum magnetic order.
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arxiv:0901.1299
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Many X-ray observations of GigaHertz Peaked Spectrum and Compact Steep Spectrum sources have been made with Chandra X-ray Observatory and XMM-Newton Observatory over the last few years. The X-ray spectra contribute the important information to the total energy distribution of the compact radio sources. In addition the spatial resolution of Chandra allows for studies of the X-ray morphology of these sources on arcsec scales and provide a direct view of their environments. This paper gives a review of the current status of the X-ray observations and their contribution to our understanding of the nature of these compact radio sources. It also describes primary physical processes that lead to the observed X-ray emission and summarize X-ray emission properties expected from interactions between an expanding radio source and the intergalactic environment.
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arxiv:0901.1327
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For a proper subfield $K$ of $\QQ$ we show the existence of an algebraic number $\alpha$ such that no power $\alpha^n$, $n\geq 1$, lies in $K$. As an application it is shown that these numbers, multiplied by convenient Gaussian numbers, can be written in the form $P(T)^{Q(T)}$ for some transcendental numbers $T$ where $P$ and $Q$ are arbitrarily prescribed non-constant rational functions over $\QQ$.
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arxiv:0901.1335
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There is a growing interest in the literature for adaptive Markov chain Monte Carlo methods based on sequences of random transition kernels $\{P_n\}$ where the kernel $P_n$ is allowed to have an invariant distribution $\pi_n$ not necessarily equal to the distribution of interest $\pi$ (target distribution). These algorithms are designed such that as $n\to\infty$, $P_n$ converges to $P$, a kernel that has the correct invariant distribution $\pi$. Typically, $P$ is a kernel with good convergence properties, but one that cannot be directly implemented. It is then expected that the algorithm will inherit the good convergence properties of $P$. The equi-energy sampler of [Ann. Statist. 34 (2006) 1581--1619] is an example of this type of adaptive MCMC. We show in this paper that the asymptotic variance of this type of adaptive MCMC is always at least as large as the asymptotic variance of the Markov chain with transition kernel $P$. We also show by simulation that the difference can be substantial.
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arxiv:0901.1378
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Heavy baryon/meson ratios $\Lambda_c/D^0$ and $\Lambda_b/\bar{B}^0$ in relativistic heavy ion collisions are studied in the quark coalescence model. For heavy baryons, we include production from coalescence of heavy quarks with free light quarks as well as with bounded light diquarks that might exist in the strongly coupled quark-gluon plasma produced in these collisions. Including the contribution from decays of heavy hadron resonances and also that due to fragmentation of heavy quarks that are left in the system after coalescence, the resulting $\Lambda_c/D^0$ and $\Lambda_b/\bar{B}^0$ ratios in midrapidity ($|y|\le 0.5$) from central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV are about a factor of five and ten, respectively, larger than those given by the thermal model, and about a factor of ten and twelve, respectively, larger than corresponding ratios in the PYTHIA model for $pp$ collisions. These ratios are reduced by a factor of about 1.6 if there are no diquarks in the quark-gluon plasma. The transverse momentum dependence of the heavy baryon/meson ratios is found to be sensitive to the heavy quark mass, with the $\Lambda_b/\bar{B}^0$ ratio being much flatter than the $\Lambda_c/D^0$ ratio. The latter peaks at the transverse momentum $p_T^{} \simeq 0.8$ GeV but the peak shifts to $p_T^{} \simeq 2$ GeV in the absence of diquarks.
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arxiv:0901.1382
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F\"ur die freien orthogonalen Quantengruppen $A_o(n)$ wird ein vollst\"a ndiges Reduktionssystem angegeben und verifiziert. F\"ur den Fall $n = 2$ wird ein endlicher Automat angegeben, der s\"amtliche der Basiselemente findet. Weiterhin wird eine Basis f\"ur die f\"ur die Kerne einer freien Aufl\"osung von $A_o(n)$ als Bimodul bewiesen. Abschlie{\ss}end wird mit der nun verifizierten Aufl\"osung die Homologie von $A_o(n)$ explizit berechnet.
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arxiv:0901.1391
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An elasto-plasticity model with coupled hardening variables of strain type is presented. In the theoretical framework of generalized associativity, the formulation of this model is based on the introduction of two hardening variables with a coupled evolution. Even if the corresponding hardening rules are linear, the stress-strain hardening evolution is non-linear. The numerical implementation by a standard return mapping algorithm is discussed and some numerical simulations of cyclic behaviour in the univariate case are presented.
