A spectral method for elliptic equations: the Dirichlet problem

An elliptic partial differential equation Lu=f with a zero Dirichlet boundary condition is converted to an equivalent elliptic equation on the unit ball. A spectral Galerkin method is applied to the reformulated problem, using multivariate polynomials as the approximants. For a smooth boundary and smooth problem parameter functions, the method is proven to converge faster than any power of 1/n with n the degree of the approximate Galerkin solution. Examples in two and three variables are given as numerical illustrations. Empirically, the condition number of the associated linear system increases like O(N), with N the order of the linear system.Comment: This is latex with the standard article style, produced using Scientific Workplace in a portable format. The paper is 22 pages in length with 8 figure

Realism, Objectivity, and Evaluation

I discuss Benacerraf's epistemological challenge for realism about areas like mathematics, metalogic, and modality, and describe the pluralist response to it. I explain why normative pluralism is peculiarly unsatisfactory, and use this explanation to formulate a radicalization of Moore's Open Question Argument. According to the argument, the facts -- even the normative facts -- fail to settle the practical questions at the center of our normative lives. One lesson is that the concepts of realism and objectivity, which are widely identified, are actually in tension

A simple cobalt-based catalyst system for the controlled dehydropolymerisation of H3B·NMeH2 on the gram-scale

A simple Co(ii)-based amine-borane dehydropolymerisation catalyst system is reported that operates at low loadings, to selectively give (H2BNMeH)n polymer on scale, with catalyst control over Mn, narrow dispersities and low residual metal content

Computation of Asymptotic Expansions of Turning Point Problems via Cauchy's Integral Formula: Bessel Functions

Linear second-order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two infinite series, the coefficients of which are usually difficult to compute. By considering the series as asymptotic expansions for two explicitly defined analytic functions, Cauchy's integral formula is employed to compute the coefficient functions to a high order of accuracy. The method employs a certain exponential form of Liouville´Green expansions for solutions of the differential equation, as well as for the Airy function. We illustrate the use of the method with the high accuracy computation of Airy-type expansions of Bessel functions of complex argument.The authors acknowledge support from Ministerio de Economía y Competitividad, project MTM2015-67142-P (MINECO/FEDER, UE). A.G. and J.S. acknowledge support from Ministerio de Economía y Competitividad, project MTM2012-34787. A.G. acknowledges the Fulbright/MEC Program for support during her stay at SDSU. J.S. acknowledges the Salvador de Madariaga Program for support during his stay at SDSU

The incidence of myocardial injury following post-operative Goal Directed Therapy.

BACKGROUND: Studies suggest that Goal Directed Therapy (GDT) results in improved outcome following major surgery. However, there is concern that pre-emptive use of inotropic therapy may lead to an increased incidence of myocardial ischaemia and infarction. METHODS: Post hoc analysis of data collected prospectively during a randomised controlled trial of the effects of post-operative GDT in high-risk general surgical patients. Serum troponin T concentrations were measured at baseline and on day 1 and day 2 following surgery. Continuous ECG monitoring was performed during the eight hour intervention period. Patients were followed up for predefined cardiac complications. A univariate analysis was performed to identify any associations between potential risk factors for myocardial injury and elevated troponin T concentrations. RESULTS: GDT was associated with fewer complications, and a reduced duration of hospital stay. Troponin T concentrations above 0.01 microg l-1 were identified in eight patients in the GDT group and six in the control group. Values increased above 0.05 microg l-1 in four patients in the GDT group and two patients in the control group. There were no overall differences in the incidence of elevated troponin T concentrations. The incidence of cardiovascular complications was also similar. None of the patients, in whom troponin T concentrations were elevated, developed ECG changes indicating myocardial ischaemia during the intervention period. The only factor to be associated with elevated troponin T concentrations following surgery was end-stage renal failure. CONCLUSION: The use of post-operative GDT does not result in an increased incidence of myocardial injury

Background risk of breast cancer and the association between physical activity and mammographic density

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Are genetic risk factors for psychosis also associated with dimension-specific psychotic experiences in adolescence?

