ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Inducing mineral precipitation in groundwater by addition of phosphate

<p>Abstract</p> <p>Background</p> <p>Induced precipitation of phosphate minerals to scavenge trace elements from groundwater is a potential remediation approach for contaminated aquifers. The success of engineered precipitation schemes depends on the particular phases generated, their rates of formation, and their long term stability. The purpose of this study was to examine the precipitation of calcium phosphate minerals under conditions representative of a natural groundwater. Because microorganisms are present in groundwater, and because some proposed schemes for phosphate mineral precipitation rely on stimulation of native microbial populations, we also tested the effect of bacterial cells (initial densities of 10⁵and 10⁷mL^-1) added to the precipitation medium. In addition, we tested the effect of a trace mixture of propionic, isovaleric, formic and butyric acids (total concentration 0.035 mM).</p> <p>Results</p> <p>The general progression of mineral precipitation was similar under all of the study conditions, with initial formation of amorphous calcium phosphate, and transformation to poorly crystalline hydroxylapatite (HAP) within one week. The presence of the bacterial cells appeared to delay precipitation, although by the end of the experiments the overall extent of precipitation was similar for all treatments. The stoichiometry of the final precipitates as well as Rietveld structure refinement using x-ray diffraction data indicated that the presence of organic acids and bacterial cells resulted in an increasing <it>a </it>and decreasing <it>c </it>lattice parameter, with the higher concentration of cells resulting in the greatest distortion. Uptake of Sr into the solids was decreased in the treatments with cells and organic acids, compared to the control.</p> <p>Conclusions</p> <p>Our results suggest that the minerals formed initially during an engineered precipitation application for trace element sequestration may not be the ones that control long-term immobilization of the contaminants. In addition, the presence of bacterial cells appears to be associated with delayed HAP precipitation, changes in the lattice parameters, and reduced incorporation of trace elements as compared to cell-free systems. Schemes to remediate groundwater contaminated with trace metals that are based on enhanced phosphate mineral precipitation may need to account for these phenomena, particularly if the remediation approach relies on enhancement of <it>in situ </it>microbial populations.</p

Variation in MSRA Modifies Risk of Neonatal Intestinal Obstruction in Cystic Fibrosis

Meconium ileus (MI), a life-threatening intestinal obstruction due to meconium with abnormal protein content, occurs in approximately 15 percent of neonates with cystic fibrosis (CF). Analysis of twins with CF demonstrates that MI is a highly heritable trait, indicating that genetic modifiers are largely responsible for this complication. Here, we performed regional family-based association analysis of a locus that had previously been linked to MI and found that SNP haplotypes 5′ to and within the MSRA gene were associated with MI (P = 1.99×10−5 to 1.08×10−6; Bonferroni P = 0.057 to 3.1×10−3). The haplotype with the lowest P value showed association with MI in an independent sample of 1,335 unrelated CF patients (OR = 0.72, 95% CI [0.53–0.98], P = 0.04). Intestinal obstruction at the time of weaning was decreased in CF mice with Msra null alleles compared to those with wild-type Msra resulting in significant improvement in survival (P = 1.2×10−4). Similar levels of goblet cell hyperplasia were observed in the ilea of the Cftr−/− and Cftr−/−Msra−/− mice. Modulation of MSRA, an antioxidant shown to preserve the activity of enzymes, may influence proteolysis in the developing intestine of the CF fetus, thereby altering the incidence of obstruction in the newborn period. Identification of MSRA as a modifier of MI provides new insight into the biologic mechanism of neonatal intestinal obstruction caused by loss of CFTR function

Systematic interpretation of pH-degradation profiles. A critical review

Abstract In this study we discuss the application of the general models for pH degradation profiles for specific acid, solvent and base catalysis, both in the absence and presence of ligands, and for the general acid and base catalysis, that we have published recently, we also present a systematic step by step procedure for the interpretation of pH profiles, which we apply to a number of recent publications. To facilitate the comparison of the mathematical treatment of the data the model equations reported in these studies have been transformed analogous to our equations. Many of these studies raise minor to serious objections. These objectives vary from unjustified conclusions regarding the content of specific reactions to the degradation, mathematical errors in the model equations, unjustified neglect of pK a values close to or within the pH range investigated, unjustified linearization of non linear relationships to the application of model equations with non integer exponents without any theoretical foundation. Application of our model equations explains discrepancies in some of the original publications and offers acceptable alternatives to some rather stretched hypotheses. © 1997 Elsevier Science B.V