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.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

Consensus Report: 2nd European Workshop on Tobacco Use Prevention and Cessation for Oral Health Professionals

Tobacco use has been identified as a major risk factor for oral disorders such as cancer and periodontal disease. Tobacco use cessation (TUC) is associated with the potential for reversal of precancer, enhanced outcomes following periodontal treatment, and better periodontal status compared to patients who continue to smoke. Consequently, helping tobacco users to quit has become a part of both the responsibility of oral health professionals and the general practice of dentistry. TUC should consist of behavioural support, and if accompanied by pharmacotherapy, is more likely to be successful. It is widely accepted that appropriate compensation of TUC counselling would give oral health professionals greater incentives to provide these measures. Therefore, TUC-related compensation should be made accessible to all dental professionals and be in appropriate relation to other therapeutic interventions. International and national associations for oral health professionals are urged to act as advocates to promote population, community and individual initiatives in support of tobacco use prevention and cessation (TUPAC) counselling, including integration in undergraduate and graduate dental curricula. In order to facilitate the adoption of TUPAC strategies by oral health professionals, we propose a level of care model which includes 1) basic care: brief interventions for all patients in the dental practice to identify tobacco users, assess readiness to quit, and request permission to re-address at a subsequent visit, 2) intermediate care: interventions consisting of (brief) motivational interviewing sessions to build on readiness to quit, enlist resources to support change, and to include cessation medications, and 3) advanced care: intensive interventions to develop a detailed quit plan including the use of suitable pharmacotherapy. To ensure that the delivery of effective TUC becomes part of standard care, continuing education courses and updates should be implemented and offered to all oral health professionals on a regular basis.

Identification of problems in functioning of people with sleep disorders in a clinical setting using the International Classification of Functioning Disability and Health (ICF) Checklist

We conducted an explorative, cross-sectional, multi-centre study in order to identify the most common problems of people with any kind of (primary) sleep disorder in a clinical setting using the International Classification of Functioning, Disability and Health (ICF) as a frame of reference. Data were collected from patients using a structured face-to-face interview of 45-60 min duration. A case record form for health professionals containing the extended ICF Checklist, sociodemographic variables and disease-specific variables was used. The study centres collected data of 99 individuals with sleep disorders. The identified categories include 48 (32%) for body functions, 13 (9%) body structures, 55 (37%) activities and participation and 32 (22%) for environmental factors. 'Sleep functions' (100%) and 'energy and drive functions', respectively, (85%) were the most severely impaired second-level categories of body functions followed by 'attention functions' (78%) and 'temperament and personality functions' (77%). With regard to the component activities and participation, patients felt most restricted in the categories of 'watching' (e.g. TV) (82%), 'recreation and leisure' (75%) and 'carrying out daily routine' (74%). Within the component environmental factors the categories 'support of immediate family', 'health services, systems and policies' and 'products or substances for personal consumption [medication]' were the most important facilitators; 'time-related changes', 'light' and 'climate' were the most important barriers. The study identified a large variety of functional problems reflecting the complexity of sleep disorders. The ICF has the potential to provide a comprehensive framework for the description of functional health in individuals with sleep disorders in a clinical setting.

[Mastitis management in Swiss dairy farms with udder health problems]

The objective of this study was to describe the udder health management in Swiss dairy herds with udder health problems. One hundred dairy herds with a yield-corrected somatic cell count of 200'000 to 300'000 cells/ml during 2010 were selected. Data concerning farm structure, housing system, milking technique, milking procedures, dry-cow and mastitis management were collected during farm visits between September and December 2011. In addition, quarter milk samples were collected for bacteriological culturing from cows with a composite somatic cell count ≥ 150'000 cells/ml. The highest quarter level prevalence was 12.3 % for C. bovis. Eighty-two percent of the pipeline milking machines in tie-stalls and 88 % of the milking parlours fulfilled the criteria for the vacuum drop, and only 74 % of the pipeline milking machines met the criteria of the 10-l-water test. Eighty-five percent of the farms changed their milk liners too late. The correct order of teat preparation before cluster attachment was carried out by 37 % of the farmers only. With these results, Swiss dairy farmers and herd health veterinarians can be directed to common mistakes in mastitis management. The data will be used for future information campaigns to improve udder health in Swiss dairy farms.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Memory and attention problems in children with brain tumors at diagnosis

Purpose: Results from previous studies indicate that children with brain tumors (BT) might present with cognitive problems at diagnosis and thus before the start of any medical treatment. The question remains whether these problems are due to the underlying tumor itself or due to the high level of emotional and physical stress which is involved at diagnosis of a malignant disorder. All children with a de novo oncological diagnosis not involving the central nervous systems (CNS) are usually exposed to a comparable level of distress. However, patients with cancer not involving the CNS are not expected to show disease-related cognitive problems. Thus they serve as a well-balanced control group (CG) to help distinguish between the probable causes of the effect. Method: In a pilot study we analyzed an array of cognitive functions in 16 children with BT and 17 control patients. In both groups, tests were administered in-patient at diagnosis before any therapeutic intervention such as surgery, chemotherapy od irradiation. Results: Performance of children with BT was comparable to that of CG patients in the areas of intelligence, perceptual reasoning, verbal comprehension, working memory, and processing speed. In contrast, however, BT patients performded significantly worse in verbal memory and attention. Conclusion: Memory and attention seem to be the most vulnerable funstions affected by BT, with other functions being preserved at the time of diagnosis. It ist to be expected that this vulnerability might exacerbate the cognitive decline after chemotherapy and radiation treatment - known to impair intellectual performance. The findings highlight the need of early cognitive assessments in children with BT in order to introduce cognitive training as early as possible to minimize or even prevent cognitive long-term sequelae. This might improve long-term academic and professional outcome of these children, but especially helps their return to school after hospitalization.

