Dynamics of Epidemics

This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where the disease can expand to an epidemic, the probability distribution function is the sum of two parts; one which is static at long times, and another whose mean grows exponentially. The time development of the mean number of infected individuals is obtained analytically. When epidemics occur, the probability distributions are very broad, and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals.Comment: 4 pages and 3 figure

Wavelength Dependent PSFs and their impact on Weak Lensing Measurements

We measure and model the wavelength dependence of the PSF in the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) survey. We find that PSF chromaticity is present in that redder stars appear smaller than bluer stars in the $g, r,$ and $i$-bands at the 1-2 per cent level and in the $z$ and $y$-bands at the 0.1-0.2 per cent level. From the color dependence of the PSF, we fit a model between the monochromatic PSF trace radius, $R$, and wavelength of the form $R(\lambda)\propto \lambda^{b}$. We find values of $b$ between -0.2 and -0.5, depending on the epoch and filter. This is consistent with the expectations of a turbulent atmosphere with an outer scale length of $\sim 10-100$ m, indicating that the atmosphere is dominating the chromaticity. We find evidence in the best seeing data that the optical system and detector also contribute some wavelength dependence. Meyers and Burchat (2015) showed that $b$ must be measured to an accuracy of $\sim 0.02$ not to dominate the systematic error budget of the Large Synoptic Survey Telescope (LSST) weak lensing (WL) survey. Using simple image simulations, we find that $b$ can be inferred with this accuracy in the $r$ and $i$-bands for all positions in the LSST field of view, assuming a stellar density of 1 star arcmin$^{-2}$ and that the optical PSF can be accurately modeled. Therefore, it is possible to correct for most, if not all, of the bias that the wavelength-dependent PSF will introduce into an LSST-like WL survey.Comment: 14 pages, 10 figures. Submitted to MNRAS. Comments welcom

Feasibility model of a high reliability five-year tape transport, volume 2

Analysis of the design features of the modularized tape transport renders a life expectancy in excess of five years. Tests performed on the tape transport were directed toward determining its performance capability. These tests revealed that the tape jitter and skew are in the range achieved by high quality digital tape transports. Guidance of the tape in the lateral sense by the use of the two hybrid crowned rollers proved to be excellent. Tracking was maintained within less than one thousandth inch (approximately 2 micrometers). The guidance capability demonstrated makes possible the achievement of the performance objective of 7.2 x 10 to the 9th power storage capability employing 1500 ft. of one inch wide tape with a packing density of 5,000 bits per inch per track on 80 tracks. Also, the machine showed excellent characteristics operating over a wide range of tape speeds. The basic design concept lends itself to growth and adaptation to a wide range of recorder requirements

Feasibility model of a high reliability five-year tape transport, Volume 1

The development, performance, and test results for the spaceborne magnetic tape transport are discussed. An analytical model of the tape transport was used to optimize its conceptual design. Each of the subsystems was subjected to reliability analyses which included structural integrity, maintenance of system performance within acceptable bounds, and avoidance of fatigue failure. These subsystems were also compared with each other in order to evaluate reliability characteristics. The transport uses no mechanical couplings. Four drive motors, one for each reel and one for each of two capstans, are used in a differential mode. There are two hybrid, spherical, cone tapered-crown rollers for tape guidance. Storage of the magnetic tape is provided by a reel assembly which includes the reel, a reel support structure and bearings, dust seals, and a dc drive motor. A summary of transport test results on tape guidance, flutter, and skew is provided

Children's construction task performance and spatial ability: controlling task complexity and predicting mathematics performance.

