Local Analysis of Inverse Problems: H\"{o}lder Stability and Iterative Reconstruction

We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however, the data space can be an arbitrary Banach space. We study sequences of parameter functions generated by a nonlinear Landweber iteration and conditions under which these strongly converge, locally, to the solutions within an appropriate distance. We express the conditions for convergence in terms of H\"{o}lder stability of the inverse maps, which ties naturally to the analysis of inverse problems

Utility of 2013 American College of Cardiology/American Heart Association Cholesterol Guidelines in HIV-Infected Adults With Carotid Atherosclerosis.

BackgroundAlthough HIV is associated with increased atherosclerotic cardiovascular disease (CVD) risk, it is unknown whether guidelines can identify HIV-infected adults who may benefit from statins. We compared the 2013 American College of Cardiology/American Heart Association and 2004 Adult Treatment Panel III recommendations in HIV-infected adults and evaluated associations with carotid artery intima-media thickness and plaque.Methods and resultsCarotid artery intima-media thickness was measured at baseline and 3 years later in 352 HIV-infected adults without clinical atherosclerotic CVD and not on statins. Plaque was defined as IMT >1.5 mm in any segment. At baseline, the median age was 43 (interquartile range, 39-49), 85% were men, 74% were on antiretroviral medication, and 50% had plaque. The American College of Cardiology/American Heart Association guidelines were more likely to recommend statins compared with the Adult Treatment Panel III guidelines, both overall (26% versus 14%; P<0.001), in those with plaque (32% versus 17%; P=0.0002), and in those without plaque (16% versus 7%; P=0.025). In multivariable analysis, older age, higher low-density lipoprotein cholesterol, pack per year of smoking, and history of opportunistic infection were associated with baseline plaque. Baseline IMT (hazard ratio, 1.18 per 10% increment; 95% confidence interval, 1.05-1.33; P=0.005) and plaque (hazard ratio, 2.06; 95% confidence interval, 1.02-4.08; P=0.037) were each associated with all-cause mortality, independent of traditional CVD risk factors.ConclusionsAlthough the American College of Cardiology/American Heart Association guidelines recommended statins to a greater number of HIV-infected adults compared with the Adult Treatment Panel III guidelines, both failed to recommend therapy in the majority of HIV-affected adults with carotid plaque. Baseline carotid atherosclerosis but not atherosclerotic CVD risk scores was an independent predictor of mortality. HIV-specific guidelines that include detection of subclinical atherosclerosis may help to identify HIV-infected adults who are at increased atherosclerotic CVD risk and may be considered for statins

Nonparametric instrumental regression with non-convex constraints

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, like integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition

Electronic Portfolios in the Classroom: Factors Impacting Teachers’ Integration of New Technologies and New Pedagogies

This article presents the findings of a study on the use of an electronic portfolio (EP) in 16 elementary classrooms across Canada. Using a mixed-methods approach, data were collected to understand how teachers used EPs in their classrooms, to what extent they integrated the EP into their practice, and the factors influencing their use. Using expectancy theory, findings indicate that low implementers experienced significant technical obstacles and/or were reluctant to change their established practices, whereas high implementers reported feeling supported by their administration, experiencing growth in their teaching practice, and using more pedagogical practices that support self-regulated learning as a result of the scaffolding provided by the software

Measles in HIV-infected children in southern Africa

In recent years, southern Africa has experienced a widespread measles outbreak. Given the high human immunodeficiency virus (HIV) prevalence in the region, the particular features of measles in HIV-infected individuals are of interest to clinicians, especially as regards children, as are measles immunisation strategies for this population. This review discusses a case ofsevere measles in an HIV-infected child in Botswana, focusing on its implications for clinical case management in Botswana and similar settings and for policies on measles immunisation

Discretization of variational regularization in Banach spaces

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data \yd of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\infty$--space