Intracavity Generation of Radially Polarized CO2 Laser Beams Based on a Simple Binary Dielectric Diffraction Grating

We present experimental results on the intracavity generation of radially polarized light by incorporation of a polarization-selective mirror in a CO2 -laser resonator. The selectivity is achieved with a simple binary dielectric diffraction grating etched in the backsurface of the mirror substrate. Very high polarization selectivity was achieved, and good agreement of simulation and experimental results is shown. The overall radial polarization purity of the generated laser beam was found to be higher than 90% .

A modified test for small-study effects in meta-analyses of controlled trials with binary endpoints

Publication bias and related bias in meta-analysis is often examined by visually checking for asymmetry in funnel plots of treatment effect against its standard error. Formal statistical tests of funnel plot asymmetry have been proposed, but when applied to binary outcome data these can give false-positive rates that are higher than the nominal level in some situations (large treatment effects, or few events per trial, or all trials of similar sizes). We develop a modified linear regression test for funnel plot asymmetry based on the efficient score and its variance, Fisher's information. The performance of this test is compared to the other proposed tests in simulation analyses based on the characteristics of published controlled trials. When there is little or no between-trial heterogeneity, this modified test has a false-positive rate close to the nominal level while maintaining similar power to the original linear regression test ('Egger' test). When the degree of between-trial heterogeneity is large, none of the tests that have been proposed has uniformly good properties.

A Faster Circular Binary Segmentation Algorithm for the Analysis of Array CGH Data

Motivation: Array CGH technologies enable the simultaneous measurement of DNA copy number for thousands of sites on a genome. We developed the circular binary segmentation (CBS) algorithm to divide the genome into regions of equal copy number (Olshen {\it et~al}, 2004). The algorithm tests for change-points using a maximal $t$-statistic with a permutation reference distribution to obtain the corresponding $p$-value. The number of computations required for the maximal test statistic is $O(N^2),$ where $N$ is the number of markers. This makes the full permutation approach computationally prohibitive for the newer arrays that contain tens of thousands markers and highlights the need for a faster. algorithm. Results: We present a hybrid approach to obtain the $p$-value of the test statistic in linear time. We also introduce a rule for stopping early when there is strong evidence for the presence of a change. We show through simulations that the hybrid approach provides a substantial gain in speed with only a negligible loss in accuracy and that the stopping rule further increases speed. We also present the analysis of array CGH data from a breast cancer cell line to show the impact of the new approaches on the analysis of real data. Availability: An R (R Development Core Team, 2006) version of the CBS algorithm has been implemented in the ``DNAcopy'' package of the Bioconductor project (Gentleman {\it et~al}, 2004). The proposed hybrid method for the $p$-value is available in version 1.2.1 or higher and the stopping rule for declaring a change early is available in version 1.5.1 or higher.

Quantifying and Comparing the Accuracy of Binary Biomarkers When Predicting a Failure Time Outcome

The positive and negative predictive value are standard measures used to quantify the predictive accuracy of binary biomarkers when the outcome being predicted is also binary. When the biomarkers are instead being used to predict a failure time outcome, there is no standard way of quantifying predictive accuracy. We propose a natural extension of the traditional predictive values to accommodate censored survival data. We discuss not only quantifying predictive accuracy using these extended predictive values, but also rigorously comparing the accuracy of two biomarkers in terms of their predictive values. Using a marginal regression framework, we describe how to estimate differences in predictive accuracy and how to test whether the observed difference is statistically significant.

A BAYESIAN SHRINKAGE MODEL FOR INCOMPLETE LONGITUDINAL BINARY DATA WITH APPLICATION TO THE BREAST CANCER PREVENTION TRIAL

We consider inference in randomized studies, in which repeatedly measured outcomes may be informatively missing due to drop out. In this setting, it is well known that full data estimands are not identified unless unverified assumptions are imposed. We assume a non-future dependence model for the drop-out mechanism and posit an exponential tilt model that links non-identifiable and identifiable distributions. This model is indexed by non-identified parameters, which are assumed to have an informative prior distribution, elicited from subject-matter experts. Under this model, full data estimands are shown to be expressed as functionals of the distribution of the observed data. To avoid the curse of dimensionality, we model the distribution of the observed data using a Bayesian shrinkage model. In a simulation study, we compare our approach to a fully parametric and a fully saturated model for the distribution of the observed data. Our methodology is motivated and applied to data from the Breast Cancer Prevention Trial.

A unified approach to modeling multivariate binary data using copulas over partitions

Many seemingly disparate approaches for marginal modeling have been developed in recent years. We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the proposed copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.

