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Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe several such approaches in the common framework of graphical models. We give a unified overview of models previously introduced in the literature, which is simpler and more comprehensive than previous descriptions and enables us to highlight commonalities and differences among models that were not observed in the past. In addition, we present several new models and inference routines, which are naturally derived within this unified viewpoint.
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arxiv:1104.1992
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We provide the first exact calculation of the height distribution at arbitrary time $t$ of the continuum KPZ growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer (DP) with one end fixed, one free, and the Bethe Ansatz for the replicated attractive boson model. We obtain the generating function of the moments of the DP partition sum as a Fredholm Pfaffian. Our formula, valid for all times, exhibits convergence of the free energy (i.e. KPZ height) distribution to the GOE Tracy Widom distribution at large time.
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arxiv:1104.1993
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Using the contraction of the SU(3) algebra to the algebra of the rigid rotator in the large boson number limit of the Interacting Boson Approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical line of the first order shape/phase transition separating the spherical and prolate deformed phases, and lies within the Alhassid--Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices amidst chaotic regions. In addition to providing an explanation for the existence of the arc of regularity, the present line represents the first example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state (and its rotational band) become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons.
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arxiv:1104.2104
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We use ab initio calculations to examine thermodynamic factors that could promote the formation of recently proposed unique oP10-FeB4 and oP12-FeB2 compounds. We demonstrate that these compact boron-rich phases are stabilized further under pressure. We also show that chromium tetraboride is more stable in the new oP10 rather than the reported oI10 structure which opens up the possibility of realizing an oP10-Fe(x)Cr(1-x)B4 pseudobinary material. In addition to exhibiting remarkable electronic features, oP10-FeB4 and oP12-FeB2 are expected to be harder than the known Fe-B compounds commonly used for hard coating applications.
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arxiv:1104.2136
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Quartic gravity theory is considered with the Einstein-Hilbert Lagrangean $R+aR^{2}+bR_{\mu \nu}R^{\mu \nu},$ $R_{\mu \nu}$ being Ricci\'s tensor and R the curvature scalar. The parameters $a$ and $b$ are taken of order 1 km$^{2}.$ Arguments are given which suggest that the effective theory so obtained may be a plausible approximation of a viable theory. A numerical integration is performed of the field equations for a free neutron gas. As in the standard Oppenheimer-Volkoff calculation the star mass increases with increasing central density until about 1 solar mass and then decreases. However a dramatic difference exists in the behaviour of the baryon number, which increases monotonically. The calculation suggests that the theory allows stars in equilibrium with arbitrary baryon number, no matter how large.
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arxiv:1104.2140
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We establish a coupled fixed points theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on existence of quasisolutions and solutions to first--order functional differential equations with state--dependent deviating arguments. Our results are very general and can be applied to functional equations featuring discontinuities with respect to all of their arguments, but we emphasize that they are new even for differential equations with continuously state--dependent delays.
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arxiv:1104.2159
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The thermal conductivity k of the iron-arsenide superconductor LiFeAs (Tc ~ 18K) was measured in single crystals at temperatures down to T~50mK and in magnetic fields up to H=17T, very close to the upper critical field Hc2~18T. For both directions of the heat current, parallel and perpendicular to the tetragonal c-axis, a negligible residual linear term k/T is found as T ->0, revealing that there are no zero-energy quasiparticles in the superconducting state. The increase in k with magnetic field is the same for both current directions and it follows closely the dependence expected for an isotropic superconducting gap. There is no evidence of multi-band character, whereby the gap would be different on different Fermi-surface sheets. These findings show that the superconducting gap in LiFeAs is isotropic in 3D, without nodes or deep minima anywhere on the Fermi surface. Comparison with other iron-pnictide superconductors suggests that a nodeless isotropic gap is a common feature at optimal doping (maximal Tc).
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arxiv:1104.2209
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A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of the Lie algebra $\g$ of $G$. A hermitian Lie group is a central extension of the identity component of the automorphism group of a hermitian Hilbert symmetric space. In the present paper we classify the irreducible semibounded unitary representations of hermitian Lie groups corresponding to infinite dimensional irreducible symmetric spaces. These groups come in three essentially different types: those corresponding to negatively curved spaces (the symmetric Hilbert domains), the unitary groups acting on the duals of Hilbert domains, such as the restricted Gra\ss{}mannian, and the motion groups of flat spaces.
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arxiv:1104.2234
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We study a scalar field with non-minimal kinetic coupling to itself and to the curvature. The slow rolling conditions allowing an inflationary background have been found. The quadratic and Higgs type potentials have been considered, and the corresponding values for the scalar fields at the end of inflation allows to recover the connection with particle physics.
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arxiv:1104.2253
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Photons (bosons) confined in a hollow waveguide containing an atomic gas could show spin-charge separation, which is more commonly associated with one-dimensional fermions.
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arxiv:1104.2297
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We perform a time-dependent ionization analysis to constrain plasma heating requirements during a fast partial halo coronal mass ejection (CME) observed on 2000 June 28 by the Ultraviolet Coronagraph Spectrometer (UVCS) aboard the Solar and Heliospheric Observatory (SOHO). We use two methods to derive densities from the UVCS measurements, including a density sensitive O V line ratio at 1213.85 and 1218.35 Angstroms, and radiative pumping of the O VI 1032,1038 doublet by chromospheric emission lines. The most strongly constrained feature shows cumulative plasma heating comparable to or greater than the kinetic energy, while features observed earlier during the event show cumulative plasma heating of order or less than the kinetic energy. SOHO Michelson Doppler Imager (MDI) observations are used to estimate the active region magnetic energy. We consider candidate plasma heating mechanisms and provide constraints when possible. Because this CME was associated with a relatively weak flare, the contribution by flare energy (e.g., through thermal conduction or energetic particles) is probably small; however, the flare may have been partially behind the limb. Wave heating by photospheric motions requires heating rates significantly larger than those previously inferred for coronal holes, but the eruption itself could drive waves which heat the plasma. Heating by small-scale reconnection in the flux rope or by the CME current sheet is not significantly constrained. UVCS line widths suggest that turbulence must be replenished continually and dissipated on time scales shorter than the propagation time in order to be an intermediate step in CME heating.
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arxiv:1104.2298
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The Bernoulli sieve is the infinite "balls-in-boxes" occupancy scheme with random frequencies $P_k=W_1...W_{k-1}(1-W_k)$, where $(W_k)_{k\in\mn}$ are independent copies of a random variable $W$ taking values in $(0,1)$. Assuming that the number of balls equals $n$, let $L_n$ denote the number of empty boxes within the occupancy range. The paper proves that, under a regular variation assumption, $L_n$, properly normalized without centering, weakly converges to a functional of an inverse stable subordinator. Proofs rely upon the observation that $(\log P_k)$ is a perturbed random walk. In particular, some results for general perturbed random walks are derived. The other result of the paper states that whenever $L_n$ weakly converges (without normalization) the limiting law is mixed Poisson.
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arxiv:1104.2299
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We investigate the low temperature thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsion in an external magnetic field via the thermodynamic Bethe ansatz method. The exact thermodynamics of the model in a weak magnetic field is derived with the help of Wiener-Hopf techniques. It turns out that the low energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(2) Heisenberg spin chain. However, these two types of conformally invariant low-lying excitations may break down as excitations take place far away from the Fermi points. The long distance asymptotics of the correlation functions and the critical exponents for the model in the presence of a magnetic field at zero temperature are derived in detail by solving dressed charge equations and by conformal mapping. Furthermore, we calculate the conformal dimensions for particular cases of correlation functions. The leading terms of these correlation functions are given explicitly for a weak magnetic field $H\ll 1$ and for a magnetic field close to the critical field $H\rightarrow H_{c}$. Our analytical results provide insights into universal thermodynamics and criticality in one-dimensional many-body physics.
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arxiv:1104.2352
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When two particles attract via a resonant short-range interaction, three particles always form an infinite tower of bound states characterized by a discrete scaling symmetry. It has been considered that this Efimov effect exists only in three dimensions. Here we review how the Efimov physics can be liberated from three dimensions by considering two-body and three-body interactions in mixed dimensions and four-body interaction in one dimension. In such new systems, intriguing phenomena appear, such as confinement-induced Efimov effect, Bose-Fermi crossover in Efimov spectrum, and formation of interlayer Efimov trimers. Some of them are observable in ultracold atom experiments and we believe that this study significantly broadens our horizons of universal Efimov physics.
