Adaptive Thresholding for Sparse Covariance Matrix Estimation

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal thresholding estimators are shown to be sub-optimal over the same parameter spaces. Support recovery is also discussed. The adaptive thresholding estimators are easy to implement. Numerical performance of the estimators is studied using both simulated and real data. Simulation results show that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators. The method is also illustrated in an analysis on a dataset from a small round blue-cell tumors microarray experiment. A supplement to this paper which contains additional technical proofs is available online.Comment: To appear in Journal of the American Statistical Associatio

Testing equality of variances in the analysis of repeated measurements

The problem of comparing the precisions of two instruments using repeated measurements can be cast as an extension of the Pitman-Morgan problem of testing equality of variances of a bivariate normal distribution. Hawkins (1981) decomposes the hypothesis of equal variances in this model into two subhypotheses for which simple tests exist. For the overall hypothesis he proposes to combine the tests of the subhypotheses using Fisher's method and empirically compares the component tests and their combination with the likelihood ratio test. In this paper an attempt is made to resolve some discrepancies and puzzling conclusions in Hawkins's study and to propose simple modifications.\ud \ud The new tests are compared to the tests discussed by Hawkins and to each other both in terms of the finite sample power (estimated by Monte Carlo simulation) and theoretically in terms of asymptotic relative efficiencies

Hydrogen thermal conductivity at temperatures from 2000 to 4000 deg F Final report

Hydrogen thermal conductivity at temperatures from 2000 to 4600 deg

A spectrum of carbon dioxide from 800 to 5500 cm-1

An atlas of CO2 lines obtained from long path length samples at 296 K is presented. Many of the line centers are marked and their positions tabulated

Discovery of distant high luminosity infrared galaxies

We have developed a method for selecting the most luminous galaxies detected by IRAS based on their extreme values of R, the ratio of 60 micron and B-band luminosity. These objects have optical counterparts that are close to or below the limits of Schmidt surveys. We have tested our method on a 1079 deg^2 region of sky, where we have selected a sample of IRAS sources with 60 micron flux densities greater than 0.2 Jy, corresponding to a redshift limit z~1 for objects with far-IR luminosities of 10^{13} L_sun. Optical identifications for these were obtained from the UK Schmidt Telescope plates, using the likelihood ratio method. Optical spectroscopy has been carried out to reliably identify and measure the redshifts of six objects with very faint optical counterparts, which are the only objects with R>100 in the sample. One object is a hyperluminous infrared galaxy (HyLIG) at z=0.834. Of the remaining, fainter objects, five are ultraluminous infrared galaxies (ULIGs) with a mean redshift of 0.45, higher than the highest known redshift of any non-hyperluminous ULIG prior to this study. High excitation lines reveal the presence of an active nucleus in the HyLIG, just as in the other known infrared-selected HyLIGs. In contrast, no high excitation lines are found in the non-hyperluminous ULIGs. We discuss the implications of our results for the number density of HyLIGs at z<1 and for the evolution of the infrared galaxy population out to this redshift, and show that substantial evolution is indicated. Our selection method is robust against the presence of gravitational lensing if the optical and infrared magnification factors are similar, and we suggest a way of using it to select candidate gravitationally lensed infrared galaxies.Comment: 6 pages, accepted for publication in A&

Evaluation of an exercise field test using heart rate monitors to assess cardiorespiratory fitness and heart rate recovery in an asymptomatic population.

PurposeMeasures of cardiorespiratory fitness (CRF) and heart rate recovery (HRR) can improve risk stratification for cardiovascular disease, but these measurements are rarely made in asymptomatic individuals due to cost. An exercise field test (EFT) to assess CRF and HRR would be an inexpensive method for cardiovascular disease risk assessment in large populations. This study assessed 1) the predictive accuracy of a 12-minute run/walk EFT for estimating CRF ([Formula: see text]) and 2) the accuracy of HRR measured after an EFT using a heart rate monitor (HRM) in an asymptomatic population.MethodsFifty subjects (48% women) ages 18-45 years completed a symptom-limited exercise tolerance test (ETT) (Bruce protocol) and an EFT on separate days. During the ETT, [Formula: see text] was measured by a metabolic cart, and heart rate was measured continuously by a HRM and a metabolic cart.ResultsEFT distance and sex independently predicted[Formula: see text]. The average absolute difference between observed and predicted [Formula: see text] was 0.26 ± 3.27 ml·kg-1·min-1 for our model compared to 7.55 ± 3.64 ml·kg-1·min-1 for the Cooper model. HRM HRR data were equivalent to respective metabolic cart values during the ETT. HRR at 1 minute post-exercise during ETT compared to the EFT had a moderate correlation (r=0.75, p&lt;0.001).ConclusionA more accurate model to estimate CRF from a 12-minute run/walk EFT was developed, and HRR can be measured using a HRM in an asymptomatic population outside of clinical settings

Conicoid Mirrors

The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources.Comment: 9 page

Reducing smoking in adolescents: cost-effectiveness results from the cluster randomized ASSIST (A Stop Smoking In Schools Trial)

Introduction: School-based smoking prevention programmes can be effective, but evidence on cost-effectiveness is lacking. We conducted a cost-effectiveness analysis of a school-based “peer-led” intervention.&lt;p&gt;&lt;/p&gt; Methods: We evaluated the ASSIST (A Stop Smoking In Schools Trial) programme in a cluster randomized controlled trial. The ASSIST programme trained students to act as peer supporters during informal interactions to encourage their peers not to smoke. Fifty-nine secondary schools in England and Wales were randomized to receive the ASSIST programme or usual smoking education. Ten thousand seven hundred and thirty students aged 12–13 years attended participating schools. Previous work has demonstrated that the ASSIST programme achieved a 2.1% (95% CI = 0%–4.2%) reduction in smoking prevalence. We evaluated the public sector cost, prevalence of weekly smoking, and cost per additional student not smoking at 24 months.&lt;p&gt;&lt;/p&gt; Results: The ASSIST programme cost of £32 (95% CI = £29.70–£33.80) per student. The incremental cost per student not smoking at 2 years was £1,500 (95% CI = £669–£9,947). Students in intervention schools were less likely to believe that they would be a smoker at age 16 years (odds ratio [OR] = 0.80; 95% CI = 0.66–0.96).&lt;p&gt;&lt;/p&gt; Conclusions: A peer-led intervention reduced smoking among adolescents at a modest cost. The intervention is cost-effective under realistic assumptions regarding the extent to which reductions in adolescent smoking lead to lower smoking prevalence and/or earlier smoking cessation in adulthood. The annual cost of extending the intervention to Year 8 students in all U.K. schools would be in the region of £38 million and could result in 20,400 fewer adolescent smokers.&lt;p&gt;&lt;/p&gt