Component-based variation reduction

This procedure was used mainly to aehieve a reduction of dimensionality, i.e., to fit a A -dimensional subspace to the original / -variate observations p k). The statistics used to summarize the most important results was the percent of the total variation explained by the first k (usually two or three) components. In the case at hand the interpretation of PCA results was based on the diagrams of coefficients of variables (total concentrations of metals in the samples) and the scatter plot of samples (the stations separated in coastal, intermediate and offshore stations). 

Steefel et al. ([23] and references therein) noted that the approach does not account for pH, competitive ion effects or oxidation-reduction reactions. As a consequence, values may vary by orders of magnitude from one set of conditions to another. Chen [25] also highlighted these limitations by comparing numerical modeling results of contaminant transport using a multi-component coupled reactive mass transport model and a based transport model. The conclusion from this work was that values vary with location and time and this variation could not be accounted for in the model. 

The intensity of the ESR signal provides a measure of the radical concentration and is evaluated by double integration of the ESR signal, based on an intensity reference. Variation of the ESR intensity indicated the entrance-exit of a paramagnetic probe from the dendritic box, or the oxidation-reduction of a paramagnetic label or ion belonging to the dendrimer. Variation of relative intensify of a spectral component provided a measure of the distribution of paramagnetic species in different locations and environments at the external and/or internal surface of the dendrimers. 

PCA is a method based on the Karhunen-Loeve transformation (KL transformation) of the data points in the feature space. In KL transformation, the data points in the feature space are rotated such that the new coordinates of the sample points become the linear combination of the original coordinates. And the first principal component is chosen to be the direction with largest variation of the distribution of sample points. After the KL transformation and the neglect of the components with minor variation of coordinates of sample points, we can make dimension reduction without significant loss of the information about the distribution of sample points in the feature space. Up to now PCA is probably the most widespread multivariate statistical technique used in chemometrics. Within the chemical community the first major application of PCA was reported in 1970s, and form the foundation of many modem chemometric methods. Conventional approaches are univariate in which only one independent variable is used per sample, but this misses much information for the multivariate problem of SAR, in which many descriptors are available on a number of candidate compounds. PCA is one of several multivariate methods that allow us to explore patterns in multivariate data, answering questions about similarity and classification of samples on the basis of projection based on principal components. 

A preliminary, simple system state point evaluation was performed to estimate the system performance impacts for various leak sizes. This evaluation was non-conservative because the effects of reduced compressor efficiency and the increased pressure losses in the system were not considered in the evaluation. The effects of leak size on system performance are summarized in Figure 9-34. Included in this figure are the state point assumptions. Based on bypass control analysis performed in Reference 9- 64 an additional reduction in overall system performance is expected based on more detailed system models which capture the effects of system pressure, variations in component pressure drop and turbine/compressor efficiency variations. For a 10% bypass flow on the compressor side of the 100 kWe Brayton system in Reference 9- 64 a reduction in electrical output of approximately 37% was calculated compared to 24% predicted by the simpler state point model. 

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