We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in plasma physics -the flow of magnetic field lines and the guiding center motion of magnetized charged particles -resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates, i.e., coordinates lacking the familiar (q, p) partitioning. Recent efforts made progress toward non-canonical symplectic integration of these systems by appealing to the variational integration framework; however, those integrators were multistep methods and later found to be numerically unstable due to parasitic mode instabilities. This work eliminates the multistep character and, therefore, the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem "degenerate variational integration". Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that their resultant Euler-Lagrange equations are systems of first-order ODEs. We show that retaining the same degree of degeneracy when constructing a discrete Lagrangian yields one-step variational integrators preserving a non-canonical symplectic structure on the original Hamiltonian phase space. The advantages of the new algorithms are demonstrated via numerical examples, demonstrating superior stability compared to existing variational integrators for these systems and superior qualitative behavior compared to non-conservative algorithms. a) Electronic mail: ellison6@llnl.gov b) Present address: Tibbar Plasma Technologies, 274 DP Rd, Los Alamos, NM 87544, USA 2

This is a report on 126 prospectively registered and controlled complications in 29,695 consecutive endoscopic procedures of the lower gastrointestinal tract. The overall complication rate is 0.4%. All endoscopic procedures were performed in our institution; no referrals "from other hospitals" are included. The therapy and prognosis of occurring complications are described. Especially after therapeutic endoscopy--above all, after polypectomy--the complication rate of 0.83% is not negligible. A serious aspect is the average interval of 30 h from endoscopically caused complication to the onset of symptoms. Bleeding could be managed conservatively in 76% of cases. Nevertheless perforation and transmural burn injuries required surgical intervention in 78% of cases. The authors conclude that in the case of transmural burn an attempt at "active conservative treatment" is justified if the patient is under close surgical control, if the symptoms improve, and if there is a possibility of immediate surgery.

Purpose To study the natural evolution of cartilage T2 relaxation times in knees with various extents of morphological cartilage abnormalities, assessed with 3T MRI from the Osteoarthritis Initiative. Materials and Methods Right knee MRIs of 245, 45–60 year old individuals without radiographic OA were included. Cartilage was segmented and T2 maps were generated in five compartments (patella, medial and lateral femoral condyle, medial and lateral tibia) at baseline and two-year follow-up. We examined the association of T2 values and two-year change of T2 values with various Whole-Organ MR Imaging Scores (WORMS). Statistical analysis was performed with ANOVA and Students t-tests. Results Higher baseline T2 was associated with more severe cartilage defects at baseline and subsequent cartilage loss (P<0.001). However, longitudinal T2 change was inversely associated with both baseline (P=0.038) and follow-up (P=0.002) severity of cartilage defects. Knees that developed new cartilage defects had smaller increases in T2 than subjects without defects (P=0.045). Individuals with higher baseline T2 showed smaller T2 increases over time (P<0.001). Conclusion An inverse correlation of longitudinal T2 changes versus baseline T2 values and morphological cartilage abnormalities suggests that once morphological cartilage defects occur, T2 values may be limited for evaluating further cartilage degradation.

Objective To evaluate the association of metabolic risk factors with severity and two-year progression of early degenerative cartilage changes at the knee, measured with T2 relaxation times in middle-aged subjects from the Osteoarthritis Initiative. Methods Cartilage segmentation and T2 map generation was performed in 3T knee MR images from 403, 45 – 60 year old subjects without radiographic osteoarthritis (OA). The influence of risk factors on baseline and longitudinal progression of T2 was analyzed using linear regression, adjusting for age, gender and other OA risk factors. Results Four metabolic risk factors (i) high abdominal circumference (P<0.001), (ii) hypertension (P=0.040), (iii) high fat consumption (P=0.019) and (iv) self-reported diabetes (P=0.012) were individually associated with higher baseline T2. When the four metabolic risk factors were considered in a multivariate regression model, higher T2 remained significantly associated with abdominal circumference (P<0.001) and diabetes (P=0.031) and there was a trend for high fat consumption (P=0.096). Of individual risk factors, only diabetes remained associated with higher baseline T2 after adjustment for BMI. After adjustment for BMI, baseline T2 increased in dose-reponse fashion with the number of metabolic risk factors present (P=0.032 for linear trend), and subjects with ≥3 metabolic factors (versus <3) had significantly higher baseline T2 (mean difference, 1.2ms; lower 95% confidence interval (CI), 0.3ms; upper 95% CI, 2.1ms; P=0.011). Metabolic risk factors were not significantly associated with increases in T2 during follow-up. Conclusion Metabolic risk factors are associated with higher T2, suggesting that increased cartilage degeneration may be caused by modifiable metabolic disorders.

We present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinitedimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonic behavior of entropy are guaranteed for finite element discretizations in general, independently of the mesh configuration.

Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian via Noether's theorem. An inevitable prerequisite for the derivation of variational integrators is the existence of a variational formulation for the considered problem. Even though for a large class of systems this requirement is fulfilled, there are many interesting examples which do not belong to this class, e.g., equations of advectiondiffusion type frequently encountered in fluid dynamics or plasma physics.On the other hand, it is always possible to embed an arbitrary dynamical system into a larger Lagrangian system using the method of formal (or adjoint) Lagrangians. We investigate the application of the variational integrator method to formal Lagrangians, and thereby extend the application domain of variational integrators to include potentially all dynamical systems.The theory is supported by physically relevant examples, such as the advection equation and the vorticity equation, and numerically verified. Remarkably, the integrator for the vorticity equation combines Arakawa's discretisation of the Poisson brackets with a symplectic time stepping scheme in a fully covariant way such that the discrete energy is exactly preserved. In the presentation of the results, we try to make the geometric framework of variational integrators accessible to non specialists.

From 50 subjects included (mean age 56.1 ± 8.8 years, 60.0% males, mean body mass index 28.3 ± 5.2) 2'400 measurements were obtained. Interobserver agreement was excellent for all muscle compartments (PDFF: ICC0.99, CSA: ICC0.98) with only minor absolute and relative differences (-0.2 ± 0.5%, 31 ± 44.7 mm; -2.6 ± 6.4% and 2.7 ± 3.9%, respectively). Intra-observer reproducibility was similarly excellent (PDFF: ICC1.0, 0.0 ± 0.4%, 0.4%; CSA: ICC1.0, 5.5 ± 25.3 mm, 0.5%, absolute and relative differences, respectively). All agreement was independent of age, gender, body mass index, body height and visceral adipose tissue (ICC0.96-1.0). Furthermore, PDFF reproducibility was independent of CSA (ICC0.93-0.99).  Conclusions:  Quantification of skeletal muscle fat content and area by MRI using an anatomical landmark-based, manual skeletal muscle segmentation is highly reproducible. Advances in knowledge: An anatomical landmark-based, manual skeletal muscle segmentation provides high reproducibility of skeletal muscle fat content and area and may therefore serve as a robust proxy for myosteatosis and sarcopenia in large cohort studies.