Estimation of signal backgrounds on multivariate loadings improves model generation in face of complex variation in backgrounds and constituents

The present study is designed to understand further implications of using multivariate loadings for the correction of background signal, which has previously been shown to be highly reproducible even for very low quality signals. Singular value decomposition (SVD)‐based background correction was compared with the traditional per‐signal paradigm for a biomedical dataset to generate qualitative and quantitative models. The qualitative effect on a principal component analysis model and the quantitative effect on a partial least square regression model were assessed for these background correction methods. The chosen quantitative parameter was the concentration of a pathologically relevant protein modification, pentosidine. Of the approaches tested, the SVD‐based paradigm provided the regression model with the highest correlations, highest accuracy (lowest standard error of prediction) and repeatability (lowest sampling error). Contrasted against the traditional approaches, it was determined that the improved accuracy and repeatability of the SVD‐based approach arises from its ability to simultaneously handle very complex background shapes alongside the complex variation in biochemical species that resulted in Raman signals with incompatible baseline regions. A better understanding of the interaction of SVD‐based baseline correction, and data will give the reader more insight into the potential applicability of the procedure for other datasets. Copyright © 2012 John Wiley & Sons, Ltd.     

Balanced Bilinear Forms on Matrix and Matrix-Like Coalgebras

In this short note, we determine all balanced bilinear forms for a matrix coalgebra and for one type of matrix-like coalgebra.     

Convergence rates for intermediate problems

Convergence rate estimates are derived for a variant of Aronszajn-type intermediate problems that is both computationally feasible and known to be convergent for problems with nontrivial essential spectrum. Implementation of these derived bounds is discussed in general and illustrated on differential eigenvalue problems. Convergence rates are derived for the commonly used method of simple truncation.The work of the first author was partially supported by AFOSR Grant 84-0326. The work of the second author was partially supported by NSF Grant MCS-8301402     

Inertia-preserving secant updates

A class of rank-two, inertia-preserving updates for symmetric matricesH _c is studied. To ensure that inertia is preserved, the updates are chosen to be of the formH ₊=FH _c F ^t, whereF=I+qr ^t, withq andr selected so that the secant equation is satisfied. A characterization is given for all such updates. Using a parameterization of this family of updates, the connection between them and the Broyden class of updates is established. Also, parameter selection criteria that can be used to choose the optimally conditioned update or the update closest to the SR1 update are discussed.The work of the first author was partially supported by AFOSR Grant 84-0326. The work of the second author was partially supported by NSF Grant EAR-82-18743.     

Alkane activation by homogeneous palladium complexes

The conversion of adamantane exclusively to 1-adamantyl trifluoroacetate in a refluxing trifluoroacetic acid solution of palladium acetate at 1 atm of air or nitrogen was confirmed. The conversion can be made quantitative. The 1-adamantyl trifluoroacetate was hydrolysed to yield 1-adamantanol in 90% isolated yield. The adamantane functionalization is accompanied by concomitant formation of a palladium mirror.     

Chemistry of cobalt acetate. 7. Electrochemical oxidation of mu3-oxo-centered cobalt(III) acetate trimers

Electrochemical and spectroelectrochemical properties of five cobalt(III) acetate complexes [CoIII3(mu3-O)(CH3CO2)5(OR)(py)3][PF6] are described, where py=pyridine and R=OCCH3 (A), H (B), CH3 (C), CH2CH=CH2 (D), and CH2C6H5 (E). Each is reduced irreversibly as observed by cyclic voltammetry at room temperature and at -40 degrees C in acetonitrile at scan rates up to 20 V s(-1), but oxidized reversibly to a mixed-valence Co(III)2Co(IV) species at approximately 1.23 V vs the ferrocenium/ferrocene couple. Controlled potential coulometry confirmed a one-electron-oxidation process. Spectroelectrochemical oxidation of A at 5 degrees C showed isosbestic points in the electronic absorption spectrum that showed the oxidized complex to be stable in solution for at least 1 h.