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arxiv:1104.2387
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{\em Riemannian cubics} are curves in a manifold $M$ that satisfy a variational condition appropriate for interpolation problems. When $M$ is the rotation group SO(3), Riemannian cubics are track-summands of {\em Riemannian cubic splines}, used for motion planning of rigid bodies. Partial integrability results are known for Riemannian cubics, and the asymptotics of Riemannian cubics in SO(3) are reasonably well understood. The mathematical properties and medium-term behaviour of Riemannian cubics in SO(3) are known to be be extremely rich, but there are numerical methods for calculating Riemannian cubic splines in practice. What is missing is an understanding of the short-term behaviour of Riemannian cubics, and it is this that is important for applications. The present paper fills this gap by deriving approximations to nearly geodesic Riemannian cubics in terms of elementary functions. The high quality of these approximations depends on mathematical results that are specific to Riemannian cubics.
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arxiv:1104.2397
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We consider the universe as a huge $\nu_R$-sphere formed with degenerate relic neutrinos and suggest that its constant energy density play a role of an effective cosmological constant. We construct the sphere as a bubble of true vacuum in a field theory model with a spontaneously broken U(1) global symmetry, and we interpret the sphere-forming time as the transition time for recent acceleration of the universe. The coincidence problem may be regarded as naturally resolved in this model, because the relic neutrinos can make the $\nu_R$-sphere at the recent past time during the matter-dominated era.
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arxiv:1104.2413
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Thermoelectric properties of the layered cobalt oxide system LixCoO2 were investigated in a wide range of Li composition, 0.98 >= x >= 0.35. Single-phase bulk samples of LixCoO2 were successfully obtained through electrochemical deintercalation of Li from the pristine LiCoO2 phase. While LixCoO2 with x >= 0.94 is semiconductive, the highly Li-deficient phase (0.75 >= x >= 0.35) exhibits metallic conductivity. The magnitude of Seebeck coefficient at 293 K (S293K) significantly depends on the Li content (x). The S293K value is as large as +70 ~ +100 uV/K for x >= 0.94, and it rapidly decreases from +90 uV/K to +10 uV/K as x is lowered within a Li composition range of 0.75 >= x >= 0.50. This behavior is in sharp contrast to the results of x <= 0.40 for which the S293K value is small and independent of x (+10 uV/K), indicating that a discontinuous change in the thermoelectric characteristics takes place at x = 0.40 ~ 0.50. The unusually large Seebeck coefficient and metallic conductivity are found to coexist in a narrow range of Li composition at about x = 0.75. The coexistence, which leads to an enhanced thermoelectric power factor, may be attributed to unusual electronic structure of the two-dimensional CoO2 block.
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arxiv:1104.2419
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Thomas has recently derived scaling laws for X-ray radiation from electrons accelerated in plasma bubbles, as well as a threshold for the self-injection of background electrons into the bubble [A. G. R. Thomas, Phys. Plasmas 17, 056708 (2010)]. To obtain this threshold, the equations of motion for a test electron are studied within the frame of the bubble model, where the bubble is described by prescribed electromagnetic fields and has a perfectly spherical shape. The author affirms that any elliptical trajectory of the form x'^2/{\gamma}_p^2 + y'^2 = R^2 is solution of the equations of motion (in the bubble frame), within the approximation p'_y^2/p'_x^2 \ll 1. In addition, he highlights that his result is different from the work of Kostyukov et al. [Phys. Rev. Lett. 103, 175003 (2009)], and explains the error committed by Kostyukov-Nerush-Pukhov-Seredov (KNPS). In this comment, we show that numerically integrated trajectories, based on the same equations than the analytical work of Thomas, lead to a completely different result for the self-injection threshold, the result published by KNPS [Phys. Rev. Lett. 103, 175003 (2009)]. We explain why the analytical analysis of Thomas fails and we provide a discussion based on numerical simulations which show exactly where the difference arises. We also show that the arguments of Thomas concerning the error of KNPS do not hold, and that their analysis is mathematically correct. Finally, we emphasize that if the KNPS threshold is found not to be verified in PIC (Particle In Cell) simulations or experiments, it is due to a deficiency of the model itself, and not to an error in the mathematical derivation.
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arxiv:1104.2449
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In the next years the data transmission connections will constitute one of the principal tools of communication among cities, enterprises and public administration. With their enhanced connectivity, the systems and nets of information are now exposed to an increased vulnerability and new safety problems are emerging. Insofar Quantum Key Distribution (QKD) has matured to real world applications and can enhance the safety of the communication nets. In this paper we present the QKD network designed and implemented by Selex-SI and we give an overview of the obtained results.
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arxiv:1104.2475
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We study the basic holographic insulator and superconductor phase transition in the AdS soliton background by generalizing the spontaneous breaking of a global U(1) symmetry to occur via St$\ddot{u}$ckelberg mechanism. We construct the soliton solutions with backreaction and examine the effects of the backreaction on the condensation of the scalar hair in the generalized St$\ddot{u}$ckelberg Lagrangian. We disclose rich physics in various phase transitions. In addition to the AdS soliton configuration, we also examine the property of the phase transition in the AdS black hole background.
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arxiv:1104.2478
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We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a three-dimensional square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced in [Van den Nest et al., Phys. Rev. A 80, 052334 (2009)] and extended here.
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arxiv:1104.2517
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We investigate new shapes of local primordial non-Gaussianities in the CMB. Allowing for a primordial isocurvature mode along with the main adiabatic one, the angular bispectrum is in general a superposition of six distinct shapes: the usual adiabatic term, a purely isocurvature component and four additional components that arise from correlations between the adiabatic and isocurvature modes. We present a class of early Universe models in which various hierarchies between these six components can be obtained, while satisfying the present upper bound on the isocurvature fraction in the power spectrum. Remarkably, even with this constraint, detectable non-Gaussianity could be produced by isocurvature modes. We finally discuss the prospects of detecting these new shapes with the Planck satellite.
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arxiv:1104.2567
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In this paper we will make the computation of the Onsager-Machlup functional of an inhomogeneous uniformly elliptic diffusion process. This functional will have formally the same picture as in the homogeneous case, the only difference come from the infinitesimal variation of the volume. For example in the Ricci flow case, we find some functional which is not so far to the $\mathcal L_{0} $ distance used by Lott to study this flow \cite{Lott:08}. We finish by a application to small ball probability for weighted sup norm, for inhomogeneous diffusion.
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arxiv:1104.2678
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We present a high-performance N-body code for self-gravitating collisional systems accelerated with the aid of a new SIMD instruction set extension of the x86 architecture: Advanced Vector eXtensions (AVX), an enhanced version of the Streaming SIMD Extensions (SSE). With one processor core of Intel Core i7-2600 processor (8 MB cache and 3.40 GHz) based on Sandy Bridge micro-architecture, we implemented a fourth-order Hermite scheme with individual timestep scheme (Makino and Aarseth, 1992), and achieved the performance of 20 giga floating point number operations per second (GFLOPS) for double-precision accuracy, which is two times and five times higher than that of the previously developed code implemented with the SSE instructions (Nitadori et al., 2006b), and that of a code implemented without any explicit use of SIMD instructions with the same processor core, respectively. We have parallelized the code by using so-called NINJA scheme (Nitadori et al., 2006a), and achieved 90 GFLOPS for a system containing more than N = 8192 particles with 8 MPI processes on four cores. We expect to achieve about 10 tera FLOPS (TFLOPS) for a self-gravitating collisional system with N 105 on massively parallel systems with at most 800 cores with Sandy Bridge micro-architecture. This performance will be comparable to that of Graphic Processing Unit (GPU) cluster systems, such as the one with about 200 Tesla C1070 GPUs (Spurzem et al., 2010). This paper offers an alternative to collisional N-body simulations with GRAPEs and GPUs.
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arxiv:1104.2700
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Estimating the black hole mass at the center of galaxies is a fundamental step not only for understanding the physics of accretion, but also for the cosmological evolution of galaxies. Recently a new method, based solely on X-ray data, was successfully applied to determine the black hole mass in Galactic systems. Since X-rays are thought to be produced via Comptonization process both in stellar and supermassive black holes, in principle, the same method may be applied to estimate the mass in supermassive black holes. In this work we test this hypothesis by performing a systematic analysis of a sample of AGNs, whose black hole mass has been already determined via reverberation mapping and which possess high quality XMM-Newton archival data. The good agreement obtained between the black hole masses derived with this novel scaling technique and the reverberation mapping values suggests that this method is robust and works equally well on stellar and supermassive black holes, making it a truly scale-independent technique for black hole determination.
