Necessary conditions for variational regularization schemes

We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization method, we start with an investigation of the converse question: How could necessary conditions for a variational method to provide a regularization method look like? To this end, we formalize the notion of a variational scheme and start with comparison of three different instances of variational methods. Then we focus on the data space model and investigate the role and interplay of the topological structure, the convergence notion and the discrepancy functional. Especially, we deduce necessary conditions for the discrepancy functional to fulfill usual continuity assumptions. The results are applied to discrepancy functionals given by Bregman distances and especially to the Kullback-Leibler divergence.Comment: To appear in Inverse Problem

SHOX2 DNA Methylation is a Biomarker for the diagnosis of lung cancer based on bronchial aspirates

<p>Abstract</p> <p>Background</p> <p>This study aimed to show that SHOX2 DNA methylation is a tumor marker in patients with suspected lung cancer by using bronchial fluid aspirated during bronchoscopy. Such a biomarker would be clinically valuable, especially when, following the first bronchoscopy, a final diagnosis cannot be established by histology or cytology. A test with a low false positive rate can reduce the need for further invasive and costly procedures and ensure early treatment.</p> <p>Methods</p> <p>Marker discovery was carried out by differential methylation hybridization (DMH) and real-time PCR. The real-time PCR based HeavyMethyl technology was used for quantitative analysis of DNA methylation of SHOX2 using bronchial aspirates from two clinical centres in a case-control study. Fresh-frozen and Saccomanno-fixed samples were used to show the tumor marker performance in different sample types of clinical relevance.</p> <p>Results</p> <p>Valid measurements were obtained from a total of 523 patient samples (242 controls, 281 cases). DNA methylation of SHOX2 allowed to distinguish between malignant and benign lung disease, i.e. abscesses, infections, obstructive lung diseases, sarcoidosis, scleroderma, stenoses, at high specificity (68% sensitivity [95% CI 62-73%], 95% specificity [95% CI 91-97%]).</p> <p>Conclusions</p> <p>Hypermethylation of SHOX2 in bronchial aspirates appears to be a clinically useful tumor marker for identifying subjects with lung carcinoma, especially if histological and cytological findings after bronchoscopy are ambiguous.</p

Pelagic molybdenum concentration anomalies and the impact of sediment resuspension on the molybdenum budget in two tidal systems of the North Sea

The seasonal dynamics of molybdenum (Mo) were studied in the water column of two tidal basins of the German Wadden Sea (Sylt-Rømø and Spiekeroog) between 2007 and 2011. In contrast to its conservative behaviour in the open ocean, both, losses of more than 50% of the usual concentration level of Mo in seawater and enrichments up to 20% were observed repeatedly in the water column of the study areas. During early summer, Mo removal by adsorption on algae-derived organic matter (e.g. after Phaeocystis blooms) is postulated to be a possible mechanism. Mo bound to organic aggregates is likely transferred to the surface sediment where microbial decomposition enriches Mo in the pore water. First δ98/95Mo data of the study area disclose residual Mo in the open water column being isotopically heavier than MOMo (Mean Ocean Molybdenum) during a negative Mo concentration anomaly, whereas suspended particulate matter shows distinctly lighter values. Based on field observations a Mo isotope enrichment factor of ε = −0.3‰ has been determined which was used to argue against sorption on metal oxide surfaces. It is suggested here that isotope fractionation is caused by biological activity and association to organic matter. Pelagic Mo concentration anomalies exceeding the theoretical salinity-based concentration level, on the other hand, cannot be explained by replenishment via North Sea waters alone and require a supply of excess Mo. Laboratory experiments with natural anoxic tidal flat sediments and modelled sediment displacement during storm events suggest fast and effective Mo release during the resuspension of anoxic sediments in oxic seawater as an important process for a recycling of sedimentary sulphide bound Mo into the water column