求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

Joint L1/Lp-regularized minimization in video recovery of remote sensing based on compressed sensing

L₁ regularization and L_p regularization are proposed for processing recovered images based on compressed sensing (CS). L₁ regularization can be solved as a convex optimization problem but is less sparse than L_p (0 < p < 1). L_p regularization is sparser than L₁ regularization but is more difficult to solve. This paper proposes joint L₁/L_p (0 < p < 1) regularization, which combines L_p regularization and L₁ regularization. This joint regularization is applied to recover video of remote sensing based on CS. Joint regularization is sparser than L₁ regularization but is as easy to solve as L₁ regularization. A linearized Bregman reweighted iteration algorithm is proposed to solve the joint L₁/L_p regularization problem. The performance and capabilities of the linearized Bregman algorithm and linearized Bregman reweighted algorithm for solving the joint L₁/L_p regularization model are analyzed and compared through numerical simulations.     

A vectorial algorithm with finite element method for prediction of powder segregation in metal injection molding

The design of the mold and the choice of the injection parameters for metal injection molding (MIM) is required to maintain homogeneity of the filled mixture. However, powder segregation is unavoidable in MIM because of the significant difference in densities of the metallic powder and the polymer binder. To achieve an effective prediction of segregation effect, a biphasic model based on mixture theory is employed. The viscous behaviors of each phase and the interaction coefficient between the flows of the two phases should be determined. The solution of two coupled Navier–Stokes equations results in a tremendous computation effort. The previous development of an explicit algorithm makes the biphasic simulation much faster than that of the classic methods. However, it is strongly desired to reduce or even eliminate the numerous global solutions for pressure fields at each time step. Hence, a new vectorial algorithm is proposed and developed to perform the simulation only by vectorial operations. It provides the anticipated efficiency in the simulation of biphasic modeling, and the advantage to use the classic elements of equal‐order interpolations. Some results produced by the two algorithms are compared with the experimental values to validate the new vectorial algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

The lifetime of CFC substitutes studied by a network trained with chaotic mapping modified genetic algorithm and DFT calculations

The hydrohaloalkanes have attracted much attention as potential substitutes of chlorofluorocarbons (CFCs) that deplete the ozone layer and lead to great high global warming. Having a short atmospheric lifetime is very important for the potential substitutes that may also induce ozone depletion and yield high global warming gases to be put in use. Quantitative structure–activity relationship (QSAR) studies were presented for their lifetimes aided by the quantum chemistry parameters including net charges, Mulliken overlaps, E _HOMO and E _LUMO based on the density functional theory (DFT) at B3PW91 level, and the C-H bond dissociation energy based on AM1 calculations. Outstanding features of the logistic mapping, a simple chaotic system, especially the inherent ability to search the space of interest exhaustively have been utilized. The chaotic mapping aided genetic algorithm artificial neural network training scheme (CGANN) showed better performance than the conventional genetic algorithm ANN training when the structure of the data set was not favorable. The lifetimes of HFCs and HCs appeared to be greatly dependent on their energies of the highest occupied molecular orbitals. The perference of the RMSRE comparing to RMSE as objective function of ANN training was better for the samples of interest with relatively short lifetimes. C₂H₆ and C₃H₈ as potential green substitutes of CFCs present relatively short lifetimes.     

Hierarchical Model-Based Clustering for Large Datasets

In recent years, hierarchical model-based clustering has provided promising results in a variety of applications. However, its use with large datasets has been hindered by a time and memory complexity that are at least quadratic in the number of observations. To overcome this difficulty, this article proposes to start the hierarchical agglomeration from an efficient classification of the data in many classes rather than from the usual set of singleton clusters. This initial partition is derived from a subgraph of the minimum spanning tree associated with the data. To this end, we develop graphical tools that assess the presence of clusters in the data and uncover observations difficult to classify. We use this approach to analyze two large, real datasets: a multiband MRI image of the human brain and data on global precipitation climatology. We use the real datasets to discuss ways of integrating the spatial information in the clustering analysis. We focus on two-stage methods, in which a second stage of processing using established methods is applied to the output from the algorithm presented in this article, viewed as a first stage.     

Composite Likelihood Inference in a Discrete Latent Variable Model for Two-Way “Clustering-by-Segmentation” Problems

We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g., exchangeable observational units or features) and contiguous groups, or segments, along the other (e.g., consecutively ordered times or locations). The model relies on a hidden Markov structure but, given its complexity, cannot be estimated by full maximum likelihood. Therefore, we introduce a composite likelihood methodology based on considering different subsets of the data. The proposed approach is illustrated by simulation, and with an application to genomic data.     

An improved watermarking method based on double random phase encoding technique

An improved watermarking method, based on the double random phase encoding technique and the cascaded-phases iterative algorithm and random-phase-shift algorithm, is proposed. This method can significantly reduce the needs of watermarking information storage for different multimedia products, and provide a reasonable criterion of determining the authenticity of a product for the copyright owner. This method can also be applied to track the source of copies. The effectiveness of this method was verified through numerical simulations.     

Spectrum of a Rudin–Shapiro-like sequence

We show that a recently proposed Rudin–Shapiro-like sequence, with balanced weights, has purely singular continuous diffraction spectrum, in contrast to the well-known Rudin–Shapiro sequence whose diffraction is absolutely continuous. This answers a question that had been raised about this new sequence.     

Real‐Time Measurement of the Size Distribution of Diesel Exhaust Particles using a Portable 4‐stage Electrical Low Pressure Impactor

For this study, a 4 stage electrical low pressure impactor was designed to measure the real‐time size distribution of diesel particulate matter (DPM). For the performance evaluation, sodium chloride (NaCl) particles and dioctyl sebacate (DOS) particles were used. After evaluating the collection efficiency of each stage of the impactor, the size distributions of test particles were estimated using electrical current data and their inversion algorithm, and this was found to agree with the results obtained by a scanning mobility particle sizer (SMPS). For measurement of DPM, a common‐rail direct injection (CRDI) diesel engine, for engine speeds of 1,200 rpm and 1,500 rpm at 2.7 kgf·m, was used. Therefore, it was found that the size distribution of the DPM could be easily obtained, with the currents measured by the impactor and the data inversion algorithm, in less than 5 seconds. Furthermore, the effective density of the DPM could be obtained using the calculated results and the SMPS data.     

Parallel Schwarz alternating methods for anisotropic diffusion of speckled medical images

This paper deals with ultrasound medical image processing, particularly to filter the noise while preserving the edges and structures of information. The mathematical processing consists in solving by a numerical way a nonlinear evolutive boundary value problem. Several numerical semi-implicit time marching schemes are considered and analyzed. At each time step, parallel synchronous or asynchronous Schwarz alternating methods are used to solve the linear system and its convergence is studied. Lastly, the results of sequential and parallel simulations are presented.