On Asymmetric Coverings and Covering Numbers

An asymmetric covering D(n,R) is a collection of special subsets S of an n-set such that every subset T of the n-set is contained in at least one special S with |S| - |T| <= R. In this paper we compute the smallest size of any D(n,1) for n <= 8. We also investigate ``continuous'' and ``banded'' versions of the problem. The latter involves the classical covering numbers C(n,k,k-1), and we determine the following new values: C(10,5,4) = 51, C(11,7,6,) =84, C(12,8,7) = 126, C(13,9,8)= 185 and C(14,10,9) = 259. We also find the number of nonisomorphic minimal covering designs in several cases.Comment: 11 page

An Analysis of the Impacts of Including Income in Determining Community Wealth in the Maine K-12 School Funding Formula

A key feature of K‐12 school funding formulas is establishing an ability‐to‐pay provision in the formula. With the exception of Hawaii, all states share the funding of their K‐12 school system between the State and local communities. And all school formulas use some mechanism to determine the ability of a local community to pay its equitable share of the costs of education. For Maine, as well as a majority of other states, local property wealth is used to determine ability‐to‐pay. The theory is that communities with higher property wealth are more wealthy communities, and, thus, more able to pay for the costs of their local school system. In contrast, communities with lower property wealth are considered to be less wealthy communities, less able to pay for the costs of their local school system, and, thus, eligible for more state aid. This report presents an analysis of three alternative strategies for defining ability‐ to‐pay in Maine, all three of which add income into the calculation of ability‐to‐pay. In Spring 2009 the Joint Standing Committee for Education and Cultural Affairs of the Maine Legislature approved a multi‐faceted research plan for the review of Maine’s school funding formula

OntoMathPROOntoMath^{PRO} Ontology: A Linked Data Hub for Mathematics

In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.Comment: 15 pages, 6 images, 1 table, Knowledge Engineering and the Semantic Web - 5th International Conferenc

Long-term Outcomes of the FRESH START Trial: Exploring the Role of Self-efficacy in Cancer Survivors’ Maintenance of Dietary Practices and Physical Activity

Background: This study examined whether changes in self-efficacy explain the effects of a mailed print intervention on long-term dietary practices of breast and prostate cancer survivors. The relationship between change in self-efficacy and long-term physical activity (PA) also was examined. Methods: Breast and prostate cancer survivors (N = 543) from 39 US states and two Canadian provinces participated in the FRESH START intervention trial. Participants were randomly assigned to receive a 10-month program of mailed print materials on diet and PA available in the public domain or a 10-month program of tailored materials designed to increase fruit and vegetable (F&V) intake, decrease fat intake, and/or increase PA. Changes in self-efficacy for F&V intake and fat restriction were analyzed as potential mediators of the intervention's effects on diet at 2-year follow-up. Because we previously found that change in self-efficacy for PA did not vary by group assignment, the relationship between change in self-efficacy and PA at 2-year follow-up was examined across study conditions. Results: Results suggest that change in self-efficacy for fat restriction partially explained the intervention's effect on fat intake (mean indirect effect = -0.28), and change in self-efficacy for F&V consumption partially explained the intervention's effect on daily F&V intake (mean indirect effect = .11). Change in self-efficacy for fat restriction partially accounted for the intervention's impact on overall diet quality among men only (mean indirect effect = 0.60). Finally, change in self-efficacy for PA predicted PA at 2-year follow-up. Conclusions: Findings suggest that self-efficacy may influence long-term maintenance of healthy lifestyle practices among cancer survivors

Long-Term Dietary Outcomes of the FRESH START Intervention for Breast and Prostate Cancer Survivors

