Votes and a half-binomial

AbstractIn two party elections with popular vote ratio pq, 12≤p=1 −q, a theoretical model suggests replacing the so-called MacMahon cube law approximation (pq)3, for the ratio PQ of candidates elected, by the ratio ƒk(p)ƒk(q) of the two half sums in the binomial expansion of (p+q)2k+1 for some k. This ratio is nearly (pq)3 when k = 6. The success probability gk(p)=(pa(pa+qa) for the power law (pq)a≐PQ is shown to so closely approximate ƒk(p)=Σ0k(r2k+1)p2k+1−rqr, if we choose a = ak=(2k+1)!4kk!k!, that 1≤ƒk(p)gk(p)≤1.01884086 for k≥1 if 12≤p≤1. Computationally, we avoid large binomial coefficients in computing ƒk(p) for k>22 by expressing 2ƒk(p)−1 as the sum (p−q) Σ0k(4pq)sas(2s+1), whose terms decrease by the factors (4pq)(1−12s). Setting K = 4k+3, we compute ak for the large k using a continued fraction πak2=K+12(2K+32(2K+52(2K+…))) derived from the ratio of π to the finite Wallis product approximation

Stellar Spin-Orbit Misalignment in a Multiplanet System

Stars hosting hot Jupiters are often observed to have high obliquities, whereas stars with multiple co-planar planets have been seen to have low obliquities. This has been interpreted as evidence that hot-Jupiter formation is linked to dynamical disruption, as opposed to planet migration through a protoplanetary disk. We used asteroseismology to measure a large obliquity for Kepler-56, a red giant star hosting two transiting co-planar planets. These observations show that spin-orbit misalignments are not confined to hot-Jupiter systems. Misalignments in a broader class of systems had been predicted as a consequence of torques from wide-orbiting companions, and indeed radial-velocity measurements revealed a third companion in a wide orbit in the Kepler-56 system.Comment: Accepted for publication in Science, published online on October 17 2013; PDF includes main article and supplementary materials (65 pages, 27 figures, 7 tables); v2: small correction to author lis

The APOKASC Catalog: An Asteroseismic and Spectroscopic Joint Survey of Targets in the Kepler Fields

We present the first APOKASC catalog of spectroscopic and asteroseismic properties of 1916 red giants observed in the Kepler fields. The spectroscopic parameters provided from the Apache Point Observatory Galactic Evolution Experiment project are complemented with asteroseismic surface gravities, masses, radii, and mean densities determined by members of the Kepler Asteroseismology Science Consortium. We assess both random and systematic sources of error and include a discussion of sample selection for giants in the Kepler fields. Total uncertainties in the main catalog properties are of order 80 K in Teff , 0.06 dex in [M/H], 0.014 dex in log g, and 12% and 5% in mass and radius, respectively; these reflect a combination of systematic and random errors. Asteroseismic surface gravities are substantially more precise and accurate than spectroscopic ones, and we find good agreement between their mean values and the calibrated spectroscopic surface gravities. There are, however, systematic underlying trends with Teff and log g. Our effective temperature scale is between 0-200 K cooler than that expected from the Infrared Flux Method, depending on the adopted extinction map, which provides evidence for a lower value on average than that inferred for the Kepler Input Catalog (KIC). We find a reasonable correspondence between the photometric KIC and spectroscopic APOKASC metallicity scales, with increased dispersion in KIC metallicities as the absolute metal abundance decreases, and offsets in Teff and log g consistent with those derived in the literature. We present mean fitting relations between APOKASC and KIC observables and discuss future prospects, strengths, and limitations of the catalog data.Comment: 49 pages. ApJSupp, in press. Full machine-readable ascii files available under ancillary data. Categories: Kepler targets, asteroseismology, large spectroscopic survey

Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars

Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell. Once a red giant is sufficiently evolved, the helium in the core also undergoes fusion. Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface before helium ignition and the amount of internal mixing from rotation and other processes. Progress is hampered by our inability to distinguish between red giants burning helium in the core and those still only burning hydrogen in a shell. Asteroseismology offers a way forward, being a powerful tool for probing the internal structures of stars using their natural oscillation frequencies. Here we report observations of gravity-mode period spacings in red giants that permit a distinction between evolutionary stages to be made. We use high-precision photometry obtained with the Kepler spacecraft over more than a year to measure oscillations in several hundred red giants. We find many stars whose dipole modes show sequences with approximately regular period spacings. These stars fall into two clear groups, allowing us to distinguish unambiguously between hydrogen-shell-burning stars (period spacing mostly about 50 seconds) and those that are also burning helium (period spacing about 100 to 300 seconds).Comment: to appear as a Letter to Natur