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arxiv:1104.2758
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Functional MRI (fMRI) has become the most common method for investigating the human brain. However, fMRI data present some complications for statistical analysis and modeling. One recently developed approach to these data focuses on estimation of computational encoding models that describe how stimuli are transformed into brain activity measured in individual voxels. Here we aim at building encoding models for fMRI signals recorded in the primary visual cortex of the human brain. We use residual analyses to reveal systematic nonlinearity across voxels not taken into account by previous models. We then show how a sparse nonparametric method [J. Roy. Statist. Soc. Ser. B 71 (2009b) 1009-1030] can be used together with correlation screening to estimate nonlinear encoding models effectively. Our approach produces encoding models that predict about 25% more accurately than models estimated using other methods [Nature 452 (2008a) 352--355]. The estimated nonlinearity impacts the inferred properties of individual voxels, and it has a plausible biological interpretation. One benefit of quantitative encoding models is that estimated models can be used to decode brain activity, in order to identify which specific image was seen by an observer. Encoding models estimated by our approach also improve such image identification by about 12% when the correct image is one of 11,500 possible images.
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arxiv:1104.2805
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We report the discovery of WASP-43b, a hot Jupiter transiting a K7V star every 0.81 d. At 0.6-Msun the host star has the lowest mass of any star hosting a hot Jupiter. It also shows a 15.6-d rotation period. The planet has a mass of 1.8 Mjup, a radius of 0.9 Rjup, and with a semi-major axis of only 0.014 AU has the smallest orbital distance of any known hot Jupiter. The discovery of such a planet around a K7V star shows that planets with apparently short remaining lifetimes owing to tidal decay of the orbit are also found around stars with deep convection zones.
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arxiv:1104.2823
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We report the detection of WASP-35b, a planet transiting a metal-poor ([Fe/H] = -0.15) star in the Southern hemisphere, WASP-48b, an inflated planet which may have spun-up its slightly evolved host star of 1.75 R_sun in the Northern hemisphere, and the independent discovery of HAT-P-30b / WASP-51b, a new planet in the Northern hemisphere. Using WASP, RISE, FTS and TRAPPIST photometry, with CORALIE, SOPHIE and NOT spectroscopy, we determine that WASP-35b has a mass of 0.72 +/- 0.06 M_J and radius of 1.32 +/- 0.03 R_J, and orbits with a period of 3.16 days, WASP-48b has a mass of 0.98 +/- 0.09 M_J, radius of 1.67 +/- 0.08 R_J and orbits in 2.14 days, while WASP-51b, with an orbital period of 2.81 days, is found to have a mass of 0.76 +/- 0.05 M_J and radius of 1.42 +/- 0.04 R_J, agreeing with values of 0.71 +/- 0.03 M_J and 1.34 +/- 0.07 R_J reported for HAT-P-30b.
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arxiv:1104.2827
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In this work, the complete one loop calculation of meson-meson scattering amplitudes within U(3)\otimes U(3) chiral perturbation theory with explicit resonance states is carried out for the first time. Partial waves are unitarized from the perturbative calculation employing a non-perturbative approach based on the N/D method. Once experimental data are reproduced in a satisfactory way we then study the resonance properties, such as the pole positions, corresponding residues and their N_C behaviors. The resulting N_C dependence is the first one in the literature that takes into account the fact that the \eta_1 becomes the ninth Goldstone boson in the chiral limit for large N_C. Within this scheme the vector resonances studied, \rho(770), K^*(892) and \phi(1020), follow an N_C trajectory in agreement with their standard \bar{q}q interpretation. The scalars f_0(1370), a_0(1450) and K^*(1430) also have for large N_C a \bar{q}q pole position trajectory and all of them tend to a bare octet of scalar resonances around 1.4 GeV. The f_0(980) tends asymptotically to the bare pole position of a singlet scalar resonance around 1 GeV. The \sigma, \kappa and a_0(980) scalar resonances have a very different N_C behavior. The case of the \sigma resonance is analyzed with special detail.
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arxiv:1104.2849
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We present follow-up observations to those of Geballe & Oka (2010), who found high column densities of H3+ ~100 pc off of the Galactic center (GC) on the lines of sight to 2MASS J17432173-2951430 (J1743) and 2MASS J17470898-2829561 (J1747). The wavelength coverages on these sightlines have been extended in order to observe two key transitions of H3+, R(3,3)l and R(2,2)l, that constrain the temperatures and densities of the environments. The profiles of the H3+ R(3,3)l line, which is due only to gas in the GC, closely matches the differences between the H3+ R(1,1)l and CO line profiles, just as it does for previously studied sightlines in the GC. Absorption in the R(2,2)l line of H3+ is present in J1747 at velocities between -60 and +100 km/s. This is the second clear detection of this line in the interstellar medium after GCIRS 3 in the Central Cluster. The temperature of the absorbing gas in this velocity range is 350 K, significantly warmer than in the diffuse clouds in other parts of the Central Molecular Zone. This indicates that the absorbing gas is local to Sgr B molecular cloud complex. The warm and diffuse gas revealed by Oka et al. (2005) apparently extends to ~100 pc, but there is a hint that its temperature is somewhat lower in the line of sight to J1743 than elsewhere in the GC. The observation of H3+ toward J1747 is compared with the recent Herschel observation of H2O+ toward Sgr B2 and their chemical relationship and remarkably similar velocity profiles are discussed.
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arxiv:1104.2902
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The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes: the research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.
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arxiv:1104.2910
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These proceedings present the unfolding techniques used so far in ATLAS. Two representative examples are discussed in detail; one using bin-by-bin correction factors, and the other iterative unfolding.
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arxiv:1104.2962
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For a given quantum state $\rho$ and two quantum operations $\Phi$ and $\Psi$, the information encoded in the quantum state $\rho$ is quantified by its von Neumann entropy $\S(\rho)$. By the famous Choi-Jamio{\l}kowski isomorphism, the quantum operation $\Phi$ can be transformed into a bipartite state, the von Neumann entropy $\S^{\mathrm{map}}(\Phi)$ of the bipartite state describes the decoherence induced by $\Phi$. In this Letter, we characterize not only the pairs $(\Phi, \rho)$ which satisfy $\S(\Phi(\rho))=\S(\rho)$, but also the pairs $(\Phi, \Psi)$ which satisfy $\S^{\mathrm{map}}(\Phi\circ\Psi) = \S^{\mathrm{map}}(\Psi)$.
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arxiv:1104.2992
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The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of Thermodynamics. On the contrary, the formulation in terms of internal powers is more general, because it is a priori defined on the basis of the constitutive equations. Besides it allows to highlight, without ambiguity, the contribution of the internal powers in the variation of the thermodynamic potentials. Finally, in this paper, we consider some examples of non-local materials and derive the proper expressions of their internal powers from the power balance laws.
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arxiv:1104.3000
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Minimal deterministic finite automata (DFAs) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the input DFA, by [Gawrychowski and Je\.z: Hyper-minimisation made efficient. Proc. MFCS, LNCS 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyper-minimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. Both algorithms return a DFA that is as small as possible, while only committing a finite number of errors. These algorithms are further improved to return a DFA that commits the least number of errors at the expense of an increased (quadratic) run-time. This solves an open problem of [Badr, Geffert, and Shipman: Hyper-minimizing minimized deterministic finite state automata. RAIRO Theor. Inf. Appl. 43, 2009]. In addition, an experimental study on random automata is performed and the effects of the existing algorithms and the new algorithm are reported.
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arxiv:1104.3007
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In this paper, we complete the global qualitative analysis of the well-known FitzHugh-Nagumo neuronal model. In particular, studying global limit cycle bifurcations and applying the Wintner-Perko termination principle for multiple limit cycles, we prove that the corresponding dynamical system has at most two limit cycles.
