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

Lions-type compactness and Rubik actions on the Heisenberg group

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group TeX is provided by the unitary group U(n) × {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein’s horizontal Sobolev space TeX. As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Ground reaction force profiles after partial and pancarpal arthrodesis in dogs

OBJECTIVES: To evaluate and compare long-term functional outcome after partial carpal arthrodesis and pancarpal arthrodesis in dogs using kinetic gait analysis. METHODS: Fourteen dogs with 19 partial carpal or pancarpal arthrodeses were retrospectively examined and underwent force-plate gait analysis. Mean times since surgery were 29.4 and 24.4 months for pancarpal and partial carpal arthrodesis respectively. Vertical and braking-propulsive ground reaction force profiles were compared between treatment groups, and to those of normal dogs (control group) using Kruskal-Wallis one-way analysis of variance. RESULTS: With the exception of time to vertical peak that occurred earlier in dogs with pancarpal than in dogs with partial carpal arthrodesis (p <0.01), there was no difference between the two treatment groups. Several parameters differed significantly between operated and healthy dogs (p <0.01): vertical impulses were significantly lower in both treatment groups, braking forces and impulses were also reduced after both techniques. Propulsive forces and impulses were only reduced in dogs with pancarpal arthrodesis. When comparing gait parameters of sound limbs of unilateral operated dogs to those of control dogs, braking forces and impulses (p <0.01; p <0.05) were significantly higher in the sound legs of unilateral operated dogs. CLINICAL SIGNIFICANCE: Long-term outcome after partial carpal and pancarpal arthrodesis is good and comparable to each other. Propulsive action may be altered more in dogs with pancarpal arthrodesis.

A comparison of estimated glomerular filtration rates using Cockcroft−Gault and the Chronic Kidney Disease Epidemiology Collaboration estimating equations in HIV infection

OBJECTIVES: The aim of this study was to determine whether the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI)- or Cockcroft-Gault (CG)-based estimated glomerular filtration rates (eGFRs) performs better in the cohort setting for predicting moderate/advanced chronic kidney disease (CKD) or end-stage renal disease (ESRD). METHODS: A total of 9521 persons in the EuroSIDA study contributed 133 873 eGFRs. Poisson regression was used to model the incidence of moderate and advanced CKD (confirmed eGFR < 60 and < 30 mL/min/1.73 m(2) , respectively) or ESRD (fatal/nonfatal) using CG and CKD-EPI eGFRs. RESULTS: Of 133 873 eGFR values, the ratio of CG to CKD-EPI was ≥ 1.1 in 22 092 (16.5%) and the difference between them (CG minus CKD-EPI) was ≥ 10 mL/min/1.73 m(2) in 20 867 (15.6%). Differences between CKD-EPI and CG were much greater when CG was not standardized for body surface area (BSA). A total of 403 persons developed moderate CKD using CG [incidence 8.9/1000 person-years of follow-up (PYFU); 95% confidence interval (CI) 8.0-9.8] and 364 using CKD-EPI (incidence 7.3/1000 PYFU; 95% CI 6.5-8.0). CG-derived eGFRs were equal to CKD-EPI-derived eGFRs at predicting ESRD (n = 36) and death (n = 565), as measured by the Akaike information criterion. CG-based moderate and advanced CKDs were associated with ESRD [adjusted incidence rate ratio (aIRR) 7.17; 95% CI 2.65-19.36 and aIRR 23.46; 95% CI 8.54-64.48, respectively], as were CKD-EPI-based moderate and advanced CKDs (aIRR 12.41; 95% CI 4.74-32.51 and aIRR 12.44; 95% CI 4.83-32.03, respectively). CONCLUSIONS: Differences between eGFRs using CG adjusted for BSA or CKD-EPI were modest. In the absence of a gold standard, the two formulae predicted clinical outcomes with equal precision and can be used to estimate GFR in HIV-positive persons.

Comparison of partial least squares regression and principal component regression for pelvic shape prediction.

This paper studied two different regression techniques for pelvic shape prediction, i.e., the partial least square regression (PLSR) and the principal component regression (PCR). Three different predictors such as surface landmarks, morphological parameters, or surface models of neighboring structures were used in a cross-validation study to predict the pelvic shape. Results obtained from applying these two different regression techniques were compared to the population mean model. In almost all the prediction experiments, both regression techniques unanimously generated better results than the population mean model, while the difference on prediction accuracy between these two regression methods is not statistically significant (α=0.01).

