18,796 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
Multipartite entanglement in four-qubit cluster-class states
Based on quantitative complementarity relations (QCRs), we analyze the
multipartite correlations in four-qubit cluster-class states. It is proven
analytically that the average multipartite correlation is entanglement
monotone. Moreover, it is also shown that the mixed three-tangle is a
correlation measure compatible with the QCRs in this kind of quantum states.
More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement
measures is obtained rigorously in the present system.Comment: 7 pages, 3 figs, version 3, some refs. are adde
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs
We consider the adjacency matrix of a large random graph and study
fluctuations of the function
with .
We prove that the moments of fluctuations normalized by in the limit
satisfy the Wick relations for the Gaussian random variables. This
allows us to prove central limit theorem for and then extend
the result on the linear eigenvalue statistics of any
function which increases, together with its
first two derivatives, at infinity not faster than an exponential.Comment: 22 page
Quantum state redistribution based on a generalized decoupling
We develop a simple protocol for a one-shot version of quantum state
redistribution, which is the most general two-terminal source coding problem.
The protocol is simplified from a combination of protocols for the fully
quantum reverse Shannon and fully quantum Slepian-Wolf problems, with its
time-reversal symmetry being apparent. When the protocol is applied to the case
where the redistributed states have a tensor power structure, more natural
resource rates are obtained
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
The Performance of CRTNT Fluorescence Light Detector for Sub-EeV Cosmic Ray Observation
Cosmic Ray Tau Neutrino Telescopes (CRTNT) using for sub-EeV cosmic ray
measurement is discussed. Performances of a stereoscope configuration with a
tower of those telescopes plus two side-triggers are studied. This is done by
using a detailed detector simulation driven by Corsika. Detector aperture as a
function of shower energy above 10^17 eV is calculated. Event rate of about 20k
per year for the second knee measurement is estimated. Event rate for cross
calibration with detectors working on higher energy range is also estimated.
Different configurations of the detectors are tried for optimization.Comment: 5 pages, 4 figures, submitted to HEP & N
Summary Report of AF1 to Snowmass 2021: Beam Physics and Accelerator Education within the Accelerator Frontier
This report summarizes the findings of the AF1 Topical Subgroup to Snowmass
2021, which investigates beam physics and accelerator education within the
accelerator frontiers (AF). The report focuses primarily on opportunities for
basic accelerator and beam physics, formulated into four grand challenges. In
addition, the report also studies the current status of accelerator education,
outreach and diversity issues. Physics limits of ultimate beams for future
colliders are also briefly discussed.Comment: arXiv admin note: text overlap with arXiv:2203.0681
Existence problem of proton semi-bubble structure in the state of Si
The fully self-consistent Hartree-Fock (HF) plus random phase approximation
(RPA) based on Skyrme-type interaction is used to study the existence problem
of proton semi-bubble structure in the state of Si. The
experimental excitation energy and the B(E2) strength of the state in
Si can be reproduced quite well. The tensor effect is also studied. It
is shown that the tensor interaction has a notable impact on the excitation
energy of the state and a small effect on the B(E2) value. Besides, its
effect on the density distributions in the ground and state of
Si is negligible. Our present results with T36 and T44 show that the
state of Si is mainly caused by proton transiton from orbit to orbit, and the existence of a proton
semi-bubble structure in this state is very unlikely.Comment: 6 pages, 3 figures, 3 table
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