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arxiv:0901.1449
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Let (H_t) be the Ornstein-Uhlenbeck semigroup on R^d with covariance matrix I and drift matrix \lambda(R-I), where \lambda>0 and R is a skew-adjoint matrix and denote by \gamma_\infty the invariant measure for (H_t). Semigroups of this form are the basic building blocks of Ornstein-Uhlenbeck semigroups which are normal on L^2(\gamma_\infty). We prove that if the matrix R generates a one-parameter group of periodic rotations then the maximal operator associated to the semigroup is of weak type 1 with respect to the invariant measure. We also prove that the maximal operator associated to an arbitrary normal Ornstein-Uhlenbeck semigroup is bounded on L^p(\gamma_\infty) if and only if 1<p\le \infty.
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arxiv:0901.1455
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We examine the hydrodynamic limit of non-conformal branes using the recently developed precise holographic dictionary. We first streamline the discussion of holography for backgrounds that asymptote locally to non-conformal brane solutions by showing that all such solutions can be obtained from higher dimensional asymptotically locally AdS solutions by suitable dimensional reduction and continuation in the dimension. As a consequence, many holographic results for such backgrounds follow from the corresponding results of the Asymptotically AdS case. In particular, the hydrodynamics of non-conformal branes is fully determined in terms of conformal hydrodynamics. Using previous results on the latter we predict the form of the non-conformal hydrodynamic stress tensor to second order in derivatives. Furthermore we show that the ratio between bulk and shear viscosity is fixed by the generalized conformal structure to be \zeta/\eta = 2(1/(d-1) - c_s^2), where c_s is the speed of sound in the fluid.
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arxiv:0901.1487
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A complete and user-friendly directory of tails of Archimedean copulas is presented which can be used in the selection and construction of appropriate models with desired properties. The results are synthesized in the form of a decision tree: Given the values of some readily computable characteristics of the Archimedean generator, the upper and lower tails of the copula are classified into one of three classes each, one corresponding to asymptotic dependence and the other two to asymptotic independence. For a long list of single-parameter families, the relevant tail quantities are computed so that the corresponding classes in the decision tree can easily be determined. In addition, new models with tailor-made upper and lower tails can be constructed via a number of transformation methods. The frequently occurring category of asymptotic independence turns out to conceal a surprisingly rich variety of tail dependence structures.
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arxiv:0901.1521
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The mean free path of light ($l^*$) calculated for elastic scattering on a system of nanoparticles with spatially correlated disorder is found to have a minimum when the correlation length is of the order of the wavelength of light. For a typical choice of parameters for the scattering system, this minimum mean free path ($l^*_{min}$) turns out to satisfy the Ioffe-Regel criterion for wave localization, $l^*_{min} \sim \lambda$, over a range of the correlation length, defining thus a stop-band for light transmission. It also provides a semi-phenomenological explanation for several interesting findings reported recently on the transmission/ reflection and the trapping/storage of light in a magnetically tunable ferrofluidic system. The subtle effect of structural anisotropy, induced by the external magnetic field on the scattering by the medium, is briefly discussed in physical terms of the anisotropic Anderson localization.
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arxiv:0901.1522
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The fireshell model for Gamma-Ray Bursts (GRBs) naturally leads to a canonical GRB composed of a proper-GRB (P-GRB) and an afterglow. P-GRBs, introduced by us in 2001, are sometimes considered "precursors" of the main GRB event in the current literature. We show in this paper how the fireshell model leads to the understanding of the structure of GRBs, with precise estimates of the time sequence and intensities of the P-GRB and the of the afterglow. It leads as well to a natural classification of the canonical GRBs which overcomes the traditional one in short and long GRBs.
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arxiv:0901.1545
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We study theories of spaces of random variables: first, we consider random variables with values in the interval $[0,1]$, then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: i) The randomisation of a stable structure is stable. ii) The randomisation of a simple unstable structure is not simple. We also prove that in the randomised structure, every type is a Lascar type.
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arxiv:0901.1584
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State-of-the-art quantum chemical methods are applied to the study of the multiorbital correlated electronic structure of a Fe-As compound, the recently discovered LiFeAs. Our calculations predict a high-spin, S=2, ground-state configuration for the Fe ions, which shows that the on-site Coulomb interactions are substantial. Also, orbital degeneracy in the (xz,yz) sector and a three-quarter filling of these levels suggest the presence of strong fluctuations and are compatible with a low metallic conductivity in the normal state. The lowest electron-removal states have As 4p character, in analogy to the ligand hole states in p-type cuprate superconductors.
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arxiv:0901.1594
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We prove the Erdos-Turan equidistribution inequality, using a construction due to Chebyshev, Markov, and Stieltjes. The method is applicable in a more general setting. As an example, we state another inequality that can be proved using this method. The inequality can be used to get an error estimate in Wigner's law which is sharp near the edge.
