Relative ordering of square-norm distance correlations in open quantum systems

We investigate the square-norm distance correlation dynamics of the Bell-diagonal states under different local deco- herence channels, including phase flip, bit flip, and bit-phase flip channels by employing the geometric discord （GD） and its modified geometric discord （MGD）, as the measures of the square-norm distance correlations. Moreover, an explicit comparison between them is made in detail. The results show that there is no distinct dominant relative ordering between them. Furthermore, we obtain that the GD just gradually deceases to zero, while MGD initially has a large freezing interval, and then suddenly changes in evolution. The longer the freezing interval, the less the MGD is. Interestingly, it is shown that the dynamic behaviors of the two geometric discords under the three noisy environments for the Werner-type initial states are the same.

Correlation Analysis of Genetic Distance and Heterosis of the Major Brassica napus L. Cultivars in Yunnan Province

[Objective] The correlation between genetic distance and heterosis of the major Brassica napus L. cultivars in Yunnan Province was analyzed. [Method] The genetic distances among the 8 major Brassica napus L. cultivars in Yunnan Province were investigated with the SSR molecular marker technique. Moreover, the correlation between genetic distance and field appearance of heterosis was ana-lyzed. [Result] There was a certain correlation between the genetic distance and heterosis of crossing parents （P〉0.05）. [Conclusion] It is difficult to predict the het-erosis of Brassica napus L. cultivars and to screen parents by using the SSR molecular marker technique.

Exact Statistical Distribution and Correlation of Human Height and Weight: Analysis and Experimental Confirmation

The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, and the biology of human development. Yet, after more than a century of anthropometric measurements and analyses, there has been no consensus on this relationship. The purpose of this article is to provide a definitive statistical distribution function from which all desired statistics (probabilities, moments, and correlation functions) can be determined. The statistical analysis reported in this article provides strong evidence that height and weight in a diverse population of healthy adults constitute correlated bivariate lognormal random variables. This conclusion is supported by a battery of independent tests comparing empirical values of 1) probability density patterns, 2) linear and higher order correlation coefficients, 3) statistical and hyperstatistics moments up to 6th order, and 4) distance correlation (dCor) values to corresponding theoretical quantities: 1) predicted by the lognormal distribution and 2) simulated by use of appropriate random number generators. Furthermore, calculation of the conditional expectation of weight, given height, yields a theoretical power law that specifies conditions under which body mass index (BMI) can be a valid proxy of obesity. The consistency of the empirical data from a large, diverse anthropometric survey partitioned by gender with the predictions of a correlated bivariate lognormal distribution was found to be so extensive and close as to suggest that this outcome is not coincidental or approximate, but may be a consequence of some underlying biophysical mechanism.

A selective overview of feature screening for ultrahigh-dimensional data

High-dimensional data have frequently been collected in many scientific areas including genomewide association study, biomedical imaging, tomography, tumor classifications, and finance. Analysis of highdimensional data poses many challenges for statisticians. Feature selection and variable selection are fundamental for high-dimensional data analysis. The sparsity principle, which assumes that only a small number of predictors contribute to the response, is frequently adopted and deemed useful in the analysis of high-dimensional data.Following this general principle, a large number of variable selection approaches via penalized least squares or likelihood have been developed in the recent literature to estimate a sparse model and select significant variables simultaneously. While the penalized variable selection methods have been successfully applied in many highdimensional analyses, modern applications in areas such as genomics and proteomics push the dimensionality of data to an even larger scale, where the dimension of data may grow exponentially with the sample size. This has been called ultrahigh-dimensional data in the literature. This work aims to present a selective overview of feature screening procedures for ultrahigh-dimensional data. We focus on insights into how to construct marginal utilities for feature screening on specific models and motivation for the need of model-free feature screening procedures.

The abstract of doctoral dissertation‘Some research on hypothesis testing and nonparametric variable screening problems for high dimensional data’

In this thesis,we construct test statistic for association test and independence test in high dimension,respectively,and study the corresponding theoretical properties under some regularity conditions.Meanwhile,we propose a nonparametric variable screening procedure for sparse additive model with multivariate response in untra-high dimension and established some screening properties.

Dimension reduction graph-based sparse subspace clustering for intelligent fault identification of rolling element bearings

Sparse subspace clustering(SSC)is a spectral clustering methodology.Since high-dimensional data are often dispersed over the union of many low-dimensional subspaces,their representation in a suitable dictionary is sparse.Therefore,SSC is an effective technology for diagnosing mechanical system faults.Its main purpose is to create a representation model that can reveal the real subspace structure of high-dimensional data,construct a similarity matrix by using the sparse representation coefficients of high-dimensional data,and then cluster the obtained representation coefficients and similarity matrix in subspace.However,the design of SSC algorithm is based on global expression in which each data point is represented by all possible cluster data points.This leads to nonzero terms in nondiagonal blocks of similar matrices,which reduces the recognition performance of matrices.To improve the clustering ability of SSC for rolling bearing and the robustness of the algorithm in the presence of a large number of background noise,a simultaneous dimensionality reduction subspace clustering technology is provided in this work.Through the feature extraction of envelope signal,the dimension of the feature matrix is reduced by singular value decomposition,and the Euclidean distance between samples is replaced by correlation distance.A dimension reduction graph-based SSC technology is established.Simulation and bearing data of Western Reserve University show that the proposed algorithm can improve the accuracy and compactness of clustering.