Principal component analysis of the

The essential degrees of freedom are found by a principal component analysis of the position correlation matrix Cy of the cartesian coordinate displacements Xi with respect to their averages xi), as gathered during a long MD run ... 

Principal components analysis of the characteristics of the coals in each of the three groups showed that the interrelationships between coal properties were markedly different that is, the trends of properties with increasing rank are different, in... 

The authors wanted to select indicators that specifically tap melancholic depression. To evaluate this construct, a principal components analysis of the joint pool of K-SADS and BDI items was performed. Two independent statistical tests suggested a two-component solution, but the resulting components appeared to reflect method factors, rather than substantive factors. Specifically, all of the BDI items loaded on the first component (except for three items that did not load on either component) and nearly all of the K-SADS items loaded on the second component. In fact, the first component correlated. 98 with the BDI and the second component correlated. 93 with the K-SADS. Ambrosini et al., however, concluded that the first component reflected depression severity and the second component reflected melancholic depression. This interpretation was somewhat at odds with the data. Specifically, the second component included some K-SADS items that did not tap symptoms of melancholia (e.g., irritability and anger) and did not include some BDI items that measure symptoms of melancholia (e.g., loss of appetite). 

Figure 4.12 Principal component analysis of the major elements in Coumiac limestones. 91 percent of the variance is explained by the first two components. The data can be explained by the combination of three chemical end-members calcitic (CaO and C02), detrital (Si02 and A1203), and organic (organic C and Fe203). Because of the closure condition these three end-members translate into only two significant components.

Figure 4.13 Principal component analysis of the mean isotopic data for oceanic islands (courtesy of Vincent Salters). In the top left corner, the plane of the first two components (the Mantle Plane of Zindler et al, 1982) explains 93 percent of the variance. Component 1 is dominated by lead isotopes, component 2 by Sr and Nd isotopes. Other components are plotted for reference. In the top right corner, the Mantle Plane is viewed sideways along the direction of the second component, so the distance of each point to the plane can be easily seen. In the bottom left corner, it is viewed along the axis of the first component. The bottom right corner shows how little variance is left with components 3 and 4.

Fig. 8. Principal component analysis of the distribution of the predicted folds in bacterial, archaeal, and eukaryotic proteomes. (a) First and second principal components (b) third and fourth principal components. Aae, Aquifex aeolicus Mge, Mycoplasm genitalium Mpn, Mycoplasma pneumoniae Rpr, Rickettsia prowazekii Bbu, Borrelia burgdorferi Bsu, Bacillus subtilis, Hin, Haemophilus influenzae, Hpy, Helicobacter pylori Tma, Thermotoga mari-...

Important conclusions about the interrelationship among aromaticity indices drawn from energetic, structural, and magnetic criteria stem from principal component analysis of the problem (89JA7). The scheme of principal components is given by... 

Other strong advantages of PCR over other methods of calibration are that the spectra of the analytes have not to be known, the number of compounds contributing to the signal have not to be known on the beforehand, and the kind and concentration of the interferents should not be known. If interferents are present, e.g. NI, then the principal components analysis of the matrix, D, will reveal that there are NC = NA -I- NI significant eigenvectors. As a consequence the dimension of the factor score matrix A becomes (NS x NC). Although there are NC components present in the samples, one can suffice to relate the concentrations of the NA analytes to the factor score matrix by C = A B and therefore, it is not necessary to know the concentrations of the interferents. 

LPRINT PRINCIPAL COMPONENT ANALYSIS OF THE CORRELATION MATRIX ... 

The first part of the output contains the principal component analysis of the correlation matrix discussed later in Section 3.5. In addition to the residuals, goodness-of-fit, parameter estimates and bounds, the Durbin-Wattson D statistics is also printed by the module. 

Unfortunately, there are some technical difficulties associated with the determinant criterion (ref. 28). Minimizing the determinant (3.66) is not a trivial task. In addition, the method obviously does not apply if det[ V(p) ] is zero or nearly zero for all parameter values. This is the case if there exist affine linear relationships among the responses y, y2,. .., yny, as we discussed in Section 1.8.7. To overcome this problem the principal component analysis of the observations is applied before the estimation step. 

