Stationary harmonic maps into complete Riemannian manifold

The stationary for harmonic maps is considered from a Riemannian manifoldM into a complete Riemannian manifoldN without boundary, and it is proved that its singular set is contained inQ ¹ 2MQ ³ Project supported partially by the Development Foundation Science of Shanghai, China.     

On equilibration and sparse factorization of matrices arising in finite element solutions of partial differential equations

Investigations of scaling and equilibration of general matrices have been traditionally aimed at the effects on the stability and accuracy of LU factorizations—the so‐called scaling problem. Notably, Skeel (1979) concludes that no systematic scaling procedure can be concocted for general matrices exempt from the danger of disastrous effects. Other researchers suggest that scaling procedures are not beneficial and should be abandoned altogether. Stability and accuracy issues notwithstanding, we show that this unglamorous technique has a profound impact on the sparsity of the resulting LU factors. In the modern era of fast computing, equilibration can play a key role in constructing incomplete sparse factorizations to solve a problem unstably, but quickly and iteratively. This article presents practical evidence, on the basis of sparsity, that scaling is an indispensable companion for sparse factorization algorithms when applied to realistic problems of industrial interest. In light of our findings, we conclude that equilibration with the ∞‐norm is superior than equilibration with the 2‐norm. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 11–29, 2000     

基于实数编码遗传算法的稀布阵列综合

针对有孔径和阵元总数约束的线性阵列,提出了一种基于实数编码遗传算法的稀布阵列综合方法。算法中每条染色体基因主要由阵元间距和激励幅度共同组成,采用双变量组合优化的方式为阵列性能优化提供了更多的自由度。采用十进制实数量化编码的方式,省去了二进制编码过程中的解码运算,使算法程序更为简洁,效率更高。以降低阵列方向图的峰值旁瓣电平为目标函数,运用提出的改进遗传算法针对几种不同的线性阵列进行优化仿真,在同等约束条件下将该算法与其他改进遗传算法进行了优化对比,结果表明该算法表现更为出色。     

应用粒子滤波及先验概率模型进行图像分割的新算法

基于粒子滤波在非线性非高斯情况下具有较好的预测结果,本文提出了一种自适应背景图像分割新算法,该算法利用粒子滤波对下一帧的前景区域进行预测,进而计算出下一帧各像素点属于背景的概率以指导下一帧图像分割;在前景像素值与背景像素值相近的情况下利用先验知识进行图像分割是一种较好的方法,本文以粒子滤波预测结果与先验概率模型计算结果的均值作为当前像素点属于背景的概率来进行图像分割,实验结果表明,该方法在背景变化范围较大的情况下,可以减少前景点误分割为背景点的概率.     

角度模糊对天基稀疏孔径GMTI雷达的影响与抑制方法

天基稀疏阵实现地面运动目标指示具有很大吸引力.然而稀疏阵存在栅瓣,理论分析与仿真结果表明栅瓣会产生盲速和虚假目标.本文提出一种消除角度模糊影响的简单方法:首先对均匀稀疏阵阵元位置施加随机误差消除测速盲区;随后采用陷零空时自适应处理剔除虚假目标.仿真结果表明该方法稳健、有效.     

基于频域单源区间的具有延迟的欠定盲分离

本文研究如何分离具有延迟而无回波的混叠信号.提出了欠定情况(即感知器少于源信号)下具有时间延迟的信道估计算法,称为单源区间衰减和延迟恢复(AD-MRISSI)算法;它在理论上能无偏差地估计信道,在应用中能准确地估计延迟和精确地估计衰减.也提出了一个基于稀疏原则的源信号重建算法,能避免Bofill算法中的求解二阶锥规划问题.几个语音信号实验展示了其有效性和实用性.     

矩量法中阻抗矩阵的稀疏化研究

将高阶叠层矢量基函数及最大正交高阶矢量基函数应用于电磁场积分方程方法,提出将阻抗矩阵按稀疏阵处理的方法.通过文中的处理,使得存储阻抗矩阵的内存需求量和求解矩阵方程的迭代求解时间大为降低.本文还结合适当算例,分析了判断门限的选取对阻抗矩阵的存储量与迭代法求解的计算量的影响.     

基于局部通信的有限元分析并行算法优化研究

针对有限元分析的计算问题,在现有采用全局通信方案的简单并行算法基础上,对其所涉核心算法,采用稀疏数据结构与局部通信进行并行算法优化设计,有效减少了通信所涉及的处理器个数与通信量.同时,通过采用非阻塞通信,并将与通信无关计算进行分离与前置的方法,进行计算与通信重叠,以有效隐藏通信开销的影响.实验结果表明,优化所得算法相比...     

Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection

Motivated by mobile devices that record data at a high frequency, we propose a new methodological framework for analyzing a semi-parametric regression model that allow us to study a nonlinear relationship between a scalar response and multiple functional predictors in the presence of scalar covariates. Utilizing functional principal component analysis (FPCA) and the least-squares kernel machine method (LSKM), we are able to substantially extend the framework of semi-parametric regression models of scalar responses on scalar predictors by allowing multiple functional predictors to enter the nonlinear model. Regularization is established for feature selection in the setting of reproducing kernel Hilbert spaces. Our method performs simultaneously model fitting and variable selection on functional features. For the implementation, we propose an effective algorithm to solve related optimization problems in that iterations take place between both linear mixed-effects models and a variable selection method (e.g., sparse group lasso). We show algorithmic convergence results and theoretical guarantees for the proposed methodology. We illustrate its performance through simulation experiments and an analysis of accelerometer data.     

Beyond Equal-Power Sparse NOMA: Two User Classes and Closed-Form Bounds on the Achievable Region

Non-orthogonal multiple access (NOMA) is a promising technology for future beyond-5G wireless networks, whose fundamental information-theoretic limits are yet to be fully explored. Considering regular sparse code-domain NOMA (with a fixed and finite number of orthogonal resources allocated to any designated user and vice versa), this paper extends previous results by the authors to a setting comprising two classes of users with different power constraints. Explicit rigorous closed-form analytical inner and outer bounds on the achievable rate (total class throughput) region in the large-system limit are derived and comparatively investigated in extreme-SNR regimes. The inner bound is based on the conditional vector entropy power inequality (EPI), while the outer bound relies on a recent strengthened version of the EPI. Valuable insights are provided into the potential performance gains of regular sparse NOMA in practically oriented settings, comprising, e.g., a combination of low-complexity devices and broadband users with higher transmit power capabilities, or combinations of cell-edge and cell-center users. The conditions for superior performance over dense code-domain NOMA (taking the form of randomly spread code-division multiple access), as well as a relatively small gap to the ultimate performance limits, are identified. The proposed bounds are also applicable for the analysis of interference networks, e.g., Wyner-type cellular models.