关于矩阵乘积特征值估计的一点注记

由矩阵奇异值的表示定理,给出了一个关于矩阵乘积的特征值的估计,进而说明[1]、[2]的结果都是没有意义的。     

求解线性互补问题的AOR算法

建立了求解线性互补问题的加速松驰迭代算法，并在一定条件下，证明了新算法的收敛性。     

新型吡唑去甲斑蝥酰亚胺衍生物的核磁共振波谱分析

利用1,3-偶极环加成合成了新的去甲去氢斑蝥素衍生物,借助1HNMR、13CNMR及相关的2DNMR谱的分析,对斑蝥素衍生物的氢谱和碳谱进行了归属,并确证了该类化合物的构象.     

On the estimation of the spectral density for continuous spatial processes

In this work, we study the asymptotic properties of smoothed nonparametric kernel spectral density estimators for the spatial spectral density. We consider the case of continuous stationary spatial processes under a shrinking asymptotic framework. Expressions for the bias and the covariance structure are obtained and the implications for the edge effect bias of the choice of the kernel, bandwidth and spacing parameter in the design are also discussed, both for tapered and untapered estimates. Results are illustrated with a simulation study.     

The limiting spectral distribution for large sample covariance matrices with unbounded m-dependent entries

ABSTRACT

In this note, the limiting spectral distribution for large sample covariance matrices with unbounded m-dependent structure is obtained under the third moment for the entries. This partially extends the results of Hui and Pan (Comm. Statist. Theory and Methods, 2010, 39: 935–941).     

Estimation of the population spectral distribution from a large dimensional sample covariance matrix

This paper introduces a new method to estimate the spectral distribution of a population covariance matrix from high-dimensional data. The method is founded on a meaningful generalization of the seminal Mar?enko–Pastur equation, originally defined in the complex plane, to the real line. Beyond its easy implementation and the established asymptotic consistency, the new estimator outperforms two existing estimators from the literature in almost all the situations tested in a simulation experiment. An application to the analysis of the correlation matrix of S&P 500 daily stock returns is also given.     

产品级再使用的绩效测度

产品级再使用绩效测度有助于总结再使用的经验,加强停用产品的资源化管理,实现产品的最大再利用价值,提出了从技术先进性、绿色性、经济性和心理因素4个方面测度产品级再使用全过程绩效,建立了产品级再使用子系统和特征矩阵,提出了基于谱范数的测度方法,该方法充分利用了产品级再使用全过程的指标信息,并在不同阶段给予指标不同的权重。针对绩效测度指标过多的问题,提出了两阶段的层次分析法,在多指标权重确定中具有应用价值,另一方面也解决了专家的权威与共识问题。以电视再使用为案例,验证了提出的理论和方法能有效测度再使用绩效,并进行了结果分析,给出了再使用建议。     

基于谱分析的安徽省经济波动研究

科学地测定经济周期,有利于从更深层次理解和把握安徽经济系统的运行状态,对于安徽国民经济实现又好又快地发展具有十分重要的理论定义与现实意义。目前国内学者对安徽宏观经济波动的研究还比较少,故采用增长周期法,剔除安徽省国内生产总值指数长期趋势,生成人工序列,并对其进行加汉宁窗的谱分析,得到相应谱密度曲线;确定安徽省经济波动周期分量的长度与类型,对安徽经济周期波动情况进行回顾,发现固定资产投资的周期波动是造成安徽经济周期波动最直接的内在原因。安徽省应加强宏观经济调控,以减缓经济波动造成的影响。     

Community detection with structural and attribute similarities

An important problem in network analysis is to identify significant communities. Most of the real-world data sets exhibit a certain topological structure between nodes and the attributes describing them. In this paper, we propose a new community detection criterion considering both structural similarities and attribute similarities. The clustering method integrates the cost of clustering node attributes with the cost of clustering the structural information via the normalized modularity. We show that the joint clustering problem can be formulated as a spectral relaxation problem. The proposed algorithm is capable of learning the degree of contributions of individual node attributes. A number of numerical studies involving simulated and real data sets demonstrate the effectiveness of the proposed method.