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arxiv:0901.1620
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Three planets with minimum masses less than 10 Earth masses orbit the star HD 40307, suggesting these planets may be rocky. However, with only radial velocity data, it is impossible to determine if these planets are rocky or gaseous. Here we exploit various dynamical features of the system in order to assess the physical properties of the planets. Observations allow for circular orbits, but a numerical integration shows that the eccentricities must be at least 0.0001. Also, planets b and c are so close to the star that tidal effects are significant. If planet b has tidal parameters similar to the terrestrial planets in the Solar System and a remnant eccentricity larger than 0.001, then, going back in time, the system would have been unstable within the lifetime of the star (which we estimate to be 6.1 +/- 1.6 Gyr). Moreover, if the eccentricities are that large and the inner planet is rocky, then its tidal heating may be an order of magnitude greater than extremely volcanic Io, on a per unit surface area basis. If planet b is not terrestrial, e.g. Neptune-like, these physical constraints would not apply. This analysis suggests the planets are not terrestrial-like, and are more like our giant planets. In either case, we find that the planets probably formed at larger radii and migrated early-on (via disk interactions) into their current orbits. This study demonstrates how the orbital and dynamical properties of exoplanet systems may be used to constrain the planets' physical properties.
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arxiv:0901.1698
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We present a new inner bound for the rate region of the $t$-stage successive-refinement problem with side-information. We also present a new upper bound for the rate-distortion function for lossy-source coding with multiple decoders and side-information. Characterising this rate-distortion function is a long-standing open problem, and it is widely believed that the tightest upper bound is provided by Theorem 2 of Heegard and Berger's paper "Rate Distortion when Side Information may be Absent", \emph{IEEE Trans. Inform. Theory}, 1985. We give a counterexample to Heegard and Berger's result.
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arxiv:0901.1705
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Let L be the Lie algebra of a simple algebraic group defined over a field F and let H be a split Cartan subalgebra of L. Then L has a Chevalley basis with respect to H. If the characteristic of F is not 2 or 3, it is known how to find it. In this paper, we treat the remaining two characteristics. To this end, we present a few new methods, implemented in Magma, which vary from the computation of centralisers of one root space in another to the computation of a specific part of the Lie algebra of derivations of $L$.
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arxiv:0901.1717
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We extend the hadronic SU(3) non-linear sigma model to include quark degrees of freedom. The choice of potential for the Polyakov loop as a function of temperature and chemical potential allows us to construct a realistic phase diagram from the analysis of the order parameters of the system. These parameters are the chiral condensate, for the chiral symmetry restoration and the Polyakov loop, for the deconfinement to quark matter. Besides reproducing lattice QCD results, for zero and low chemical potential, we are in agreement with neutron star observations for zero temperature.
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arxiv:0901.1748
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We propose an explanation for the far-infrared/radio correlation of galaxies in terms of the energy balance of the interstellar medium and determine the flux from high-energy photons and neutrinos from starburst galaxies. We present a catalog of the 127 brightest starburst galaxies with redshifts of z<0.03. In order to investigate the correlation between radio- and far-infrared emission, we apply the leaky box approximation. Further, we derive photon- and neutrino spectra from proton-proton interactions in supernova remnants (SNRs). Here, we assume that a fraction of the SNR's energy is transferred to the acceleration of cosmic rays. We also investigate the possibility of detecting Gamma Ray Bursts from nearby starburst galaxies, using the catalog defined here. We show that the radio emission is only weakly dependent on the magnetic field. It turns out that the intensity of the radio signal is directly proportional to the number of supernova explosions, which scales with the far-infrared luminosity. In addition, we find that high-energy photons from proton-proton interactions in SNRs in starbursts can make up several percent of the diffuse gamma-ray background. The neutrino flux from the same sources has a maximum energy of ~1e5 GeV. Neutrinos can, on the other hand, can be observed if a Gamma Ray Burst happens in a nearby starburst. About 0.03 GRBs per year are expected to occur in the entire catalog. The true number is expected to be even higher, since we only include the brightest sources. The number of events per burst in IceCube varies between about one event and more than 1000 events. This provides good prospects for IceCube to detect a significant event, since the background for a GRB search is close to zero.
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arxiv:0901.1775
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The standard theory of ideal gases ignores the interaction of the gas particles with the thermal radiation (photon gas) that fills the otherwise vacuum space between them. This is an unphysical feature since every material absorbs and radiates thermal energy. This interaction may be important in gases since the latter, unlike solids and liquids are capable of undergoing conspicuous volume changes. Taking it into account makes the behaviour of the ideal gases more realistic and removes Gibbs' paradox.
