The sparse probabilistic Boolean network (SPBN) model has been applied in various fields of industrial engineering and management. The goal of this model is to find a sparse probability distribution based on a given transition-probability matrix and a set of Boolean networks (BNs). In this paper, a partial proximal-type operator splitting method is proposed to solve a separable minimization problem arising from the study of the SPBN model. All the subproblem-solvers of the proposed method do not involve matrix multiplication, and consequently the proposed method can be used to deal with large-scale problems. The global convergence to a critical point of the proposed method is proved under some mild conditions. Numerical experiments on some real probabilistic Boolean network problems show that the proposed method is effective and efficient compared with some existing methods.
Mesh generation is a challenge for high-performance numerical simulation, one reason is the complex geometry representing solution domain makes pre-processing difficult, especially for those assembly model containing hundreds and thousands of components involving misaligned interfaces between neighboring parts, and no state-of-art meshing tools could provide automatic functions for processing such complex model, another reason is hundreds of millions or even billions meshes should be generated quickly, which also exceeds the capabilities of available tools. In this paper, a novel parallel and automatic mesh generation method is proposed. Firstly, a surface imprinting algorithm based on the hybrid representation of discrete and continuous surfaces is proposed to process misaligned assembly model automatically. Then, the repaired assembly model is used as an input for a carefully designed mesh generation pipeline which connects the procedures of mesh sizing control, and three-level parallel tetrahedral mesh generation in order. This proposed method could produce hundreds of millions consistent mesh qualified for high-performance numerical simulation based on thousands of geometry components. Numerical experiments on a giant dam model and an integrated circuit board model demonstrates the effectiveness of this method.
A new cost function based on diagonalization of the correlation matrices is proposed to measure the independency of output signills in this paper. In order to expand the search space and decrease the crasssorrelation among the sub-sources, we . propose to perform nonlinear transformation for the cost function. The real coded genetic algorithm is also proposed to search the optimum solution, which can overcome the drawbacks of traditional gradient search technique being likely tend to fall into local minimums. This novel method can be, applicable to instantaneous or convolutive mixture models with stationary or non-stationary input signals. Simulation results demonstrate the algorithm not only has fast convergence performance and high accuracy, hut also can improve the output SNR greatly.
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