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arxiv:1104.3019
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We consider intrinsic contributions to the spin Hall and spin Nernst effects in a bilayer graphene. The relevant electronic spectrum is obtained from the tight binding Hamiltonian, which also includes the intrinsic spin-orbit interaction. The corresponding spin Hall and spin Nernst conductivities are compared with those obtained from effective Hamiltonians appropriate for states in the vicinity of the Fermi level of a neutral bilayer graphene. Both conductivities are determined within the linear response theory and Green function formalism. The influence of an external voltage between the two atomic sheets is also included. We found transition from the topological spin Hall insulator phase at low voltages to conventional insulator phase at larger voltages.
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arxiv:1104.3036
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We investigate the possibility of habitable Trojan planets in the HD 23079 star-planet system. This system consists of a solar-type star and a Jupiter-type planet, which orbits the star near the outer edge of the stellar habitable zone in an orbit of low eccentricity. We find that in agreement with previous studies Earth-mass habitable Trojan planets are possible in this system, although the success of staying within the zone of habitability is significantly affected by the orbital parameters of the giant planet and by the initial condition of the theoretical Earth-mass planet. In one of our simulations, the Earth-mass planet is captured by the giant planet and thus becomes a habitable moon.
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arxiv:1104.3092
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In classical general relativity the Cauchy horizon within a two-horizon black hole is unstable via a phenomenon known as mass inflation, in which the mass parameter (and the spacetime curvature) of the black hole diverges at the Cauchy horizon. Here we study this effect for loop black holes -- quantum gravitationally corrected black holes from loop quantum gravity -- whose construction alleviates the $r=0$ singularity present in their classical counterparts. We use a simplified model of mass inflation, which makes use of the generalized DTR relation, to conclude that the Cauchy horizon of loop black holes indeed results in a curvature singularity similar to that found in classical black holes. The DTR relation is of particular utility in the loop black hole because it does not directly rely upon Einstein's field equations. We elucidate some of the interesting and counterintuitive properties of the loop black hole, and corroborate our results using an alternate model of mass inflation due to Ori.
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arxiv:1104.3126
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Community structure appears to be an intrinsic property of many complex real-world networks. However, recent work shows that real-world networks reveal even more sophisticated modules than classical cohesive (link-density) communities. In particular, networks can also be naturally partitioned according to similar patterns of connectedness among the nodes, revealing link-pattern communities. We here propose a propagation based algorithm that can extract both link-density and link-pattern communities, without any prior knowledge of the true structure. The algorithm was first validated on different classes of synthetic benchmark networks with community structure, and also on random networks. We have further applied the algorithm to different social, information, technological and biological networks, where it indeed reveals meaningful (composites of) link-density and link-pattern communities. The results thus seem to imply that, similarly as link-density counterparts, link-pattern communities appear ubiquitous in nature and design.
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arxiv:1104.3162
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Allometric growth is found in many tagging systems online. That is, the number of new tags (T) is a power law function of the active population (P), or T P^gamma (gamma!=1). According to previous studies, it is the heterogeneity in individual tagging behavior that gives rise to allometric growth. These studies consider the power-law distribution model with an exponent beta, regarding 1/beta as an index for heterogeneity. However, they did not discuss whether power-law is the only distribution that leads to allometric growth, or equivalently, whether the positive correlation between heterogeneity and allometric growth holds in systems of distributions other than power-law. In this paper, the authors systematically examine the growth pattern of systems of six different distributions, and find that both power-law distribution and log-normal distribution lead to allometric growth. Furthermore, by introducing Shannon entropy as an indicator for heterogeneity instead of 1/beta, the authors confirm that the positive relationship between heterogeneity and allometric growth exists in both cases of power-law and log-normal distributions.
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arxiv:1104.3179
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The eccentric connectivity index $\xi^c$ is a distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. We prove that the broom has maximum $\xi^c$ among trees with a fixed maximum vertex degree, and characterize such trees with minimum $\xi^c$\,. In addition, we propose a simple linear algorithm for calculating $\xi^c$ of trees.
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arxiv:1104.3206
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Markov Logic Networks (MLNs) have emerged as a powerful framework that combines statistical and logical reasoning; they have been applied to many data intensive problems including information extraction, entity resolution, and text mining. Current implementations of MLNs do not scale to large real-world data sets, which is preventing their wide-spread adoption. We present Tuffy that achieves scalability via three novel contributions: (1) a bottom-up approach to grounding that allows us to leverage the full power of the relational optimizer, (2) a novel hybrid architecture that allows us to perform AI-style local search efficiently using an RDBMS, and (3) a theoretical insight that shows when one can (exponentially) improve the efficiency of stochastic local search. We leverage (3) to build novel partitioning, loading, and parallel algorithms. We show that our approach outperforms state-of-the-art implementations in both quality and speed on several publicly available datasets.
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arxiv:1104.3216
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In order to prevent detection and evade signature-based scanning methods, which are normally exploited by antivirus software, metamorphic viruses use several various obfuscation approaches. They transform their code in new instances as look entirely or partly different and contain dissimilar sequences of string, but their behavior and function remain unchanged. This obfuscation process allows them to stay away from the string based signature detection. In this research, we use a statistical technique to compare the similarity between two files infected by two morphed versions of a given metamorphic virus. Our proposed solution based on static analysis and it uses the histogram of machine instructions frequency in various offspring of obfuscated viruses. We use Euclidean histogram distance metric to compare a pair of portable executable (PE) files. The aim of this study is to show that for some particular obfuscation methods, the presented solution can be exploited to detect morphed varieties of a file. Hence, it can be utilized by non-string based signature scanning to identify whether a file is a version of a metamorphic virus or not.
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arxiv:1104.3228
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An entanglement bound based on local measurements is introduced for multipartite pure states. It is the upper bound of the geometric measure and the relative entropy of entanglement. It is the lower bound of minimal measurement entropy. For pure bipartite states, the bound is equal to the entanglement entropy. The bound is applied to pure tripartite qubit states and the exact tripartite relative entropy of entanglement is obtained for a wide class of states.
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arxiv:1104.3280
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This paper is devoted to the study of the nonrelativitic limit of Amelino-Camelia Doubly Special Relativity, and the corresponding modified Klein-Gordon and Dirac equations. We show that these equations reduce to the Schrodinger equations for the particle and the antiparticle with different inertial masses. However, their rest masses are the same. M. Coraddu and S. Mignemi have studied recently the non relativistic limit of the Magueijo-Smolin Doubly Special Relativity. We compare their results with our study, and show that these two models are reciprocal to each other in the nonrelativitic limit. The different inertial masses also leads to the CPT violation.
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arxiv:1104.3322
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Cosmic string wakes lead to a large signal in 21 cm redshift maps at redshifts larger than that corresponding to reionization. Here, we compute the angular power spectrum of 21 cm radiation as predicted by a scaling distribution of cosmic strings whose wakes have undergone shock heating.
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arxiv:1104.3337
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We show that the group of homeomorphisms of the Cantor set $H(K)$ has ample generics, that is, for every $m$ the diagonal conjugacy action $g\cdot(h_1,h_2,..., h_m)=(gh_1g^{-1},gh_2g^{-1},..., gh_mg^{-1})$ of $H(K)$ on $H(K)^m$ has a comeager orbit. This answers a question of Kechris and Rosendal. We show that the generic tuple in $H(K)^m$ can be taken to be the limit of a certain projective Fraisse family. We also present a proof of the existence of the generic homeomorphism of the Cantor set in the context of the projective Fraisse theory.
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arxiv:1104.3340
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In this paper we define the Schwartz linear operators among spaces of tempered distributions. These operators are the analogous of linear continuous operators among separable Hilbert spaces, but in the case of spaces endowed with Schwartz bases having a continuous index set. The Schwartz linear operators enjoy properties very similar to those enjoyed by linear operators in the finite dimensional case. The Schwartz operators are one possible rigorous mathematical model for the operators and observables used in Quantum Mechanics.
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arxiv:1104.3380
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Star polymer is a typical nonlinear macromolecule possessing special thermodynamic behaviors for the existence of a jointing point. The thermodynamic transitions of a single star polymer are systematically studied with bond fluctuation model using Wang-Landau sampling technique. A new analysis method applying the shape factor is proposed to determine coil-globule (CG) and liquid-crystal (LC) transitions, which shows higher efficiency and precision than canonical specific heat function. It is found that the LC transition of star polymer at lower temperature obeys the identical scaling law as linear polymer. With the increase of the arm density of star polymer, however, the CG transition point, corresponding to {\theta} temperature, shifts towards the LC transition and the reason comes from the high density arms of star polymer, which requires the lower temperature for attracting force to overcome the volume excluding effects of chain. This work clearly demonstrates that the distinction of linear and star polymers in structures only affects CG transition and has no influence on LC transition.
