Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

A boundary value problem approach to too-short arc optical track association

Given a short-arc optical observation with estimated angle-rates, the admissible region is a compact region in the range / range-rate space defined such that all likely and relevant orbits are contained within it. An alternative boundary value problem formulation has recently been proposed where range / range hypotheses are generated with two angle measurements from two tracks as input. In this paper, angle-rate information is reintroduced as a means to eliminate hypotheses by bounding their constants of motion before a more computationally costly Lambert solver or differential correction algorithm is run.

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.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

Therapeutic drug monitoring of once daily aminoglycoside dosing: comparison of two methods and investigation of the optimal blood sampling strategy.

PURPOSE Therapeutic drug monitoring of patients receiving once daily aminoglycoside therapy can be performed using pharmacokinetic (PK) formulas or Bayesian calculations. While these methods produced comparable results, their performance has never been checked against full PK profiles. We performed a PK study in order to compare both methods and to determine the best time-points to estimate AUC0-24 and peak concentrations (C max). METHODS We obtained full PK profiles in 14 patients receiving a once daily aminoglycoside therapy. PK parameters were calculated with PKSolver using non-compartmental methods. The calculated PK parameters were then compared with parameters estimated using an algorithm based on two serum concentrations (two-point method) or the software TCIWorks (Bayesian method). RESULTS For tobramycin and gentamicin, AUC0-24 and C max could be reliably estimated using a first serum concentration obtained at 1 h and a second one between 8 and 10 h after start of the infusion. The two-point and the Bayesian method produced similar results. For amikacin, AUC0-24 could reliably be estimated by both methods. C max was underestimated by 10-20% by the two-point method and by up to 30% with a large variation by the Bayesian method. CONCLUSIONS The ideal time-points for therapeutic drug monitoring of once daily administered aminoglycosides are 1 h after start of a 30-min infusion for the first time-point and 8-10 h after start of the infusion for the second time-point. Duration of the infusion and accurate registration of the time-points of blood drawing are essential for obtaining precise predictions.

Short-arc tracklet association for geostationary objects

Measurement association and initial orbit determination is a fundamental task when building up a database of space objects. This paper proposes an efficient and robust method to determine the orbit using the available information of two tracklets, i.e. their line-of-sights and their derivatives. The approach works with a boundary-value formulation to represent hypothesized orbital states and uses an optimization scheme to find the best fitting orbits. The method is assessed and compared to an initial-value formulation using a measurement set taken by the Zimmerwald Small Aperture Robotic Telescope of the Astronomical Institute at the University of Bern. False associations of closely spaced objects on similar orbits cannot be completely eliminated due to the short duration of the measurement arcs. However, the presented approach uses the available information optimally and the overall association performance and robustness is very promising. The boundary-value optimization takes only around 2% of computational time when compared to optimization approaches using an initial-value formulation. The full potential of the method in terms of run-time is additionally illustrated by comparing it to other published association methods.

Influence of previous surgery on patient-rated outcome after surgery for degenerative disorders of the lumbar spine.

PURPOSE Few studies have used multivariate models to quantify the effect of multiple previous spine surgeries on patient-oriented outcome after spine surgery. This study sought to quantify the effect of prior spine surgery on 12-month postoperative outcomes in patients undergoing surgery for different degenerative disorders of the lumbar spine. METHODS The study included 4940 patients with lumbar degenerative disease documented in the Spine Tango Registry of EUROSPINE, the Spine Society of Europe, from 2004 to 2015. Preoperatively and 12 months postoperatively, patients completed the multidimensional Core Outcome Measures Index (COMI; 0-10 scale). Patients' medical history and surgical details were recorded using the Spine Tango Surgery 2006 and 2011 forms. Multiple linear regression models were used to investigate the relationship between the number of previous surgeries and the 12-month postoperative COMI score, controlling for the baseline COMI score and other potential confounders. RESULTS In the adjusted model including all cases, the 12-month COMI score showed a 0.37-point worse value [95 % confidence intervals (95 % CI) 0.29-0.45; p < 0.001] for each additional prior spine surgery. In the subgroup of patients with lumbar disc herniation, the corresponding effect was 0.52 points (95 % CI 0.27-0.77; p < 0.001) and in lumbar degenerative spondylolisthesis, 0.40 points (95 % CI 0.17-0.64; p = 0.001). CONCLUSIONS We were able to demonstrate a clear "dose-response" effect for previous surgery: the greater the number of prior spine surgeries, the systematically worse the outcome at 12 months' follow-up. The results of this study can be used when considering or consenting a patient for further surgery, to better inform the patient of the likely outcome and to set realistic expectations.

