Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant

The purpose of this paper is to establish that for any compact, connected C^{\infty} Riemannian manifold there exists a robust family of kernels of increasing smoothness that are well suited for interpolation. They generate Lagrange functions that are uniformly bounded and decay away from their center at an exponential rate. An immediate corollary is that the corresponding Lebesgue constant will be uniformly bounded with a constant whose only dependence on the set of data sites is reflected in the mesh ratio, which measures the uniformity of the data. The analysis needed for these results was inspired by some fundamental work of Matveev where the Sobolev decay of Lagrange functions associated with certain kernels on \Omega \subset R^d was obtained. With a bit more work, one establishes the following: Lebesgue constants associated with surface splines and Sobolev splines are uniformly bounded on R^d provided the data sites \Xi are quasi-uniformly distributed. The non-Euclidean case is more involved as the geometry of the underlying surface comes into play. In addition to establishing bounded Lebesgue constants in this setting, a "zeros lemma" for compact Riemannian manifolds is established.Comment: 33 pages, 2 figures, new title, accepted for publication in SIAM J. on Math. Ana

Physical Activity and Quality of Life in Retinitis Pigmentosa

Purpose. Aerobic exercise has been found to be neuroprotective in animal models of retinal degeneration. This study aims to report physical activity levels in patients with RP and investigate the relationship between physical activity and vision-related quality-of-life (QOL). Materials and Methods. A retrospective study of adult patients with RP examined in 2005–2014. Physical activity levels were assessed using the Godin Exercise Questionnaire. The NEI-Visual Function Questionaire-25 (VFQ-25), SF-36 General Health survey, and Pepper Assessment Tool for Disability (PAT-D) were administered. Results. 143 patients participated. 81 (56.6%) patients were classified as “active” and 62 (43.4%) as “insufficiently active” by Godin score. VFQ-25 revealed statistically significant differences between the active and insufficiently active patients, including overall visual function (53.3 versus 45.1, p=0.010), color vision (73.8 versus 52.9, p<0.001), and peripheral vision (34.3 versus 23.8, p=0.021). The physical component of the SF-36 and the PAT-D survey also demonstrated statistically significant differences (47.2 versus 52.9, p=0.002; 24.3 versus 30.0, p=0.010). Active patients had a higher initial Goldmann visual field (GVF) score (74.8 versus 60.1 degrees, p=0.255) and final GVF score (78.7 versus 47.1 degrees, p=0.069) but did not reach statistical significance. Conclusions. In RP, increased physical activity is associated with greater self-reported visual function and QOL

What’s Sex (Composition) Got to Do with It? The Importance of Sex Composition of Gangs for Female and Male Members’ Offending and Victimization

Sex composition of groups has been theorized in organizational sociology and found in prior work to structure female and male members’ behaviors and experiences. Peer group and gang literature similarly finds that the sex gap in offending varies across groups of differing sex ratios. Drawing on this and other research linking gang membership, offending, and victimization, we examine whether sex composition of gangs is linked to sex differences in offending in this sample, further assess whether sex composition similarly structures females’ and males’ victimization experiences, and if so, why. Self-report data from gang members in a multi-site, longitudinal study of 3,820 youths are employed. Results support previous findings about variations in member delinquency by both sex and sex composition of the gang and also indicate parallel variations in members’ victimization. These results are further considered within the context of facilitating effects such as gender dynamics, gang characteristics, and normative orientation

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

The Atacama Cosmology Telescope: Two-Season ACTPol Spectra and Parameters

We present the temperature and polarization angular power spectra measured by the Atacama Cosmology Telescope Polarimeter (ACTPol). We analyze night-time data collected during 2013-14 using two detector arrays at 149 GHz, from 548 deg$^2$ of sky on the celestial equator. We use these spectra, and the spectra measured with the MBAC camera on ACT from 2008-10, in combination with Planck and WMAP data to estimate cosmological parameters from the temperature, polarization, and temperature-polarization cross-correlations. We find the new ACTPol data to be consistent with the LCDM model. The ACTPol temperature-polarization cross-spectrum now provides stronger constraints on multiple parameters than the ACTPol temperature spectrum, including the baryon density, the acoustic peak angular scale, and the derived Hubble constant. Adding the new data to planck temperature data tightens the limits on damping tail parameters, for example reducing the joint uncertainty on the number of neutrino species and the primordial helium fraction by 20%.Comment: 23 pages, 25 figure

A multi-decade record of high quality fCO2 data in version 3 of the Surface Ocean CO2 Atlas (SOCAT)

The Surface Ocean CO2 Atlas (SOCAT) is a synthesis of quality-controlled fCO2 (fugacity of carbon dioxide) values for the global surface oceans and coastal seas with regular updates. Version 3 of SOCAT has 14.7 million fCO2 values from 3646 data sets covering the years 1957 to 2014. This latest version has an additional 4.6 million fCO2 values relative to version 2 and extends the record from 2011 to 2014. Version 3 also significantly increases the data availability for 2005 to 2013. SOCAT has an average of approximately 1.2 million surface water fCO2 values per year for the years 2006 to 2012. Quality and documentation of the data has improved. A new feature is the data set quality control (QC) flag of E for data from alternative sensors and platforms. The accuracy of surface water fCO2 has been defined for all data set QC flags. Automated range checking has been carried out for all data sets during their upload into SOCAT. The upgrade of the interactive Data Set Viewer (previously known as the Cruise Data Viewer) allows better interrogation of the SOCAT data collection and rapid creation of high-quality figures for scientific presentations. Automated data upload has been launched for version 4 and will enable more frequent SOCAT releases in the future. High-profile scientific applications of SOCAT include quantification of the ocean sink for atmospheric carbon dioxide and its long-term variation, detection of ocean acidification, as well as evaluation of coupled-climate and ocean-only biogeochemical models. Users of SOCAT data products are urged to acknowledge the contribution of data providers, as stated in the SOCAT Fair Data Use Statement. This ESSD (Earth System Science Data) “living data” publication documents the methods and data sets used for the assembly of this new version of the SOCAT data collection and compares these with those used for earlier versions of the data collection (Pfeil et al., 2013; Sabine et al., 2013; Bakker et al., 2014). Individual data set files, included in the synthesis product, can be downloaded here: doi:10.1594/PANGAEA.849770. The gridded products are available here: doi:10.3334/CDIAC/OTG.SOCAT_V3_GRID