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arxiv:0901.1799
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The performance of several popular water models (TIP3P, TIP4P, TIP5P and TIP4P/2005) is analysed. For that purpose the predictions for ten different properties of water are investigated, namely: 1. vapour-liquid equilibria (VLE) and critical temperature; 2. surface tension; 3. densities of the different solid structures of water (ices); 4. phase diagram; 5. melting point properties; 6. maximum in density at room pressure and thermal coefficients $\alpha$ and $\kappa_T$; 7. structure of liquid water and ice; 8. equation of state at high pressures; 9. diffusion coefficient; 10. dielectric constant. For each property, the performance of each model is analysed in detail with a critical discussion of the possible reason of the success or failure of the model. A final judgement on the quality of these models is provided. TIP4P/2005 provides the best description of almost all properties of the list, with the only exception of the dielectric constant. In the second position, TIP5P and TIP4P yield an overall similar performance, and the last place with the poorest description of the water properties is provided by TIP3P. The ideas leading to the proposal and design of the TIP4P/2005 are also discussed in detail. TIP4P/2005 is probably close to the best description of water that can be achieved with a non polarizable model described by a single Lennard-Jones (LJ) site and three charges.
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arxiv:0901.1803
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In this work the high pressure region of the phase diagram of water has been studied by computer simulation by using the TIP4P/2005 model of water. Free energy calculations were performed for ices VII and VIII and for the fluid phase to determine the melting curve of these ices. In addition molecular dynamics simulations were performed at high temperatures (440K) observing the spontaneous freezing of the liquid into a solid phase at pressures of about 80000 bar. The analysis of the structure obtained lead to the conclusion that a plastic crystal phase was formed. In the plastic crystal phase the oxygen atoms were arranged forming a body center cubic structure, as in ice VII, but the water molecules were able to rotate almost freely. Free energy calculations were performed for this new phase, and it was found that for TIP4P/2005 this plastic crystal phase is thermodynamically stable with respect to ices VII and VIII for temperatures higher than about 400K, although the precise value depends on the pressure. By using Gibbs Duhem simulations, all coexistence lines were determined, and the phase diagram of the TIP4P/2005 model was obtained, including ices VIII and VII and the new plastic crystal phase. The TIP4P/2005 model is able to describe qualitatively the phase diagram of water. It would be of interest to study if such a plastic crystal phase does indeed exist for real water. The nearly spherical shape of water makes possible the formation of a plastic crystal phase at high temperatures. The formation of a plastic crystal phase at high temperatures (with a bcc arrangements of oxygen atoms) is fast from a kinetic point of view occurring in about 2ns. This is in contrast to the nucleation of ice Ih which requires simulations of the order of hundreds of ns.
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arxiv:0901.1828
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We report on partially overlapping XMM-Newton (~260 ks) and Suzaku (~100 ks) observations of the iron K band in the nearby, bright Seyfert 1 galaxy Mrk 509. The source shows a resolved neutral Fe K line, most probably produced in the outer part of the accretion disc. Moreover, the source shows further emission blue-ward of the 6.4 keV line due to ionized material. This emission is well reproduced by a broad line produced in the accretion disc, while it cannot be easily described by scattering or emission from photo-ionized gas at rest. The summed spectrum of all XMM-Newton observations shows the presence of a narrow absorption line at 7.3 keV produced by highly ionized outflowing material. A spectral variability study of the XMM-Newton data shows an indication for an excess of variability at 6.6-6.7 keV. These variations may be produced in the red wing of the broad ionized line or by variation of a further absorption structure. The Suzaku data indicate that the neutral Fe Kalpha line intensity is consistent with being constant on long timescales (of a few years) and they also confirm as most likely the interpretation of the excess blueshifted emission in terms of a broad ionized Fe line. The average Suzaku spectrum differs from the XMM-Newton one for the disappearance of the 7.3 keV absorption line and around 6.7 keV, where the XMM-Newton data alone suggested variability.
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arxiv:0901.1882
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We present a practical algorithm to decode erasures of Reed-Solomon codes over the q elements binary field in O(q \log_2^2 q) time where the constant implied by the O-notation is very small. Asymptotically fast algorithms based on fast polynomial arithmetic were already known, but even if their complexity is similar, they are mostly impractical. By comparison our algorithm uses only a few Walsh transforms and has been easily implemented.
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arxiv:0901.1886
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We consider a randomly perturbed Korteweg-de Vries equation. The perturbation is a random potential depending both on space and time, with a white noise behavior in time, and a regular, but stationary behavior in space. We investigate the dynamics of the soliton of the KdV equation in the presence of this random perturbation, assuming that the amplitude of the perturbation is small. We estimate precisely the exit time of the perturbed solution from a neighborhood of the modulated soliton, and we obtain the modulation equations for the soliton parameters. We moreover prove a central limit theorem for the dispersive part of the solution, and investigate the asymptotic behavior in time of the limit process.
