An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Plasma NGAL and glomerular filtration rate in cardiac transplant recipients treated with standard or reduced calcineurin inhibitor levels.

AIM Predictors of renal recovery following conversion from calcineurin inhibitor- to proliferation signal inhibitor-based therapy are lacking. We hypothesized that plasma NGAL (P-NGAL) could predict improvement in glomerular filtration rate (GFR) after conversion to everolimus. PATIENTS & METHODS P-NGAL was measured in 88 cardiac transplantation patients (median 5 years post-transplant) with renal dysfunction randomized to continuation of conventional calcineurin inhibitor-based immunosuppression or switching to an everolimus-based regimen. RESULTS P-NGAL correlated with measured GFR (mGFR) at baseline (R(2) = 0.21; p < 0.001). Randomization to everolimus improved mGFR after 1 year (median [25-75 % percentiles]: ΔmGFR 5.5 [-0.5-11.5] vs -1 [-7-4] ml/min/1.73 m(2); p = 0.006). Baseline P-NGAL predicted mGFR after 1 year (R(2) = 0.18; p < 0.001), but this association disappeared after controlling for baseline mGFR. CONCLUSION P-NGAL and GFR correlate with renal dysfunction in long-term heart transplantation recipients. P-NGAL did not predict improvement of renal function after conversion to everolimus-based immunosuppression.

Newton-Cartan supergravity with torsion and Schrödinger supergravity

We derive a torsionfull version of three-dimensional N=2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The “superconformal” theory that we start with is Schrödinger supergravity which we obtain by gauging the Schrödinger superalgebra. We present two non-relativistic N=2 matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call “old minimal” and “new minimal” Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.

The cystatin C/creatinine ratio, a marker of glomerular filtration quality: associated factors, reference intervals, and prediction of morbidity and mortality in healthy seniors.

The ratio of cystatin C (cysC) to creatinine (crea) is regarded as a marker of glomerular filtration quality associated with cardiovascular morbidities. We sought to determine reference intervals for serum cysC-crea ratio in seniors. Furthermore, we sought to determine whether other low-molecular weight molecules exhibit a similar behavior in individuals with altered glomerular filtration quality. Finally, we investigated associations with adverse outcomes. A total of 1382 subjectively healthy Swiss volunteers aged 60 years or older were enrolled in the study. Reference intervals were calculated according to Clinical & Laboratory Standards Institute (CLSI) guideline EP28-A3c. After a baseline exam, a 4-year follow-up survey recorded information about overall morbidity and mortality. The cysC-crea ratio (mean 0.0124 ± 0.0026 mg/μmol) was significantly higher in women and increased progressively with age. Other associated factors were hemoglobin A1c, mean arterial pressure, and C-reactive protein (P < 0.05 for all). Participants exhibiting shrunken pore syndrome had significantly higher ratios of 3.5-66.5 kDa molecules (brain natriuretic peptide, parathyroid hormone, β2-microglobulin, cystatin C, retinol-binding protein, thyroid-stimulating hormone, α1-acid glycoprotein, lipase, amylase, prealbumin, and albumin) and creatinine. There was no such difference in the ratios of very low-molecular weight molecules (urea, uric acid) to creatinine or in the ratios of molecules larger than 66.5 kDa (transferrin, haptoglobin) to creatinine. The cysC-crea ratio was significantly predictive of mortality and subjective overall morbidity at follow-up in logistic regression models adjusting for several factors. The cysC-crea ratio exhibits age- and sex-specific reference intervals in seniors. In conclusion, the cysC-crea ratio may indicate the relative retention of biologically active low-molecular weight compounds and can independently predict the risk for overall mortality and morbidity in the elderly.