Background Cancer survivors are at increased risk for secondary cancers and other diseases. Healthy dietary practices may improve cancer survivors' health and well-being. Objective The durability of the effects of the FRESH START intervention, a program of sequentially tailored mailed materials, and standardized mailed materials (for controls) on cancer survivors' dietary outcomes was assessed over a 2-year period. Greater dietary gains were expected for FRESH START participants relative to controls. Design Participants were randomized to receive tailored vs standardized 10-month mailed print interventions promoting diet and exercise behaviors. Data were collected at baseline and 1- and 2-year follow-ups. Participants/setting Breast and prostate cancer survivors (n=543) were recruited from 39 states and two provinces within North America. A total of 489 participants completed the 2-year follow-up assessment (10% attrition). Intervention Participants were randomly assigned to either a 10-month program of tailored mailed print materials promoting fruit and vegetable consumption, reduced total and saturated fat intake, and/or increased exercise or to a 10-month program of publicly available mailed materials on diet and exercise. Main outcome measures Telephone surveys (supported with blood biomarkers) assessed dietary habits at baseline and 1- and 2-year follow-ups. Statistical analyses performed Paired-samples t tests were conducted to examine the durability of the intervention's effects on dietary outcomes within each study arm. Arm differences in follow-up outcomes were then tested with the general linear model, controlling for the baseline value of the outcomes. Results Both arms reported decreased saturated fat intake, increased servings of fruits and vegetables, and better overall diet quality at year 2 relative to baseline. However, FRESH START participants reported better overall diet quality and lower total and saturated fat intake compared to controls at the 2-year follow-up. Conclusions Results suggest that mailed material interventions, especially those that are tailored, can produce long-term dietary improvement among cancer survivors

Change in self-efficacy partially mediates the effects of the FRESH START intervention on cancer survivors' dietary outcomes

Objective: This study examined change in self-efficacy as a mediator of the effects of a mailed print intervention on the dietary and exercise practices of newly diagnosed breast and prostate cancer survivors. Method: A total of 543 breast and prostate cancer patients were recruited from 39 states and two provinces within North America. Participants were randomly assigned to receive a 10-month program of tailored mailed print materials that aimed to increase fruit and vegetable consumption, reduce fat intake, and/or increase exercise or a 10-month program of publically available materials on diet and exercise. Telephone surveys conducted at baseline and 1 year assessed dietary practices, physical activity, and self-efficacy for engaging in these health behaviors. Results: Results indicated that changes in self-efficacy for fat restriction and eating more fruits and vegetables were significant mediators of the intervention's effects on dietary outcomes at 1-year follow-up. The intervention did not significantly affect self-efficacy for exercise; however, a significant, positive relationship was found between self-efficacy for exercise and exercise duration at follow-up. Conclusions: Findings are largely consistent with Social Cognitive Theory and support the use of strategies to increase self-efficacy in health promotion interventions for cancer survivors. Copyright © 2008 John Wiley & Sons, Ltd

Characterizing 51 Eri b from 1-5 μ\mum: a partly-cloudy exoplanet

We present spectro-photometry spanning 1-5 $\mu$m of 51 Eridani b, a 2-10 M$_\text{Jup}$ planet discovered by the Gemini Planet Imager Exoplanet Survey. In this study, we present new $K1$ (1.90-2.19 $\mu$m) and $K2$ (2.10-2.40 $\mu$m) spectra taken with the Gemini Planet Imager as well as an updated $L_P$ (3.76 $\mu$m) and new $M_S$ (4.67 $\mu$m) photometry from the NIRC2 Narrow camera. The new data were combined with $J$ (1.13-1.35 $\mu$m) and $H$ (1.50-1.80 $\mu$m) spectra from the discovery epoch with the goal of better characterizing the planet properties. 51 Eri b photometry is redder than field brown dwarfs as well as known young T-dwarfs with similar spectral type (between T4-T8) and we propose that 51 Eri b might be in the process of undergoing the transition from L-type to T-type. We used two complementary atmosphere model grids including either deep iron/silicate clouds or sulfide/salt clouds in the photosphere, spanning a range of cloud properties, including fully cloudy, cloud free and patchy/intermediate opacity clouds. Model fits suggest that 51 Eri b has an effective temperature ranging between 605-737 K, a solar metallicity, a surface gravity of $\log$(g) = 3.5-4.0 dex, and the atmosphere requires a patchy cloud atmosphere to model the SED. From the model atmospheres, we infer a luminosity for the planet of -5.83 to -5.93 ($\log L/L_{\odot}$), leaving 51 Eri b in the unique position as being one of the only directly imaged planet consistent with having formed via cold-start scenario. Comparisons of the planet SED against warm-start models indicates that the planet luminosity is best reproduced by a planet formed via core accretion with a core mass between 15 and 127 M$_{\oplus}$.Comment: 27 pages, 19 figures, Accepted for publication in The Astronomical Journa