Nitrogen oxides in the firn air at Summit, Greenland

Measurements of NOx within the snowpack at Summit, Greenland were carried out from June 2008 to July 2010, using a novel system to sample firn air with minimal disruption of the snowpack. These long-term measurements were motivated by the need of improving the representation of air-snow interactions in global models. Results indicated that the NOx budget within the snowpack was on the order of 550 pptv as maximum, and was constituted primarily for NO2. NOx production was observed within the first 50 cm of the snowpack during the sunlight season between February and August. Presence of NOx at larger depths was attributed to high speed wind and vertical transport processes. Production of NO correlated with the seasonal incoming radiation profile, while NO2 maximum was observed in April. These measurements constitute the larger data set of NOx within the firn and will improve the representation of processes driving snow photochemistry at Summit.

Spin-strain coupling in a 3-D transition metal oxides

ab-initio Hartree Fock (HF), density functional theory (DFT) and hybrid potentials were employed to compute the optimized lattice parameters and elastic properties of perovskite 3-d transition metal oxides. The optimized lattice parameters and elastic properties are interdependent in these materials. An interaction is observed between the electronic charge, spin and lattice degrees of freedom in 3-d transition metal oxides. The coupling between the electronic charge, spin and lattice structures originates due to localization of d-atomic orbitals. The coupling between the electronic charge, spin and crystalline lattice also contributes in the ferroelectric and ferromagnetic properties in perovskites. The cubic and tetragonal crystalline structures of perovskite transition metal oxides of ABO3 are studied. The electronic structure and the physics of 3-d perovskite materials is complex and less well considered. Moreover, the novelty of the electronic structure and properties of these perovskites transition metal oxides exceeds the challenge offered by their complex crystalline structures. To achieve the objective of understanding the structure and property relationship of these materials the first-principle computational method is employed. CRYSTAL09 code is employed for computing crystalline structure, elastic, ferromagnetic and other electronic properties. Second-order elastic constants (SOEC) and bulk moduli (B) are computed in an automated process by employing ELASTCON (elastic constants) and EOS (equation of state) programs in CRYSTAL09 code. ELASTCON, EOS and other computational algorithms are utilized to determine the elastic properties of tetragonal BaTiO3, rutile TiO2, cubic and tetragonal BaFeO3 and the ferromagentic properties of 3-d transition metal oxides. Multiple methods are employed to crosscheck the consistency of our computational results. Computational results have motivated us to explore the ferromagnetic properties of 3-d transition metal oxides. Billyscript and CRYSTAL09 code are employed to compute the optimized geometry of the cubic and tetragonal crystalline structure of transition metal oxides of Sc to Cu. Cubic crystalline structure is initially chosen to determine the effect of lattice strains on ferromagnetism due to the spin angular momentum of an electron. The 3-d transition metals and their oxides are challenging as the basis functions and potentials are not fully developed to address the complex physics of the transition metals. Moreover, perovskite crystalline structures are extremely challenging with respect to the quality of computations as the latter requires the well established methods. Ferroelectric and ferromagnetic properties of bulk, surfaces and interfaces are explored by employing CRYSTAL09 code. In our computations done on cubic TMOs of Sc-Fe it is observed that there is a coupling between the crystalline structure and FM/AFM spin polarization. Strained crystalline structures of 3-d transition metal oxides are subjected to changes in the electromagnetic and electronic properties. The electronic structure and properties of bulk, composites, surfaces of 3-d transition metal oxides are computed successfully.

Nitrogen Oxides in the North Atlantic Troposphere: Impacts of Boreal Wildfire and Anthropogenic Emissions

