Variants of the Varimax Rotation Method

In the present paper we present an example proving that the Varimax rotation method commonly used in factor analysis (see H. F. KAISER, 1958) need not give a unique solution. We also show that changing the original algorithm more than one local maximum of the criterion “V” can be achieved. Hence the loadings of factors and practical interpretations of solutions are affected in this way.     

Development of a New Index of Balance in Adults with Intellectual and Developmental Disabilities

Purposes

The first objective was to propose a new model representing the balance level of adults with intellectual and developmental disabilities (IDD) using Principal Components Analysis (PCA); and the second objective was to use the results from the PCA recorded by regression method to construct and validate summative scales of the standardized values of the index, which may be useful to facilitate a balance assessment in adults with IDD.

Methods

A total of 801 individuals with IDD (509 males) mean 33.1±8.5 years old, were recruited from Special Olympic Games in Spain 2009 to 2012. The participants performed the following tests: the timed-stand test, the single leg stance test with open and closed eyes, the Functional Reach Test, the Expanded Timed-Get-up-and-Go Test. Data was analyzed using principal components analysis (PCA) with Oblimin rotation and Kaiser normalization. We examined the construct validity of our proposed two-factor model underlying balance for adults with IDD. The scores from PCA were recorded by regression method and were standardized.

Results

The Component Plot and Rotated Space indicated that a two-factor solution (Dynamic and Static Balance components) was optimal. The PCA with direct Oblimin rotation revealed a satisfactory percentage of total variance explained by the two factors: 51.6 and 21.4%, respectively. The median score standardized for component dynamic and static of the balance index for adults with IDD is shown how references values.

Conclusions

Our study may lead to improvements in the understanding and assessment of balance in adults with IDD. First, it confirms that a two-factor model may underlie the balance construct, and second, it provides an index that may be useful for identifying the balance level for adults with IDD.     

Supervised principal component analysis for gene set enrichment of microarray data with continuous or survival outcomes

MOTIVATION: Gene set analysis allows formal testing of subtle but coordinated changes in a group of genes, such as those defined by Gene Ontology (GO) or KEGG Pathway databases. We propose a new method for gene set analysis that is based on principal component analysis (PCA) of genes expression values in the gene set. PCA is an effective method for reducing high dimensionality and capture variations in gene expression values. However, one limitation with PCA is that the latent variable identified by the first PC may be unrelated to outcome. RESULTS: In the proposed supervised PCA (SPCA) model for gene set analysis, the PCs are estimated from a selected subset of genes that are associated with outcome. As outcome information is used in the gene selection step, this method is supervised, thus called the Supervised PCA model. Because of the gene selection step, test statistic in SPCA model can no longer be approximated well using t-distribution. We propose a two-component mixture distribution based on Gumbel exteme value distributions to account for the gene selection step. We show the proposed method compares favorably to currently available gene set analysis methods using simulated and real microarray data. SOFTWARE: The R code for the analysis used in this article are available upon request, we are currently working on implementing the proposed method in an R package.     

Fluorescence polarization immunoassay: detection of antibody to Brucella abortus

Fluorescence polarization immunoassay (FPA) is a homogeneous immunoassay useful for rapid and accurate detection of antibody or antigen. The principle of the assay is that a fluorescent dye (attached to an antigen or an antibody fragment) can be excited by plane-polarized light at the appropriate wavelength. As a rule, a small molecule rotates faster when in solution than a larger molecule. The rotation rate may be assessed by measuring light intensity in the vertical and horizontal planes. Generally, the time it takes a molecule to rotate through a given angle is an indication of its size. When a small molecule that rotates rapidly is bound to a larger molecule, the rotation rate is decreased and this decrease is measured. Because it is a primary antigen-antibody interaction, the rate of reaction is very rapid and usually a result may be obtained in minutes. This technology was applied to the detection of antibody to Brucella abortus in serum and milk, providing for the first time a rapid primary binding assay that is cost effective for use in the field.     