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arxiv:1104.3411
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The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.
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arxiv:1104.3498
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We define Stasheff polytopes in the space of tropical points of cluster A-varieties. We study the supports of products of elements of canonical bases for cluster X-varieties. We prove that, for the cluster X-variety of type A_n, such supports are Stasheff polytopes.
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arxiv:1104.3528
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We revisit the process $e^+e^- \to \gamma Z$ at the ILC with transverse beam polarization in the presence of anomalous CP-violating $\gamma Z Z$ coupling $\lambda_1$ and $\gamma \gamma Z$ coupling $\lambda_2$. We point out that if the final-state spins are resolved, then it becomes possible to fingerprint the anomalous coupling {\rm Re}$\lambda_1$.90% confidence level limit on {\rm Re}$\lambda_1$ achievable at ILC with center-of-mass energy of 500 GeV or 800 GeV with realistic initial beam polarization and integrated luminosity is of the order of few times of $10^{-2}$ when the helicity of $Z$ is used and $10^{-3}$ when the helicity of $\gamma$ is used. The resulting corrections at quadratic order to the cross section and its influence on these limits are also evaluated and are shown to be small. The benefits of such polarization programmes at the ILC are compared and contrasted for the process at hand. We also discuss possible methods by which one can isolate events with a definite helicity for one of the final-state particles.
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arxiv:1104.3645
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We discuss recent results on the heavy fermion superconductor CeRhIn$_5$ which presents ideal conditions to study the strong coupling between the suppression of antiferromagnetic order and the appearance of unconventional superconductivity. The appearance of superconductivity as function of pressure is strongly connected to the suppression of the magnetic order. Under magnetic field, the re-entrance of magnetic order inside the superconducting state shows that antiferromagnetism nucleates in the vortex cores. The suppression of antiferromagnetism in CeRhIn$_5$ by Sn doping is compared to that under hydrostatic pressure.
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arxiv:1104.3656
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We present the results of an experimental and theoretical study of the electronically excited $\tripletex$ state of $^{87}$Rb$_2$ molecules. The vibrational energies are measured for deeply bound states from the bottom up to $v'=15$ using laser spectroscopy of ultracold Rb$_2$ Feshbach molecules. The spectrum of each vibrational state is dominated by a 47\,GHz splitting into a $\cog$ and $\clg$ component caused mainly by a strong second order spin-orbit interaction. Our spectroscopy fully resolves the rotational, hyperfine, and Zeeman structure of the spectrum. We are able to describe to first order this structure using a simplified effective Hamiltonian.
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arxiv:1104.3674
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This Letter reports results from the NEMO-3 experiment based on an exposure of 1275 days with 661g of 130Te in the form of enriched and natural tellurium foils. The double beta decay rate of 130Te is found to be greater than zero with a significance of 7.7 standard deviations and the half-life is measured to be T1/2 = (7.0 +/- 0.9(stat) +/- 1.1(syst)) x 10^{20} yr. This represents the most precise measurement of this half-life yet published and the first real-time observation of this decay.
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arxiv:1104.3716
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A complete classification of binary doubly even self-dual codes of length 40 is given. As a consequence, a classification of binary extremal self-dual codes of length 38 is also given.
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arxiv:1104.3727
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A self-contained Fortran-77 program for goodness of fit tests for histograms with weighted entries as well as with unweighted entries is presented. The code calculates test statistics for case of histogram with normalized weights of events and in case of unnormalized weights of events.
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arxiv:1104.3733
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We present 2817 new southern proper motion systems with 0.40 "/yr > mu > 0.18 "/yr and declination between -47 degrees and 00 degrees. This is a continuation of the SuperCOSMOS-RECONS (SCR) proper motion searches of the southern sky. We use the same photometric relations as previous searches to provide distance estimates based on the assumption that the objects are single main sequence stars. We find 79 new red dwarf systems predicted to be within 25 pc, including a few new components of previously known systems. Two systems - SCR 1731-2452 at 9.5 pc and SCR 1746-3214 at 9.9 pc - are anticipated to be within 10 pc. We also find 23 new white dwarf candidates with distance estimates of 15-66 pc, as well as 360 new red subdwarf candidates. With this search, we complete the SCR sweep of the southern sky for stars with mu > 0.18 "/yr and R_59F < 16.5, resulting in a total of 5042 objects in 4724 previously unreported proper motion systems. Here we provide selected comprehensive lists from our SCR proper motion search to date, including 152 red dwarf systems estimated to be within 25 pc (nine within 10 pc), 46 white dwarfs (ten within 25 pc), and 598 subdwarf candidates. The results of this search suggest that there are more nearby systems to be found at fainter magnitudes and lower proper motion limits than those probed so far.
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arxiv:1104.3765
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The moment method is an image analysis technique for sub-pixel estimation of particle positions. The total error in the calculated particle position includes effects of pixel locking and random noise in each pixel. Pixel locking, also known as peak locking, is an artifact where calculated particle positions are concentrated at certain locations relative to pixel edges. We report simulations to gain an understanding of the sources of error and their dependence on parameters the experimenter can control. We suggest an algorithm, and we find optimal parameters an experimenter can use to minimize total error and pixel locking. Simulating a dusty plasma experiment, we find that a sub-pixel accuracy of 0.017 pixel or better can be attained. These results are also useful for improving particle position measurement and particle tracking velocimetry (PTV) using video microscopy, in fields including colloids, biology, and fluid mechanics.
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arxiv:1104.3776
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In this paper we prove some new series for $1/\pi$ as well as related congruences. We also raise several new kinds of series for $1/\pi$ and present some related conjectural congruences involving representations of primes by binary quadratic forms.
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arxiv:1104.3856
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An even hole is an induced chordless cycle of even length at least four. A diamond is an induced subgraph isomorphic to K_4-e. We show that graphs without even holes and without diamonds can be decomposed via clique-separators into graphs that have uniformly bounded cliquewidth.
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arxiv:1104.3920
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The strength of light emission near metallic nanostructures can scale anomalously with frequency and dimensionality. We find that light-matter interactions in plasmonic systems confined in two dimensions (e.g., near metal nanowires) strengthen with decreasing frequency owing to strong mode confinement away from the surface plasmon frequency. The anomalous scaling also applies to the modulation speed of plasmonic light sources, including lasers, with modulation bandwidths growing at lower carrier frequencies. This allows developing optical devices that exhibit simultaneously femto-second response times at the nano-meter scale, even at longer wavelengths into the mid IR, limited only by non-local effects and reversible light-matter coupling.
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arxiv:1104.3946
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The two-dimensional homogeneous Euclidean algorithm is the central motivation for the definition of the classical multidimensional continued fraction algorithms, as Jacobi-Perron, Poincar\'e, Brun and Selmer algorithms. The Rauzy induction, a generalization of the Euclidean algorithm, is a key tool in the study of interval exchange transformations. Both maps are known to be dissipative and ergodic with respect to Lebesgue measure. Here we prove that they are exact.
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arxiv:1104.3980
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For each $t>0,$ up to the number $n=N(t),$ the exact estimations of all initial taylor coefficients in the class $B_t$ were found, where $B_t$ is a set of holomorphic in unit disk functions $f,$ $0<|f|<1,$ $f(0)=e^{-t}.$
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arxiv:1104.3984
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We revisit the phase diagram of the frustrated s=1/2 spin ladder with antiferromagnetic rung and diagonal couplings. In particular, we reexamine the evidence for the columnar dimer phase, which has been predicted from analytic treatment of the model and has been claimed to be found in numerical calculations. By considering longer chains and by keeping more states than in previous work using the density-matrix renormalization group, we show that the numerical evidence presented previously for the existence of the dimerized phase is not unambiguous in view of the present more careful analysis. While we cannot completely rule out the possibility of a dimerized phase in the cross-coupled ladder, we do set limits on the maximum possible value of the dimer order parameter that are much smaller than those found previously.