Height Systems and Vertical Datums: a Review in the Australian Context

This paper reviews (without equations) the various definitions of height systems and vertical geodetic datum surfaces, together with their practical realisation for users in Australia. Excluding geopotential numbers, a height system is a one-dimensional coordinate system used to express the metric distance (height) of a point from some reference surface. Its definition varies according to the reference surface chosen and the path along which the height is measured. A vertical geodetic datum is the practical realisation of a height system and its reference surface for users, nominally tied to mean sea level. In Australia, the normal-orthometric height system is used, which is embedded in the Australian Height Datum (AHD). The AHD was realised by the adjustment of ~195,000 km of spirit-levelling observations fixed to limited-term observations of mean sea level at multiple tide-gauges. The paper ends by giving some explanation of the problems with the AHD and of the differences between the AHD and the national geoid model, pointing out that it is preferable to recompute the AHD

Versailles project on advanced materials and standards (VAMAS) interlaboratory study on measuring the number concentration of colloidal gold nanoparticles

We describe the outcome of a large international interlaboratory study of the measurement of particle number concentration of colloidal nanoparticles, project 10 of the technical working area 34, "Nanoparticle Populations" of the Versailles Project on Advanced Materials and Standards (VAMAS). A total of 50 laboratories delivered results for the number concentration of 30 nm gold colloidal nanoparticles measured using particle tracking analysis (PTA), single particle inductively coupled plasma mass spectrometry (spICP-MS), ultraviolet-visible (UV-Vis) light spectroscopy, centrifugal liquid sedimentation (CLS) and small angle X-ray scattering (SAXS). The study provides quantitative data to evaluate the repeatability of these methods and their reproducibility in the measurement of number concentration of model nanoparticle systems following a common measurement protocol. We find that the population-averaging methods of SAXS, CLS and UV-Vis have high measurement repeatability and reproducibility, with between-labs variability of 2.6%, 11% and 1.4% respectively. However, results may be significantly biased for reasons including inaccurate material properties whose values are used to compute the number concentration. Particle-counting method results are less reproducibile than population-averaging methods, with measured between-labs variability of 68% and 46% for PTA and spICP-MS respectively. This study provides the stakeholder community with important comparative data to underpin measurement reproducibility and method validation for number concentration of nanoparticles

Versailles project on advanced materials and standards (VAMAS) interlaboratory study on measuring the number concentration of colloidal gold nanoparticles

We describe the outcome of a large international interlaboratory study of the measurement of particle number concentration of colloidal nanoparticles, project 10 of the technical working area 34, "Nanoparticle Populations" of the Versailles Project on Advanced Materials and Standards (VAMAS). A total of 50 laboratories delivered results for the number concentration of 30 nm gold colloidal nanoparticles measured using particle tracking analysis (PTA), single particle inductively coupled plasma mass spectrometry (spICP-MS), ultraviolet-visible (UV-Vis) light spectroscopy, centrifugal liquid sedimentation (CLS) and small angle X-ray scattering (SAXS). The study provides quantitative data to evaluate the repeatability of these methods and their reproducibility in the measurement of number concentration of model nanoparticle systems following a common measurement protocol. We find that the population-averaging methods of SAXS, CLS and UV-Vis have high measurement repeatability and reproducibility, with between-labs variability of 2.6%, 11% and 1.4% respectively. However, results may be significantly biased for reasons including inaccurate material properties whose values are used to compute the number concentration. Particle-counting method results are less reproducibile than population-averaging methods, with measured between-labs variability of 68% and 46% for PTA and spICP-MS respectively. This study provides the stakeholder community with important comparative data to underpin measurement reproducibility and method validation for number concentration of nanoparticles

The Early Growth Genetics (EGG) and EArly Genetics and Lifecourse Epidemiology (EAGLE) consortia : design, results and future prospects

The impact of many unfavorable childhood traits or diseases, such as low birth weight and mental disorders, is not limited to childhood and adolescence, as they are also associated with poor outcomes in adulthood, such as cardiovascular disease. Insight into the genetic etiology of childhood and adolescent traits and disorders may therefore provide new perspectives, not only on how to improve wellbeing during childhood, but also how to prevent later adverse outcomes. To achieve the sample sizes required for genetic research, the Early Growth Genetics (EGG) and EArly Genetics and Lifecourse Epidemiology (EAGLE) consortia were established. The majority of the participating cohorts are longitudinal population-based samples, but other cohorts with data on early childhood phenotypes are also involved. Cohorts often have a broad focus and collect(ed) data on various somatic and psychiatric traits as well as environmental factors. Genetic variants have been successfully identified for multiple traits, for example, birth weight, atopic dermatitis, childhood BMI, allergic sensitization, and pubertal growth. Furthermore, the results have shown that genetic factors also partly underlie the association with adult traits. As sample sizes are still increasing, it is expected that future analyses will identify additional variants. This, in combination with the development of innovative statistical methods, will provide detailed insight on the mechanisms underlying the transition from childhood to adult disorders. Both consortia welcome new collaborations. Policies and contact details are available from the corresponding authors of this manuscript and/or the consortium websites.Peer reviewe