The effect of boundary conditions on epicardial potential distributions

This study presents a comparison of semi-analytical and numerical solution techniques for solving the passive bidomain equation in simple tissue geometries containing a region of subendocardial ischaemia. When the semi-analytical solution is based on Fourier transforms, recovering the solution from the frequency domain via fast Fourier transforms imposes a periodic boundary condition on the solution of the partial differential equation. On the other hand, the numerical solution uses an insulation boundary condition. When these techniques are applied to calculate the epicardial surface potentials, both yield a three well potential distribution which is identical if fibre rotation within the tissue is ignored. However, when fibre rotation is included, the resulting three-well distribution rotates, but through different angles, depending on the solution method. A quantitative comparison between the semi-analytical and numerical solutiontechniques is presented in terms of the effect fibre rotation has on the rotation of the epicardial potential distribution. It turns out that the Fourier transform approach predicts a larger rotation of the epicardial potential distribution than the numerical solution. The conclusion from this study is that it is not always possible to use analytical or semi-analytical solutions to check the accuracy of numerical solution procedures. For the problem considered here, this checking is only possible when it is assumed that there is no fibre rotation through the tissue.     

A principal components analysis of human odontometrics

It has long been recognized that tooth crown diameters in hominoids are all positively intercorrelated one with another. This study reports on sex-specific correlation matrices derived from 2,650 individuals from the Solomon Islands, Melanesia. Mesiodistal and buccolingual diameters of all permanent teeth from one side are used, excluding third molars. Analysis discloses significant sex dimorphism in the strengths of the intercorrelations, with females being better integrated. Principal components analysis (PCA) provides an objective means of data reduction (shown here to be preferable to simple size summation methods) and decorrelation of the resulting linear combinations. Four components are extracted (with results being virtually identical in the two sexes) and arguments are put forth that varimax rotation to "a simpler solution" may be counterproductive. Before rotation, the four components are 1) overall size, 2) buccolingual widths contrasted with mesiodistal lengths, 3) anterior (I,C) contrasted with posterior (P,M) teeth, and 4) premolars contrasted with molars. Most of the explained (shared) variance (63%) extracted by PCA is in overall size of the dentition. There is a strong urge to view the results of these principal components analyses as reflective of biologically and genetically meaningful entities.     

Multivariate denoising methods combining wavelets and principal component analysis for mass spectrometry data

The identification of new diagnostic or prognostic biomarkers is one of the main aims of clinical cancer research. In recent years, there has been a growing interest in using mass spectrometry for the detection of such biomarkers. The MS signal resulting from MALDI‐TOF measurements is contaminated by different sources of technical variations that can be removed by a prior pre‐processing step. In particular, denoising makes it possible to remove the random noise contained in the signal. Wavelet methodology associated with thresholding is usually used for this purpose. In this study, we adapted two multivariate denoising methods that combine wavelets and PCA to MS data. The objective was to obtain better denoising of the data so as to extract the meaningful proteomic biological information from the raw spectra and reach meaningful clinical conclusions. The proposed methods were evaluated and compared with the classical soft thresholding denoising method using both real and simulated data sets. It was shown that taking into account common structures of the signals by adding a dimension reduction step on approximation coefficients through PCA provided more effective denoising when combined with soft thresholding on detail coefficients.     

Parallel Analysis: a method for determining significant principal components

Abstract. Numerous ecological studies use Principal Components Analysis (PCA) for exploratory analysis and data reduction. Determination of the number of components to retain is the most crucial problem confronting the researcher when using PCA. An incorrect choice may lead to the underextraction of components, but commonly results in overextraction. Of several methods proposed to determine the significance of principal components, Parallel Analysis (PA) has proven consistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. All components with eigenvalues below this threshold value should be considered spurious. We illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis (FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separated into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was applied for each PCA/FA found in the literature. Of 39 analy ses (in 22 articles), 29 (74.4 %) considered no threshold rule, presumably retaining interpretable components. According to the PA results, 26 (66.7 %) overextracted components. This overextraction may have resulted in potentially misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase confidence in the results and reduce the subjective interpretation of supposedly objective methods.     

