Differential equations for the cuspoid canonical integrals

Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

Bulge plus disc and S\'ersic decomposition catalogues for 16,908 galaxies in the SDSS Stripe 82 co-adds: A detailed study of the ugrizugriz structural measurements

Quantitative characterization of galaxy morphology is vital in enabling comparison of observations to predictions from galaxy formation theory. However, without significant overlap between the observational footprints of deep and shallow galaxy surveys, the extent to which structural measurements for large galaxy samples are robust to image quality (e.g., depth, spatial resolution) cannot be established. Deep images from the Sloan Digital Sky Survey (SDSS) Stripe 82 co-adds provide a unique solution to this problem - offering $1.6-1.8$ magnitudes improvement in depth with respect to SDSS Legacy images. Having similar spatial resolution to Legacy, the co-adds make it possible to examine the sensitivity of parametric morphologies to depth alone. Using the Gim2D surface-brightness decomposition software, we provide public morphology catalogs for 16,908 galaxies in the Stripe 82 $ugriz$ co-adds. Our methods and selection are completely consistent with the Simard et al. (2011) and Mendel et al. (2014) photometric decompositions. We rigorously compare measurements in the deep and shallow images. We find no systematics in total magnitudes and sizes except for faint galaxies in the $u$-band and the brightest galaxies in each band. However, characterization of bulge-to-total fractions is significantly improved in the deep images. Furthermore, statistics used to determine whether single-S\'ersic or two-component (e.g., bulge+disc) models are required become more bimodal in the deep images. Lastly, we show that asymmetries are enhanced in the deep images and that the enhancement is positively correlated with the asymmetries measured in Legacy images.Comment: 27 pages, 14 figures. MNRAS accepted. Our catalogs are available in TXT and SQL formats at http://orca.phys.uvic.ca/~cbottrel/share/Stripe82/Catalogs

Improving clerkship preparedness: a hospital medicine elective for pre-clerkship students.

BackgroundMedical students often struggle to apply their nascent clinical skills in clerkships. While transitional clerkships can orient students to new roles and logistics, students may benefit from developing clinical skills in inpatient environments earlier in their curriculum to improve readiness for clerkships.InterventionOur four- to six-session elective provides pre-clerkship students with individualized learning in the inpatient setting with the aim of improving clerkship preparedness. Students work one-on-one with faculty who facilitate individualized learning through mentoring, deliberate practice, and directed feedback. Second-year medical students are placed on an attending-only, traditionally 'non-teaching' service in the hospital medicine division of a Veterans Affairs (VA) hospital for half-day sessions. Most students self-select into the elective following a class-wide advertisement. The elective also accepts students who are referred for remediation of their clinical skills.OutcomeIn the elective's first two years, 25 students participated and 47 students were waitlisted. We compared participant and waitlisted (non-participant) students' self-efficacy in several clinical and professional domains during their first clerkship. Elective participants reported significantly higher clerkship preparedness compared to non-participants in the areas of physical exam, oral presentation, and formulation of assessments and plans.ConclusionsStudents found the one-on-one feedback and personalized attention from attending physicians to be a particularly useful aspect of the course. This frequently cited benefit points to students' perceived needs and the value they place on individualized feedback. Our innovation harnesses an untapped resource - the hospital medicine 'non-teaching' service - and serves as an attainable option for schools interested in enhancing early clinical skill-building for all students, including those recommended for remediation.AbbreviationsA&P: Assessment and plan; H&P: History and physical; ILP: Individual learning plan

Using Spatial Density to Characterize Volcanic Fields on Mars

We introduce a new tool to planetary geology for quantifying the spatial arrangement of vent fields and volcanic provinces using non parametric kernel density estimation. Unlike parametricmethods where spatial density, and thus the spatial arrangement of volcanic vents, is simplified to fit a standard statistical distribution, non parametric methods offer more objective and data driven techniques to characterize volcanic vent fields. This method is applied to Syria Planum volcanic vent catalog data as well as catalog data for a vent field south of Pavonis Mons. The spatial densities are compared to terrestrial volcanic fields

Thermal Radiation Analysis System (TRASYS)

A user's manual is presented for TRASYS, which is a digital software system with a generalized capability for solving radiation problems. Subroutines, file, and variable definitions are presented along with subroutine and function descriptions for the preprocessor. Definitions and descriptions of components of the processor are also presented

Eclipsing Expectations: How a Third Grader Set His Own Goals (And Taught Us All How to Listen)

A description of an illuminating journey through the eyes of a parent, Diane, who wanted a more inclusive experience for her son Benny. For Diane and Benny, this meant becoming meaningful participants not only in Benny’s own classroom community but in the Individualized Education Program (IEP) meetings that determined his educational goals. David uses a DSE framework to analyze and highlight the importance of context, as opposed to focusing on the disability condition, in enacting inclusionary practices. The authors argue for an “adhocratic” model of education that views children, educators, and parents as allies