A Spectral Method for Elliptic Equations: The Neumann Problem

Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth. Consider solving an elliptic partial differential equation $-\Delta u+\gamma u=f$ over $\Omega$ with a Neumann boundary condition. The problem is converted to an equivalent elliptic problem over the unit ball $B$, and then a spectral Galerkin method is used to create a convergent sequence of multivariate polynomials $u_{n}$ of degree $\leq n$ that is convergent to $u$. The transformation from $\Omega$ to $B$ requires a special analytical calculation for its implementation. With sufficiently smooth problem parameters, the method is shown to be rapidly convergent. For $u\in C^{\infty}(\overline{\Omega})$ and assuming $\partial\Omega$ is a $C^{\infty}$ boundary, the convergence of $\Vert u-u_{n}\Vert_{H^{1}}$ to zero is faster than any power of $1/n$. Numerical examples in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ show experimentally an exponential rate of convergence.Comment: 23 pages, 11 figure

Testing Diagnostics of Nuclear Activity and Star Formation in Galaxies at z>1

We present some of the first science data with the new Keck/MOSFIRE instrument to test the effectiveness of different AGN/SF diagnostics at z~1.5. MOSFIRE spectra were obtained in three H-band multi-slit masks in the GOODS-S field, resulting in two hour exposures of 36 emission-line galaxies. We compare X-ray data with the traditional emission-line ratio diagnostics and the alternative mass-excitation and color-excitation diagrams, combining new MOSFIRE infrared data with previous HST/WFC3 infrared spectra (from the 3D-HST survey) and multiwavelength photometry. We demonstrate that a high [OIII]/Hb ratio is insufficient as an AGN indicator at z>1. For the four X-ray detected galaxies, the classic diagnostics ([OIII]/Hb vs. [NII]/Ha and [SII]/Ha) remain consistent with X-ray AGN/SF classification. The X-ray data also suggest that "composite" galaxies (with intermediate AGN/SF classification) host bona-fide AGNs. Nearly 2/3 of the z~1.5 emission-line galaxies have nuclear activity detected by either X-rays or the classic diagnostics. Compared to the X-ray and line ratio classifications, the mass-excitation method remains effective at z>1, but we show that the color-excitation method requires a new calibration to successfully identify AGNs at these redshifts.Comment: 7 pages, 4 figures. Accepted to ApJ Letter

Slotted Aircraft Wing

An aircraft wing includes a leading airfoil element and a trailing airfoil element. At least one slot is defined by the wing during at least one transonic condition of the wing. The slot may either extend spanwise along only a portion of the wingspan, or it may extend spanwise along the entire wingspan. In either case, the slot allows a portion of the air flowing along the lower surface of the leading airfoil element to split and flow over the upper surface of the trailing airfoil element so as to achieve a performance improvement in the transonic condition

The influence of socioeconomic deprivation on multimorbidity at different ages:a cross-sectional study

Multimorbidity occurs at a younger age in individuals in areas of high socioeconomic deprivation but little is known about the 'typology' of multimorbidity in different age groups and its association with socioeconomic status

On global-local artificial neural networks for function approximation

We present a hybrid radial basis function (RBF) sigmoid neural network with a three-step training algorithm that utilizes both global search and gradient descent training. The algorithm used is intended to identify global features of an input-output relationship before adding local detail to the approximating function. It aims to achieve efficient function approximation through the separate identification of aspects of a relationship that are expressed universally from those that vary only within particular regions of the input space. We test the effectiveness of our method using five regression tasks; four use synthetic datasets while the last problem uses real-world data on the wave overtopping of seawalls. It is shown that the hybrid architecture is often superior to architectures containing neurons of a single type in several ways: lower mean square errors are often achievable using fewer hidden neurons and with less need for regularization. Our global-local artificial neural network (GL-ANN) is also seen to compare favorably with both perceptron radial basis net and regression tree derived RBFs. A number of issues concerning the training of GL-ANNs are discussed: the use of regularization, the inclusion of a gradient descent optimization step, the choice of RBF spreads, model selection, and the development of appropriate stopping criteria

Biofilm Mediated Calculus Formation in the Urinary Tract

Mineralization and subsequent calculus formation is a common complication of biofilm infections. In the urinary tract, these infected calculi often arise from infections by urease-producing bacteria. Ammonia, liberated by bacterial urease activity, increases urine pH, resulting in the precipitation of Ca and Mg as carbonateapatite {Ca10(PO4,CO3)6(OH,CO3)2} and struvite (NH4MgP04·6H2O). These minerals become entrapped in the organic matrix which surrounds the infecting organisms and ultimately grow into mature calculi. When the causative organisms grow on urinary catheters and stents, the resulting mineralization can partially or completely obstruct urine flow. Mineralization may also exacerbate tissue damage, lead to a Joss of kidney function, and aid in the dissemination of microorganisms into deeper tissues. Several factors influence mineral formation and growth during struvite urolithiasis. These include host factors such as urine chemistry and anatomy of the urinary tract, the presence and characteristics of any foreign objects such as catheters, and bacterial factors such as the type of organisms present and their virulence factors. This review will address these and other factors which influence biofilm mineralization and calculus formation in the urinary tract

Advances in actinomycete research: an ActinoBase review of 2019

The actinomycetes are Gram-positive bacteria belonging to the order Actinomycetales within the phylum Actinobacteria. They include members with significant economic and medical importance, for example filamentous actinomycetes such as Streptomyces species, which have a propensity to produce a plethora of bioactive secondary metabolites and form symbioses with higher organisms, such as plants and insects. Studying these bacteria is challenging, but also fascinating and very rewarding. As a Microbiology Society initiative, members of the actinomycete research community have been developing a Wikipedia-style resource, called ActinoBase, the purpose of which is to aid in the study of these filamentous bacteria. This review will highlight 10 publications from 2019 that have been of special interest to the ActinoBase community, covering 4 major components of actinomycete research: (i) development and regulation; (ii) specialized metabolites; (iii) ecology and host interactions; and (iv) technology and methodology