Nitrogen oxides play a crucial role in the budget of tropospheric ozone (O sub(3)) and the formation of the hydroxyl radical. Anthropogenic activities and boreal wildfires are large sources of emissions in the atmosphere. However, the influence of the transport of these emissions on nitrogen oxides and O sub(3) levels at hemispheric scales is not well understood, in particular due to a lack of nitrogen oxides measurements in remote regions. In order to address these deficiencies, measurements of NO, NO sub(2) and NO sub(y) (total reactive nitrogen oxides) were made in the lower free troposphere (FT) over the central North Atlantic region (Pico Mountain station, 38 degree N 28 degree W, 2.3 km asl) from July 2002 to August 2005. These measurements reveal a well-defined seasonal cycle of nitrogen oxides (NO sub(x) = NO+NO sub(2) and NO sub(y)) in the background central North Atlantic lower FT, with higher mixing ratios during the summertime. Observed NO sub(x) and NO sub(y) levels are consistent with long-range transport of emissions, but with significant removal en-route to the measurement site. Reactive nitrogen largely exists in the form of PAN and HNO sub(3) ( similar to 80-90% of NO sub(y)) all year round. A shift in the composition of NO sub(y) from dominance of PAN to dominance of HNO sub(3) occurs from winter-spring to summer-fall, as a result of changes in temperature and photochemistry over the region. Analysis of the long-range transport of boreal wildfire emissions on nitrogen oxides provides evidence of the very large-scale impacts of boreal wildfires on the tropospheric NO sub(x) and O sub(3) budgets. Boreal wildfire emissions are responsible for significant shifts in the nitrogen oxides distributions toward higher levels during the summer, with medians of NO sub(y) (117-175 pptv) and NO sub(x) (9-30 pptv) greater in the presence of boreal wildfire emissions. Extreme levels of NO sub(x) (up to 150 pptv) and NO sub(y) (up to 1100 pptv) observed in boreal wildfire plumes suggest that decomposition of PAN to NO sub(x) is a significant source of NO sub(x), and imply that O sub(3) formation occurs during transport. Ozone levels are also significantly enhanced in boreal wildfire plumes. However, a complex behavior of O sub(3) is observed in the plumes, which varies from significant to lower O sub(3) production to O sub(3) destruction. Long-range transport of anthropogenic emissions from North America also has a significant influence on the regional NO sub(x) and O sub(3) budgets. Transport of pollution from North America causes significant enhancements on nitrogen oxides year-round. Enhancements of CO, NO sub(y) and NO sub(x) indicate that, consistent with previous studies, more than 95% of the NO sub(x) emitted over the U.S. is removed before and during export out of the U.S. boundary layer. However, about 30% of the NO sub(x) emissions exported out of the U.S. boundary layer remain in the airmasses. Since the lifetime of NO sub(x) is shorter than the transport timescale, PAN decomposition and potentially photolysis of HNO sub(3) provide a supply of NO sub(x) over the central North Atlantic lower FT. Observed Delta O sub(3)/ Delta NO sub(y) and large NO sub(y) levels remaining in the North American plumes suggest potential O sub(3) formation well downwind from North America. Finally, a comparison of the nitrogen oxides measurements with results from the global chemical transport (GCT) model GEOS-Chem identifies differences between the observations and the model. GEOS-Chem reproduces the seasonal variation of nitrogen oxides over the central North Atlantic lower FT, but does not capture the magnitude of the cycles. Improvements in our understanding of nitrogen oxides chemistry in the remote FT and emission sources are necessary for the current GCT models to adequately estimate the impacts of emissions on tropospheric NO sub(x) and the resulting impacts on the O sub(3) budget.

MODELING DYNAMICS OF OZONE AND NITROGEN OXIDES AT SUMMIT, GREENLAND WITH A 1-D PROCESS-SCALE MODEL

This work presents a 1-D process scale model used to investigate the chemical dynamics and temporal variability of nitrogen oxides (NOx) and ozone (O3) within and above snowpack at Summit, Greenland for March-May 2009 and estimates surface exchange of NOx between the snowpack and surface layer in April-May 2009. The model assumes the surface of snowflakes have a Liquid Like Layer (LLL) where aqueous chemistry occurs and interacts with the interstitial air of the snowpack. Model parameters and initialization are physically and chemically representative of snowpack at Summit, Greenland and model results are compared to measurements of NOx and O3 collected by our group at Summit, Greenland from 2008-2010. The model paired with measurements confirmed the main hypothesis in literature that photolysis of nitrate on the surface of snowflakes is responsible for nitrogen dioxide (NO2) production in the top ~50 cm of the snowpack at solar noon for March – May time periods in 2009. Nighttime peaks of NO2 in the snowpack for April and May were reproduced with aqueous formation of peroxynitric acid (HNO4) in the top ~50 cm of the snowpack with subsequent mass transfer to the gas phase, decomposition to form NO2 at nighttime, and transportation of the NO2 to depths of 2 meters. Modeled production of HNO4 was hindered in March 2009 due to the low production of its precursor, hydroperoxy radical, resulting in underestimation of nighttime NO2 in the snowpack for March 2009. The aqueous reaction of O3 with formic acid was the major sync of O3 in the snowpack for March-May, 2009. Nitrogen monoxide (NO) production in the top ~50 cm of the snowpack is related to the photolysis of NO2, which underrepresents NO in May of 2009. Modeled surface exchange of NOx in April and May are on the order of 1011 molecules m-2 s-1. Removal of measured downward fluxes of NO and NO2 in measured fluxes resulted in agreement between measured NOx fluxes and modeled surface exchange in April and an order of magnitude deviation in May. Modeled transport of NOx above the snowpack in May shows an order of magnitude increase of NOx fluxes in the first 50 cm of the snowpack and is attributed to the production of NO2 during the day from the thermal decomposition and photolysis of peroxynitric acid with minor contributions of NO from HONO photolysis in the early morning.

On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

OBJECTIVES: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. METHODS: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. RESULTS: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. CONCLUSION: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.