Dynamical Mass Measurement of the Young Spectroscopic Binary V343 Normae AaAb Resolved With the Gemini Planet Imager

We present new spatially resolved astrometry and photometry from the Gemini Planet Imager of the inner binary of the young multiple star system V343 Normae, which is a member of the beta Pictoris moving group. V343 Normae comprises a K0 and mid-M star in a ~4.5 year orbit (AaAb) and a wide 10" M5 companion (B). By combining these data with archival astrometry and radial velocities we fit the orbit and measure individual masses for both components of M_Aa = 1.10 +/- 0.10 M_sun and M_Ab = 0.290 +/- 0.018 M_sun. Comparing to theoretical isochrones, we find good agreement for the measured masses and JHK band magnitudes of the two components consistent with the age of the beta Pic moving group. We derive a model-dependent age for the beta Pic moving group of 26 +/- 3 Myr by combining our results for V343 Normae with literature measurements for GJ 3305, which is another group member with resolved binary components and dynamical masses.Comment: 12 pages, 7 figures. Accepted to A

Improving and Assessing Planet Sensitivity of the GPI Exoplanet Survey with a Forward Model Matched Filter

We present a new matched filter algorithm for direct detection of point sources in the immediate vicinity of bright stars. The stellar Point Spread Function (PSF) is first subtracted using a Karhunen-Lo\'eve Image Processing (KLIP) algorithm with Angular and Spectral Differential Imaging (ADI and SDI). The KLIP-induced distortion of the astrophysical signal is included in the matched filter template by computing a forward model of the PSF at every position in the image. To optimize the performance of the algorithm, we conduct extensive planet injection and recovery tests and tune the exoplanet spectra template and KLIP reduction aggressiveness to maximize the Signal-to-Noise Ratio (SNR) of the recovered planets. We show that only two spectral templates are necessary to recover any young Jovian exoplanets with minimal SNR loss. We also developed a complete pipeline for the automated detection of point source candidates, the calculation of Receiver Operating Characteristics (ROC), false positives based contrast curves, and completeness contours. We process in a uniform manner more than 330 datasets from the Gemini Planet Imager Exoplanet Survey (GPIES) and assess GPI typical sensitivity as a function of the star and the hypothetical companion spectral type. This work allows for the first time a comparison of different detection algorithms at a survey scale accounting for both planet completeness and false positive rate. We show that the new forward model matched filter allows the detection of $50\%$ fainter objects than a conventional cross-correlation technique with a Gaussian PSF template for the same false positive rate.Comment: ApJ accepte

Performance of the Gemini Planet Imager Non-Redundant Mask and spectroscopy of two close-separation binaries HR 2690 and HD 142527

The Gemini Planet Imager (GPI) contains a 10-hole non-redundant mask (NRM), enabling interferometric resolution in complement to its coronagraphic capabilities. The NRM operates both in spectroscopic (integral field spectrograph, henceforth IFS) and polarimetric configurations. NRM observations were taken between 2013 and 2016 to characterize its performance. Most observations were taken in spectroscopic mode with the goal of obtaining precise astrometry and spectroscopy of faint companions to bright stars. We find a clear correlation between residual wavefront error measured by the AO system and the contrast sensitivity by comparing phase errors in observations of the same source, taken on different dates. We find a typical 5-$\sigma$ contrast sensitivity of $2-3~\times~10^{-3}$ at $\sim\lambda/D$. We explore the accuracy of spectral extraction of secondary components of binary systems by recovering the signal from a simulated source injected into several datasets. We outline data reduction procedures unique to GPI's IFS and describe a newly public data pipeline used for the presented analyses. We demonstrate recovery of astrometry and spectroscopy of two known companions to HR 2690 and HD 142527. NRM+polarimetry observations achieve differential visibility precision of $\sigma\sim0.4\%$ in the best case. We discuss its limitations on Gemini-S/GPI for resolving inner regions of protoplanetary disks and prospects for future upgrades. We summarize lessons learned in observing with NRM in spectroscopic and polarimetric modes.Comment: Accepted to AJ, 22 pages, 14 figure