Improved conditioning of the Floater--Hormann interpolants

The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of rounding errors increases with approximation order, and can make balancing the interpolation error and rounding error difficult. This article proposes to modify the Floater--Hormann interpolants by including additional local polynomial interpolants at the ends of the interval. This appears to improve the conditioning of the interpolants and allow higher approximation orders to be used in practice.Comment: 13 pages, 4 figures, 1 tabl

The Rising Stellar Velocity Dispersion of M87 from Integrated Starlight

We have measured the line-of-sight velocity distribution from integrated stellar light at two points in the outer halo of M87 (NGC 4486), the second-rank galaxy in the Virgo Cluster. The data were taken at R = 480" ($\sim 41.5$ kpc) and R = 526" ($\sim 45.5$ kpc) along the SE major axis. The second moment for a non-parametric estimate of the full velocity distribution is $420 \pm 23$ km/s and $577 \pm 35$ km/s respectively. There is intriguing evidence in the velocity profiles for two kinematically distinct stellar components at the position of our pointing. Under this assumption we employ a two-Gaussian decomposition and find the primary Gaussian having rest velocities equal to M87 (consistent with zero rotation) and second moments of $383 \pm 32$ km/s and $446 \pm 43$ km/s respectively. The asymmetry seen in the velocity profiles suggests that the stellar halo of M87 is not in a relaxed state and confuses a clean dynamical interpretation. That said, either measurement (full or two component model) shows a rising velocity dispersion at large radii, consistent with previous integrated light measurements, yet significantly higher than globular cluster measurements at comparable radial positions. These integrated light measurements at large radii, and the stark contrast they make to the measurements of other kinematic tracers, highlight the rich kinematic complexity of environments like the center of the Virgo Cluster and the need for caution when interpreting kinematic measurements from various dynamical tracers.Comment: 16 pages, 5 figures; accepted for publication in The Astrophysical Journa

Healthcare Employees’ Perceptions on the Effects of Internal Audits

With limited research on the perceptions of internal audits, this study was able to add more literature to the subject. The study’s aim was to survey employee perceptions of the effects of internal audits. This study will provide organizations with results pertaining to how employees perceive the usefulness of internal audits. The study team conducted a single-site study and invited the healthcare organization\u27s employee population to participate in the study. The survey captured 40 responses from 361 invitees (11%). The survey explored the perceptions on six categories of internal audits: Efficiency, Ethical Behavior, Effectiveness, Auidotr-Auditee Relationship Exchange, Learning from Audit, and Top Management Support. Each category\u27s effect on internal audits was weighed by the “Strongly Agree” selection. 1.) 84 (29.9%) Top management, 2.) 55 (19.6%) Learning from Audit, 3.) 48 (17.1%) Auditor-Auditee Relationship Exchange, 4.) 42 (14.9%) Efficiency, 5.) 38 (13.5%) Ethical Behavior, and 6.) 14 (4.9%) Effectiveness. Furthermore, each category received its top response count for the selection of “Agree”. Therefore it was quite evident that each category is perceived to be an effect of internal audits. The survey results of this study can guide organizations on key areas of internal audits

Basis functions on the grain boundary space: Theory

With the increasing availability of experimental and computational data concerning the properties and distribution of grain boundaries in polycrystalline materials, there is a corresponding need to efficiently and systematically express functions on the grain boundary space. A grain boundary can be described by the rotations applied to two grains on either side of a fixed boundary plane, suggesting that the grain boundary space is related to the space of rotations. This observation is used to construct an orthornormal function basis, allowing effectively arbitrary functions on the grain boundary space to be written as linear combinations of the basis functions. Moreover, a procedure is developed to construct a smaller set of basis functions consistent with the crystallographic point group symmetries, grain exchange symmetry, and the null boundary singularity. Functions with the corresponding symmetries can be efficiently expressed as linear combinations of the symmetrized basis functions. An example is provided that shows the efficacy of the symmetrization procedure

Classification of atomic environments via the Gromov-Wasserstein distance

Interpreting molecular dynamics simulations usually involves automated classification of local atomic environments to identify regions of interest. Existing approaches are generally limited to a small number of reference structures and only include limited information about the local chemical composition. This work proposes to use a variant of the Gromov-Wasserstein (GW) distance to quantify the difference between a local atomic environment and a set of arbitrary reference environments in a way that is sensitive to atomic displacements, missing atoms, and differences in chemical composition. This involves describing a local atomic environment as a finite metric measure space, which has the additional advantages of not requiring the local environment to be centered on an atom and of not making any assumptions about the material class. Numerical examples illustrate the efficacy and versatility of the algorithm

Trends in Scottish newborn screening programme for congenital hypothyroidism 1980-2014: strategies for reducing age at notification after initial and repeat sampling

Objectives: To determine ages at first capillary sampling and notification and age at notification after second sampling in Scottish newborns referred with elevated thyroid-stimulating hormone (TSH). Subjects and methods: Referrals between 1980 and 2014 inclusive were grouped into seven 5-year blocks and analysed according to agreed standards. Results: Of 2 116 132 newborn infants screened, 919 were referred with capillary TSH elevation ≥8 mU/L of whom 624 had definite (606) or probable (18) congenital hypothyroidism. Median age at first sampling fell from 7 to 5 days between 1980 and 2014 (standard 4–7 days), with 22, 8 and 3 infants sampled >7 days during 2000–2004, 2005–2009 and 2010–2014. Median age at notification was consistently ≤14 days, range falling during 2000–2004, 2005–2009 and 2010–2014 from 6 to 78, 7–52 and 7–32 days with 12 (14.6%), 6 (5.6%) and 5 (4.3%) infants notified >14 days. However 18/123 (14.6%) of infants undergoing second sampling from 2000 onwards breached the ≤26-day standard for notification. By 2010–2014, the 91 infants with confirmed congenital hypothyroidism had shown favourable median age at first sample (5 days) with start of treatment (10.5 days) approaching age at notification. Conclusion: Most standards for newborn thyroid screening are being met by the Scottish programme, but there is a need to reduce age range at notification, particularly following second sampling. Strategies to improve screening performance include carrying out initial capillary sampling as close to 96 hours as possible; introducing 6-day laboratory reporting and use of electronic transmission for communicating repeat requests