Quantum and classical correlations for a two-qubit X structure density matrix

We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix. Based on the characteristics of the expressions, the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method. We explain the relationships among quantum discord, classical correlation, and entanglement, and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state. The new method, which is different from previous approaches, has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state, such as a mixed state.

Development of Comment Correlation Matrix for Mobile Application Recommendation

As the evolution of mobile technology, mobile devices have become an essential tool in people＇s daily life. Moreover, with the rapid growth of Internet and mobile networks, people can easily access various services provided by mobile platforms. Many services can be executed on the mobile devices with various mobile applications launched to mobile platforms. People can choose what they like to install in their mobile devices and hence make their life more convenient, entertaining, and productive. However, there are too many mobile applications for users to choose. The goal of this research is to propose a methodology which can recommend top-N lists for mobile applications. A comment correlation matrix is proposed. Furthermore, a recommendation algorithm for mobile applications based on user comments and key attributes is built. With the proposed method, it outperforms Google play and is closer to user real feelings.

Subspace decomposition-based correlation matrix multiplication

The correlation matrix, which is widely used in eigenvalue decomposition （EVD） or singular value decomposition （SVD）, usually can be denoted by R = E[yiy＇i]. A novel method for constructing the correlation matrix R is proposed. The proposed algorithm can improve the resolving power of the signal eigenvalues and overcomes the shortcomings of the traditional subspace methods, which cannot be applied to low SNR. Then the proposed method is applied to the direct sequence spread spectrum （DSSS） signal＇s signature sequence estimation. The performance of the proposed algorithm is analyzed, and some illustrative simulation results are presented.

Optimal Bounds for the Largest Eigenvalue of a 3 ×3 Correlation Matrix

A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.

Pseudo-Channel Matrix Truncation Based Spatial Correlation Mitigation in Massive MIMO

Massive multiple-input multiple-output(MIMO),a technique that can greatly increase spectral efficiency(SE)of cellular networks,has attracted significant interests in recent years.One of the major limitations of massive MIMO systems is pilot contamination,which will deteriorate the SE.The superimposed pilot-based scheme has been proved to be a viable method for pilot contamination reduction.However,it cannot break through another limitation of massive MIMO,i.e.,spatial correlation.In addition,it will also lead to interference between the pilot and user data since they are imposed together.In this paper,we try to tackle these two issues,which will be described as follows.Firstly,a column-wise asymptotically orthogonal matrix,named as pseudo-channel matrix,is developed by orthogonalization of received signal.To recover the information about the large-scale fading(LSF)coefficients,the pseudo-channel matrix is truncated according to the cardinality of adjacent users set(CAUS).By this means,spatial correlation can be mitigated effectively.Secondly,robust independent component analysis(RobustICA)is used to reduce the interference caused by user data,and as a result the system performance can be further improved.Numerical simulation results demonstrate the effectiveness of the proposed method.

Cross Correlation of Intra-day Stock Prices in Comparison to Random Matrix Theory

We propose and apply a new algorithm of principal component analysis which is suitable for a large sized, highly random time series data, such as a set of stock prices in a stock market. This algorithm utilizes the fact that the major part of the time series is random, and compare the eigenvalue spectrum of cross correlation matrix of a large set of random time series, to the spectrum derived by the random matrix theory (RMT) at the limit of large dimension (the number of independent time series) and long enough length of time series. We test this algorithm on the real tick data of American stocks at different years between 1994 and 2002 and show that the extracted principal components indeed reflects the change of leading stock sectors during this period.

Covariance Matrix Learning Differential Evolution Algorithm Based on Correlation

Differential evolution algorithm based on the covariance matrix learning can adjust the coordinate system according to the characteristics of the population, which makes the search move in a more favorable direction. In order to obtain more accurate information about the function shape, this paper proposes covariance matrix learning differential evolution algorithm based on correlation (denoted as RCLDE) to improve the search efficiency of the algorithm. First, a hybrid mutation strategy is designed to balance the diversity and convergence of the population;secondly, the covariance learning matrix is constructed by selecting the individual with the less correlation;then, a comprehensive learning mechanism is comprehensively designed by two covariance matrix learning mechanisms based on the principle of probability. Finally, the algorithm is tested on the CEC2005, and the experimental results are compared with other effective differential evolution algorithms. The experimental results show that the algorithm proposed in this paper is an effective algorithm.