Exploring the Factor Structure of Neurocognitive Measures in Older Individuals

Here we focus on factor analysis from a best practices point of view, by investigating the factor structure of neuropsychological tests and using the results obtained to illustrate on choosing a reasonable solution. The sample (n=1051 individuals) was randomly divided into two groups: one for exploratory factor analysis (EFA) and principal component analysis (PCA), to investigate the number of factors underlying the neurocognitive variables; the second to test the “best fit” model via confirmatory factor analysis (CFA). For the exploratory step, three extraction (maximum likelihood, principal axis factoring and principal components) and two rotation (orthogonal and oblique) methods were used. The analysis methodology allowed exploring how different cognitive/psychological tests correlated/discriminated between dimensions, indicating that to capture latent structures in similar sample sizes and measures, with approximately normal data distribution, reflective models with oblimin rotation might prove the most adequate.     

Classification and Visualization Based on Derived Image Features: Application to Genetic Syndromes

Data transformations prior to analysis may be beneficial in classification tasks. In this article we investigate a set of such transformations on 2D graph-data derived from facial images and their effect on classification accuracy in a high-dimensional setting. These transformations are low-variance in the sense that each involves only a fixed small number of input features. We show that classification accuracy can be improved when penalized regression techniques are employed, as compared to a principal component analysis (PCA) pre-processing step. In our data example classification accuracy improves from 47% to 62% when switching from PCA to penalized regression. A second goal is to visualize the resulting classifiers. We develop importance plots highlighting the influence of coordinates in the original 2D space. Features used for classification are mapped to coordinates in the original images and combined into an importance measure for each pixel. These plots assist in assessing plausibility of classifiers, interpretation of classifiers, and determination of the relative importance of different features.     

A weighted principal component analysis and its application to gene expression data

In this work, we introduce in the first part new developments in Principal Component Analysis (PCA) and in the second part a new method to select variables (genes in our application). Our focus is on problems where the values taken by each variable do not all have the same importance and where the data may be contaminated with noise and contain outliers, as is the case with microarray data. The usual PCA is not appropriate to deal with this kind of problems. In this context, we propose the use of a new correlation coefficient as an alternative to Pearson's. This leads to a so-called weighted PCA (WPCA). In order to illustrate the features of our WPCA and compare it with the usual PCA, we consider the problem of analyzing gene expression data sets. In the second part of this work, we propose a new PCA-based algorithm to iteratively select the most important genes in a microarray data set. We show that this algorithm produces better results when our WPCA is used instead of the usual PCA. Furthermore, by using Support Vector Machines, we show that it can compete with the Significance Analysis of Microarrays algorithm.     

Myosin motor domain lever arm rotation is coupled to ATP hydrolysis

We have investigated coupling of lever arm rotation to the ATP binding and hydrolysis steps for the myosin motor domain. In several current hypotheses of the mechanism of force production by muscle, the primary mechanical feature is the rotation of a lever arm that is a subdomain of the myosin motor domain. In these models, the lever arm rotates while the myosin motor domain is free, and then reverses the rotation to produce force while it is bound to actin. These mechanical steps are coupled to steps in the ATP hydrolysis cycle. Our hypothesis is that ATP hydrolysis induces lever arm rotation to produce a more compact motor domain that has stored mechanical energy. Our approach is to use transient electric birefringence techniques to measure changes in hydrodynamic size that result from lever arm rotation when various ligands are bound to isolated skeletal muscle myosin motor domain in solution. Results for ATP and CTP, which do support force production by muscle fibers, are compared to those of ATPgammaS and GTP, which do not. Measurements are also made of conformational changes when the motor domain is bound to NDP's and PP(i) in the absence and presence of the phosphate analogue orthovanadate, to determine the roles the nucleoside moieties of the nucleotides have on lever arm rotation. The results indicate that for the substrates investigated, rotation does not occur upon substrate binding, but is coupled to the NTP hydrolysis step. The data are consistent with a model in which only substrates that produce a motor domain-NDP-P(i) complex as the steady-state intermediate make the motor domain more compact, and only those substrates support force production.     

