行(列)对称矩阵的满秩分解和正交对角分解

提出了行(列)转置矩阵与行(列)对称矩阵的概念,研究了其性质,给出了行(列)对称矩阵的满秩分解和正交对角分解公式,极大地减少了行(列)对称矩阵的满秩分解和正交对角分解的计算量与存储量,且没有降低数值精度.     

Hadamard matrix methods in identifying differentially expressed genes from microarray experiments

Identifying differentially expressed genes is a basic objective in microarray experiments. Many statistical methods for detecting differentially expressed genes in multiple-slide experiments have been proposed. However, sometimes with limited experimental resources, only a single cDNA array or two Oligonuleotide arrays could be made or only insufficient replicated arrays could be conducted. Many current statistical models cannot be used because of the non-availability of replicated data. Simply using fold changes is also unreliable and inefficient [Chen et al. 1997. Ratio-based decisions and the quantitative analysis of cDNA microarray images. J. Biomed. Optics 2, 364–374; Newton et al. 2001. On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data. J. Comput. Biol. 8, 37–52; Pan et al. 2002. How many replicates of arrays are required to detect gene expression changes in microarray experiments? a mixture model approach. Genome Biol. 3, research0022.1-0022.10]. We propose a new method. If the log-transformed ratios for the expressed genes as well as unexpressed genes have equal variance, we use a Hadamard matrix to construct a t-test from a single array data. Basically, we test whether each doubtful gene has significantly differential expression compared to the unexpressed genes. We form some new random variables corresponding to the rows of a Hadamard matrix using the algebraic sum of gene expressions. A one-sample t-test is constructed and the p-value is calculated for each doubtful gene based on these random variables. By using any method for multiple testing, adjusted p-values could be obtained from original p-values and significance of doubtful genes can be determined. When the variance of expressed genes differs from the variance of unexpressed genes, we construct a z-statistic based on the result from application of Hadamard matrix and find the confidence interval to retain the null hypothesis. Using the interval, we determine differentially expressed genes. This method is also useful for multiple microarrays, especially when sufficient replicated data are not available for a traditional t-test. We apply our methodology to ApoAI data. The results appear to be promising. They not only confirm the early known differentially expressed genes, but also indicate more genes to be differentially expressed.     

关于有限生成模糊向量(矩阵)空间基底的注

讨论了有限生成模糊向量(矩阵)空间的基底的若干问题.     

限值响应超平面模式识别的模型及计算方法

用模式识别的观点，探讨了以本征值分解法研究响应值在窄的上下限内的限值控制问题．通过变换坐标表象（ｒｅｐｒｅｓｅｎｔａｔｉｏｎ），可以将一个超平面嵌入响应值符合控制要求的输入模式的薄分布层中，并划分出一定的模糊分界面±ｄ’，使之与响应值的限定范围±ｄ相对应．子空间中的超平面由协方差矩阵的一组本任解确定，且最小本征值所对应的本征矢为超平面的法矢．从拟合特定输入模式的分布出发，建立输入－输出之间的一般联系，减少了在模型建立和修正过程中对系统正常运行的干扰．     

用C 构造矩阵类

本文主要讨论可重用的面向对象的矩阵类的设计方法，另外，本文也注重C＋＋的编程思想和技巧，因此，源程序清单中通过给出流运算符重载、算术运算符重载、类模板等等的诸多实例，说明C＋＋的设计程序技术。     

二维到达角和极化参数的并行化设计

针对无线电波的信号频率、二维到达角和极化参数联合估计算法的运算量大、计算时间长,且不能满足实时性要求的问题,提出了对该算法进行并行化设计的解决方法。通过对联合估计算法的数学模型和串行算法的分析,设计并实现了通用并行算法。经在4台同构处理器上进行测试,表明该并行算法能有效减少计算时间,使加速比达到2倍以上。     

用矩阵讨论多元函数的极值问题

利用矩阵给出了多元函数在稳定点取极值的充分条件,提出了解决两类极值问题的代数方法.     

Aligned rank statistics for repeated measurement models with orthonormal design, employing a Chernoff–Savage approach

In this paper, aligned rank statistics are considered for testing hypotheses regarding the location in repeated measurement designs, where the design matrix for each set of measurements is orthonormal. Such a design may, for instance, be used when testing for linearity. It turns out that the centered design matrix is not of full rank, and therefore it does not quite satisfy the usual conditions in the literature. The number of degrees of freedom of the limiting chi-square distribution of the test statistic under the null hypothesis, however, is not affected, unless rather special hypotheses are tested. An independent derivation of this limiting distribution is given, using the Chernoff–Savage approach. In passing, it is observed that independence of the choice of aligner, which in the location problem is well-known to be due to cancellation, may in scale problems occur as a result of the type of score function suitable for scale tests. A possible extension to multivariate data is briefly indicated.     

基于神经网络的超声医学图像自动分割

图像分割是多维超声医学图像重建中最重要和最困难的问题。文中将传统的最近邻分类方法与自组织神经网络相结合，提出了一种超声医学图像的自动分割方法。实验表明，与传统的Ｋ平均方法相比，该方法除具有自动分割优点外，还具有稳定性好，自适应强，分割准确等优点。     

模数制渐开线直齿圆柱齿轮几何要素的测量

本文阐述了渐开线直齿圆柱齿轮顶圆直径及齿轮模数、变位系数和压力角等参数的确定方法和步骤.