32,977 research outputs found
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 .
On the other hand, assuming that the data dimension as well as the number
of regression variables are fixed while the sample size 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 and a large sample size .
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 and
large context, but also for moderately large data dimensions like or
. 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
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
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
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 -ray bands, together with our own
photometric observations for this source. The light curves show that the
variability amplitudes in -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 -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 -ray
variations, which are consistent with the leptonic models. Coincidences of
-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 -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
-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.
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