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arxiv:0901.1965
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Evolution of structure of spherical SiO2 nanoparticles upon cooling from the melt has been investigated via molecular-dynamics (MD) simulations under non-periodic boundary conditions (NPBC). We use the pair interatomic potentials which have weak Coulomb interaction and Morse type short-range interaction. The change in structure of SiO2 nanoparticles upon cooling process has been studied through the partial radial distribution functions (PRDFs), coordination number and bond-angle distributions at different temperatures. The core and surface structures of nanoparticles have been studied in details. Our results show significant temperature dependence of structure of nanoparticles. Moreover, temperature dependence of concentration of structural defects in nanoparticles upon cooling from the melt toward glassy state has been found and discussed.
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arxiv:0901.2029
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Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches.
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arxiv:0901.2060
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We revisit Merton's portfolio optimization problem under boun-ded state-dependent utility functions, in a market driven by a L\'evy process $Z$ extending results by Karatzas et. al. (1991) and Kunita (2003). The problem is solved using a dual variational problem as it is customarily done for non-Markovian models. One of the main features here is that the domain of the dual problem enjoys an explicit "parametrization", built on a multiplicative optional decomposition for nonnegative supermartingales due to F\"ollmer and Kramkov (1997). As a key step in obtaining the representation result we prove a closure property for integrals with respect to Poisson random measures, a result of interest on its own that extends the analog property for integrals with respect to a fixed semimartingale due to M\'emin (1980). In the case that (i) the L\'evy measure of $Z$ is atomic with a finite number of atoms or that (ii) $\Delta S_{t}/S_{t^{-}}=\zeta_{t} \vartheta(\Delta Z_{t})$ for a process $\zeta$ and a deterministic function $\vartheta$, we explicitly characterize the admissible trading strategies and show that the dual solution is a risk-neutral local martingale.
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arxiv:0901.2070
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Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes under descent. Inspired by structures arising in a representation theoretic approach to rational conformal field theories, we introduce geometric structure that is appropriate to define surface holonomy in more general situations: Jandl gerbes for unoriented surfaces, D-branes for surfaces with boundaries, and bi-branes for surfaces with defect lines.
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arxiv:0901.2085
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We present timing data spanning 6.4 yr for the young and energetic PSR J0205+6449, in the supernova remnant 3C 58. Data were obtained with the Rossi X-ray Timing Explorer, the Jodrell Bank Observatory and the Green Bank Telescope. We present phase-coherent timing analyses showing timing noise and two spin-up glitches with fractional frequency increases of ~3.4E-7 near MJD 52555, and ~3.8E-6 between MJDs 52777 and 53062. These glitches are unusually large if the pulsar was created in the historical supernova in 1181 as has been suggested. For the X-ray timing we developed a new unbinned maximum-likelihood method for determining pulse arrival times which performs significantly better than the traditional binned techniques. In addition, we present an X-ray pulse profile analysis of four years of RXTE data showing that the pulsar is detected up to ~40 keV. We also present the first measurement of the phase offset between the radio and X-ray pulse for this source, showing that the radio pulse leads the X-ray pulse by phi=0.10+/-0.01 in phase. We compile all known measurements of the phase offsets between radio and X-ray and radio and gamma-ray pulses for X-ray and gamma-ray pulsars. We show that there is no relationship between pulse period and phase offset, supported by our measurement of the phase offset for PSR J0205+6449.
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arxiv:0901.2119
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Combining a recent derivation of the CMB evolution equations for homogeneous but anisotropic (Bianchi) cosmologies with an account of the full linearized dynamical freedoms available in such models, I calculate and discuss the various temperature and polarisation anisotropy patterns which may be formed. Certain anisotropies can be hidden in superhorizon modes at early times, thus avoiding any constraints from nucleosynthesis while nevertheless producing non-trivial redshift-zero temperature patterns in flat and open universes. The results are likely to be more of pedagogical than observational interest, but future work will assess whether such patterns can be matched to anomalies in WMAP results.
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arxiv:0901.2122
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We map the three dimensional extent of the Virgo Over-density by combining distance information from RR Lyrae variables and projected spatial information from SEKBO (Keller et al. 2008) and Sloan Digital Sky Survey (SDSS) DR6 photometry. The Virgo Over-density is seen to comprise two filaments 14.5 x 3 degrees and 10 x 3 degrees and a circular structure 3 degrees in diameter. Together the three features span 38 degrees of right ascension and declinations of +2 to -15 degrees. RR Lyrae variables place the two filamentary features at heliocentric distances of 20 and 17 kpc respectively, with projected dimensions of 5 x 1 kpc and 3 x 1 kpc.
