2,784 research outputs found
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
Stimulus-Informed Generalized Canonical Correlation Analysis of Stimulus-Following Brain Responses
In brain-computer interface or neuroscience applications, generalized
canonical correlation analysis (GCCA) is often used to extract correlated
signal components in the neural activity of different subjects attending to the
same stimulus. This allows quantifying the so-called inter-subject correlation
or boosting the signal-to-noise ratio of the stimulus-following brain responses
with respect to other (non-)neural activity. GCCA is, however,
stimulus-unaware: it does not take the stimulus information into account and
does therefore not cope well with lower amounts of data or smaller groups of
subjects. We propose a novel stimulus-informed GCCA algorithm based on the
MAXVAR-GCCA framework. We show the superiority of the proposed
stimulus-informed GCCA method based on the inter-subject correlation between
electroencephalography responses of a group of subjects listening to the same
speech stimulus, especially for lower amounts of data or smaller groups of
subjects
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