Rejoinder: Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies

Rejoinder to "Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies" [arXiv:1102.2774]Comment: Published in at http://dx.doi.org/10.1214/08-STS244REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies

Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be done by properly quantifying the relative (to complete data) amount of available information. The problem is directly motivated by applications to studies, such as linkage analyses and haplotype-based association projects, designed to identify genetic contributions to complex diseases. In the genetic studies the relative information measures are needed for the experimental design, technology comparison, interpretation of the data, and for understanding the behavior of some of the inference tools. The central difficulties in constructing such information measures arise from the multiple, and sometimes conflicting, aims in practice. For large samples, we show that a satisfactory, likelihood-based general solution exists by using appropriate forms of the relative Kullback--Leibler information, and that the proposed measures are computationally inexpensive given the maximized likelihoods with the observed data. Two measures are introduced, under the null and alternative hypothesis respectively. We exemplify the measures on data coming from mapping studies on the inflammatory bowel disease and diabetes. For small-sample problems, which appear rather frequently in practice and sometimes in disguised forms (e.g., measuring individual contributions to a large study), the robust Bayesian approach holds great promise, though the choice of a general-purpose "default prior" is a very challenging problem.Comment: Published in at http://dx.doi.org/10.1214/07-STS244 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The thermal evolution of nuclear matter at zero temperature and definite baryon number density in chiral perturbation theory

The thermal properties of cold dense nuclear matter are investigated with chiral perturbation theory. The evolution curves for the baryon number density, baryon number susceptibility, pressure and the equation of state are obtained. The chiral condensate is calculated and our result shows that when the baryon chemical potential goes beyond $1150 \mathrm{MeV}$, the absolute value of the quark condensate decreases rapidly, which indicates a tendency of chiral restoration.Comment: 17 pages, 9 figures, revtex

Anharmonic multi-phonon nonradiative transition: An ab initio calculation approach

Nonradiative carrier recombinations at deep centers in semiconductors are of great importance for both fundamental physics and device engineering. In this article, we provide a revised analysis of Huang’s original nonradiative multi-phonon (NMP) theory with ab initio calculations. First, we confirmed at the first-principles level that Huang’s concise formula gives the same results as the matrix-based formula, and that Huang’s high-temperature formula provides an analytical expression for the coupling constant in Marcus theory. Secondly, we correct for anharmonic effects by taking into account local phonon-mode variations for different charge states of a defect. The corrected capture rates for defects in GaN and SiC agree well with experiments

The Nonlinear Permittivity Including Non-Abelian Self-interaction of Plasmons in Quark-Gluon Plasma

By decomposing the distribution functions and color field to regular and fluctuation parts, the solution of the semi-classical kinetic equations of quark-gluon plasma is analyzed. Through expanding the kinetic equations of the fluctuation parts to third order, the nonlinear permittivity including the self-interaction of gauge field is obtained and a rough numerical estimate is given out for the important \vk =0 modes of the pure gluon plasma.Comment: 7 pages, shortened version accepted by Chin.Phys.Let

Relative entropy of entanglement of a kind of two qubit entangled states

We in this paper strictly prove that some block diagonalizable two qubit entangled state with six none zero elements reaches its quantum relative entropy entanglement by the a separable state having the same matrix structure. The entangled state comprises local filtering result state as a special case.Comment: 5 page

Binary pulsars as probes of a Galactic dark matter disk

As a binary pulsar moves through a wind of dark matter particles, the resulting dynamical friction modifies the binary's orbit. We study this effect for the double disk dark matter (DDDM) scenario, where a fraction of the dark matter is dissipative and settles into a thin disk. For binaries within the dark disk, this effect is enhanced due to the higher dark matter density and lower velocity dispersion of the dark disk, and due to its co-rotation with the baryonic disk.We estimate the effect and compare it with observations for two different limits in the Knudsen number ($Kn$). First, in the case where DDDM is effectively collisionless within the characteristic scale of the binary ($Kn\gg1$) and ignoring the possible interaction between the pair of dark matter wakes. Second, in the fully collisional case ($Kn\ll1$), where a fluid description can be adopted and the interaction of the pair of wakes is taken into account. We find that the change in the orbital period is of the same order of magnitude in both limits. A comparison with observations reveals good prospects to probe currently allowed DDDM models with timing data from binary pulsars in the near future. We finally comment on the possibility of extending the analysis to the intermediate (rarefied gas) case with $Kn\sim1$.Comment: 15 pages, 6 figures. Few comments and references added, version accepted for publication in Physics of the Dark Universe (PDU