This paper presents a methodology to control construction task complexity and examined the relationships between construction performance and spatial and mathematical abilities in children. The study included three groups of children (N = 96); ages 7-8, 10-11, and 13-14 years. Each group constructed seven pre-specified objects. The study replicated and extended previous findings that indicated that the extent of component symmetry and variety, and the number of components for each object and available for selection, significantly predicted construction task difficulty. Results showed that this methodology is a valid and reliable technique for assessing and predicting construction play task difficulty. Furthermore, construction play performance predicted mathematical attainment independently of spatial ability

Some homogenization and corrector results for nonlinear monotone operators

This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form \ \ds -\limfunc{div}\left(a\left(x, x/{\varepsilon _h},Du_h\right)\right)=f_h on $\Omega$ with Dirichlet boundary conditions. The sequence $(\varepsilon _h)$ tends to $0$ and the map $a(x,y,\xi )$ is periodic in $y$, monotone in $\xi$ and satisfies suitable continuity conditions. It is proved that $u_h\rightarrow u$ weakly in $H_0^{1,2}(\Omega )$, where $u$ is the solution of a homogenized problem \ -\limfunc{div}(b(x,Du))=f on $\Omega$. We also prove some corrector results, i.e. we find $(P_h)$ such that $Du_h-P_h(Du)\rightarrow 0$ in $L^2(\Omega ,R^n)$

Building a comprehensive mentoring academy for schools of health.

Formal mentoring programs are increasingly recognized as critical for faculty career development. We describe a mentoring academy (MA) developed for faculty across tracks (i.e., researchers, clinicians, educators) within a "school of health" encompassing schools of medicine and nursing. The program is anchored dually in a clinical and translational science center and a school of health. The structure includes the involvement of departmental and center mentoring directors to achieve widespread uptake and oversight. A fundamental resource provided by the MA includes providing workshops to enhance mentoring skills. Initiatives for junior faculty emphasize establishing and maintaining strong mentoring relationships and implementing individual development plans (IDPs) for career planning. We present self-report data on competency improvement from mentor workshops and data on resources and barriers identified by junior faculty (n = 222) in their IDPs. Mentors reported statistically significantly improved mentoring competency after workshop participation. Junior faculty most frequently identified mentors (61%) and collaborators (23%) as resources for goal attainment. Top barriers included insufficient time and time-management issues (57%), funding limitations (18%), work-life balance issues (18%), including inadequate time for self-care and career development activities. Our MA can serve as a model and roadmap for providing resources to faculty across traditional tracks within medical schools

Beyond Heroes & Role Models: Using Biographies to Develop Young Change Agents

Reading, writing, and discussing biographies provide unique opportunities for teachers and students. Critical thinking can be developed through questioning, predicting, and analyzing various biographical mediums--texts, photographs and illustrations, book reviews, websites, films, news articles, etc.--to learn more about an individual\u27s life experiences and choices. Decision making skills can be enhanced when students juxtapose their perceptions of heroes and role models to that of a change agent, even considering how their own life experiences and choices may be contributing to larger actions of change. In this article, the authors discuss six biographies that could be used with young people in the elementary classroom to study change agents. The authors carefully selected and organized their literary choices into four categories: (1) familiar historical figures, (2) familiar living persons, (3) less familiar figures, and finally (4) students and teachers themselves--because they can act as change agents today on a local and personal level

Epitaxial growth of (111)-oriented LaAlO3_3/LaNiO3_3 ultra-thin superlattices

The epitaxial stabilization of a single layer or superlattice structures composed of complex oxide materials on polar (111) surfaces is severely burdened by reconstructions at the interface, that commonly arise to neutralize the polarity. We report on the synthesis of high quality LaNiO$_3$/mLaAlO$_3$ pseudo cubic (111) superlattices on polar (111)-oriented LaAlO$_3$, the proposed complex oxide candidate for a topological insulating behavior. Comprehensive X-Ray diffraction measurements, RHEED, and element specific resonant X-ray absorption spectroscopy affirm their high structural and chemical quality. The study offers an opportunity to fabricate interesting interface and topology controlled (111) oriented superlattices based on ortho-nickelates

Singularities of Nonlinear Elliptic Systems

Through Morrey's spaces (plus Zorko's spaces) and their potentials/capacities as well as Hausdorff contents/dimensions, this paper estimates the singular sets of nonlinear elliptic systems of the even-ordered Meyers-Elcrat type and a class of quadratic functionals inducing harmonic maps.Comment: 18 pages Communications in Partial Differential Equation