Induction of monocyte procoagulant activity with OKT3 antibody

OKT3 monoclonal antibody (MoAb), a mouse MoAb against cluster of differentiation 3 (CD3) molecule, induced a large amount of procoagulant activity (PCA) in human peripheral blood mononuclear cells (PBM). The PCA-inducing capability in OKT3 MoAb was abolished by absorption with T lymphocytes or Sepharose-conjugated antibody to mouse IgG. Most of the PCA in PBM was associated with monocytes. There was a dose-dependent increase in PCA when increasing numbers of T cells were added to the monocytes in the presence of OKT3 MoAb. OKT3 MoAb did not induce PCA in either T cells or monocytes alone. T cells pulsed with OKT3 MoAb only in the presence of monocytes could induce PCA in monocytes. Culture supernatants (CS) from PBM stimulated with OKT3 MoAb did not enhance PCA in monocytes; however, it did induce PCA in the human monocyte-like cell line (U937) which differs in some properties from monocytes; this activity could be abolished by the MoAb against human interferon-gamma (IFN-gamma). Nevertheless, neither human IFN-gamma nor interleukin 1 or 2 had significant direct effect in inducing PCA in U937 cells; CS from either monocytes or T cells alone stimulated with OKT3 MoAb did not induce PCA in U937 cells. This apparent discrepancy suggests that there may be factors in CS that induce PCA in U937 cells only in the presence of IFN-gamma. The PCA induced in monocytes or U937 cells was tissue factor-like because of the dependence on coagulation factors V, VII, and X. These observations suggest that OKT3 MoAb is a potent T cell-dependent monocyte PCA inducer and stimulates T cells only in the presence of monocytes. The direct cellular interaction between monocytes and stimulated T cells appears to be necessary to elicit monocyte PCA with OKT3 MoAb stimulation. Thus, monocytes may play a dual role, not only as effector cells, but also as cells that collaborate with T cells after OKT3 MoAb stimulation so as to produce PCA.     

湖南辣椒地方品种资源的因子分析及数量分类

本文对40个湖南辣椒地方品种进行因子分析,并将其分为7大类.结果表明,数量分类的结果基本上反映辣椒品种间的遗传差异,符合实际情况.当主因子的特征值累计贡献率大于75%时,主因子值就能基本反映原来性状的遗传特征.果重、果数和株型是辣椒品种主因子的重要影响变量.Promax斜交旋转后的主因子比方差极大正交旋转后的主因子更能代表品种遗传特性.比较不同的系统聚类方法,类平均法能较好适合辣椒品种的数量分类.     

Influence of gait speed on free vertical moment during walking

Free vertical moment (FVM) of ground reaction is recognized to be a meaningful indicator of torsional stress on the lower limbs when walking. The purpose of this study was to examine whether and how gait speed influences the FVM when walking. Fourteen young healthy adults performed a series of overground walking trials at three different speeds: low, preferred and fast. FVM was measured during the stance phase of the dominant leg using a force platform embedded in a 10 m-long walkway. Transverse plane kinematic parameters of the foot and pelvis were measured using a motion capture system. Results showed a significant decrease in peak abduction FVM (i.e., resisting internal foot rotation) and an increase in peak adduction FVM (i.e., resisting external foot rotation), together with an increase in gait speed. Concomitantly, we observed a decrease in the foot progression angle and an increase in the peak pelvis rotation velocity in the transverse plane with an increase in gait speed. A significant positive correlation was found between the pelvis rotation velocity and the peak adduction moment, suggesting that pelvis rotation influences the magnitude of adduction FVM. Furthermore, we also found significant correlations between the peak adduction FVM and both the step length and frequency, indicating that the alterations in FVM may be ascribed to changes in these two key variables of gait speed. These speed-related changes in FVM should be considered when this parameter is used in gait assessment, particularly when used as an index for rehabilitation and injury prevention.     