Apoptosis of ligamentous cells of the cranial cruciate ligament from stable stifle joints of dogs with partial cranial cruciate ligament rupture

OBJECTIVE To describe the presence and amount of apoptotic ligamentous cells in different areas of partially ruptured canine cranial cruciate ligaments (prCCLs) and to compare these findings with apoptosis of ligamentous cells in totally ruptured cranial cruciate ligaments (trCCLs). ANIMALS 20 dogs with prCCLs and 14 dogs with trCCLs. PROCEDURES Dogs with prCCLs or trCCLs were admitted to the veterinary hospital for stifle joint treatment. Biopsy specimens of the intact area of prCCLs (group A) and the ruptured area of prCCLs (group B) as well as specimens from trCCLs (group C) were harvested during arthroscopy. Caspase-3 and poly (ADP-ribose) polymerase (PARP) detection were used to detect apoptotic ligamentous cells by immunohistochemistry. RESULTS No difference was found in the degree of synovitis or osteophytosis between prCCLs and trCCLs. No difference was found in degenerative changes in ligaments between groups A and B. A substantial amount of apoptotic cells could be found in > 90% of all stained slides. A correlation (r(s) = 0.71) was found between the number of caspase-3-and PARP-positive cells. No significant difference was found in the amount of apoptotic cells among the 3 groups. No significant correlation could be detected between the degree of synovitis and apoptotic cells or osteophyte production and apoptotic cells. CONCLUSIONS AND CLINICAL RELEVANCE The lack of difference between the 3 groups indicates that apoptosis could be a factor in the internal disease process leading to CCL rupture and is not primarily a consequence of the acute rupture of the ligament.

Roy-Steiner equations for piN scattering

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.

5-year results of accelerated partial breast irradiation using sole interstitial multicatheter brachytherapy versus whole-breast irradiation with boost after breast-conserving surgery for low-risk invasive and in-situ carcinoma of the female breast: a randomised, phase 3, non-inferiority trial.

BACKGROUND In a phase 3, randomised, non-inferiority trial, accelerated partial breast irradiation (APBI) for patients with stage 0, I, and IIA breast cancer who underwent breast-conserving treatment was compared with whole-breast irradiation. Here, we present 5-year follow-up results. METHODS We did a phase 3, randomised, non-inferiority trial at 16 hospitals and medical centres in seven European countries. 1184 patients with low-risk invasive and ductal carcinoma in situ treated with breast-conserving surgery were centrally randomised to either whole-breast irradiation or APBI using multicatheter brachytherapy. The primary endpoint was local recurrence. Analysis was done according to treatment received. This trial is registered with ClinicalTrials.gov, number NCT00402519. FINDINGS Between April 20, 2004, and July 30, 2009, 551 patients had whole-breast irradiation with tumour-bed boost and 633 patients received APBI using interstitial multicatheter brachytherapy. At 5-year follow-up, nine patients treated with APBI and five patients receiving whole-breast irradiation had a local recurrence; the cumulative incidence of local recurrence was 1·44% (95% CI 0·51-2·38) with APBI and 0·92% (0·12-1·73) with whole-breast irradiation (difference 0·52%, 95% CI -0·72 to 1·75; p=0·42). No grade 4 late side-effects were reported. The 5-year risk of grade 2-3 late side-effects to the skin was 3·2% with APBI versus 5·7% with whole-breast irradiation (p=0·08), and 5-year risk of grade 2-3 subcutaneous tissue late side-effects was 7·6% versus 6·3% (p=0·53). The risk of severe (grade 3) fibrosis at 5 years was 0·2% with whole-breast irradiation and 0% with APBI (p=0·46). INTERPRETATION The difference between treatments was below the relevance margin of 3 percentage points. Therefore, adjuvant APBI using multicatheter brachytherapy after breast-conserving surgery in patients with early breast cancer is not inferior to adjuvant whole-breast irradiation with respect to 5-year local control, disease-free survival, and overall survival. FUNDING German Cancer Aid.

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.