Respiratory-related leg movements and their relationship with periodic leg movements during sleep

STUDY OBJECTIVES: To describe the time structure of leg movements (LM) in obstructive sleep apnea (OSA) syndrome, in order to advance understanding of their clinical significance. LOCATION: Sleep Research Centre, Oasi Institute (IRCCS), Troina, Italy. SETTING: Sleep laboratory. PATIENTS: Eighty-four patients (16 females, 68 males, mean age 55.1 y, range 29-74 y). METHODS: Respiratory-related leg movements (RRLM) and those unrelated to respiratory events (NRLM) were examined within diagnostic polysomnograms alone and together for their distributions within the sleep period and for their periodicity. MEASUREMENTS AND RESULTS: Patients with OSA and RRLM exhibited more periodic leg movements in sleep (PLMS), particularly in NREM sleep. A gradual decrease in number of NRLM across the sleep period was observed in patients with RRLM. This pattern was less clear for RRLM. Frequency histograms of intermovement intervals of all LMs in patients with RRLM showed a prominent first peak at 4 sec, and a second peak at approximately 24 sec coincident with that of PLMS occurring in the absence of OSA. A third peak of lowest amplitude was the broadest with a maximum at approximately 42 sec. In patients lacking RRLM, NRLM were evident with a single peak at 2-4 sec. A stepwise linear regression analysis showed that, after controlling for a diagnosis of restless legs syndrome and apnea-hypopnea index, PLMS remained significantly associated with RRLM. CONCLUSION: The time structure of leg movements occurring in conjunction with respiratory events exhibit features of periodic leg movements in sleep occurring alone, only with a different and longer period. This brings into question the validity, both biologic and clinical, of scoring conventions with their a priori exclusion from consideration as periodic leg movements in sleep.

An MILP-based heuristic for staff scheduling problems with acceptance levels

We present a real-world staff-assignment problem that was reported to us by a provider of an online workforce scheduling software. The problem consists of assigning employees to work shifts subject to a large variety of requirements related to work laws, work shift compatibility, workload balancing, and personal preferences of employees. A target value is given for each requirement, and all possible deviations from these values are associated with acceptance levels. The objective is to minimize the total number of deviations in ascending order of the acceptance levels. We present an exact lexicographic goal programming MILP formulation and an MILP-based heuristic. The heuristic consists of two phases: in the first phase a feasible schedule is built and in the second phase parts of the schedule are iteratively re-optimized by applying an exact MILP model. A major advantage of such MILP-based approaches is the flexibility to account for additional constraints or modified planning objectives, which is important as the requirements may vary depending on the company or planning period. The applicability of the heuristic is demonstrated for a test set derived from real-world data. Our computational results indicate that the heuristic is able to devise optimal solutions to non-trivial problem instances, and outperforms the exact lexicographic goal programming formulation on medium- and large-sized problem instances.

Chronological Order of Appearance of Extraintestinal Manifestations Relative to the Time of IBD Diagnosis in the Swiss Inflammatory Bowel Disease Cohort.

BACKGROUND Data evaluating the chronological order of appearance of extraintestinal manifestations (EIMs) relative to the time of inflammatory bowel disease (IBD) diagnosis is currently lacking. We aimed to assess the type, frequency, and chronological order of appearance of EIMs in patients with IBD. METHODS Data from the Swiss Inflammatory Bowel Disease Cohort Study were analyzed. RESULTS The data on 1249 patients were analyzed (49.8% female, median age: 40 [interquartile range, 30-51 yr], 735 [58.8%] with Crohn's disease, 483 [38.7%] with ulcerative colitis, and 31 [2.5%] with indeterminate colitis). A total of 366 patients presented with EIMs (29.3%). Of those, 63.4% presented with 1, 26.5% with 2, 4.9% with 3, 2.5% with 4, and 2.7% with 5 EIMs during their lifetime. Patients presented with the following diseases as first EIMs: peripheral arthritis 70.0%, aphthous stomatitis 21.6%, axial arthropathy/ankylosing spondylitis 16.4%, uveitis 13.7%, erythema nodosum 12.6%, primary sclerosing cholangitis 6.6%, pyoderma gangrenosum 4.9%, and psoriasis 2.7%. In 25.8% of cases, patients presented with their first EIM before IBD was diagnosed (median time 5 mo before IBD diagnosis: range, 0-25 mo), and in 74.2% of cases, the first EIM manifested itself after IBD diagnosis (median: 92 mo; range, 29-183 mo). CONCLUSIONS In one quarter of patients with IBD, EIMs appeared before the time of IBD diagnosis. Occurrence of EIMs should prompt physicians to look for potential underlying IBD.

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.