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Principal Component Analyses in Anthropological Genetics  [PDF]
Xingdong Chen, Chao Chen, Li Jin
Advances in Anthropology (AA) , 2011, DOI: 10.4236/aa.2011.12002
Abstract: Principal component analyses (PCA) is a statistical method for exploring and making sense of datasets with a large number of measurements (which can be thought of as dimensions) by reducing the dimensions to the few principal components (PCs) that explain the main patterns. Thus, the first PC is the mathematical combination of measurements that accounts for the largest amount of variability in the data. Here, we gave an interpretation about the principle of PCA and its original mathematical algorithm, singular variable decomposition (SVD). PCA can be used in study of gene expression; also PCA has a population genetics interpretation and can be used to identify differences in ancestry among populations and samples, through there are some limitations due to the dynamics of microevolution and historical processes, with advent of molecular techniques, PCA on Y chromosome, mtDNA, and nuclear DNA gave us more accurate interpretations than on classical markers. Furthermore, we list some new extensions and limits of PCA.
A MATLAB-Based Numerical and GUI Implementation of Cross-Gradients Joint Inversion of Gravity and Magnetic Data  [PDF]
Junjie Zhou, Xingdong Zhang, Chunxiao Xiu
Journal of Software Engineering and Applications (JSEA) , 2015, DOI: 10.4236/jsea.2015.82010
Abstract: The cross-gradients joint inversion technique has been applied to multiple geophysical data with a significant improvement on compatibility, but its numerical implementation for practical use is rarely discussed in the literature. We present a MATLAB-based three-dimensional cross-gradients joint inversion program with application to gravity and magnetic data. The input and output information was examined with care to create a rational, independent design of a graphical user interface (GUI) and computing kernel. For 3D visualization and data file operations, UBC-GIF tools are invoked using a series of I/O functions. Some key issues regarding the iterative joint inversion algorithm are also discussed: for instance, the forward difference of cross gradients, and matrix pseudo inverse computation. A synthetic example is employed to illustrate the whole process. Joint and separate inversions can be performed flexibly by switching the inversion mode. The resulting density model and susceptibility model demonstrate the correctness of the proposed program.
Simultaneous Structure-Coupled Joint Inversion of Gravity and Magnetic Data Based on a Damped Least-Squares Technique  [PDF]
Junjie Zhou, Chunxiao Xiu, Xingdong Zhang
International Journal of Geosciences (IJG) , 2015, DOI: 10.4236/ijg.2015.62011
Abstract: The structure-coupled joint inversion method of gravity and magnetic data is a powerful tool fordeveloping improved physical property models with high resolution and compatible features;however, the conventional procedure is inefficient due to the truncated singular values decomposition(SVD) process at each iteration. To improve the algorithm, a technique using damped leastsquaresis adopted to calculate the structural term of model updates, instead of the truncated SVD. Thisproduces structural coupled density and magnetization images with high efficiency. A so-calledcoupling factor is introduced to regulate the tuning of the desired final structural similarity level.Synthetic examples show that the joint inversion results are internally consistent and achievehigherresolution than separated. The acceptable runtime performance of the damped least squarestechnique used in joint inversion indicates that it is more suitable for practical use than the truncated SVD method.
Lithological Characterization and Its Application Based on Three-Dimensional Structure-Coupled Joint Inversion of Gravity and Magnetic Data  [PDF]
Junjie Zhou, Xingdong Zhang, Chunxiao Xiu
International Journal of Geosciences (IJG) , 2015, DOI: 10.4236/ijg.2015.63016
Abstract: Incorporating structural-coupling constraint, known as the cross-gradients criterion, helps to improve the focussing trend in cross-plot of multiple physical properties. Based on this feature, apost-processing technique is studied to characterize the lithological types of subsurface geological materials after joint inversion. A simple domain transform, which converts two kinds of participant physical properties into an artificial complex array, is adopted to extract anomalies manually from homogenous host rock. A synthetic example shows that structure-coupled joint inverted results tend to concentrate on the feature trends in the cross-plot, and the main geological targets are recovered well by a radius-azimuth plot. In a field data example, the lithological characterizationreveals that the main rock types interpreted in the study area agree with the geological information, thus demonstrating the feasibility of this technique.
Reproducibility and Relative Validity of a Food Frequency Questionnaire Developed for Adults in Taizhou, China
Maoqiang Zhuang, Ziyu Yuan, Lanfang Lin, Bin Hu, Xiaofeng Wang, Yajun Yang, Xingdong Chen, Li Jin, Ming Lu, Weimin Ye
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0048341
Abstract: Objective To evaluate the reproducibility and validity of a food frequency questionnaire (FFQ) developed to investigate the relationship between dietary factors and diseases in the adult Chinese population in East China. Methods A total of 78 males and 129 females aged 30–75 years completed four inconsecutive 24-hour dietary recalls (24-HRs, served as a reference method) and two FFQs (FFQ1 and FFQ2) over a nine-month interval. The reproducibility of the FFQ was estimated with correlation coefficients, cross-classification, and weighted kappa statistic. The validity was assessed by comparing the data obtained from FFQ and 24-HRs. Results The median nutrient intakes assessed with FFQs were higher than the average of four 24-HRs. For the food groups, Spearman, Pearson, and intraclass correlation coefficients between FFQ1 and FFQ2 ranged from 0.23 to 0.61, 0.27 to 0.64, and 0.26 to 0.65, respectively. For total energy and nutrient intakes, the corresponding coefficients ranged from 0.25 to 0.61, 0.28 to 0.64, and 0.28 to 0.62, respectively. The correlations between FFQ1 and FFQ2 for most nutrients decreased after adjustment with total energy intake. More than 70% of the subjects were classified into the same and adjacent categories by both FFQs. For food groups, the crude, energy-adjusted, and de-attenuated Spearman correlation coefficients between FFQ2 and the 24-HRs ranged from 0.17 to 0.59, 0.10 to 0.57, and 0.11 to 0.64, respectively. For total energy and nutrient intakes, the corresponding coefficients ranged from 0.20 to 0.58, 0.08 to 0.54, and 0.09 to 0.56, respectively. More than 67% of the subjects were classified into the same and adjacent categories by both instruments. Both weighted kappa statistic and Bland-Altman Plots showed reasonably acceptable agreement between the FFQ2 and 24-HRs. Conclusion The FFQ developed for adults in the Taizhou area is reasonably reliable and valid for assessment of most food and nutrient intakes.
