Data matrix, compositional analysis

Three main patterns of contamination were resolved by MCR-ALS analysis of [SE SO] data matrix (105 samples x 15 variables). Composition profiles (loadings) of the resolved components are shown in Fig. 11 (plots on the left). Variables are identified with a number in the x axis. In the y axis, the relative contribution of every scaled variable to the identified contamination pattern is given. Temporal and spatial sample distribution profiles of the contamination patterns (scores) are represented in Fig. 11 (plots on the right). In the x axis, samples are identified for the two compartments, SE and SO, successively ordered from first to third campaign and, within each campaign, form North-West to South-East. The y axis displays the contribution of every resolved contamination pattern to samples. 

After device construction, structural and functional analysis are critical. One might argue that only the second issue matters, but structural data often give insights into why devices perform suboptimally, and provide important clues about how to improve device function. We routinely use protein analytics (matrix-assisted laser desorption-ionization mass spectroscopy, amino acid composition analysis, gel electrophoresis, Western blotting, circular dichroism, vari-... 

After finding NC, we must determine the composition of each mineral. It is very helpful at this point to have a qualitative mlneraloglcal analysis, such as XRD, to provide initial estimates of compositions. In addition, libraries of mineral compositions are extremely useful. Methods based on searching the original data matrix for candidate minerals also are helpful and in some instances may provide the best compositions for real samples. 

Multivariate methods, on the other hand, resolve the major sources by analyzing the entire ambient data matrix. Factor analysis, for example, examines elemental and sample correlations in the ambient data matrix. This analysis yields the minimum number of factors required to reproduce the ambient data matrix, their relative chemical composition and their contribution to the mass variability. A major limitation in common and principal component factor analysis is the abstract nature of the factors and the difficulty these methods have in relating these factors to real world sources. Hopke, et al. (13.14) have improved the methods ability to associate these abstract factors with controllable sources by combining source data from the F matrix, with Malinowski s target transformation factor analysis program. (15) Hopke, et al. (13,14) as well as Klelnman, et al. (10) have used the results of factor analysis along with multiple regression to quantify the source contributions. Their approach is similar to the chemical mass balance approach except they use a least squares fit of the total mass on different filters Instead of a least squares fit of the chemicals on an individual filter. 

The term factor is a catch-all for the concept of an identifiable property of a system whose quantity value might have some effect on the response. Factor tends to be used synonymously with the terms variable and parameter, although each of these terms has a special meaning in some branches of science. In factor analysis, a multivariate method that decomposes a data matrix to identify independent variables that can reconstitute the observed data, the term latent variable or latent factor is used to identify factors of the model that are composites of input variables. A latent factor may not exist outside the mathematical model, and it might not therefore influence... 

FIGURE 11.19 Composition (loading) profiles of resolved components in the MCR-ALS analysis of raw augmented data matrix. Top components explain more variance bottom components explain less variance. Names for the compounds are defined in the caption to Figure 11.17. 

A data matrix produced by compositional analysis commonly contains 10 or more metric variables (elemental concentrations) determined for an even greater number of observations. The bridge between this multidimensional data matrix and the desired archaeological interpretation is multivariate analysis. The purposes of multivariate analysis are data exploration, hypothesis generation, hypothesis testing, and data reduction. Application of multivariate techniques to data for these purposes entails an assumption that some form of structure exists within the data matrix. The notion of structure is therefore fundamental to compositional investigations. 

Dhawan and Trivedi [127] studied the thermal stability of conducting polypyrrole film, grown on the FeCU spray-coated polyvinylacetate film, exposed to pyrrole vapours under mild vacuum. The thermogravi-metric analysis data for the conductive polypyrrole composite showed its stability up to I50°C and after that a continuous weight loss was observed up to 450°C implying the breakdown of the host polymer, polyvinylacetate matrix. The differential thermal analysi.s of the composite also showed first inflection at 205°C followed by a major transformation at 296°C. 

Repeated attempts to obtain the band at 1030 cm 1 in spectra of the respective solids of various compositions did not furnish the desired result. Nevertheless, the band was observed in IR transmission spectra of gaseous components that separated from molten K2NbF7 and were collected in a standard gas phase cell with Csl windows appropriate for IR measurements. Fig. 85 presents the structure of the band and exact wave numbers of its components. Storage of the gas in the cell for several days resulted in a yellow deposit on the windows due to oxidation and subsequent separation of iodine. Analysis of available reported data [364 - 367] enables to assign the band observed at -1030 cm 1 to vibrations of OF radicals. It should be emphasized that a single mode was observed for OF in the argon matrix while in the case of nitrogen, two modes were indicated [367]. 

The table data show that the stress/strain properties of compositions are improved by additional dispersion (mixing). Ultrasonic analysis is sufficiently reliable and informative as a means of mixing quality assessment. The very small change of the characteristics for filled compositions (chalk + kaolin) can be due to the fact that these fillers are readily distributed in the matrix as they are. 

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