Mean values of multiplicative functions over function fields

We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical difficulties that arise over the integers disappear in the function field setting, which helps bring out more clearly the main ideas of the proofs over number fields. We also obtain Lipschitz estimates showing the slow variation of mean values of multiplicative functions over function fields, which display some features that are not present in the integer situation

Imaging the dynamical atmosphere of the red supergiant Betelgeuse in the CO first overtone lines with VLTI/AMBER

We present the first 1-D aperture synthesis imaging of the red supergiant Betelgeuse in the individual CO first overtone lines with VLTI/AMBER. The reconstructed 1-D projection images reveal that the star appears differently in the blue wing, line center, and red wing of the individual CO lines. The 1-D projection images in the blue wing and line center show a pronounced, asymmetrically extended component up to ~1.3 stellar radii, while those in the red wing do not show such a component. The observed 1-D projection images in the lines can be reasonably explained by a model in which the CO gas within a region more than half as large as the stellar size is moving slightly outward with 0--5 km s^-1, while the gas in the remaining region is infalling fast with 20--30 km s^-1. A comparison between the CO line AMBER data taken in 2008 and 2009 shows a significant time variation in the dynamics of the CO line-forming region in the photosphere and the outer atmosphere. In contrast to the line data, the reconstructed 1-D projection images in the continuum show only a slight deviation from a uniform disk or limb-darkened disk. We derive a uniform-disk diameter of 42.05 +/- 0.05 mas and a power-law-type limb-darkened disk diameter of 42.49 +/- 0.06 mas and a limb-darkening parameter of (9.7 +/- 0.5) x 10^{-2}. This latter angular diameter leads to an effective temperature of 3690 +/- 54 K for the continuum-forming layer. These diameters confirm that the near-IR size of Betelgeuse was nearly constant over the last 18 years, in marked contrast to the recently reported noticeable decrease in the mid-IR size. The continuum data taken in 2008 and 2009 reveal no or only marginal time variations, much smaller than the maximum variation predicted by the current 3-D convection simulations.Comment: 21 pages, 12 figures, accepted for publication in Astronomy and Astrophysic

Helium, Oxygen, Proton, and Electron (HOPE) Mass Spectrometer for the Radiation Belt Storm Probes Mission

The HOPE mass spectrometer of the Radiation Belt Storm Probes (RBSP) mission (renamed the Van Allen Probes) is designed to measure the in situ plasma ion and electron fluxes over 4π sr at each RBSP spacecraft within the terrestrial radiation belts. The scientific goal is to understand the underlying physical processes that govern the radiation belt structure and dynamics. Spectral measurements for both ions and electrons are acquired over 1 eV to 50 keV in 36 log-spaced steps at an energy resolution ΔE FWHM/E≈15 %. The dominant ion species (H+, He+, and O+) of the magnetosphere are identified using foil-based time-of-flight (TOF) mass spectrometry with channel electron multiplier (CEM) detectors. Angular measurements are derived using five polar pixels coplanar with the spacecraft spin axis, and up to 16 azimuthal bins are acquired for each polar pixel over time as the spacecraft spins. Ion and electron measurements are acquired on alternate spacecraft spins. HOPE incorporates several new methods to minimize and monitor the background induced by penetrating particles in the harsh environment of the radiation belts. The absolute efficiencies of detection are continuously monitored, enabling precise, quantitative measurements of electron and ion fluxes and ion species abundances throughout the mission. We describe the engineering approaches for plasma measurements in the radiation belts and present summaries of HOPE measurement strategy and performance

Reduced regional brain cortical thickness in patients with heart failure.

