Efficient diagnosis of multiprocessor systems under probabilistic models

The problem of fault diagnosis in multiprocessor systems is considered under a probabilistic fault model. The focus is on minimizing the number of tests that must be conducted in order to correctly diagnose the state of every processor in the system with high probability. A diagnosis algorithm that can correctly diagnose the state of every processor with probability approaching one in a class of systems performing slightly greater than a linear number of tests is presented. A nearly matching lower bound on the number of tests required to achieve correct diagnosis in arbitrary systems is also proven. Lower and upper bounds on the number of tests required for regular systems are also presented. A class of regular systems which includes hypercubes is shown to be correctly diagnosable with high probability. In all cases, the number of tests required under this probabilistic model is shown to be significantly less than under a bounded-size fault set model. Because the number of tests that must be conducted is a measure of the diagnosis overhead, these results represent a dramatic improvement in the performance of system-level diagnosis techniques

Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method

For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual polynomial than the stationary iteration, and thus converges much faster. We show in this paper that also for non-linear problems, domain decomposition methods can either be used directly as iterative solvers, or one can use them as preconditioners for Newton's method. For the concrete case of the parallel Schwarz method, we show that we obtain a preconditioner we call RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all components directly defined by the iterative method. This has the advantage that RASPEN already converges when used as an iterative solver, in contrast to ASPIN, and we thus get a substantially better preconditioner for Newton's method. The iterative construction also allows us to naturally define a coarse correction using the multigrid full approximation scheme, which leads to a convergent two level non-linear iterative domain decomposition method and a two level RASPEN non-linear preconditioner. We illustrate our findings with numerical results on the Forchheimer equation and a non-linear diffusion problem

Christianity and homosexuality: contradictory or complimentary? A qualitative study of the experiences of Christian homosexual university students

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Fortnightly modulation of the estuarine circulation in Juan de Fuca Strait

Riverine discharge into the Strait of Georgia sets up a well-defined estuarine circulation within Juan de Fuca Strait, the main path for the freshwater outflow to the continental shelf. At the landward end of Juan de Fuca Strait, the water flows through narrow channels in which strong tidal currents are known to induce significant mixing of the water column, and a spring-neap modulation of the estuarine exchange. A three-dimensional prognostic numerical model has been developed to study the circulation around Vancouver Island, British Columbia. In a series of simulations, the estuarine circulation within Juan de Fuca Strait is established by the Fraser River freshwater discharge. A fortnightly modulation is imposed on the mixing over the various sills to simulate the spring-neap tidal mixing regime. The resulting variation in the estuarine circulation is found to be largely limited to the eastern section of Juan de Fuca Strait, in the vicinity of the sills. Data from current meter moorings and surface salinity data from lighthouse stations compare favorably with the model results. The effect of local wind forcing on the estuarine exchange is also examined. The model is capable of simulating those rare events during which a concurrence of river freshet, neap tide and northwest wind allows a stronger pulse of fresh surface water to escape relatively unmixed into the eastern end of Juan de Fuca Strait. The disturbance then propagates along the northern shore of the strait as a first mode internal Kelvin wave. Finally, the effect of the fortnightly modulation on the export of freshwater onto the continental shelf is examined. It is found that small amplitude coastal trapped waves are generated near the mouth of Juan de Fuca. However, this fortnightly signal is weak in comparison to the energetic wind-induced variations typically found over the shelf