As seen from Fig. 5.3, the substrate concentration is most sensitive to the parameters around t = 7 hours. It is therefore advantageous to select more observation points in this region when designing identification experiments (see Section 3.10.2). The sensitivity functions, especially with respect to Ks and Kd, seem to be proportional to each other, and the near—linear dependence of the columns in the Jacobian matrix may lead to ill-conditioned parameter estimation problem. Principal component analysis of the matrix STS is a powerful help in uncovering such parameter dependences. The approach will be discussed in Section 5.8.1. 

Principal component analysis of the normalized sensitivity matrix both concentrations observed... 

Practical identifiability is not the only problem that can be adressed by principal component analysis of the sensitivity matrix. In (refs. 29-30) several examples of model reduction based on this technique are discussed. 

Figure 2. Plot of the first two factors (accounting for 69 percent of the variance) from a principal components analysis of the residential soil sample data (n = 38) from El Coyote using 11 chemical elements (Al, Ba, Ca, Fe, K, Mg Mn, Na, P, Sr, Ti). Ovens tend to have higher concentrations ofBa, Fe, and Na (which are all highly correlated, r>.7) compared to hearths, while hearths tend to have higher concentrations of P, K, Al, Mg and Ti (which are all highly correlated, r>0.7) compared to ovens.

With these patterns in mind, we conducted a principal components analysis of the two datasets using a covariance matrix, since some of the elements have especially high concentrations that could swamp those with lower concentrations in the analysis (Figure S). Here we can see that, in the plaza, samples from the north half vary by P concentration, while those of the south vary according to levels of Ba and Mg the reverse is true for western versus eastern samples (not pictured). In the patio, all samples tend to vary along Factor 1, in which Al, Ba, Fe, and Mn account for most of the variance in the data. This suggests that activity loci in the plaza and patio vary by comer or quadrant. 

Although the radius of gyration provides the overall size of the molecule, the full scattering profile contains much additional information. Segel et al. (1999) introduced the use of principal component analysis of the kinetics (see also Doniach, 2001) to separate scattering profiles of intermediate states... 

The approach taken to observe the impact of the copper smelter on mesoscale variations rainwater composition was to determine the spatial, temporal, and experimental components of the variability of a number of appropriate chemical species in the rainwater. This paper presents results for 1985, during smelter operation, and includes (1) estimates of the experimental variability in chemical composition, (2) an approach for a two step chemical and statistical screening of the data set, (3) the spatial variation in rainwater composition for a storm collected on February 14-15, and (4) a principal component analysis of the rainwater concentrations to help identify source factors influencing our samples. 

The principal component analysis of the dynamics revealed the hingebending motions of the protein. One end of the screw axis of the motions... 

Principal component analysis of the aldehydes and the ketones, respectively, afforded two significant components which accounted for 78% (aldehydes) and 88% (ketones) of the total variance. A score plot of the ketones is shown in the example of the Fischer indole synthesis given in Sect. 5.3.2. For a score plot of the aldehydes, see [61]. 

Principal component analysis of the response matrix afforded one significant component (cross-validation) which described 82% of total variance in Y. As all responses are of the same kind (percentage yield) the data were not autoscaled prior to analysis. The response y1]L was deleted as it did not vary. The scores and loadings are also given in Table 14. The score values were used to fit a second-order... 

Interestingly, a statistical principal component analysis of the solvatochromic shift data sets previously used by Kamlet and Taft in defining the n scale has shown that, rather than one [n ), two solvent parameters (0ik and 02k) are necessary to describe the solvent-induced band shifts of the studied solvatochromic indicators [236]. This is not unexpected since the n parameters are assumed to consist of a blend of dipolarity and polarizability contributions to the solute/solvent interactions. 

Statistical analyses. Three-way analyses of variance treating judges as a random effect were performed on each descriptive term using SAS Institute Inc. IMP 3.1 (Cary, North Carolina). Principal component analysis of the correlation matrix of the mean intensity ratings was performed with Varimax rotation. Over 200 GC peaks... 

Molecules in the dataset were divided into a training set (331 compounds) and a test set (39 molecules). The test set was chosen to cover the activity data span of the two subsets of data uniformly. The dataset was divided into three groups according to the activity value. (2.02-1.45, 1.43-0.95, 0.90.3) Then 13 molecules from each group were randomly chosen. The principal component analysis of the complete dataset was performed to analyze the structural variance of both the training and test sets. The PCA scores plot (Fig. 9.10) showed that there was no structural outlier present in the dataset and that the training set and test set shared the same chemical space. 

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