Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms

This paper considers the regularized Tyler's scatter estimator for elliptical distributions, which has received considerable attention recently. Various types of shrinkage Tyler's estimators have been proposed in the literature and proved work effectively in the "small n large p" scenario. Nevertheless, the existence and uniqueness properties of the estimators are not thoroughly studied, and in certain cases the algorithms may fail to converge. In this work, we provide a general result that analyzes the sufficient condition for the existence of a family of shrinkage Tyler's estimators, which quantitatively shows that regularization indeed reduces the number of required samples for estimation and the convergence of the algorithms for the estimators. For two specific shrinkage Tyler's estimators, we also proved that the condition is necessary and the estimator is unique. Finally, we show that the two estimators are actually equivalent. Numerical algorithms are also derived based on the majorization-minimization framework, under which the convergence is analyzed systematically

Environmental public health tracking of childhood asthma using California health interview survey, traffic, and outdoor air pollution data.

BackgroundDespite extensive evidence that air pollution affects childhood asthma, state-level and national-level tracking of asthma outcomes in relation to air pollution is limited.ObjectivesOur goals were to evaluate the feasibility of linking the 2001 California Health Interview Survey (CHIS), air monitoring, and traffic data; estimate associations between traffic density (TD) or outdoor air pollutant concentrations and childhood asthma morbidity; and evaluate the usefulness of such databases, linkages, and analyses to Environmental Public Health Tracking (EPHT).MethodsWe estimated TD within 500 feet of residential cross-streets of respondents and annual average pollutant concentrations based on monitoring station measurements. We used logistic regression to examine associations with reported asthma symptoms and emergency department (ED) visits/hospitalizations.ResultsAssignment of TD and air pollution exposures for cross-streets was successful for 82% of children with asthma in Los Angeles and San Diego, California, Counties. Children with asthma living in high ozone areas and areas with high concentrations of particulate matter < 10 microm in aerodynamic diameter experienced symptoms more frequently, and those living close to heavy traffic reported more ED visits/hospitalizations. The advantages of the CHIS for asthma EPHT include a large and representative sample, biennial data collection, and ascertainment of important socio-demographic and residential address information. Disadvantages are its cross-sectional design, reliance on parental reports of diagnoses and symptoms, and lack of information on some potential confounders.ConclusionsDespite limitations, the CHIS provides a useful framework for examining air pollution and childhood asthma morbidity in support of EPHT, especially because later surveys address some noted gaps. We plan to employ CHIS 2003 and 2005 data and novel exposure assessment methods to re-examine the questions raised here

Astrophysical constraints on the proton-to-electron mass ratio with FAST

That the laws of physics are the same at all times and places throughout the Universe is one of the basic assumptions of physics. Astronomical observations provide the only means to test this basic assumption on cosmological time and distance scales. The possibility of variations in the dimensionless physical constant {\mu} - the proton-to-electron mass ratio, can be tested by comparing astronomical measurements of the rest frequency of certain spectral lines at radio wavelengths with laboratory determinations. Different types of molecular transitions have different dependencies on {\mu} and so observations of two or more spectral lines towards the same astronomical source can be used to test whether there is any evidence for either temporal or spatial changes in the physical fundamental constants. {\mu} will change if the relative strength of the strong nuclear force compared to the electromagnetic force varies. Theoretical studies have shown that the rotational transitions of some molecules which have transitions in the frequency range that will be covered by FAST (e.g., CH3OH, OH and CH) are sensitive to changes in {\mu}. A number of studies looking for possible variations in {\mu} have been undertaken with existing telescopes, however, the greater sensitivity of FAST means it will open new opportunities to significantly improve upon measurements made to date. In this paper, we discuss which molecular transitions and sources (both in the Galaxy and external galaxies) are likely targets for providing improved constraints on {\mu} with FAST

Effects of fiber/matrix interactions on the properties of graphite/epoxy composites

A state-of-the-art literature review of the interactions between fibers and resin within graphite epoxy composite materials was performed. Emphasis centered on: adhesion theory; wetting characteristics of carbon fiber; load transfer mechanisms; methods to evaluate and measure interfacial bond strengths; environmental influence at the interface; and the effect of the interface/interphase on composite performance, with particular attention to impact toughness. In conjunction with the literature review, efforts were made to design experiments to study the wetting behavior of carbon fibers with various finish variants and their effect on adhesion joint strength. The properties of composites with various fiber finishes were measured and compared to the base-line properties of a control. It was shown that by tailoring the interphase properties, a 30% increase in impact toughness was achieved without loss of mechanical properties at both room and elevated temperatures

Health Status of the Uninsured: Opportunities for Improvement

Provides estimates of the geographic variations in the rates of self-reported fair or poor health status, asthma, and hypertension among uninsured children and adults in California