Cross-correlation matrix analysis of Chinese and American bank stocks in subprime crisis

In order to study the universality of the interactions among different markets, we analyze the cross-correlation matrix of the price of the Chinese and American bank stocks. We then find that the stock prices of the emerging market are more correlated than that of the developed market. Considering that the values of the components for the eigenvector may be positive or negative, we analyze the differences between two markets in combination with the endogenous and exogenous events which influence the financial markets. We find that the sparse pattern of components of eigenvectors out of the threshold value has no change in American bank stocks before and after the subprime crisis. However, it changes from sparse to dense for Chinese bank stocks. By using the threshold value to exclude the external factors, we simulate the interactions in financial markets.

Using shapes correlation for active contour segmentation of uterine fibroid ultrasound images in computer-aided therapy

Segmenting the lesion regions from the ultrasound （US） images is an important step in the intra-operative planning of some computer-aided therapies. High-Intensity Focused Ultrasound （HIFU）, as a popular computer-aided therapy, has been widely used in the treatment of uterine fibroids. However, such segmentation in HIFU remains challenge for two reasons： （1） the blurry or missing boundaries of lesion regions in the HIFU images and （2） the deformation of uterine fibroids caused by the patient＇s breathing or an external force during the US imaging process, which can lead to complex shapes of lesion regions. These factors have prevented classical active contour-based segmentation methods from yielding desired results for uterine fibroids in US images. In this paper, a novel active contour-based segmentation method is proposed, which utilizes the correlation information of target shapes among a sequence of images as prior knowledge to aid the existing active contour method. This prior knowledge can be interpreted as a unsupervised clustering of shapes prior modeling. Meanwhile, it is also proved that the shapes correlation has the low-rank property in a linear space, and the theory of matrix recovery is used as an effective tool to impose the proposed prior on an existing active contour model. Finally, an accurate method is developed to solve the proposed model by using the Augmented Lagrange Multiplier （ALM）. Experimental results from both synthetic and clinical uterine fibroids US image sequences demonstrate that the proposed method can consistently improve the performance of active contour models and increase the robustness against missing or misleading boundaries, and can greatly improve the efficiency of HIFU therapy.

Correlation of coordinate transformation parameters

Coordinate transformation parameters between two spatial Cartesian coordinate systems can be solved from the positions of non-colinear corresponding points. Based on the characteristics of translation, rotation and zoom components of the transformation, the complete solution is divided into three steps. Firstly, positional vectors are regulated with respect to the centroid of sets of points in order to separate the translation compo- nents. Secondly, the scale coefficient and rotation matrix are derived from the regulated positions independent- ly and correlations among transformation model parameters are analyzed. It is indicated that this method is applicable to other sets of non-position data to separate the respective attributions for transformation parameters.

Ternary Zero Correlation Zone Sequence Sets for Asynchronous DS-CDMA

In this paper we propose a new class of ternary Zero Correlation Zone (ZCZ) sequence sets based on binary ZCZ sequence sets construction. It is shown that the proposed ternary ZCZ sequence sets can reach the upper bound on the ZCZ sequences. The performance of the proposed sequences set in asynchronous Direct Sequence-Code Division Multiple Access (DS-CDMA) system is evaluated. In the simulation we used two types of channels: Additive White Gaussian Noise (AWGN) and frequency non-selective fading with AWGN noise. The proposed ternary ZCZ sequence sets show better results, in term of Bit Error Rate (BER), than Hayashi’s ternary ZCZ sequence sets.