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arxiv:0901.2145
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We present new XMM-Newton observations of the supernova remnant N120 in the LMC, and numerical simulations on the evolution of this supernova remnant which we compare with the X-ray observations. The supernova remnant N120, together with several HII regions, forms a large nebular complex5D (also called N120) whose shape resembles a semicircular ring. From the XMM-Newton data we generate images and spectra of this remnant in the energy band between 0.2 to 2.0 keV. The images show that the X-ray emission is brighter towards the east (i.e., towards the rim of the large nebular complex). The EPIC/MOS1 and MOS2 data reveal a thermal spectrum in soft X-rays. 2D axisymmetric numerical simulations with the Yguaz\'u-a code were carried out assuming that the remnant is expanding into an inhomogeneous ISM with an exponential density gradient and showing that thermal conduction effects are negligible. Simulated X-ray emission maps were obtained from the numerical simulations in order to compare them with the observations. We find good agreement between the XMM-Newton data, previous optical kinematic data, and the numerical simulations; the simulations reproduce the observed X-ray luminosity and surface brightness distribution. We have also detected more extended diffuse X-ray emission probably due to the N120 large HII complex or superbubble.
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arxiv:0901.2146
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We consider quantum random walks (QRW) on the integers, a subject that has been considered in the last few years in the framework of quantum computation. We show how the theory of CMV matrices gives a natural tool to study these processes and to give results that are analogous to those that Karlin and McGregor developed to study (classical) birth-and-death processes using orthogonal polynomials on the real line. In perfect analogy with the classical case the study of QRWs on the set of non-negative integers can be handled using scalar valued (Laurent) polynomials and a scalar valued measure on the circle. In the case of classical or quantum random walks on the integers one needs to allow for matrix valued versions of these notions. We show how our tools yield results in the well known case of the Hadamard walk, but we go beyond this translation invariant model to analyze examples that are hard to analyze using other methods. More precisely we consider QRWs on the set of non- negative integers. The analysis of these cases leads to phenomena that are absent in the case of QRWs on the integers even if one restricts oneself to a constant coin. This is illustrated here by studying recurrence properties of the walk, but the same method can be used for other purposes. The presentation here aims at being selfcontained, but we re- frain from trying to give an introduction to quantum random walks, a subject well surveyed in the literature we quote. For two excellent reviews, see [1, 18]. See also the recent notes [19].
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arxiv:0901.2244
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In this paper we show that the space of nodal rational curves, which is so called a Severi variety (of rational curves), on any non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N.Hitchin. As geometric objects naturally associated to Einstein-Weyl structure, we investigate null surfaces and geodesics on the Severi varieties. Also we see that if the projective surface has an appropriate real structure, then the real locus of the Severi variety becomes a positive definite Einstein-Weyl manifold. Moreover we construct various explicit examples of rational surfaces having 3-dimensional Severi varieties of rational curves.
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arxiv:0901.2264
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Examples are given of non-elementary properties that are preserved under C-filtrations for various classes C of Abelian groups. The Baer-Specker group is never the union of a chain of proper subgroups with cotorsionfree quotients. Cotorsion-free groups form an abstract elementary class (AEC). The Kaplansky invariants of the Baer-Specker group are used to determine the AECs defined by the perps of the Baer-Specker quotient groups that are obtained by factoring the Baer-Specker group B of a ZFC extension by the Baer-Specker group A of the ground model, under various hypotheses, yielding information about its stability spectrum.
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arxiv:0901.2291
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As it is known, finitely presented quivers correspond to Dynkin graphs (Gabriel, 1972) and tame quivers -- to extended Dynkin graphs (Donovan and Freislich, Nazarova, 1973). In the article "Locally scalar reresentations of graphs in the category of Hilbers spaces" (Func. Anal. and Appl., 2005) authors showed the way to tranfer these results to Hilbert spaces, constructed Coxeter functors and proved an analogue of Gabriel theorem fol locally scalar (orthoscalar in the sequel) representations (up to the unitary equivalence). The category of orthoscalar representations of a quiver can be considered as a subcategory in the category of all representations (over a field $\mathbb C$). In the present paper we study the connection between indecomposable orthoscalar representations in the subcategory and in the category of all representations. For the quivers, corresponded to extended Dynkin graphs, orthoscalar representations which cannot be obtained from the simplest by Coxeter functors (regular representations) are classified.
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arxiv:0901.2296
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It is shown, using sutured manifold theory, that if there are any 2-component counterexamples to the Generalized Property R Conjecture, then any knot of least genus among components of such counterexamples is not a fibered knot. The general question of what fibered knots might appear as a component of such a counterexample is further considered; much can be said about the monodromy of the fiber, particularly in the case in which the fiber is of genus two.
