Factor analysis has proven an effective approach for distilling high dimensional spectral-image data into a limited number of components that describe the spatial and spectral characteristics of the imaged sample. Principal Component Analysis (PCA) is the most commonly used factor analysis tool; however, PCA constrains both the spectral and abundance factors to be orthogonal, and forces the components to serially maximize the variance that each accounts for. Neither constraint has any basis in physical reality; thus, principal components are abstract and not easily interpreted. The mathematical properties of PCA scores and loadings also differ subtly, which has implications for how they can be used in abstract factor 'rotation' procedures such as Varimax. The Singular Value Decomposition (SVD) is a mathematical technique that is frequently used to compute PCA. In this talk, we will argue that SVD itself provides a more flexible framework for spectral image analysis since spatial-domain and spectral-domain singular vectors are treated in a symmetrical fashion. We will also show that applying an abstract rotation in our choice of either the spatial or spectral domain relaxes the orthogonality requirement in the complementary domain. For instance, samples are often approximately orthogonal in a spatial sense, that is, they consist of relatively discrete chemical phases. In such cases, rotating the singular vectors in a way designed to maximize the simplicity of the spatial representation yields physically acceptable and readily interpretable estimates of the pure-component spectra. This talk will demonstrate that this approach can achieve excellent results for difficult-to-analyze data sets obtained by a variety of spectroscopic imaging techniques.
This short-term, late-start LDRD examined the effects of nutritional deprivation on the energy harvesting complex in microalgae. While the original experimental plan involved a much more detailed study of temperature and nutrition on the antenna system of a variety of TAG producing algae and their concomitant effects on oil production, time and fiscal constraints limited the scope of the study. This work was a joint effort between research teams at Sandia National Laboratories, New Mexico and California. Preliminary results indicate there is a photosystem response to silica starvation in diatoms that could impact the mechanisms for lipid accumulation.
In this study, (CFx)n cathode reaction during discharge has been investigated using in situ X-ray diffraction (XRD). Mathematical treatment of the in situ XRD data set was performed using multivariate curve resolution with alternating least squares (MCR–ALS), a technique of multivariate analysis. MCR–ALS analysis successfully separated the relatively weak XRD signal intensity due to the chemical reaction from the other inert cell component signals. The resulting dynamic reaction component revealed the loss of (CFx)n cathode signal together with the simultaneous appearance of LiF by-product intensity. Careful examination of the XRD data set revealed an additional dynamic component which may be associated with the formation of an intermediate compound during the discharge process.