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arxiv:1104.3990
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It is known that the Principal Poincar\'e Pontryagin Function is generically an Abelian integral. In non generic cases it is an iterated integral. In previous papers one of the authors gives a precise description of the Principal Poincar\'e Pontryagin Function, an iterated integral af length at most 2, involving a logarithmic function with only one ramification at a point at infinity. We show here that this property can be generalized to Hamiltonians having real points at infinity and satisfying some properties.
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arxiv:1104.4021
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The magnetic properties of the ferrimagnetic cobaltite CaBaCo$_4$O$_7$ are systematically investigated. We find that the susceptibility exhibits a downward deviation below $\sim$ 360 K, suggesting the occurrence of short range magnetic correlations at temperature well above $T_C$. The effective moment is determined to be 4.5 $\mu_B$/f.u, which is consistent with that expected for the Co$^{2+}$/Co$^{3+}$ high spin species. Using a criterion given by Banerjee [Phys. Lett. \textbf{12}, 16 (1964)], we demonstrate that the paramagnetic to ferrimagnetic transition in CaBaCo$_4$O$_7$ has a first order character.
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arxiv:1104.4032
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The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw_1), a random walk along the line of natural time, happening in operational time; (rw_2), a random walk along the line of space, happening in operational time;(rw_3), the inversion of (rw_1), namely a random walk along the line of operational time, happening in natural time. Via the general integral equation of CTRW and appropriate rescaling, the transition to the diffusion limit is carried out for each of these three random walks. Combining the limits of (rw_1) and (rw_2) we get the method of parametric subordination for generating particle paths, whereas combination of (rw_2) and (rw_3) yields the subordination integral for the sojourn probability density in space-time fractional diffusion.
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arxiv:1104.4041
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We study surface plasmons localized on interfaces between topologically trivial and topologically non-trivial time reversal invariant materials in three dimensions. For the interface between a metal and a topological insulator the magnetic polarization of the surface plasmon is rotated out of the plane of the interface; this effect should be experimentally observable by exciting the surface plasmon with polarized light. More interestingly, we argue that the same effect also is realized on the interface between vacuum and a doped topological insulator with non-vanishing bulk carrier density.
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arxiv:1104.4125
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The exponential increase of multimedia services by the mobile users requires seamless connectivity with cost effective Quality of Service QoS provisioning. For providing such on-demand QoS, the network needs to utilize the radio channels among the Mobile Hosts (MHs) effectively. We use vector genetic algorithm VGA for temporal imploration of sharable channel(s) from the neighbouring cells to fulfill the needs of a cell. We propose a new micro-level temporal channel imploration mechanism MiCi, which promptly allocates available borrowing channel s of the neighbouring cell(s) to the needy cell. The novelty of MiCi is scalability, high availability, and on demand allocation of the channels to the desired cells. The performance of our model has been tested by simulation against a standard FCA scheme as well as a Greedy Borrowing Heuristic. In all the test cases MiCi shows promising results in comparison to both the schemes.
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arxiv:1104.4204
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Asteroid sizes can be directly measured by observing occultations of stars by asteroids. When there are enough observations across the path of the shadow, the asteroid's projected silhouette can be reconstructed. Asteroid shape models derived from photometry by the lightcurve inversion method enable us to predict the orientation of an asteroid for the time of occultation. By scaling the shape model to fit the occultation chords, we can determine the asteroid size with a relative accuracy of typically ~ 10%. We combine shape and spin state models of 44 asteroids (14 of them are new or updated models) with the available occultation data to derive asteroid effective diameters. In many cases, occultations allow us to reject one of two possible pole solutions that were derived from photometry. We show that by combining results obtained from lightcurve inversion with occultation timings, we can obtain unique physical models of asteroids.
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arxiv:1104.4227
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The effect of a diluted Planckian radiation field on a Xe gas at the electron temperature of 100 eV is investigated within the framework of a Collisional Radiative Model, using the HULLAC code. The atomic model spans 19 charge states, includes 20 375 configurations and contains more than 2 10^6 levels. We have simulated detailed spectra comprising more than 10^9 transitions with the Mixed UTA model. The radiation temperature Tr is varied from 0 to 1.5 Te. The dilution factor, D, applied to decrease the radiation field, is varied independently from 0 to 3 at fixed Tr = Te. In both cases, the average charge state Z* increases from 15 to 27, but in different ways. It is shown that even a dilution D = 0.01 changes Z* by more than 1.5. Different combinations of Tr and D yielding exactly the same Z*, may give line ratios sufficiently different to be observed. This fact is explained by the interplay of the shape of the radiation field and the atomic structure.
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arxiv:1104.4248
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Wire chambers are routinely operated as tracking detectors in magnetic spectrometers at high-intensity continuous electron beams. Especially in experiments studying reactions with small cross-sections the reaction yield is limited by the background rate in the chambers. One way to determine the track of a charged particle through a multi-wire proportional chamber (MWPC) is the measurement of the charge distribution induced on its cathodes. In practical applications of this read-out method, the algorithm to relate the measured charge distribution to the avalanche position is an important factor for the achievable position resolution and for the track reconstruction efficiency. An algorithm was developed for operating two large-sized MWPCs in a strong background environment with multiple-particle tracks. Resulting efficiencies were determined as a function of the electron beam current and on the signal amplitudes. Because of the different energy-losses of pions, kaons, and protons in the momentum range of the spectrometer the efficiencies depend also on the particle species.
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arxiv:1104.4254
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This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random sensing matrices. Necessary and sufficient conditions on the number of measurements required are provided. It is shown that these conditions are sharp and the minimum-rank decoder is asymptotically optimal. The reliability function of this decoder is also derived by appealing to de Caen's lower bound on the probability of a union. The sufficient condition also holds when the sensing matrices are sparse - a scenario that may be amenable to efficient decoding. More precisely, it is shown that if the n\times n-sensing matrices contain, on average, \Omega(nlog n) entries, the number of measurements required is the same as that when the sensing matrices are dense and contain entries drawn uniformly at random from the field. Analogies are drawn between the above results and rank-metric codes in the coding theory literature. In fact, we are also strongly motivated by understanding when minimum rank distance decoding of random rank-metric codes succeeds. To this end, we derive distance properties of equiprobable and sparse rank-metric codes. These distance properties provide a precise geometric interpretation of the fact that the sparse ensemble requires as few measurements as the dense one. Finally, we provide a non-exhaustive procedure to search for the unknown low-rank matrix.
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arxiv:1104.4302
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One of the most dramatic manifestations of solar activity are large-scale coronal bright fronts (CBFs) observed in extreme ultraviolet (EUV) images of the solar atmosphere. To date, the energetics and kinematics of CBFs remain poorly understood, due to the low image cadence and sensitivity of previous EUV imagers and the limited methods used to extract the features. In this paper, the trajectory and morphology of CBFs was determined in order to investigate the varying properties of a sample of CBFs, including their kinematics and pulse shape, dispersion, and dissipation. We have developed a semi-automatic intensity profiling technique to extract the morphology and accurate positions of CBFs in 2.5-10 min cadence images from STEREO/EUVI. The technique was applied to sequences of 171A and 195A images from STEREO/EUVI in order to measure the wave properties of four separate CBF events. Following launch at velocities of ~240-450kms^{-1} each of the four events studied showed significant negative acceleration ranging from ~ -290 to -60ms^{-2}. The CBF spatial and temporal widths were found to increase from ~50 Mm to ~200 Mm and ~100 s to ~1500 s respectively, suggesting that they are dispersive in nature. The variation in position-angle averaged pulse-integrated intensity with propagation shows no clear trend across the four events studied. These results are most consistent with CBFs being dispersive magnetoacoustic waves.
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arxiv:1104.4334
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We present mid-infrared narrow-band images of the Orion BN/KL region, and N-band low-resolution spectra of IRc2 and the nearby radio source "I." The distributions of the silicate absorption strength and the color temperature have been revealed with a sub-arcsecond resolution. The detailed structure of the 7.8 micron/12.4 micron color temperature distribution was resolved in the vicinity of IRc2. A mid-infrared counterpart to source I has been detected as a large color temperature peak. The color temperature distribution shows an increasing gradient from IRc2 toward source I, and no dominant temperature peak is seen at IRc2. The spectral energy distribution of IRc2 could be fitted by a two-temperature component model, and the "warmer component" of the infrared emission from IRc2 could be reproduced by scattering of radiation from source I. IRc2 itself is not self-luminous, but is illuminated and heated by an embedded luminous young stellar object located at source I.
