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

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

Fast parallel algorithms for a broad class of nonlinear variational diffusion approaches

Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during the last years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implement at ions of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Numerical results confirm that, depending on the parametrization, this approximation can be made quite accurate. Our results provide a perspective for uniform implement at ions of both nonlinear variational models and diffusion filters on parallel architectures

Association of low level viremia with inflammation and mortality in HIV-infected adults.

BackgroundWhether HIV viremia, particularly at low levels is associated with inflammation, increased coagulation, and all-cause mortality is unclear.MethodsThe associations of HIV RNA level with C-reactive protein (CRP), fibrinogen, interleukin (IL)-6 and mortality were evaluated in 1116 HIV-infected participants from the Study of Fat Redistribution and Metabolic Change in HIV infection. HIV RNA level was categorized as undetectable (i.e., "target not detected"), 1-19, 20-399, 400-9999, and ≥ 10,000 copies/ml. Covariates included demographics, lifestyle, adipose tissue, and HIV-related factors.ResultsHIV RNA level had little association with CRP. Categories of HIV RNA below 10,000 copies/ml had similar levels of IL-6 compared with an undetectable HIV RNA level, while HIV RNA ≥ 10,000 copies/ml was associated with 89% higher IL-6 (p<0.001). This association was attenuated by ~50% after adjustment for CD4+ cell count. Higher HIV RNA was associated with higher fibrinogen. Compared to an undetectable HIV RNA level, fibrinogen was 0.6%, 1.9%, 4.5%, 4.6%, and 9.4% higher across HIV RNA categories, respectively, and statistically significant at the highest level (p = 0.0002 for HIV RNA ≥ 10,000 copies/ml). Higher HIV RNA was associated with mortality during follow-up in unadjusted analysis, but showed little association after adjustment for CD4+ cell count and inflammation.ConclusionHIV RNA ≥ 10,000 copies/ml was associated with higher IL-6 and fibrinogen, but lower levels of viremia appeared similar, and there was little association with CRP. The relationship of HIV RNA with IL-6 was strongly affected by CD4 cell depletion. After adjustment for CD4+ cell count and inflammation, viremia did not appear to be substantially associated with mortality risk over 5 years

Survival of gastrointestinal stromal tumor patients in the imatinib era: life raft group observational registry

<p>Abstract</p> <p>Background</p> <p>Gastrointestinal stromal tumors (GIST), one of the most common mesenchymal tumors of the gastrointestinal tract, prior to routine immunohistochemical staining and the introduction of tyrosine kinase inhibitors, were often mistaken for neoplasms of smooth muscle origin such as leiomyomas, leiomyosarcomas or leiomyoblastomas. Since the advent of imatinib, GIST has been further delineated into adult- (KIT or PDGFRα mutations) and pediatric- (typified by wild-type GIST/succinate dehydrogenase deficiencies) types. Using varying gender ratios at age of diagnosis we sought to elucidate prognostic factors for each sub-type and their impact on overall survival.</p> <p>Methods</p> <p>This is a long-term retrospective analysis of a large observational study of an international open cohort of patients from a GIST research and patient advocacy's lifetime registry. Demographic and disease-specific data were voluntarily supplied by its members from May 2000-October 2010; the primary outcome was overall survival. Associations between survival and prognostic factors were evaluated by univariate Cox proportional hazard analyses, with backward selection at <it>P </it>< 0.05 used to identify independent factors.</p> <p>Results</p> <p>Inflections in gender ratios by age at diagnosis in years delineated two distinct groups: above and below age 35 at diagnosis. Closer analysis confirmed the above 35 age group as previously reported for adult-type GIST, typified by mixed primary tumor sites and gender, KIT or PDGFRα mutations, and shorter survival times. The pediatric group (< age 18 at diagnosis) was also as previously reported with predominantly stomach tumors, females, wild-type GIST or SDH mutations, and extended survival. "Young adults" however formed a third group aged 18-35 at diagnosis, and were a clear mix of these two previously reported distinct sub-types.</p> <p>Conclusions</p> <p>Pediatric- and adult-type GIST have been previously characterized in clinical settings and these observations confirm significant prognostic factors for each from a diverse real-world cohort. Additionally, these findings suggest that extra diligence be taken with "young adults" (aged 18-35 at diagnosis) as pediatric-type GIST may present well beyond adolescence, particularly as these distinct sub-types have different causes, and consequently respond differently to treatments.</p

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

Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data

In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations \gdag = F( ag) where \gdag is an integrable, non-negative function. We assume that data are drawn from a Poisson process with density t\gdag where $t>0$ may be interpreted as an exposure time. Such problems occur in many photonic imaging applications including positron emission tomography, confocal fluorescence microscopy, astronomic observations, and phase retrieval problems in optics. Our approach uses a Kullback-Leibler-type data fidelity functional and allows for general convex penalty terms. We prove convergence rates of the expectation of the reconstruction error under a variational source condition as $t\to\infty$ both for an a priori and for a Lepski{\u\i}-type parameter choice rule

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of H\"older type