Psychosis has been hypothesised to be a continuously distributed quantitative phenotype and disorders such as schizophrenia and bipolar disorder represent its extreme manifestations. Evidence suggests that common genetic variants play an important role in liability to both schizophrenia and bipolar disorder. Here we tested the hypothesis that these common variants would also influence psychotic experiences measured dimensionally in adolescents in the general population. Our aim was to test whether schizophrenia and bipolar disorder polygenic risk scores (PRS), as well as specific single nucleotide polymorphisms (SNPs) previously identified as risk variants for schizophrenia, were associated with adolescent dimension-specific psychotic experiences. Self-reported Paranoia, Hallucinations, Cognitive Disorganisation, Grandiosity, Anhedonia, and Parent-rated Negative Symptoms, as measured by the Specific Psychotic Experiences Questionnaire (SPEQ), were assessed in a community sample of 2,152 16-year-olds. Polygenic risk scores were calculated using estimates of the log of odds ratios from the Psychiatric Genomics Consortium GWAS stage-1 mega-analysis of schizophrenia and bipolar disorder. The polygenic risk analyses yielded no significant associations between schizophrenia and bipolar disorder PRS and the SPEQ measures. The analyses on the 28 individual SNPs previously associated with schizophrenia found that two SNPs in TCF4 returned a significant association with the SPEQ Paranoia dimension, rs17512836 (p-value=2.57x10-4) and rs9960767 (p-value=6.23x10-4). Replication in an independent sample of 16-year-olds (N=3,427) assessed using the Psychotic-Like Symptoms Questionnaire (PLIKS-Q), a composite measure of multiple positive psychotic experiences, failed to yield significant results. Future research with PRS derived from larger samples, as well as larger adolescent validation samples, would improve the predictive power to test these hypotheses further. The challenges of relating adult clinical diagnostic constructs such as schizophrenia to adolescent psychotic experiences at a genetic level are discussed

Breast cancer risk factors and a novel measure of volumetric breast density: cross-sectional study

We conducted a cross-sectional study nested within a prospective cohort of breast cancer risk factors and two novel measures of breast density volume among 590 women who had attended Glasgow University (1948–1968), replied to a postal questionnaire (2001) and attended breast screening in Scotland (1989–2002). Volumetric breast density was estimated using a fully automated computer programme applied to digitised film-screen mammograms, from medio-lateral oblique mammograms at the first-screening visit. This measured the proportion of the breast volume composed of dense (non-fatty) tissue (Standard Mammogram Form (SMF)%) and the absolute volume of this tissue (SMF volume, cm3). Median age at first screening was 54.1 years (range: 40.0–71.5), median SMF volume 70.25 cm3 (interquartile range: 51.0–103.0) and mean SMF% 26.3%, s.d.=8.0% (range: 12.7–58.8%). Age-adjusted logistic regression models showed a positive relationship between age at last menstrual period and SMF%, odds ratio (OR) per year later: 1.05 (95% confidence interval: 1.01–1.08, P=0.004). Number of pregnancies was inversely related to SMF volume, OR per extra pregnancy: 0.78 (0.70–0.86, P<0.001). There was a suggestion of a quadratic relationship between birthweight and SMF%, with lowest risks in women born under 2.5 and over 4 kg. Body mass index (BMI) at university (median age 19) and in 2001 (median age 62) were positively related to SMF volume, OR per extra kg m−2 1.21 (1.15–1.28) and 1.17 (1.09–1.26), respectively, and inversely related to SMF%, OR per extra kg m−2 0.83 (0.79–0.88) and 0.82 (0.76–0.88), respectively, P<0.001. Standard Mammogram Form% and absolute SMF volume are related to several, but not all, breast cancer risk factors. In particular, the positive relationship between BMI and SMF volume suggests that volume of dense breast tissue will be a useful marker in breast cancer studies

Grifonin-1: A Small HIV-1 Entry Inhibitor Derived from the Algal Lectin, Griffithsin

Background: Griffithsin, a 121-residue protein isolated from a red algal Griffithsia sp., binds high mannose N-linked glycans of virus surface glycoproteins with extremely high affinity, a property that allows it to prevent the entry of primary isolates and laboratory strains of T- and M-tropic HIV-1. We used the sequence of a portion of griffithsin's sequence as a design template to create smaller peptides with antiviral and carbohydrate-binding properties. Methodology/Results: The new peptides derived from a trio of homologous β-sheet repeats that comprise the motifs responsible for its biological activity. Our most active antiviral peptide, grifonin-1 (GRFN-1), had an EC50 of 190.8±11.0 nM in in vitro TZM-bl assays and an EC50 of 546.6±66.1 nM in p24gag antigen release assays. GRFN-1 showed considerable structural plasticity, assuming different conformations in solvents that differed in polarity and hydrophobicity. Higher concentrations of GRFN-1 formed oligomers, based on intermolecular β-sheet interactions. Like its parent protein, GRFN-1 bound viral glycoproteins gp41 and gp120 via the N-linked glycans on their surface. Conclusion: Its substantial antiviral activity and low toxicity in vitro suggest that GRFN-1 and/or its derivatives may have therapeutic potential as topical and/or systemic agents directed against HIV-1