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

Darwinian Data Structure Selection

Data structure selection and tuning is laborious but can vastly improve an application's performance and memory footprint. Some data structures share a common interface and enjoy multiple implementations. We call them Darwinian Data Structures (DDS), since we can subject their implementations to survival of the fittest. We introduce ARTEMIS a multi-objective, cloud-based search-based optimisation framework that automatically finds optimal, tuned DDS modulo a test suite, then changes an application to use that DDS. ARTEMIS achieves substantial performance improvements for \emph{every} project in $5$ Java projects from DaCapo benchmark, $8$ popular projects and $30$ uniformly sampled projects from GitHub. For execution time, CPU usage, and memory consumption, ARTEMIS finds at least one solution that improves \emph{all} measures for $86\%$ ($37/43$) of the projects. The median improvement across the best solutions is $4.8\%$, $10.1\%$, $5.1\%$ for runtime, memory and CPU usage. These aggregate results understate ARTEMIS's potential impact. Some of the benchmarks it improves are libraries or utility functions. Two examples are gson, a ubiquitous Java serialization framework, and xalan, Apache's XML transformation tool. ARTEMIS improves gson by $16.5$\%, $1\%$ and $2.2\%$ for memory, runtime, and CPU; ARTEMIS improves xalan's memory consumption by $23.5$\%. \emph{Every} client of these projects will benefit from these performance improvements.Comment: 11 page

Nondeterminstic ultrafast ground state cooling of a mechanical resonator

We present an ultrafast feasible scheme for ground state cooling of a mechanical resonator via repeated random time-interval measurements on an auxiliary flux qubit. We find that the ground state cooling can be achieved with \emph{several} such measurements. The cooling efficiency hardly depends on the time-intervals between any two consecutive measurements. The scheme is also robust against environmental noises.Comment: 4 pages, 3 figure

Effects of losses in the hybrid atom-light interferometer

Enhanced Raman scattering can be obtained by injecting a seeded light field which is correlated with the initially prepared collective atomic excitation. This Raman amplification process can be used to realize atom-light hybrid interferometer. We numerically calculate the phase sensitivities and the signal-to-noise ratios of this interferometer with the method of homodyne detection and intensity detection, and give their differences between this two methods. In the presence of loss of light field and atomic decoherence the measure precision will be reduced which can be explained by the break of the intermode decorrelation conditions of output modesComment: 9 pages, 7 figure

Optical study of MgTi2_2O4_4: Evidence for an orbital-Peierls state

Dimension reduction due to the orbital ordering has recently been proposed to explain the exotic charge, magnetic and structural transitions in some three-dimensional (3D) transitional metal oxides. We present optical measurement on a spinel compound MgTi$_2$O$_4$ which undergoes a sharp metal-insulator transition at 240 K, and show that the spectral change across the transition can be well understood from the proposed picture of 1D Peierls transition driven by the ordering of $d_{yz}$ and $d_{zx}$ orbitals. We further elaborate that the orbital-driven instability picture applies also very well to the optical data of another spinel CuIr$_2$S$_4$ reported earlier.Comment: 5 pages, 6 figures, to be published in Phys. Rev.