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.