31,988 research outputs found

    Testing linear hypotheses in high-dimensional regressions

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    For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say p≤20p\le 20. On the other hand, assuming that the data dimension pp as well as the number qq of regression variables are fixed while the sample size nn grows, several asymptotic approximations are proposed in the literature for Wilk's \bLa including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension pp and a large sample size nn. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large pp and large nn context, but also for moderately large data dimensions like p=30p=30 or p=50p=50. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in MANOVA which is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages and 2 table

    Parametrization of the Driven Betatron Oscillation

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    An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam motion in a synchrotron. By observing this coherent motion, the optical parameters can be directly measured at the beam position monitor locations. The driven oscillation induced by an AC dipole will generate a phase space ellipse which differs from that of the free oscillation. If not properly accounted for, this difference can lead to a misinterpretation of the actual optical parameters, for instance, of 6% or more in the cases of the Tevatron, RHIC, or LHC. The effect of an AC dipole on the linear optics parameters is identical to that of a thin lens quadrupole. By introducing a new amplitude function to describe this new phase space ellipse, the motion produced by an AC dipole becomes easier to interpret. Beam position data taken under the influence of an AC dipole, with this new interpretation in mind, can lead to more precise measurements of the normal Courant-Snyder parameters. This new parameterization of the driven motion is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.Comment: 8 pages, 8 figures, and 1 tabl

    Structural difference rule for amorphous alloy formation by ion mixing

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    We formulate a rule which establishes a sufficient condition that an amorphous binary alloy will be formed by ion mixing of multilayered samples when the two constituent metals are of different crystalline structure, regardless of their atomic sizes and electronegativities. The rule is supported by the experimental results we have obtained on six selected binary metal systems, as well as by the previous data reported in the literature. The amorphization mechanism is discussed in terms of the competition between two different structures resulting in frustration of the crystallization process

    v4 for identified particles at RHIC from viscous hydrodynamics

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    Using ideal and viscous hydrodynamics, the ratio of azimuthal moments v4/(v2)^2 is calculated for pions, protons, and kaons in sqrt{s}=200 A*GeV Au+Au collisions. For any value of viscosity here is little dependence on particle species. Ideal hydrodynamics and data show a flat curve as a function of pt. Adding viscosity in the standard way destroys this flatness. However, it can be restored by replacing the standard quadratic ansatz for delta f (the viscous correction to the distribution function at freeze-out) with a weaker momentum dependence.Comment: Proceedings of Hot Quarks 2010, 21-26 June 2010 La Londe Les Maures, 4 pages, 2 figure

    Effect of aging on the reinforcement efficiency of carbon nanotubes in epoxy matrix

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    The reinforcement efficiency of carbon nanotubes (CNTs) in epoxy matrix was investigated in the elastic regime. Cyclic uniaxial tensile tests were performed at constant strain amplitude and increasing maximum strain. Post-curing of the epoxy and its composite at a temperature close to the glass transition temperature allowed us to explore the effect of aging on the reinforcement efficiency of CNT. It is found that the reinforcement efficiency is compatible with a mean field mixture rule of stress reinforcement by random inclusions. It also diminishes when the maximum strain increased and this effect is amplified by aging. The decrease of elastic modulus with increasing cyclic maximum strain is quite similar to the one observed for filled elastomers with increasing strain amplitude, a phenomenon often referred as the Payne effect

    Multiwavelength Observations of the BL Lacertae Object PKS 2155-304 with XMM-Newton

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    The optical-UV and X-ray instruments on-board XMM-Ndewton provide an excellent opportunity to perform simultaneous observations of violently variable objects over a broad wavelength range. The UV and X-ray bright BL Lac object PKS 2155-304 has been repeatedly observed with XMM-Ndewton about twice per year. In this paper, we present a detailed analysis of the simultaneous multiwavelength variability of the source from optical to X-rays, based on the currently available XMM-Ndewton observations. These observations probed the intra-day multiwavelength variability at optical-UV and X-ray wavelengths of the source. The UV variability amplitude is substantially smaller than the X-ray one, and the hardness ratios of the UV to X-rays correlates with the X-ray fluxes: the brighter the source, the flatter the UV-X-ray spectra. On 2000 May 30-31 the UV and X-ray light curves were weakly correlated, while the UV variations followed the X-ray ones with no detectable lags on 2000 November 19-21. On 2001 November 30 the source exhibited a major X-ray flare that was not detected in the optical. The intra-day UV and X-ray variability presented here is not similar to the inter-day UV and X-ray variability obtained from the previous coordinated extensive multiwavelength campaigns on the source, indicating that different ``modes'' of variability might be operating in PKS 2155-304 on different timescales or from epoch to epoch.Comment: Accepted by Ap

    Sequential nature of damage annealing and activation in implanted GaAs

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    Rapid thermal processing of implanted GaAs reveals a definitive sequence in the damage annealing and the electrical activation of ions. Removal of implantation-induced damage and restoration of GaAs crystallinity occurs first. Irrespective of implanted species, at this stage the GaAs is n-type and highly resistive with almost ideal values of electron mobility. Electrical activation is achieved next when, in a narrow anneal temperature window, the material becomes n- or p-type, or remains semi-insulating, commensurate to the chemical nature of the implanted ion. Such a two-step sequence in the electrical doping of GaAs by ion implantation may be unique of GaAs and other compound semiconductors

    Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices

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    We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A.Lytova and L.Pastur in J. Stat. Phys., v.134, 147-159 (2009). Our results are valid provided the off-diagonal matrix entries have finite fourth moment, the diagonal matrix entries have finite second moment, and the test functions have four continuous derivatives in a neighborhood of the support of the Wigner semicircle law.Comment: minor corrections; the manuscript will appear in the Journal of Statistical Physic

    Random matrices: Universality of local eigenvalue statistics up to the edge

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    This is a continuation of our earlier paper on the universality of the eigenvalues of Wigner random matrices. The main new results of this paper are an extension of the results in that paper from the bulk of the spectrum up to the edge. In particular, we prove a variant of the universality results of Soshnikov for the largest eigenvalues, assuming moment conditions rather than symmetry conditions. The main new technical observation is that there is a significant bias in the Cauchy interlacing law near the edge of the spectrum which allows one to continue ensuring the delocalization of eigenvectors.Comment: 24 pages, no figures, to appear, Comm. Math. Phys. One new reference adde
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