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arxiv:1104.4394
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A method for computing the mixed moments of (not necessarily commutative) random vectors from the first order moments, the $q$-commutators between the annihilation and creation operators, and the $q$-commutators between the annihilation and preservation operators, is presented. The method is illustrated by a relevant characterization of $q$-Gaussian vectors.
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arxiv:1104.4395
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We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification of stochastic resonance induced by turbulent fluctuations, i.e. the amplitude of the external periodic perturbation needed for stochastic resonance to occur is much smaller than the one estimated by the equilibrium probability distribution of the unperturbed system. We argue that similar amplifications can be observed in many physical systems where turbulent fluctuations are needed to maintain large scale equilibria.
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arxiv:1104.4417
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This paper concerns the H(2)-unknotting numbers of links related to 2-bridge links. It consists of three parts. In the first part, we consider a necessary and sufficient condition for a 2-bridge link to have H(2)-unknotting number one. The second part concerns an explicit form of composite links with H(2)-unknotting number one. In the last part, we develop a method of studying the H(2)-unknotting numbers of some tangle unknotting number one knots via 2-bridge knots.
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arxiv:1104.4435
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A tetrad-based procedure is presented for solving Einstein's field equations for spherically-symmetric systems; this approach was first discussed by Lasenby et al. in the language of geometric algebra. The method is used to derive metrics describing a point mass in a spatially-flat, open and closed expanding universe respectively. In the spatially-flat case, a simple coordinate transformation relates the metric to the corresponding one derived by McVittie. Nonetheless, our use of non-comoving (`physical') coordinates greatly facilitates physical interpretation. For the open and closed universes, our metrics describe different spacetimes to the corresponding McVittie metrics and we believe the latter to be incorrect. In the closed case, our metric possesses an image mass at the antipodal point of the universe. We calculate the geodesic equations for the spatially-flat metric and interpret them. For radial motion in the Newtonian limit, the force acting on a test particle consists of the usual $1/r^2$ inwards component due to the central mass and a cosmological component proportional to $r$ that is directed outwards (inwards) when the expansion of the universe is accelerating (decelerating). For the standard $\Lambda$CDM concordance cosmology, the cosmological force reverses direction at about $z\approx 0.67$. We also derive an invariant fully general-relativistic expression, valid for arbitrary spherically-symmetric systems, for the force required to hold a test particle at rest relative to the central point mass.
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arxiv:1104.4447
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Opportunistic analysis has traditionally relied on independence assumptions that break down in many interesting and useful network topologies. This paper develops techniques that expand opportunistic analysis to a broader class of networks, proposes new opportunistic methods for several network geometries, and analyzes them in the high-SNR regime. For each of the geometries studied in the paper, we analyze the opportunistic DMT of several relay protocols, including amplify-and-forward, decode-and-forward, compress-and-forward, non-orthogonal amplify-forward, and dynamic decode-forward. Among the highlights of the results: in a variety of multi-user single-relay networks, simple selection strategies are developed and shown to be DMT-optimal. It is shown that compress-forward relaying achieves the DMT upper bound in the opportunistic multiple-access relay channel as well as in the opportunistic nxn user network with relay. Other protocols, e.g. dynamic decode-forward, are shown to be near optimal in several cases. Finite-precision feedback is analyzed for the opportunistic multiple-access relay channel, the opportunistic broadcast relay channel, and the opportunistic gateway channel, and is shown to be almost as good as full channel state information.
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arxiv:1104.4491
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In these torsional oscillator experiments the samples of solid $^4$He were characterized by measuring their thermal conducitvity. Polycrystalline samples of helium of either high isotopic purity or natural concentration of $^3$He were grown in an annular container by the blocked-capillary method and investigated before and after annealing. No correlation has been found between the magnitude of the low-temperature shift of the torsional oscillator frequency and the amount of crystalline defects as measured by the thermal conductivity. In samples with the natural $^3$He concentration a substantial excess thermal conductivity over the usual $T^3$ dependence was observed below 120 mK.
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arxiv:1104.4555
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Recently the CDF collaboration has reported the excess in the dijet invariant-mass distribution of the Wjj events, corresponding to a significance of 3.2 standard deviations. Considering the lack of similar excesses in the $\gamma jj$ and $Z jj$ events yet, we propose a new Z' model: Z' couples only to the second generation quarks. Single production of $\zsc$ as well as associated production with $W,\gamma, Z$ are mainly from the sea quarks. Only $W Z'$ production has additional contribution from one valence quark and one sea quark, which is allowed by CKM mixing. We found that if the new gauge coupling is large enough, marginally permitted by perturbativity, this new model can explain the observed CDF $Wjj$ anomaly as well as the lack of $\gm jj$ and $Z jj$ anomalies. Vanishing coupling of Z'-b-b protects this model from the constraint of p pbar ->WH -> l\nu b \bar{b}.
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arxiv:1104.4560
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Understanding the origin of infectious diseases provides scientifically based rationales for implementing public health measures that may help to avoid or mitigate future epidemics. The recent ancestors of a pandemic virus provide invaluable information about the set of minimal genomic alterations that transformed a zoonotic agent into a full human pandemic. Since the first confirmed cases of the H1N1 pandemic virus in the spring of 2009, several hypotheses about the strain's origins have been proposed. However, how, where, and when it first infected humans is still far from clear. The only way to piece together this epidemiological puzzle relies on the collective effort of the international scientific community to increase genomic sequencing of influenza isolates, especially ones collected in the months prior to the origin of the pandemic.
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arxiv:1104.4568
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We study resource requirements for tracking the state of an open qubit subject to continuous observation. This problem is of great importance for quantum control.
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arxiv:1104.4579
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Context. The identification of the carriers of diffuse interstellar bands (DIBs) remains one of the long-standing mysteries in astronomy. The detection of a polarisation signal in a DIB profile can be used to distinguish between a dust or gas-phase carrier. The polarisation profile can give additional information on the grain or molecular properties of the absorber. In order to detect and measure the linear and circular polarisation of the DIBs we observed reddened lines of sight showing continuum polarisation. For this study we selected two stars HD 197770 and HD 194279. We used high-resolution (R~64.000) spectropolarimetry in the wavelength range from 3700 to 10480 Angstrom with the ESPaDOnS echelle spectrograph mounted at the CFHT. Results. High S/N and high resolution Stokes V (circular), Q and U (linear) spectra were obtained. We constrained upper limits by a factor of 10 for previously observed DIBs. Furthermore, we analysed ~30 additional DIBs for which no spectropolarimetry data has been obtained before. This included the 9577 A DIB and the 8621 A DIB. Conclusions. The lack of polarisation in 45 DIB profiles suggests that none of the absorption lines is induced by a grain-type carrier. The strict upper limits, less than ~0.01%, derived for the observed lines-of-sight imply that if DIBs are due to gas-phase molecules these carriers have polarisation efficiencies which are at least 6 times, and up to 300 times, smaller than those predicted for grain-related carriers.
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arxiv:1104.4581
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The emerging need for mobile ad hoc networks and secured data transmission phase is of crucial importance depending upon the environments like military. In this paper, a new way to improve the reliability of message transmission is presented. In the open collaborative MANET environment, any node can maliciously or selfishly disrupt and deny communication of other nodes. Dynamic changing topology makes it hard to determine the adversary nodes that affect the communication in MANET. An SMT protocol provides a way to secure message transmission by dispersing the message among several paths with minimal redundancy. The multiple routes selected are known as APS -Active Path Set. This paper describes a technique for fault discovery process to identify Byzantine failures which include nodes that drop, modify, or mis-route packets in an attempt to disrupt the routing service. An adaptive probing technique detects a malicious link through binary search and according to the nodes behavior, these links are avoided in the active path by multiplicatively increasing their weights. The proposed scheme provides secure communication even with increased number of adversaries.