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arxiv:0901.2319
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We propose a microscopic approach describing the interaction of an ideal gas of hydrogenlike atoms with a weak electromagnetic field. This approach is based on the Green-function formalism and an approximate formulation of the method of second quantization for quantum many-particle systems in the presence of bound states of particles. The dependencies of the propagation velocity and damping rate of electromagnetic pulses on the microscopic characteristics of the system are studied for a gas of hydrogenlike atoms. For a Bose-Einstein condensate of alkali-metal atoms we find the conditions when the electromagnetic waves of both the optical and microwave regions are slowed. In the framework of the proposed approach, the influence of an external homogeneous and static magnetic field on the slowing phenomenon is studied.
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arxiv:0901.2425
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In this paper, we investigate the mean curvature flow having equifocal submanifolds as initial data. The investigation are performed by investigating the mean curvature flow having the lifted submanifolds to a Hilbert space through a Riemannian submersion as initial data.
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arxiv:0901.2432
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One outlines here in brief how the work of $Gian Carlo Rota$ had influenced my group research and life, starting from the end of the last century up to present time state of $The Internet Gian Carlo Rota Polish Seminar$. This note has been written for the $Rota Memorial Conference$ to be held on 16-18 Feb 2009, Milan, Italy.
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arxiv:0901.2571
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Nonsequential double ionization (NSDI) of helium in an intense few-cycle laser pulse is investigated by applying the three-dimensional semi-classical re-scattering method. It is found that the momentum distribution of He$^{2+}$ shows a single-double-single peak structure as the pulse intensity increases. According to the different mechanisms dominating the NSDI process, the laser intensity can be classified into three regimes where the momentum distribution of He$^{2+}$ exhibits different characteristics. In the relatively high intensity regime, an NSDI mechanism named the "laser-assisted collision ionization" is found to be dominating the NSDI process and causing the single peak structure. This result can shed light on the study of non-sequential ionization of a highly charged ion in a relatively intense laser pulse.
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arxiv:0901.2607
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Given a finitely presented group $G$, Hopf's formula expresses the second integral homology of $G$ in terms of generators and relators. We give an algorithm that exploits Hopf's formula to estimate $H_2(G;k)$, with coefficients in a finite field k, and give examples using $G=SL_2$ over specific rings of integers. These examples are related to a conjecture of Quillen.
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arxiv:0901.2610
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Accurate calculations of the fine and hyperfine splitting of the 2P state in Li and Be$^+$ isotopes using the explicitly correlated Hylleraas basis set are presented. Theoretical predictions including the mixing of $P_{1/2}$ and $P_{3/2}$ states, relativistic and quantum electrodynamics effects on hyperfine interactions, are compared with experimental values. It is concluded that precise spectroscopic determination of the nuclear magnetic moments requires elimination of nuclear structure effects by combining measurements for two different states.
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arxiv:0901.2633
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We propose an efficient framework for enabling secure multi-party numerical computations in a Peer-to-Peer network. This problem arises in a range of applications such as collaborative filtering, distributed computation of trust and reputation, monitoring and other tasks, where the computing nodes is expected to preserve the privacy of their inputs while performing a joint computation of a certain function. Although there is a rich literature in the field of distributed systems security concerning secure multi-party computation, in practice it is hard to deploy those methods in very large scale Peer-to-Peer networks. In this work, we try to bridge the gap between theoretical algorithms in the security domain, and a practical Peer-to-Peer deployment. We consider two security models. The first is the semi-honest model where peers correctly follow the protocol, but try to reveal private information. We provide three possible schemes for secure multi-party numerical computation for this model and identify a single light-weight scheme which outperforms the others. Using extensive simulation results over real Internet topologies, we demonstrate that our scheme is scalable to very large networks, with up to millions of nodes. The second model we consider is the malicious peers model, where peers can behave arbitrarily, deliberately trying to affect the results of the computation as well as compromising the privacy of other peers. For this model we provide a fourth scheme to defend the execution of the computation against the malicious peers. The proposed scheme has a higher complexity relative to the semi-honest model. Overall, we provide the Peer-to-Peer network designer a set of tools to choose from, based on the desired level of security.