On Testing Equality of K Multiple Correlation Matrices

Coutsourides derived an ad hoc nuisance paratmeter removal test for testing equality of two multiple correlation matrices of two independent p variate normal populations under the assumption that a sample of size n is available from each population. This paper presents a likelihood ratio test criterion for testing equality of K multiple correlation matrices and extends the results to the testing of equality of K partial correlation matrices.

AN NMF ALGORITHM FOR BLIND SEPARATION OF CONVOLUTIVE MIXED SOURCE SIGNALS WITH LEAST CORRELATION CONSTRAINS

Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are non- negative and mutual statistically dependent signals. When the observations are nonnegative linear combinations of nonnegative sources, the correlation coefficients of the observations are larger than these of source signals. In this letter, a novel Nonnegative Matrix Factorization (NMF) algorithm with least correlated component constraints to blind separation of convolutive mixed sources is proposed. The algorithm relaxes the source independence assumption and has low-complexity algebraic com- putations. Simulation results on blind source separation including real face image data indicate that the sources can be successfully recovered with the algorithm.

Area-Correlated Spectral Unmixing Based on Bayesian Nonnegative Matrix Factorization

To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed me-thod, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of the adjacent areas are used to estimate the priori probability density func-tions of the endmembers in the current area, which works as a type of constraint in the iterative spectral unmixing process. Experimental results demonstrate the effectivity and efficiency of the proposed method both for synthetic and real hyperspectral images, and it can provide a useful tool for spatial correlation and comparation analysis between ad-jacent or similar areas.

Estimation of a Linear Model in Terms of Intra-Class Correlations of the Residual Error and the Regressors

Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.

The radial correlation of atomic electrons in (e,2e) reaction

We perform a research of the influence of atomic electrons correlation to some characteristics of the (e,2e) process on helium. The Hilleraas type J-matrix approach was used for numerical calculations.

Philosophical Matrix as a System of Categories of Pure Mind

The article is a study devoted to the development of the concept of the philosophical matrix as a system of categories of pure reason.The author proposes a new approach to understanding the philosophical system of categories by putting forward unambiguous comparative concepts that serve as the basis for natural sciences.While the foundations of specific sciences are the concepts of“practical reason”,the author finds the categories of“pure reason”to be the foundations of philosophy,understood as“knowledge of the universal”.The article shows that relying on the senses and the concepts of“practical reason”allows for the verification of knowledge,while their generalization,removed from knowledge obtained empirically,gives categories of“pure reason”,which are accepted as the building material of the matrix.In this way,the author proposes a new system of philosophical categories that describes the fundamental aspects of human reasoning and its interaction with the world.At the same time,the categories of the philosophical matrix are not related to such ambiguous classificatory concepts as space,time,being,existence,consciousness,and others.The article draws attention to the fact that the matrix can be used not only to analyze philosophical theories but also to develop new concrete scientific approaches,for example,for the intellectual development of children.In addition,the article suggests the possibility of applying the philosophical matrix in other areas of the humanities,including psychology,linguistics,and sociology.As a result of the conducted research,the human intellect is divided into three ascending stages,designated by me in the following words-reason,mind,and wisdom,with the subsequent use of these concepts in philosophy and other fields of knowledge.