Calibration of LAI-2000 canopy analyser with leaf area index in a young eucalypt stand

Plant area index (PAI) measured with a LI-COR LAI-2000 plant canopy analyser (PCA) was calibrated with leaf area index (LAI) in a young stand of Eucalyptus grandis in the KwaZulu-Natal Midlands, South Africa. Destructive sampling and allometric equations were used to estimate LAI at 2 and 3 years after planting. Significant correlations (P<0.001) were found between LAI and PAI for each age with different equations being generated for the two ages (LAI=1.0594(PAI)−0.892 at 2 years of age, and LAI=1.0393(PAI) at 3 years of age). The equations differed from those reported in other eucalypt studies, as the PCA in this study over-predicted LAI at 2 years, and slightly under-predicted at 3 years, of age. It is argued that the stage of growth influenced this calibration, as the canopy and foliar structure may have been different in the young stands, affecting the basic assumptions for the PCA. A broad conversion from PCA derived PAI to LAI may not necessarily be valid for young, short rotation eucalypt plantations.     

Myosin-V makes two brownian 90 degrees rotations per 36-nm step

Myosin-V processively walks on actin filaments in a hand-over-hand fashion. The identical structures of the heads predict a symmetric hand-over-hand mechanism where regular, unidirectional rotation occurs during a 36-nm step. We investigated this by observing how fixed myosin-V rotates actin filaments. Actin filaments randomly rotated 90 degrees both clockwise and counter-clockwise during each step. Furthermore, ATP-dependent rotations were regularly followed by ATP-independent ones. Kinetic analysis indicated that the two 90 degrees rotations relate to the coordinated unbinding and rebinding of the heads with actin. We propose a 'brownian rotation hand-over-hand' model, in which myosin-V randomly rotates by thermally twisting its elastic neck domains during the 36-nm step. The brownian rotation may be advantageous for cargo transport through a crowded actin meshwork and for carrying cargoes reliably via multiple myosin-V molecules in the cell.     

Using Principal Components and Factor Analysis in Animal Behaviour Research: Caveats and Guidelines

Principal component (PCA) and factor analysis (FA) are widely used in animal behaviour research. However, many authors automatically follow questionable practices implemented by default in general‐purpose statistical software. Worse still, the results of such analyses in research reports typically omit many crucial details which may hamper their evaluation. This article provides simple non‐technical guidelines for PCA and FA. A standard for reporting the results of these analyses is suggested. Studies using PCA and FA must report: (1) whether the correlation or covariance matrix was used; (2) sample size, preferably as a footnote to the table of factor loadings; (3) indices of sampling adequacy; (4) how the number of factors was assessed; (5) communalities when sample size is small; (6) details of factor rotation; (7) if factor scores are computed, present determinacy indices; (8) preferably they should publish the original correlation matrix.     

Purine but not pyrimidine nucleotides support rotation of F(1)-ATPase

The binding change model for the F(1)-ATPase predicts that its rotation is intimately correlated with the changes in the affinities of the three catalytic sites for nucleotides. If so, subtle differences in the nucleotide structure may have pronounced effects on rotation. Here we show by single-molecule imaging that purine nucleotides ATP, GTP, and ITP support rotation but pyrimidine nucleotides UTP and CTP do not, suggesting that the extra ring in purine is indispensable for proper operation of this molecular motor. Although the three purine nucleotides were bound to the enzyme at different rates, all showed similar rotational characteristics: counterclockwise rotation, 120 degrees steps each driven by hydrolysis of one nucleotide molecule, occasional back steps, rotary torque of approximately 40 piconewtons (pN).nm, and mechanical work done in a step of approximately 80 pN.nm. These latter characteristics are likely to be determined by the rotational mechanism built in the protein structure, which purine nucleotides can energize. With ATP and GTP, rotation was observed even when the free energy of hydrolysis was -80 pN.nm/molecule, indicating approximately 100% efficiency. Reconstituted F(o)F(1)-ATPase actively translocated protons by hydrolyzing ATP, GTP, and ITP, but CTP and UTP were not even hydrolyzed. Isolated F(1) very slowly hydrolyzed UTP (but not CTP), suggesting possible uncoupling from rotation.