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

Prompting Fab Yeast Surface Display Efficiency by ER Retention and Molecular Chaperon Co-expression.

For antibody discovery and engineering, yeast surface display (YSD) of antigen-binding fragments (Fabs) and coupled fluorescence activated cell sorting (FACS) provide intact paratopic conformations and quantitative analysis at the monoclonal level, and thus holding great promises for numerous applications. Using anti-TNFα mAbs Infliximab, Adalimumab, and its variants as model Fabs, this study systematically characterized complementary approaches for the optimization of Fab YSD. Results suggested that by using divergent promoter GAL1-GAL10 and endoplasmic reticulum (ER) signal peptides for co-expression of light chain and heavy chain-Aga2 fusion, assembled Fabs were functionally displayed on yeast cell surface with sigmoidal binding responses toward TNFα. Co-expression of a Hsp70 family molecular chaperone Kar2p and/or protein-disulfide isomerase (Pdi1p) significantly improved efficiency of functional display (defined as the ratio of cells displaying functional Fab over cells displaying assembled Fab). Moreover, fusing ER retention sequences (ERSs) with light chain also enhanced Fab display quality at the expense of display quantity, and the degree of improvements was correlated with the strength of ERSs and was more significant for Infliximab than Adalimumab. The feasibility of affinity maturation was further demonstrated by isolating a high affinity Fab clone from 1:103 or 1:105 spiked libraries

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

Antireflection silicon structures with hydrophobic property fabricated by three-beam laser interference

This paper demonstrates antireflective structures on silicon wafer surfaces with hydrophobic property fabricated by three-beam laser interference. In this work, a three-beam laser interference system was set up to generate periodic micro-nano hole structures with hexagonal distributions. Compared with the existing technologies, the array of hexagonally-distributed hole structures fabricated by three-beam laser interference reveals a design guideline to achieve considerably low solar-weighted reflectance (SWR) in the wavelength range of 300-780 nm. The resulting periodic hexagonally-distributed hole structures have shown extremely low SWR (1.86%) and relatively large contact angle (140°) providing with a self-cleaning capability on the solar cell surface