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

Influence of Partial Lateral Corpectomy with and without Hemilaminectomy on Canine Thoracolumbar Stability: A Biomechanical Study

OBJECTIVE: To analyze the biomechanical changes induced by partial lateral corpectomy (PLC) and a combination of PLC and hemilaminectomy in a T13-L3 spinal segment in nonchondrodystrophic dogs. STUDY DESIGN: In vitro biomechanical cadaveric study. SAMPLE POPULATION: T13-L3 spinal segments (n = 10) of nonchondrodystrophic dogs (weighing, 25-38 kg). METHODS: A computed tomography (CT) scan of each T13-L3 spinal segment was performed. A loading simulator for flexibility analysis was used to determine the range of motion (ROM) and neutral zone (NZ) during flexion/extension, lateral bending, and axial rotation. A servohydraulic testing machine was used to determine the changes in stiffness during compression, dorsoventral, and lateral shear. All spines were tested intact, after PLC in the left intervertebral space of L1-L2, and after a combination of PLC and hemilaminectomy. RESULTS: Statistically significant increases in ROM and NZ (P < .05) were detected during flexion/extension and lateral bending when PLC was performed. A significant increase in ROM (P < .001) was noted during axial rotation and flexion after PLC and hemilaminectomy. Stiffness decreased significantly during compression and dorsoventral shear after each procedure. Decreased stiffness during lateral shear was only significant after a combination of both procedures. CONCLUSION: PLC might lead to some spinal instability; these changes are enhanced when a hemilaminectomy is added.

Intraperitoneal and intra-nasal vaccination of mice with three distinct recombinant Neospora caninum antigens results in differential effects with regard to protection against experimental challenge with Neospora caninum tachyzoites

Recombinant NcPDI(recNcPDI), NcROP2(recNcROP2), and NcMAG1(recNcMAG1) were expressed in Escherichia coli and purified, and evaluated as potential vaccine candidates by employing the C57Bl/6 mouse cerebral infection model. Intraperitoneal application of these proteins suspended in saponin adjuvants lead to protection against disease in 50% and 70% of mice vaccinated with recNcMAG1 and recNcROP2, respectively, while only 20% of mice vaccinated with recNcPDI remained without clinical signs. In contrast, a 90% protection rate was achieved following intra-nasal vaccination with recNcPDI emulsified in cholera toxin. Only 1 mouse vaccinated intra-nasally with recNcMAG1 survived the challenge infection, and protection achieved with intra-nasally applied recNcROP2 was at 60%. Determination of cerebral parasite burdens by real-time PCR showed that these were significantly reduced only in recNcROP2-vaccinated animals (following intraperitoneal and intra-nasal application) and in recNcPDI-vaccinated mice (intra-nasal application only). Quantification of viable tachyzoites in brain tissue of intra-nasally vaccinated mice showed that immunization with recNcPDI resulted in significantly decreased numbers of live parasites. These data show that, besides the nature of the antigen, the protective effect of vaccination also depends largely on the route of antigen delivery. In the case of recNcPDI, the intra-nasal route provides a platform to generate a highly protective immune response.

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.

Accelerated partial breast irradiation with interstitial brachytherapy as second conservative treatment for ipsilateral breast tumour recurrence: multicentric study of the GEC-ESTRO Breast Cancer Working Group

PURPOSE To analyse the clinical outcome after salvage lumpectomy and multi-catheter brachytherapy (MCB) for ipsilateral breast tumour recurrence (IBTR). MATERIAL AND METHODS Between 09/00 and 09/10, 217 patients presenting an IBTR underwent lumpectomy and MCB (low, pulsed, or high-dose rate). Survival rates without second local recurrence (2nd LR), distant metastasis (DM), and overall survival (OS) were analysed as well as late effects and cosmetic results. Univariate and multivariate analyses (MVA) based on IBTR data were performed to find prognostic factors for 2nd LR, DM, and OS. RESULTS Median follow-up after the IBTR was 3.9 years [range: 1.1-10.3]. Five and 10-year actuarial 2nd LR rates were 5.6% [range: 1.5-9.5] and 7.2% [range: 2.1-12.1], respectively. Five and 10-year actuarial DM rates were 9.6% [range: 5.7-15.2] and 19.1% [range: 7.8-28.3], respectively. Five and 10-year actuarial OS rates were 88.7% [range: 83.1-94.8] and 76.4% [range: 66.9-87.3], respectively. In MVA, histological grade was prognostic factor for 2nd LR (p=0.008) and OS (p=0.02); while tumour size was prognostic factor for DM (p=0.03). G3-4 complication rate was 11%. Excellent/good cosmetic result was achieved in 85%. CONCLUSION This study suggests that in case of IBTR, lumpectomy plus MCB is feasible and effective in preventing 2nd LR with an OS rate at least equivalent to those achieved with salvage mastectomy.

Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

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.

Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study

Background New HIV infections in men who have sex with men (MSM) have increased in Switzerland since 2000 despite combination antiretroviral therapy (cART). The objectives of this mathematical modelling study were: to describe the dynamics of the HIV epidemic in MSM in Switzerland using national data; to explore the effects of hypothetical prevention scenarios; and to conduct a multivariate sensitivity analysis. Methodology/Principal Findings The model describes HIV transmission, progression and the effects of cART using differential equations. The model was fitted to Swiss HIV and AIDS surveillance data and twelve unknown parameters were estimated. Predicted numbers of diagnosed HIV infections and AIDS cases fitted the observed data well. By the end of 2010, an estimated 13.5% (95% CI 12.5, 14.6%) of all HIV-infected MSM were undiagnosed and accounted for 81.8% (95% CI 81.1, 82.4%) of new HIV infections. The transmission rate was at its lowest from 1995–1999, with a nadir of 46 incident HIV infections in 1999, but increased from 2000. The estimated number of new infections continued to increase to more than 250 in 2010, although the reproduction number was still below the epidemic threshold. Prevention scenarios included temporary reductions in risk behaviour, annual test and treat, and reduction in risk behaviour to levels observed earlier in the epidemic. These led to predicted reductions in new infections from 2 to 26% by 2020. Parameters related to disease progression and relative infectiousness at different HIV stages had the greatest influence on estimates of the net transmission rate. Conclusions/Significance The model outputs suggest that the increase in HIV transmission amongst MSM in Switzerland is the result of continuing risky sexual behaviour, particularly by those unaware of their infection status. Long term reductions in the incidence of HIV infection in MSM in Switzerland will require increased and sustained uptake of effective interventions.

Population pharmacokinetics of sevoflurane in conjunction with the AnaConDa: toward target-controlled infusion of volatiles into the breathing system

BACKGROUND: The Anesthetic Conserving Device (AnaConDa) uncouples delivery of a volatile anesthetic (VA) from fresh gas flow (FGF) using a continuous infusion of liquid volatile into a modified heat-moisture exchanger capable of adsorbing VA during expiration and releasing adsorbed VA during inspiration. It combines the simplicity and responsiveness of high FGF with low agent expenditures. We performed in vitro characterization of the device before developing a population pharmacokinetic model for sevoflurane administration with the AnaConDa, and retrospectively testing its performance (internal validation). MATERIALS AND METHODS: Eighteen females and 20 males, aged 31-87, BMI 20-38, were included. The end-tidal concentrations were varied and recorded together with the VA infusion rates into the device, ventilation and demographic data. The concentration-time course of sevoflurane was described using linear differential equations, and the most suitable structural model and typical parameter values were identified. The individual pharmacokinetic parameters were obtained and tested for covariate relationships. Prediction errors were calculated. RESULTS: In vitro studies assessed the contribution of the device to the pharmacokinetic model. In vivo, the sevoflurane concentration-time courses on the patient side of the AnaConDa were adequately described with a two-compartment model. The population median absolute prediction error was 27% (interquartile range 13-45%). CONCLUSION: The predictive performance of the two-compartment model was similar to that of models accepted for TCI administration of intravenous anesthetics, supporting open-loop administration of sevoflurane with the AnaConDa. Further studies will focus on prospective testing and external validation of the model implemented in a target-controlled infusion device.