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arxiv:1104.4690
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For Gaussian hypergeometric functions $F(x)= F(a,b;c;x),$ $a,b,c>0,$ we consider the quotient $ Q_F(x,y)= (F(x)+F(y))/F(z)$ and the difference $ D_F(x,y)= F(x)+F(y)-F(z)$ for $0<x,y<1$ with $z=x+y-xy \,.$ We give best possible bounds for both expressions under various hypotheses about the parameter triple $(a,b;c)\,.$
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arxiv:1104.4736
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Tracking the evolution of high redshift seed black hole masses to late times, we examine the observable signatures today. These massive initial black hole seeds form at extremely high redshifts from the direct collapse of pre-galactic gas discs. Populating dark matter halos with seeds formed in this fashion, we follow the mass assembly history of these black holes to the present time using a Monte-Carlo merger tree approach. Utilizing this formalism, we predict the black hole mass function at high redshifts and at the present time; the integrated mass density of black holes in the Universe; the luminosity function of accreting black holes as a function of redshift and the scatter in observed, local M-sigma relation. Comparing the predictions of the `light' seed model with these massive seeds we find that significant differences appear predominantly at the low mass end of the present day black hole mass function. However, all our models predict that low surface brightness, bulge-less galaxies with large discs are least likely to be sites for the formation of massive seed black holes at high redshifts. The efficiency of seed formation at high redshifts has a direct influence on the black hole occupation fraction in galaxies at z=0. This effect is more pronounced for low mass galaxies. This is the key discriminant between the models studied here and the Population III remnant `light' seed model. We find that there exists a population of low mass galaxies that do not host nuclear black holes. Our prediction of the shape of the M-sigma relation at the low mass end and increased scatter has recently been corroborated by observations.
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arxiv:1104.4797
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In this note we prove that QR-submanifolds of the hyper-Kahler manifolds under some conditions admit the $G_2$ holonomy. We give simplest examples of such QR-submanifolds namely tori. We conjecture that all $G_2$ holonomy manifolds arise in this way.
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arxiv:1104.4895
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In this paper, we investigate the hybrid tractability of binary Quantified Constraint Satisfaction Problems (QCSPs). First, a basic tractable class of binary QCSPs is identified by using the broken-triangle property. In this class, the variable ordering for the broken-triangle property must be same as that in the prefix of the QCSP. Second, we break this restriction to allow that existentially quantified variables can be shifted within or out of their blocks, and thus identify some novel tractable classes by introducing the broken-angle property. Finally, we identify a more generalized tractable class, i.e., the min-of-max extendable class for QCSPs.
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arxiv:1104.4910
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Aims. We use a sample of 83 core-dominated active galactic nuclei (AGN) selected from the MOJAVE (Monitoring of Jets in AGN with VLBA Experiments) radio-flux-limited sample and detected with the Fermi Large Area Telescope (LAT) to study the relations between non-simultaneous radio, optical, and gamma-ray measurements. Methods. We perform a multi-band statistical analysis to investigate the relations between the emissions in different bands and reproduce these relations by modeling of the spectral energy distributions of blazars. Results. There is a significant correlation between the gamma-ray luminosity and the optical nuclear and radio (15 GHz) luminosities of blazars. We report a well defined positive correlation between the gamma-ray luminosity and the radio-optical loudness for quasars and BL Lacertae type objects (BL Lacs). A strong positive correlation is found between the radio luminosity and the gamma-ray-optical loudness for quasars, while a negative correlation between the optical luminosity and the gamma-ray-radio loudness is present for BL Lacs. Modeling of these correlations with a simple leptonic jet model for blazars indicates that variations of the accretion disk luminosity (and hence the jet power) is able to reproduce the trends observed in most of the correlations. To reproduce all observed correlations, variations of several parameters, such as the accretion power, jet viewing angle, Lorentz factor, and magnetic field of the jet, are required.
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arxiv:1104.4946
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In order to improve the transmission efficiency of optical-fiber communication system with 10Gb/s+40Gb/s, an all-fiber interleaver with unequal passband is proposed and discussed, which is based on a two-stage cascaded Mach-Zehnder interferometer (MZI). The optimum value of structural parameters, such as splitting ratios of the couplers and the physical length differences of the interferometer arms, were chosen. One set of optimized data is validated in the experimental result.The experimental results and the theoretic analysis indicate that an all-fiber optical interleaver with -3dB passband width in odd channels and even channels could be obtained, which having more than 60GHz passband and 30GHz passband, for transmission speed of 40Gb/s and 10Gb/s, respectively.By assigning different portions of spectrum to the 10Gb/s and the 40 Gb/s channels, the bandwidth efficiency requirement of the 40 Gb/s channel is relieved, and therefore longer transmission distance can be achieved.Comparing with the conventional asymmetric interleaver, the most obvious benefit of the proposed interleaver is all-fiber structure.
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arxiv:1104.4947
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Atoms made of a particle and an antiparticle are unstable, usually surviving less than a microsecond. Antihydrogen, made entirely of antiparticles, is believed to be stable, and it is this longevity that holds the promise of precision studies of matter-antimatter symmetry. We have recently demonstrated trapping of antihydrogen atoms by releasing them after a confinement time of 172 ms. A critical question for future studies is: how long can anti-atoms be trapped? Here we report the observation of anti-atom confinement for 1000 s, extending our earlier results by nearly four orders of magnitude. Our calculations indicate that most of the trapped anti-atoms reach the ground state. Further, we report the first measurement of the energy distribution of trapped antihydrogen which, coupled with detailed comparisons with simulations, provides a key tool for the systematic investigation of trapping dynamics. These advances open up a range of experimental possibilities, including precision studies of CPT symmetry and cooling to temperatures where gravitational effects could become apparent.
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arxiv:1104.4982
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For any non-uniform lattice $\Gamma $ in $SL(2,R)$, we describe the limit distribution of orthogonal translates of a divergent geodesic in $\Gamma \backslash SL(2,R)$. As an application, for a quadratic form $Q$ of signature $(2,1)$, a lattice $\Gamma $ in its isometry group, and $v_0\in R^3$ with $Q(v_0)>0$, we compute the asymptotic (with a logarithmic error term) of the number of points in a discrete orbit $v_0\Gamma $ of norm at most $T$, when the stabilizer of $v_0$ in $\Gamma $ is finite. Our result in particular implies that for any non-zero integer $d$, the smoothed count for number of integral binary quadratic forms with discriminant $d^2$ and with coefficients bounded by $T$ is asymptotic to $c\cdot T \log T +O(T)$.
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arxiv:1104.4988
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The pseudogap state of high temperature superconductors is a profound mystery. It has tantalizing evidence of a number of broken symmetry states, not necessarily conventional charge and spin density waves. Here we explore a class of more exotic density wave states characterized by topological properties observed in recently discovered topological insulators. We suggest that these rich topological density wave states deserve closer attention in not only high temperature superconductors but in other correlated electron states, as in heavy fermions.
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arxiv:1104.5053
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We report the result of the analysis of the light curve of a caustic-crossing binary-lens microlensing event OGLE-2009-BLG-023/MOA-2009-BLG-028. Even though the event was observed solely by survey experiments, we could uniquely determine the mass of the lens and distance to it by simultaneously measuring the Einstein radius and lens parallax. From this, we find that the lens system is composed of M-type dwarfs with masses $(0.50\pm 0.07) \ M_\odot$ and $(0.15\pm 0.02)\ M_\odot$ located in the Galactic disk with a distance of $\sim 1.8$ kpc toward the Galactic bulge direction. The event demonstrates that physical lens parameters of binary-lens events can be routinely determined from future high-cadence lensing surveys and thus microlensing can provide a new way to study Galactic binaries.
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arxiv:1104.5091
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Recently the CMS collaboration at the LHC reported "the first direct limit on black hole production at a particle accelerator" using a data sample corresponding to an integrated luminosity of 35/pb of pp-collision at a center of mass energy of 7 TeV. Even though the result has a strong impact on future searches, the interpretation lacks enough theoretical support. In this letter, we show that the parameter range which was considered by the CMS collaboration is actually out of the validity range of semi-classical black hole picture so that the Monte-Carlo simulation result which was crucially used in the analysis still needs further solid scientific basis.
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arxiv:1104.5129
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This paper is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is based on expressing the conditional expectation E[f(St)/Ss] using the Malliavin calculus without localization. Then the variance of the estimator of E[f(St)/Ss] is reduced using closed formulas, techniques based on a conditioning and a judicious choice of the number of simulated paths. Finally, we perform the stopping times version of the dynamic programming algorithm to decrease the bias. On the one hand, we will develop the Malliavin calculus tools for exponential multi-dimensional diffusions that have deterministic and no constant coefficients. On the other hand, we will detail various nonparametric technics to reduce the variance. Moreover, we will test the numerical efficiency of our method on a heterogeneous CPU/GPU multi-core machine.
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arxiv:1104.5131
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