Electromagnetic wave propagation and absorption in magnetised plasmas: variational formulations and domain decomposition

We consider a model for the propagation and absorption of electromagnetic waves (in the time-harmonic regime) in a magnetised plasma. We present a rigorous derivation of the model and several boundary conditions modelling wave injection into the plasma. Then we propose several variational formulations, mixed and non-mixed, and prove their well-posedness thanks to a theorem by S\'ebelin et~al. Finally, we propose a non-overlapping domain decomposition framework, show its well-posedness and equivalence with the one-domain formulation. These results appear strongly linked to the spectral properties of the plasma dielectric tensor

Judicial Trial Skills Training

The University of Minnesota Law School and the Minnesota Supreme Court Office of Continuing Education for State Court Personnel have initiated a unique and dynamic Judicial Trial Skills Training Program. Newly appointed judges participate in videotaped simulated trials designed to present the participating judges with numerous evidentiary and trial relationship issues. The videotapes of these trials are reviewed and cri- tiqued by the participating judge and a senior judge to give the participat-\u27 ingjudges immediate feedback on their performance. The review session is used to discuss the various skills that judges must develop in order to conduct fair and efficient trials

Discovering and Certifying Lower Bounds for the Online Bin Stretching Problem

There are several problems in the theory of online computation where tight lower bounds on the competitive ratio are unknown and expected to be difficult to describe in a short form. A good example is the Online Bin Stretching problem, in which the task is to pack the incoming items online into bins while minimizing the load of the largest bin. Additionally, the optimal load of the entire instance is known in advance. The contribution of this paper is twofold. First, we provide the first non-trivial lower bounds for Online Bin Stretching with 6, 7 and 8 bins, and increase the best known lower bound for 3 bins. We describe in detail the algorithmic improvements which were necessary for the discovery of the new lower bounds, which are several orders of magnitude more complex. The lower bounds are presented in the form of directed acyclic graphs. Second, we use the Coq proof assistant to formalize the Online Bin Stretching problem and certify these large lower bound graphs. The script we propose certified as well all the previously claimed lower bounds, which until now were never formally proven. To the best of our knowledge, this is the first use of a formal verification toolkit to certify a lower bound for an online problem

Scheduling malleable task trees

Solving sparse linear systems can lead to processing tree workflows on a platform of processors. In this study, we use the model of malleable tasks motivated in [Prasanna96,Beaumont07] in order to study tree workflow schedules under two contradictory objectives: makespan minimization and memory minization. First, we give a simpler proof of the result of [Prasanna96] which allows to compute a makespan-optimal schedule for tree workflows. Then, we study a more realistic speed-up function and show that the previous schedules are not optimal in this context. Finally, we give complexity results concerning the objective of minimizing both makespan and memory

Computing a Minimum-Cost k-Hop Steiner Tree in Tree-Like Metrics

We consider the problem of computing a Steiner tree of minimum cost under a k-hop constraint which requires the depth of the tree to be at most k. Our main result is an exact algorithm for metrics induced by graphs of bounded treewidth that runs in time n^O(k). For the special case of a path, we give a simple algorithm that solves the problem in polynomial time, even if k is part of the input. The main result can be used to obtain, in quasi-polynomial time, a near-optimal solution that violates the k-hop constraint by at most one hop for more general metrics induced by graphs of bounded highway dimension and bounded doubling dimension