Association of Levels of Mannose-Binding Lectin and the MBL2 Gene with Type 2 Diabetes and Diabetic Nephropathy
Nana Zhang, Maoqiang Zhuang, Aixia Ma, Guochang Wang, Ping Cheng, Yajun Yang, Xiaofeng Wang, Juan Zhang, Xingdong Chen, Ming Lu
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0083059
Abstract: Objective To investigate the association of Mannose-binding lectin (MBL) and the MBL2 gene with type 2 diabetes and diabetic nephropathy and the influence of MBL2 polymorphisms on serum MBL levels. Methods The study population included 675 type 2 diabetic patients with or without nephropathy and 855 normoglycemic controls. The single nucleotide polymorphisms (SNPs) of rs1800450, rs1800451, and rs11003125 of the MBL2 gene were determined by the Multiplex Snapshot method. Serum MBL levels were measured by enzyme-linked immune sorbent assay. Results Rs1800450 and rs11003125 SNPs demonstrated strong linkage disequilibrium in the study population (r2 = 0.97). The haplotypes constructed from the G allele of rs1800450 and the C allele of rs11003125 increased the risk for type 2 diabetes (OR = 1.2, 95% CI = 1.1–1.4, P = 0.01). For rs1800450, GG and GA genotypes were associated with type 2 diabetes (P = 0.02, 0.01, respectively). For rs11003125, the GC genotype frequency was significantly different between patients and controls (18.1% vs. 24.9%, P = 0.001). Analyses of genotypes and allele frequency distributions among patients with normal UAE, microalbuminuria, and macroalbuminuria showed that there was no obvious evidence of association between the MBL2 gene and diabetic nephropathy. Subjects with the GG genotype of rs1800450 and the CC genotype of rs11003125 had much higher serum MBL levels. Conclusions The rs1800450 and rs11003125 SNPs of the MBL2 gene have strong linkage disequilibrium and are associated with type 2 diabetes in the North Chinese Han population. No association was observed between the MBL2 gene and diabetic nephropathy. Subjects with the GG genotype of rs1800450 and the CC genotype of rs11003125 had much higher serum MBL levels. An association between elevated serum MBL and diabetic nephropathy was also observed.
On a New Hilbert-Hardy-Type Integral Operator and Applications
Liu Xingdong,Yang Bicheng
Journal of Inequalities and Applications , 2010,
Abstract: By applying the way of weight functions and a Hardy's integral inequality, a Hilbert-Hardy-type integral operator is defined, and the norm of operator is obtained. As applications, a new Hilbert-Hardy-type inequality similar to Hilbert-type integral inequality is given, and two equivalent inequalities with the best constant factors as well as some particular examples are considered.
On a New Hilbert-Hardy-Type Integral Operator and Applications
Xingdong Liu,Bicheng Yang
Journal of Inequalities and Applications , 2010, DOI: 10.1155/2010/812636
Abstract:
Inference on low-rank data matrices with applications to microarray data
Xingdong Feng,Xuming He
Statistics , 2010, DOI: 10.1214/09-AOAS262
Abstract: Probe-level microarray data are usually stored in matrices, where the row and column correspond to array and probe, respectively. Scientists routinely summarize each array by a single index as the expression level of each probe set (gene). We examine the adequacy of a unidimensional summary for characterizing the data matrix of each probe set. To do so, we propose a low-rank matrix model for the probe-level intensities, and develop a useful framework for testing the adequacy of unidimensionality against targeted alternatives. This is an interesting statistical problem where inference has to be made based on one data matrix whose entries are not i.i.d. We analyze the asymptotic properties of the proposed test statistics, and use Monte Carlo simulations to assess their small sample performance. Applications of the proposed tests to GeneChip data show that evidence against a unidimensional model is often indicative of practically relevant features of a probe set.
Statistical inference based on robust low-rank data matrix approximation
Xingdong Feng,Xuming He
Statistics , 2014, DOI: 10.1214/13-AOS1186
Abstract: The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the singular value decomposition. However, the first singular values and vectors can be driven by a small number of outlying measurements. In this paper, we consider a robust alternative that moderates the effect of outliers in low-rank approximations. Under the assumption of random row effects, we provide the asymptotic representations of the robust low-rank approximation. These representations may be used in testing the adequacy of a low-rank approximation. We use oligonucleotide gene microarray data to demonstrate how robust singular value decomposition compares with the its traditional counterparts. Examples show that the robust methods often lead to a more meaningful assessment of the dimensionality of gene intensity data matrices.
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