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arxiv:0901.2689
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Multiple Sequence Alignment (MSA) is one of the most computationally intensive tasks in Computational Biology. Existing best known solutions for multiple sequence alignment take several hours (in some cases days) of computation time to align, for example, 2000 homologous sequences of average length 300. Inspired by the Sample Sort approach in parallel processing, in this paper we propose a highly scalable multiprocessor solution for the MSA problem in phylogenetically diverse sequences. Our method employs an intelligent scheme to partition the set of sequences into smaller subsets using kmer count based similarity index, referred to as k-mer rank. Each subset is then independently aligned in parallel using any sequential approach. Further fine tuning of the local alignments is achieved using constraints derived from a global ancestor of the entire set. The proposed Sample-Align-D Algorithm has been implemented on a cluster of workstations using MPI message passing library. The accuracy of the proposed solution has been tested on standard benchmarks such as PREFAB. The accuracy of the alignment produced by our methods is comparable to that of well known sequential MSA techniques. We were able to align 2000 randomly selected sequences from the Methanosarcina acetivorans genome in less than 10 minutes using Sample-Align-D on a 16 node cluster, compared to over 23 hours on sequential MUSCLE system running on a single cluster node.
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arxiv:0901.2742
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In this paper we present an analysis of the magnetic toroidal moment and its relation to the various structural modes in R3c-distorted perovskites with magnetic cations on either the perovskite A or B site. We evaluate the toroidal moment in the limit of localized magnetic moments and show that the full magnetic symmetry can be taken into account by considering small induced magnetic moments on the oxygen sites. Our results give a transparent picture of the possible coupling between magnetization, electric polarization, and toroidal moment, thereby highlighting the different roles played by the various structural distortions in multiferroic BiFeO_3 and in the recently discussed isostructural material FeTiO_3, which has been predicted to exhibit electric field-induced magnetization switching.
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arxiv:0901.2812
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We report spatially-resolved variations in the 3.4micron hydrocarbon absorption feature and the 3.3micron polycyclic aromatic hydrocarbon (PAH) emission band in the Circinus galaxy over the central few arcsec. The absorption is measured towards warm emitting dust associated with Coronal line regions to the east and west of the nucleus. There is an absorption optical depth tau(3.4um) ~0.1 in the core which decreases to the west and increases to the east. This is consistent with increased extinction out to ~40 pc east of the core, supported by the Coronal emission line intensities which are significantly lower to the east than the west. PAH emission is measured to be symmetrically distributed out to +/- 4 arcsec, outside the differential extinction region. The asymmetry in the 3.4micron absorption band reflects that seen in the 9.7micron silicate absorption band reported by Roche et al. (2006) and the ratio of the two absorption depths remains approximately constant across the central regions, with tau(3.4um) / tau(9.7um) ~ 0.06 +/-0.01. This indicates well-mixed hydrocarbon and silicate dust populations, with no evidence for significant changes near the nucleus.
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arxiv:0901.2829
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Features of rheological laws applied to solid-like granular materials are recalled and confronted to microscopic approaches via discrete numerical simulations. We give examples of model systems with very similar equilibrium stress transport properties -- the much-studied force chains and force distribution -- but qualitatively different strain responses to stress increments. Results on the stability of elastoplastic contact networks lead to the definition of two different rheological regimes, according to whether a macroscopic fragility property (propensity to rearrange under arbitrary small stress increments in the thermodynamic limit) applies. Possible consequences are discussed.
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arxiv:0901.2846
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We continue our earlier studies of quasi-periodic oscillations (QPOs) in the power spectra of accreting, rapidly-rotating black holes that originate from the geometric "light echoes" of X-ray flares occurring within the black hole ergosphere. Our present work extends our previous treatment to three-dimensional photon emission and orbits to allow for arbitrary latitudes in the positions of the distant observers and the X-ray sources in place of the mainly equatorial positions and photon orbits of the earlier consideration. Following the trajectories of a large number of photons we calculate the response functions of a given geometry and use them to produce model light curves which we subsequently analyze to compute their power spectra and autocorrelation functions. In the case of an optically-thin environment, relevant to advection-dominated accretion flows, we consistently find QPOs at frequencies of order of ~kHz for stellar-mass black hole candidates while order of ~mHz for typical active galactic nuclei (~10^7 Msun) for a wide range of viewing angles (30 to 80deg) from X-ray sources predominantly concentrated toward the equator within the ergosphere. As in our previous treatment, here too, the QPO signal is produced by the frame-dragging of the photons by the rapidly-rotating black hole, which results in photon "bunches" separated by constant time-lags, the result of multiple photon orbits around the hole. Our model predicts for various source/observer configurations the robust presence of a new class of QPOs, which is inevitably generic to curved spacetime structure in rotating black hole systems.
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arxiv:0901.2858
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According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.
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arxiv:0901.2896
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We analyze the theory and phenomenology of anomalous global chiral symmetries in the presence of an extra dimension. We propose a simple extension of the Standard Model in 5D whose signatures closely resemble those of supersymmetry with gauge mediation, and we suggest a novel scalar dark matter candidate.
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arxiv:0901.2933
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