Testing linear hypotheses in high-dimensional regressions

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 $p\le 20$. On the other hand, assuming that the data dimension $p$ as well as the number $q$ of regression variables are fixed while the sample size $n$ 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 $p$ and a large sample size $n$. 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 $p$ and large $n$ context, but also for moderately large data dimensions like $p=30$ or $p=50$. 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

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

Chemoviscosity modeling for thermosetting resins

A chemoviscosity model, which describes viscosity rise profiles accurately under various cure cycles, and correlates viscosity data to the changes of physical properties associated with structural transformations of the thermosetting resin system during cure, was established. Work completed on chemoviscosity modeling for thermosetting resins is reported

Studies on chemoviscosity modeling for thermosetting resins

A new analytical model for simulating chemoviscosity of thermosetting resins has been formulated. The model is developed by modifying the well-established Williams-Landel-Ferry (WLF) theory in polymer rheology for thermoplastic materials. By introducing a relationship between the glass transition temperature Tg(t) and the degree of cure alpha(t) of the resin system under cure, the WLF theory can be modified to account for the factor of reaction time. Temperature dependent functions of the modified WLF theory constants C sub 1 (t) and C sub 2 (t) were determined from the isothermal cure data. Theoretical predictions of the model for the resin under dynamic heating cure cycles were shown to compare favorably with the experimental data. This work represents progress toward establishing a chemoviscosity model which is capable of not only describing viscosity profiles accurately under various cure cycles, but also correlating viscosity data to the changes of physical properties associated with the structural transformation of the thermosetting resin systems during cure

Sequential nature of damage annealing and activation in implanted GaAs

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

Ratio of Hadronic Decay Rates of J\psi and \psi(2S) and the \rho\pi Puzzle

The so-called \rho\pi puzzle of J\psi and \psi(2S) decays is examined using the experimental data available to date. Two different approaches were taken to estimate the ratio of J\psi and \psi(2S) hadronic decay rates. While one of the estimates could not yield the exact ratio of \psi(2S) to J\psi inclusive hadronic decay rates, the other, based on a computation of the inclusive ggg decay rate for \psi(2S) (J\psi) by subtracting other decay rates from the total decay rate, differs by two standard deviations from the naive prediction of perturbative QCD, even though its central value is nearly twice as large as what was naively expected. A comparison between this ratio, upon making corrections for specific exclusive two-body decay modes, and the corresponding experimental data confirms the puzzles in J\psi and \psi(2S) decays. We find from our analysis that the exclusively reconstructed hadronic decays of the \psi(2S) account for only a small fraction of its total decays, and a ratio exceeding the above estimate should be expected to occur for a considerable number of the remaining decay channels. We also show that the recent new results from the BES experiment provide crucial tests of various theoretical models proposed to explain the puzzle.Comment: 8 pages, no figure, 4 table

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

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

Multi-wavelength variability properties of Fermi blazar S5 0716+714

S5 0716+714 is a typical BL Lacertae object. In this paper we present the analysis and results of long term simultaneous observations in the radio, near-infrared, optical, X-ray and $\gamma$-ray bands, together with our own photometric observations for this source. The light curves show that the variability amplitudes in $\gamma$-ray and optical bands are larger than those in the hard X-ray and radio bands and that the spectral energy distribution (SED) peaks move to shorter wavelengths when the source becomes brighter, which are similar to other blazars, i.e., more variable at wavelengths shorter than the SED peak frequencies. Analysis shows that the characteristic variability timescales in the 14.5 GHz, the optical, the X-ray, and the $\gamma$-ray bands are comparable to each other. The variations of the hard X-ray and 14.5 GHz emissions are correlated with zero-lag, so are the V band and $\gamma$-ray variations, which are consistent with the leptonic models. Coincidences of $\gamma$-ray and optical flares with a dramatic change of the optical polarization are detected. Hadronic models do not have the same nature explanation for these observations as the leptonic models. A strong optical flare correlating a $\gamma$-ray flare whose peak flux is lower than the average flux is detected. Leptonic model can explain this variability phenomenon through simultaneous SED modeling. Different leptonic models are distinguished by average SED modeling. The synchrotron plus synchrotron self-Compton (SSC) model is ruled out due to the extreme input parameters. Scattering of external seed photons, such as the hot dust or broad line region emission, and the SSC process are probably both needed to explain the $\gamma$-ray emission of S5 0716+714.Comment: 43 pages, 13 figures, 3 tables, to be appeared in Ap

A possible hadronic excess in psi(2S) decay and rho-pi puzzle

We examine the so-called rho-pi puzzle of the psi(2S) decay by incorporating two inputs: One is the relative phase between the one-photon and the gluon decay amplitude, and the other is a possible anomaly in the inclusive nonelectromagnetic decay rate of psi(2S). We propose the possibility that in the psi(2S) decay a hadronic decay process of long distance origin is important in addition to the short-distance decay process. The amplitude of this additional process should nearly cancel the three-gluon amplitude in the exclusive psi(2S)---> 1-0- and turn the sum dominantly real in contrast to the J/psi decay. We present general consequences of this mechanism and then briefly look into two models which possibly explain the course of this additional amplitude.Comment: 14 pages, 2 Tables, and 3 eps figures. Replaces the original version with a minor change in the title and inclusion of more references. The version to appear in Phys. Rev.