Convergence analysis of energy conserving explicit local time-stepping methods for the wave equation

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any explicit time-marching method. In [18] a leap-frog (LF) based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time-steps in the locally refined region and larger steps elsewhere. Here a rigorous convergence proof is presented for the fully-discrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities

Sports Activity After Short-Stem Hip Arthroplasty

Background: No data are available about the sports activity of patients with bone-conserving short-stem hip implants. Hypothesis: Patients can return to a good level of sports activity after implantation of a short-stem hip implant. Study Design: Case series; Level of evidence, 4. Methods: The sports activity level of 68 patients (76 hips) after short-stem hip arthroplasty was assessed for a minimum of 2 years after implantation. In addition to the clinical examination, a detailed evaluation of the patients’ sports pattern was obtained. Furthermore, the results were analyzed with regard to gender (female and male) and age (55 years). Results: After a mean of 2.7 years, patients showed a Harris Hip Score (HHS) of 93.6, a Western Ontario and McMaster Universities Arthritis Index (WOMAC) score of 9.5, and a University of California, Los Angeles (UCLA) activity score of 7.6, with each individual participating on average in 3.5 different disciplines after surgery compared with 3.9 before surgery. High-impact activities decreased significantly postoperatively, whereas low-impact activities increased significantly. The duration of the sports activities remained stable, while the frequency actually increased. In contrast, men participated preoperatively in more sports than women (4.3 men vs 3.3 women). However, because of a pronounced decrease in high-impact activities by men, both genders participated in an equal number of sports postoperatively (3.5 men vs 3.5 women). Finally, 45% (n = 31) reported at least one activity that they missed. Most of them were disciplines with an intermediate- or high-impact level. Conclusion: Patients with a short-stem hip implant can return to a good level of activity postoperatively. Participation in sports almost reached similar levels as preoperatively but with a shift from high- to low-impact activities. This seems desirable from a surgeon’s point of view but should also be communicated to the patient before hip replacemen

Funde neuer und bemerkenswerter Adventivarten in Braunschweig (Niedersachsen)

In the year 2003 all known neophytes of the city of Braunschweig were collected for the first time in a checklist (BRANDES 2003). As a completion to the checklist this paper informs about 26 remarkable neophytes and their habitats, size of the populations and the date of record. In individual cases further facts about the species or a vegetation relevé will be given

Stabilized leapfrog based local time-stepping method for the wave equation

Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping (LF-LTS) method was proposed for the time integration of second-order wave equations. Recently, optimal convergence rates were proved for a conforming FEM discretization, albeit under a CFL stability condition where the global time-step, $\Delta t$, depends on the smallest elements in the mesh \cite{grote_sauter_1}. In general one cannot improve upon that stability constraint, as the LF-LTS method may become unstable at certain discrete values of $\Delta t$. To remove those critical values of $\Delta t$, we apply a slight modification (as in recent work on LF-Chebyshev methods \cite{CarHocStu19}) to the original LF-LTS method which nonetheless preserves its desirable properties: it is fully explicit, second-order accurate, satisfies a three-term (leapfrog like) recurrence relation, and conserves the energy. The new stabilized LF-LTS method also yields optimal convergence rates for a standard conforming FE discretization, yet under a CFL condition where $\Delta t$ no longer depends on the mesh size inside the locally refined region

Basal core promoters control the equilibrium between negative cofactor 2 and preinitiation complexes in human cells

BACKGROUND: The general transcription factor TFIIB and its antagonist negative cofactor 2 (NC2) are hallmarks of RNA polymerase II (RNAPII) transcription. Both factors bind TATA box-binding protein (TBP) at promoters in a mutually exclusive manner. Dissociation of NC2 is thought to be followed by TFIIB association and subsequent preinitiation complex formation. TFIIB dissociates upon RNAPII promoter clearance, thereby providing a specific measure for steady-state preinitiation complex levels. As yet, genome-scale promoter mapping of human TFIIB has not been reported. It thus remains elusive how human core promoters contribute to preinitiation complex formation in vivo. RESULTS: We compare target genes of TFIIB and NC2 in human B cells and analyze associated core promoter architectures. TFIIB occupancy is positively correlated with gene expression, with the vast majority of promoters being GC-rich and lacking defined core promoter elements. TATA elements, but not the previously in vitro defined TFIIB recognition elements, are enriched in some 4 to 5% of the genes. NC2 binds to a highly related target gene set. Nonetheless, subpopulations show strong variations in factor ratios: whereas high TFIIB/NC2 ratios select for promoters with focused start sites and conserved core elements, high NC2/TFIIB ratios correlate to multiple start-site promoters lacking defined core elements. CONCLUSIONS: TFIIB and NC2 are global players that occupy active genes. Preinitiation complex formation is independent of core elements at the majority of genes. TATA and TATA-like elements dictate TFIIB occupancy at a subset of genes. Biochemical data support a model in which preinitiation complex but not TBP-NC2 complex formation is regulated

The Riverbank Flora in Town Centres Exeniplificd by the Oker Riverbanks in Brunswick (Lower Saxony)

