A multinomial quadrivariate D-vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable subjects

Diagnostic test accuracy studies observe the result of a gold standard procedure that defines the presence or absence of a disease and the result of a diagnostic test. They typically report the number of true positives, false positives, true negatives and false negatives. However, diagnostic test outcomes can also be either non-evaluable positives or non-evaluable negatives. We propose a novel model for the meta-analysis of diagnostic studies in the presence of non-evaluable outcomes, which assumes independent multinomial distributions for the true and non-evaluable positives, and, the true and non-evaluable negatives, conditional on the latent sensitivity, specificity, probability of non-evaluable positives and probability of non-evaluable negatives in each study. For the random effects distribution of the latent proportions, we employ a drawable vine copula that can successively model the dependence in the joint tails. Our methodology is demonstrated with an extensive simulation study and applied to data from diagnostic accuracy studies of coronary computed tomography angiography for the detection of coronary artery disease. The comparison of our method with the existing approaches yields findings in the real data application that change the current conclusions

Entanglement of internal and external angular momenta of a single atom

We consider the exchange of spin and orbital angular momenta between a circularly polarized Laguerre-Gaussian beam of light and a single atom trapped in a two-dimensional harmonic potential. The radiation field is treated classically but the atomic center-of-mass motion is quantized. The spin and orbital angular momenta of the field are individually conserved upon absorption, and this results in the entanglement of the internal and external degrees of freedom of the atom. We suggest applications of this entanglement in quantum information processing.Comment: 4 pages, 2 figure

Soil aggregate stability and macrofauna as indicators of soil health and sustainable agricultural systems

A healthy soil associated with sustainable crop production is likely to be considered a sustainable agricultural system. Soil health indicators only have value if they influence management decisions that support soil and food security. The surface layer (<5 cm) of a field is disproportionally affected by arable land management practices. For silty-clay soils, structural degradation of this layer leads to slaking under the impact of rain, with implications for nutrient leaching, capping, crop emergence, infiltration, runoff and erosion. Thus, aggregate stability (rapid wetting) measurements have relevance for both soil and food security. Also, earthworm activity is a major factor regulating aggregate stability, and important for both soil functions and supporting plant productivity. Three dynamic soil health indicators, aggregate mean weight diameter, earthworm populations and Lumbricus.terrestris (indicator species) midden abundance, were measured in arable field trials. Results showed that all soils tested were unstable, contained small earthworm populations and very few L. terrestris earthworms, although the actions of the limited numbers of L. terrestris anecic earthworms, specifically their middens, were associated with high biological activity and soil aggregation, highlighting their role as an ecosystem engineer. Contrary to expectations, organic amendments did not improve the indicators. A more fundamental change in management practices addressing tillage and/or cropping is likely to be needed to improve soil health and the sustainability of the agricultural system. Despite the indications of poor soil health, crop yields have been sustained and, in many cases, increased by appropriate nutrient management. However, these findings suggest that these agricultural systems may not be resilient to changes in rotation, climate and weather variabilit

Remotely controlled mirror of variable geometry for small angle x-ray diffraction with synchrotron radiation

A total-reflecting mirror of 120-cm length was designed and built to focus synchrotron radiation emanating from the electron-positron storage ring at the Stanford Linear Accelerator Center (SPEAR). The reflecting surface is of unpolished float glass. The bending and tilt mechanism allows very fine control of the curvature and selectability of the critical angle for wavelengths ranging from 0.5 to 3.0 Å. Elliptical curvature is used to minimize aberrations. The mirror is placed asymmetrically onto the ellipse so as to achieve a tenfold demagnification of the source. The bending mechanism reduces nonelastic deformation (flow) and minimizes strains and stresses in the glass despite its length. Special design features assure stability of the focused image. The mirror reduces the intensity of shorter wavelength harmonics by a factor of approximately 100

Correlated analytical studies of organic material from the Tagish Lake carbonaceous chondrite

We report on correlated studies of organic material using SIMS, FIB-SEM, and TEM

An Examination of the Factors and Characteristics that Contribute to the Success of Putnam Fellows

The William Lowell Putnam Mathematical Competition is an intercollegiate mathematics competition for students in the United States and Canada and is regarded as the most prestigious and challenging mathematics competition in North America (Alexanderson, 2004; AMS, 2020; Grossman, 2002; Reznick, 1994; Schoenfeld, 1985). Students who earn the five highest scores on the examination are named Putnam Fellows. Since its inception in 1938, only 306 individuals have won the competition and a select few have won multiple times. Clearly, being named a Putnam Fellow is a remarkable achievement and therefore, understanding the factors and characteristics that contribute to their success is important for students interested in mathematics and STEM-related fields. Twenty-five males who were named Putnam Fellows either four, three, or two times were recruited for the study. A 17-item questionnaire was created from various research sources (Campbell, 1996a, 1996b; Campbell & Wu, 1996; DeFranco, 1996), and used to collect information around four broad areas—personal experiences, formal educational experiences, the affective domain and the cognitive domain. Qualitative research techniques were used to analyze the data. The results indicated that four subcategories of personal experiences, five subcategories of formal educational experiences, seven subcategories involving the affective domain, and three subcategories of the cognitive domain all played an important role in the development of Putnam Fellows. Future research recommendations should examine the factors and characteristics of female Putnam winners and ways to promote and support them as well as the role that Pólya-like heuristics play in the development of Putnam winners

Dispersion of Klauder's temporally stable coherent states for the hydrogen atom

We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasi-classically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit.Comment: 6 pages, 2 figure

Spectral Representation for the Effective Macroscopic Response of a Polycrystal: Application to Third-Order Nonlinear Susceptibility

Erratum: In our paper, we show that the spectral representation for isotropic two-component composites also applies to uniaxial polycrystals. We have learned that this result was, in fact, first conjectured by G.W. Milton. While our derivation is more detailed, our result for the spectral function is the same as Milton's. We very much regret not having been aware of this work at the time of writing our paper. Original abstract: We extend the spectral theory used for the calculation of the effective linear response functions of composites to the case of a polycrystalline material with uniaxially anisotropic microscopic symmetry. As an application, we combine these results with a nonlinear decoupling approximation as modified by Ma et al., to calculate the third-order nonlinear optical susceptibility of a uniaxial polycrystal, assuming that the effective dielectric function of the polycrystal can be calculated within the effective-medium approximation.Comment: v2 includes erratum and the original preprin