The vacuolar-ATPase B1 subunit in distal tubular acidosis: novel mutations and mechanisms for dysfunction

Mutations in the B1 subunit of the multisubunit vacuolar ATPase cause autosomal-recessive distal renal tubular acidosis and sensorineural deafness. Here, we report a novel frameshift mutation that truncates the C-terminus of the human B1 subunit. This mutant protein failed to assemble with other subunits in the cytosol to form the complex that can be targeted to vesicular structures in mammalian cells. Loss of proton pump activity was demonstrated in a functional complementation assay in B-subunit null yeast. The mutation caused loss of a discreet C-terminal region critical for subunit interaction not related to the C-terminal PDZ motif. Co-expression studies failed to demonstrate dominant negative effects of this truncated mutant over wild-type B1. Analysis of 12 reported B1 subunit missense mutations showed one polymorphic allele had intact pump function, two point mutants had intact assembly but defective proton pumping, and the remaining nine had disrupted assembly with no pump function. One presumed polymorphic allele was actually an inactivating mutation. Our study shows that multiple mechanisms of pump dysfunction result from B1 subunit mutations with a common outcome being defective assembly. Polymorphisms of the B1 subunit in the general population may affect renal acidification and urinary chemistry.

Embedding of human vertebral bodies leads to higher ultimate load and altered damage localisation under axial compression

Computer tomography (CT)-based finite element (FE) models of vertebral bodies assess fracture load in vitro better than dual energy X-ray absorptiometry, but boundary conditions affect stress distribution under the endplates that may influence ultimate load and damage localisation under post-yield strains. Therefore, HRpQCT-based homogenised FE models of 12 vertebral bodies were subjected to axial compression with two distinct boundary conditions: embedding in polymethylmethalcrylate (PMMA) and bonding to a healthy intervertebral disc (IVD) with distinct hyperelastic properties for nucleus and annulus. Bone volume fraction and fabric assessed from HRpQCT data were used to determine the elastic, plastic and damage behaviour of bone. Ultimate forces obtained with PMMA were 22% higher than with IVD but correlated highly (R2 = 0.99). At ultimate force, distinct fractions of damage were computed in the endplates (PMMA: 6%, IVD: 70%), cortex and trabecular sub-regions, which confirms previous observations that in contrast to PMMA embedding, failure initiated underneath the nuclei in healthy IVDs. In conclusion, axial loading of vertebral bodies via PMMA embedding versus healthy IVD overestimates ultimate load and leads to distinct damage localisation and failure pattern.

Incidence of hypo- and hyper-capnia in a cross-sectional European cohort of ventilated newborn infants

OBJECTIVE To determine the incidence of hypo- and hyper-capnia in a European cohort of ventilated newborn infants. DESIGN AND SETTING Two-point cross-sectional prospective study in 173 European neonatal intensive care units. PATIENTS AND METHODS Patient characteristics, ventilator settings and measurements, and blood gas analyses were collected for endotracheally ventilated newborn infants on two separate dates. RESULTS A total of 1569 blood gas analyses were performed in 508 included patients with a mean±SD Pco2 of 48±12 mm Hg or 6.4±1.6 kPa (range 17-104 mm Hg or 2.3-13.9 kPa). Hypocapnia (Pco2<30 mm Hg or 4 kPa) and hypercapnia (Pco2>52 mm Hg or 7 kPa) was present in, respectively, 69 (4%) and 492 (31%) of the blood gases. Hypocapnia was most common in the first 3 days of life (7.3%) and hypercapnia after the first week of life (42.6%). Pco2 was significantly higher in preterm infants (49 mm Hg or 6.5 kPa) than term infants (43 mm Hg or 5.7 kPa) and significantly lower during pressure-limited ventilation (47 mm Hg or 6.3±1.6 kPa) compared with volume-targeted ventilation (51 mm Hg or 6.8±1.7 kPa) and high-frequency ventilation (50 mm Hg or 6.7±1.7 kPa). CONCLUSIONS This study shows that hypocapnia is a relatively uncommon finding during neonatal ventilation. The higher incidence of hypercapnia may suggest that permissive hypercapnia has found its way into daily clinical practice.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.