基于阵列风速仪实测的台风“苏迪罗”近地风场空间相关性研究

[目的]针对沿海区域近地台风风场的空间相关性问题进行研究.[方法]根据阵列风速仪实测的台风“苏迪罗”风速风向数据,选取4个稳定时段的288个风速样本,对台风近地风场的空间相关性进行详细的分析.首先定性研究平均风速和风向角对顺、横风向、垂直方向脉动风速的竖向和水平互相关系数的影响,然后分析平均风速和风向角对3种脉动风速竖向和水平相干函数的影响,最后对顺风向竖向相干函数、顺风向水平相干函数和横风向水平相干函数进行公式拟合,获得相关参数的取值.[结果]平均风速对顺、横风向的竖向和水平互相关系数及相干函数有一定影响,平均风速越大,相应的互相关系数和相干函数也随之增大;风向角对3种脉动风速的竖向相关性影响不大,但对顺、横风向的水平互相关系数和相干函数影响较大;各种相干函数在零频率处(f=0 Hz)的数值大都小于1.0,零频率处的数值随距离与平均风速的比值呈指数衰减规律;顺风向竖向相干函数、顺风向水平相干函数和横风向水平相干函数随距离与平均风速比值的衰减系数分别为9.3 f+0.38,3.1 f+0.18,3.2 f+0.16.[结论]基于阵列风速仪实测的近地台风数据,分析得到了台风风场的空间相关性特性,竖向和水平的互相关系数和相干函数,给出的拟合公式可用于大跨度空间结构和桥梁结构的动态响应分析计算,可有效评估工程结构的抗风安全性.

血清TLR4、TIMP-1水平与小儿热性惊厥临床特征的关系及对继发癫痫的预测价值

目的分析血清Toll样受体4(TLR4)、基质金属蛋白酶组织抑制剂(TIMP)-1水平与小儿热性惊厥(FC)临床特征的关系及对FC继发癫痫的预测价值。方法选取2019年1月至2022年6月320例FC患儿作为研究组,另选取同期发热无惊厥儿童150例作为发热组,体检健康儿童150例作为对照组。根据FC患儿是否继发癫痫分为癫痫组和无癫痫组。采用酶联免疫吸附试验检测血清TLR4、TIMP-1水平,采用Pearson相关分析TLR4、TIMP-1水平及与临床指标间的相关性。采用受试者工作特征(ROC)曲线分析血清TLR4、TIMP-1预测FC继发癫痫的价值。采用Logistic回归分析FC患儿继发癫痫的影响因素。结果FC患儿、发热无惊厥儿童、体检健康儿童血清TLR4、TIMP-1水平依次降低,且两两比较,差异均有统计学意义(P<0.05)。研究组与发热组围生期异常发生情况、肿瘤坏死因子α(TNF-α)、C-反应蛋白(CRP)、白细胞介素-1β(IL-1β)水平和振幅整合脑电图(AEEG)评分比较,差异均有统计学意义(P<0.05)。癫痫组患儿血清TLR4、TIMP-1水平明显高于无癫痫组(P<0.05)。癫痫组和无癫痫组患儿首次惊厥次数、惊厥持续时间、首次惊厥前发热时间、围生期异常发生情况、TNF-α、CRP、IL-1β水平和AEEG评分比较,差异均有统计学意义(P<0.05)。血清TLR4水平与TIMP-1呈正相关(P<0.05);血清TLR4、TIMP-1水平与TNF-α、CRP、IL-1β呈正相关(P<0.05),与AEEG评分呈负相关(P<0.05)。TLR4、TIMP-1联合预测FC患儿继发癫痫的曲线下面积(AUC)明显高于单项检测的AUC(Z_(TLR4-联合)=3.016,P=0.003;Z_(TIMP-1-联合)=2.232,P=0.026)。Logistic回归分析结果表明,TLR4、TIMP-1、TNF-α、CRP、IL-1β水平升高,AEEG评分降低均为FC继发癫痫的危险因素(P<0.05)。结论血清TLR4、TIMP-1与FC患儿临床特征密切相关,TLR4、TIMP-1可能是FC继发癫痫的影响因素。

基于重要性分数的CUR矩阵分解识别WSN异常节点

现有异常节点识别方法普遍存在精度低或者功耗大等不足,针对这些不足,提出一种基于低秩矩阵分解的无线传感器网络异常节点识别算法。根据传感器节点的特性进行特征选取和属性矩阵构建;通过改进的CUR矩阵分解方法计算异常矩阵;依据异常矩阵中节点向量的总体均值和标准差设定控制限,判断节点是否发生异常。实验结果表明,与其它异常识别方法相比,该方法具有较高的识别准确率。