The embankments of a river flowing through the centre of an old town are very rich in plant species, as the example of the river Oker in Brunswick (Federal Republic of Germany) shows. 311 different vascular plant species - almost one third of Brunswick's spontaneous flora - are present on the banks of the river Oker. 64 of the species are indigenous, 10 are archaeophytes. 14.1 are naturalized aliens and 11.9 are ephemerophytes. On embankments in the town centre Acer pseudoplatanus, Acer platanoides, Aesculus hippocastanum, Ulmus glabra are the most common trees; the most frequent shrub is Sambucus nigra. Very apparent is a high proportion of climbing plants (Hedera helix, Clematis vitatba, Bryonia dioica). As a rule nitrophilous plants are dominant in the weed layer. The proportion of neophytes is particularly high on embankments adjoining to gardens. The importance of river banks in towns for nature conservation is discussed; for several endangered species such as Parietaria officinalis or Tutipa sylvesiris they are important places of refuge. The investigations about the river bank flora in towns published so far are briefly described and compared to the own findings

Pathologic fracture of the distal radius in a 25-year-old patient with a large unicameral bone cyst

Background: Distal radius fractures (DRF) are often referred to as osteoporosis indicator fractures as their incidence increases from age 45. In the group of young adults, distal radius fractures normally result from high-energy trauma. Wrist fractures in young patients without adequate trauma thus raise suspicion of a pathologic fracture. In this report we present the case of a fractured unicameral bone cyst (UBC) at the distal radius in a young adult. To the author's best knowledge, this is the first detailed report in an UBC at the distal radius causing a pathologic DRF in an adult patient. Case presentation: A 25-year-old otherwise healthy male presented to our Emergency Department after a simple fall on his right outstretched hand. Extended diagnostics revealed a pathologic, dorsally displaced, intra-articular distal radius fracture secondary to a unicameral bone cyst occupying almost the whole metaphysis of the distal radius. To stabilize the fracture, a combined dorsal and volar approach was used for open reduction and internal fixation. A tissue specimen for histopathological examination was gathered and the lesion was filled with an autologous bone graft harvested from the ipsilateral femur using a reamer-irrigator-aspirator (RIA) system. Following one revision surgery due to an intra-articular step-off, the patient recovered without further complications. Conclusions: Pathologic fractures in young patients caused by unicameral bone cysts require extended diagnostics and adequate treatment. A single step surgical treatment is reasonable if fracture and bone cyst are treated appropriately. Arthroscopically assisted fracture repair may be considered in intra-articular fractures or whenever co-pathologies of the carpus are suspected

Cost recommendation under uncertainty in IQWiG’s efficiency frontier framework

Background: The National Institute for Quality and Efficiency in Health Care (IQWiG) employs an efficiency frontier (EF) framework to facilitate setting maximum reimbursable prices for new interventions. Probabilistic sensitivity analysis (PSA) is used when yes/no reimbursement decisions are sought based on a fixed threshold. In the IQWiG framework, an additional layer of complexity arises as the EF itself may vary its shape in each PSA iteration, and thus the willingness-to-pay, indicated by the EF segments, may vary. Objectives: To explore the practical problems arising when, within the EF approach, maximum reimbursable prices for new interventions are sought through PSA. Methods: When the EF is varied in a PSA, cost recommendations for new interventions may be determined by the mean or the median of the distances between each intervention’s point estimate and each EF. Implications of using these metrics were explored in a simulation study based on the model used by IQWiG to assess the cost-effectiveness of 4 antidepressants. Results. Depending on the metric used, cost recommendations can be contradictory. Recommendations based on the mean can also be inconsistent. Results (median) suggested that costs of duloxetine, venlafaxine, mirtazapine, and bupropion should be decreased by €131, €29, €12, and €99, respectively. These recommendations were implemented and the analysis repeated. New results suggested keeping the costs as they were. The percentage of acceptable PSA outcomes increased 41% on average, and the uncertainty associated to the net health benefit was significantly reduced. Conclusions: The median of the distances between every intervention outcome and every EF is a good proxy for the cost recommendation that would be given should the EF be fixed. Adjusting costs according to the median increased the probability of acceptance and reduced the uncertainty around the net health benefit distribution, resulting in a reduced uncertainty for decision makers

Diagnosis and treatment of acute ankle injuries: development of an evidence-based algorithm

Acute ankle injuries are among the most common injuries in emergency departments. However, there are still no standardized examination procedures or evidence-based treatment. Therefore, the aim of this study was to systematically search the current literature, classify the evidence, and develop an algorithm for the diagnosis and treatment of acute ankle injuries. We systematically searched PubMed and the Cochrane Database for randomized controlled trials, meta-analyses, systematic reviews or, if applicable, observational studies and classified them according to their level of evidence. According to the currently available literature, the following recommendations have been formulated: i) the Ottawa Ankle/Foot Rule should be applied in order to rule out fractures; ii) physical examination is sufficient for diagnosing injuries to the lateral ligament complex; iii) classification into stable and unstable injuries is applicable and of clinical importance; iv) the squeeze-, crossed leg- and external rotation test are indicative for injuries of the syndesmosis; v) magnetic resonance imaging is recommended to verify injuries of the syndesmosis; vi) stable ankle sprains have a good prognosis while for unstable ankle sprains, conservative treatment is at least as effective as operative treatment without the related possible complications; vii) early functional treatment leads to the fastest recovery and the least rate of reinjury; viii) supervised rehabilitation reduces residual symptoms and re-injuries. Taken these recommendations into account, we present an applicable and evidence-based, step by step, decision pathway for the diagnosis and treatment of acute ankle injuries, which can be implemented in any emergency department or doctor's practice. It provides quality assurance for the patient and promotes confidence in the attending physician