Status of Women and Girls in Southern Arizona 2010

With the publication of the Status of Women and Girls in Southern Arizona report in the spring of 2009, the Women's Foundation of Southern Arizona achieved one of its major goals of establishing a comprehensive and accessible resource to provide data and analysis documenting the lives of women and girls in our region. We are now very pleased to publish the first of what are intended to be annual updates to the original report. These yearly updates will allow us not only to present the most current data on women's education, health, employment and other topics, but also to track where change is needed and measure the impact we, and our partners, have in the community at arge

An Investigation into the Bonding Properties of New Generation Ceramic Brackets As Compared to a Stainless Steel Bracket

Introduction: More patients are seeking esthetic alternatives for their orthodontic treatment options, which has led to increased use of ceramic brackets in recent years. These brackets were marketed before independent scientific research was completed. Many of the early ceramic brackets used a silane coupling agent to allow for a chemical bond between the bracket and the adhesive resin. Early reports from clinicians of increased bond strengths and iatrogenic tooth damage after bracket removal were common. Manufacturers have made changes to their base designs, relying more on mechanical retention for bond strength. The goal of this study was to test the shear bond strength of two newer generations of mechanically retained ceramic brackets and compare them to a traditional stainless steel bracket. Materials and Methods: Two types of ceramic brackets, Clarity Advanced (3M Unitek, Monrovia, CA), and Avex CX (Opal Orthodontics, South Jordan, UT) and one type of metal bracket, Victory Series MBT (3M, Unitek, Monrovia, CA) were used in this study. Exemption from IRB Application was granted by the Marquette University Institutional Review Board (IRB) on 7-12-13. The shear bond strength of the three groups of brackets were examined after bonding to extracted premolars. Brackets were debonded with a universal testing machine (Instron Corporation, Canton, MA) in a motion parallel to the bracket/tooth interface. Each tooth and bracket was viewed under an optical stereomicroscope at 10x magnification and given an adhesive remnant index (ARI) score. The one way ANOVA and Tukey\u27s post hoc tests were used to determine significant differences in bond strengths, and the Kruskal-Wallis and Mann-Whitney post hoc tests were used to analyze the difference in ARI scores. Results: Statistically significant (p\u3c0.01) differences were found between the shear bond strengths of the Victory Series and Clarity Advanced groups, with the Victory Series having a mean strength of 199.4 N and the Clarity Advanced having an average of 136.0 N. Significant (p\u3c0.0001) differences in ARI scores were found between the Victory Series and both ceramic groups, with an average score of 1 for the Victory Series and an average score of 2 for both ceramic groups. The two ceramic brackets were not statistically different from each other in bond strength or ARI score. Conclusions: The shear bond strengths of the new generations of ceramic brackets are lower than those of the metal bracket tested, which suggests a safer bond to enamel. Further research on clinical debonding characteristics and behavior intra-orally are needed to support the in vitro results found in this study

Multi-resolution analysis for ENO schemes

Given an function, u(x), which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. This multi-resolution analysis was applied to essentially non-oscillatory (ENO) schemes in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. An efficient algorithm for implementing this program in the 1-D case is presented; this algorithm can be extended to the multi-dimensional case with Cartesian grids

On positive definiteness over locally compact quantum groups

The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various well-known results about positive-definite functions over groups to the quantum framework. Among these are theorems on "square roots" of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.Comment: 28 pages; v3: incorporated several changes, most at the referee's suggestion; to appear in the Canadian Journal of Mathematic

Recent developments in shock-capturing schemes

The development of the shock capturing methodology is reviewed, paying special attention to the increasing nonlinearity in its design and its relation to interpolation. It is well-known that higher-order approximations to a discontinuous function generate spurious oscillations near the discontinuity (Gibbs phenomenon). Unlike standard finite-difference methods which use a fixed stencil, modern shock capturing schemes use an adaptive stencil which is selected according to the local smoothness of the solution. Near discontinuities this technique automatically switches to one-sided approximations, thus avoiding the use of discontinuous data which brings about spurious oscillations

Covariance Estimation in Elliptical Models with Convex Structure

We address structured covariance estimation in Elliptical distribution. We assume it is a priori known that the covariance belongs to a given convex set, e.g., the set of Toeplitz or banded matrices. We consider the General Method of Moments (GMM) optimization subject to these convex constraints. Unfortunately, GMM is still non-convex due to objective. Instead, we propose COCA - a convex relaxation which can be efficiently solved. We prove that the relaxation is tight in the unconstrained case for a finite number of samples, and in the constrained case asymptotically. We then illustrate the advantages of COCA in synthetic simulations with structured Compound Gaussian distributions. In these examples, COCA outperforms competing methods as Tyler's estimate and its projection onto a convex set

Joint Covariance Estimation with Mutual Linear Structure

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered populations with different covariances, our aim is to determine the mutual structure of these covariance matrices and estimate them. Supposing that the covariances span a low dimensional affine subspace in the space of symmetric matrices, we develop a new efficient algorithm discovering the structure and using it to improve the estimation. Our technique is based on the application of principal component analysis in the matrix space. We also derive an upper performance bound of the proposed algorithm in the Gaussian scenario and compare it with the Cramer-Rao lower bound. Numerical simulations are presented to illustrate the performance benefits of the proposed method