Effects of Standardized Ileal Digestible Lysine on Growth Performance and Economic Return of 200 to 300 lb Grow-Finish Pigs

A total of 2,099 barrows and gilts (PIC 1050 × DNA 600; initially 198.6 ± 3.72 lb) were used in a 57-d study to determine the optimal dietary standardized ileal digestible (SID) Lys level for approximately 200 to 300 lb pigs in a commercial setting. Pigs were randomly allotted to 1 of 4 dietary treatments with 24 to 27 pigs per pen and 20 replications per treatment. A similar number of barrows and gilts were placed in each pen. Diets were fed over 2 phases (199 to 233 and 233 to 299 lb respectively). Dietary treatments were corn-soybean meal-based. Diets were formulated to 85, 93, 100, or 110% of the 2016 PIC (Hendersonville, TN) SID Lys gilt recommendations with phase 1 SID Lys levels of 0.65, 0.71, 0.77, 0.84%, and phase 2 levels of 0.60, 0.66, 0.71, 0.78%, respectively. Overall (d 0 to 57), increasing SID Lys increased (linear, P \u3c 0.05) overall market weight, F/G, hot carcass weight, Lys intake/d, and Lys intake/kg of gain with an increase in ADG (quadratic, P = 0.020). For economics (d 0 to 57), feed cost per lb of gain increased (linear, P \u3c 0.05) with increased SID Lys. Revenue per pig placed and income over feed cost (IOFC) increased (quadratic, P \u3c 0.10) as the amount of SID Lys increased, and marginally significant evidence of a quadratic response for feed cost per pig placed (P = 0.073). Projecting IOFC for phase 1, the quadratic polynomial (QP) and broken-line linear models estimated the requirement at 110.9% and 96.9%, respectively, to achieve maximum IOFC. For phase 2, the QP estimated the requirement at 96.6% SID Lys to maximize IOFC. In summary, the SID Lys requirement was 97% to 111% of the 2016 PIC recommended Lys requirement for phase 1 and 97% for phase 2 to maximize IOFC

Expertise differences in anticipatory judgements during a temporally and spatially occluded dynamic task

There is contradictory evidence surrounding the role of critical cues in the successful anticipation of penalty kick outcome. In the current study, skilled and less-skilled soccer goalkeepers were required to anticipate spatially (full body; hip region) and temporally (–160 ms, –80 ms before, foot–ball contact) occluded penalty kicks. The skilled group outperformed the less-skilled group in all conditions. Both groups performed better in the full body, compared to hip region condition. Later temporal occlusion conditions were associated with increased performance in the correct response and correct side analysis, but not for correct height. These data suggest that there is enough postural information from the hip region for skilled goalkeepers to make highly accurate predictions of penalty kick direction, however, other regions are needed in order to make predictions of height. These data demonstrate the evolution of cues over time and have implications for anticipation training

Effects of Standardized Ileal Digestible Lysine on Growth Performance and Economic Return of 108 to 178 lb Grow-Finish Pigs

A total of 2,124 barrows and gilts (PIC 1050 × DNA 600; initially 107.9 ± 1.31 lb) were used in a 32-d study to determine the optimal level of dietary standardized ileal digestibility (SID) Lys for 108 to 178 lb pigs in a commercial setting. Pigs were randomly allotted to 1 of 5 dietary treatments with 24 to 27 pigs per pen and 16 replications pen treatment. A similar number of barrows and gilts were placed in each pen. Diets were fed over 3 phases (108 to 129, 129 to 156, and 156 to 178 lb, respectively). Dietary treatments were corn-soybean meal-based and contained 10% (phase 1 and 2) or 5% (phase 3) DDGS. Diets were formulated to 85, 95, 103, 110, or 120% of the 2016 PIC SID Lys gilt recommendations as follows: phase 1 SID Lys levels of 0.90, 1.01, 1.09, 1.17 and 1.27%; phase 2 levels of 0.79, 0.87, 0.94, 1.03, and 1.10%; and phase 3 levels of 0.71, 0.78, 0.85, 0.92, and 0.99%, respectively. Overall (d 0 to 32), increasing SID Lys increased (linear, P \u3c 0.001) ADG, final body weight, Lys intake/d, and Lys intake/kg of gain with an improvement in F/G (quadratic, P = 0.047). Additionally, feed cost per pig, feed cost per lb of gain, total revenue per pig, and income over feed cost (IOFC) increased (linear, P ≤ 0.002) as SID Lys increased. Projecting IOFC, broken line linear and quadratic polynomial models estimated the maximum IOFC at 105.8% and 113.7% SID Lys, respectively. In summary, while growth performance increased linearly up to 120% of the 2016 PIC recommended Lys requirement, the optimal IOFC was 106% to 114%