AimsAutonomic, cognitive, and neuropsychologic deficits appear in heart failure (HF) subjects, and these compromised functions depend on cerebral cortex integrity in addition to that of subcortical and brainstem sites. Impaired autoregulation, low cardiac output, sleep-disordered-breathing, hypertension, and diabetic conditions in HF offer considerable potential to affect cortical areas by loss of neurons and glia, which would be expressed as reduced cortical thicknesses. However, except for gross descriptions of cortical volume loss/injury, regional cortical thickness integrity in HF is unknown. Our goal was to assess regional cortical thicknesses across the brain in HF, compared to control subjects.Methods and resultsWe examined localized cortical thicknesses in 35 HF and 61 control subjects with high-resolution T1-weighted images (3.0-Tesla MRI) using FreeSurfer software, and assessed group differences with analysis-of-covariance (covariates; age, gender; p<0.05; FDR). Significantly-reduced cortical thicknesses appeared in HF over controls in multiple areas, including the frontal, parietal, temporal, and occipital lobes, more markedly on the left side, within areas that control autonomic, cognitive, affective, language, and visual functions.ConclusionHeart failure subjects show reduced regional cortical thicknesses in sites that control autonomic, cognitive, affective, language, and visual functions that are deficient in the condition. The findings suggest chronic tissue alterations, with regional changes reflecting loss of neurons and glia, and presumably are related to earlier-described axonal changes. The pathological mechanisms contributing to reduced cortical thicknesses likely include hypoxia/ischemia, accompanying impaired cerebral perfusion from reduced cardiac output and sleep-disordered-breathing and other comorbidities in HF

An Integer Programming Approach to the Student-Project Allocation Problem with Preferences over Projects

The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a stable matching of students to projects (and lecturers). However, these stable matchings can have different sizes, and the problem of finding a maximum stable matching (MAX-SPA-P) is NP-hard. There are two known approximation algorithms for MAX-SPA-P, with performance guarantees of 2 and 32 . In this paper, we describe an Integer Programming (IP) model to enable MAX-SPA-P to be solved optimally. Following this, we present results arising from an empirical analysis that investigates how the solution produced by the approximation algorithms compares to the optimal solution obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets. Our main finding is that the 32 -approximation algorithm finds stable matchings that are very close to having maximum cardinality

SOFIA/EXES Observations of Water Absorption in the Protostar AFGL 2591 at High Spectral Resolution

We present high spectral resolution (~3 km/s) observations of the nu_2 ro-vibrational band of H2O in the 6.086--6.135 micron range toward the massive protostar AFGL 2591 using the Echelon-Cross-Echelle Spectrograph (EXES) on the Stratospheric Observatory for Infrared Astronomy (SOFIA). Ten absorption features are detected in total, with seven caused by transitions in the nu_2 band of H2O, two by transitions in the first vibrationally excited nu_2 band of H2O, and one by a transition in the nu_2 band of H2{18}O. Among the detected transitions is the nu_2 1(1,1)--0(0,0) line which probes the lowest lying rotational level of para-H2O. The stronger transitions appear to be optically thick, but reach maximum absorption at a depth of about 25%, suggesting that the background source is only partially covered by the absorbing gas, or that the absorption arises within the 6 micron emitting photosphere. Assuming a covering fraction of 25%, the H2O column density and rotational temperature that best fit the observed absorption lines are N(H2O)=(1.3+-0.3)*10^{19} cm^{-2} and T=640+-80 K.Comment: 6 pages, 3 figures, 1 table, accepted for publication in ApJ

Sex and Geographic Differences in Health of the Early Inhabitants of the Mariana Islands

The early inhabitants of the Mariana Islands encountered numerous challenges that likely affected their health, including island size, vulnerability to natural disasters, availability of resources, and shifts in climate. Other factors that could have led to differences in health include biological sex, social status, diet, and genetic factors (e.g., host resistance). This article examines the effects of environment and biological sex on the health of the earliest inhabitants of the Mariana Islands through an analysis of indicators of health recorded in skeletons from Guam, Rota, Tinian, and Saipan. The indicators of health investigated include cribra orbitalia (CO), linear enamel hypoplasia (LEH), stature, trauma, infection, and dental disease (antemortem tooth loss [AMTL], dental caries, alveolar defect, dental calculus, and attrition). Betel staining of teeth is also examined. To determine if there are differences attributable to sex, male and female data are compared for each island separately and then for all the islands combined. To examine differences between islands, separate comparisons of these indicators are made for males and females. Examining islands separately, no significant sex differences were observed for CO, spondylolysis, fractures, treponemal infection, AMTL, or dental calculus. Significant sex differences were observed for LEH, betel-stained teeth, and the other dental pathologies. With few exceptions, sex differences in the observed indicators were consistent across islands. Observing male and female health across the islands revealed no significant differences for stature, trauma or infections. For the remaining indicators, significant differences were observed. Similarities in health between Guam and Rota in the south and Tinian and Saipan located farther north suggest that geography, environmental constraints, and social and cultural networking were important variables affecting the health and lives of the early inhabitants of the Mariana Islands