Quantifying brain tumor tissue abundance in HR‐MAS spectra using non‐negative blind source separation techniques

Given high‐resolution magic angle spinning (HR‐MAS) spectra from several glial tumor subjects, our goal is to differentiate between tumor tissue types by separating the different sources that contribute to the profile of each spectrum. Blind source separation techniques are applied for obtaining characteristic profiles for necrosis, highly cellular tumor and border tumor tissue and providing the contribution (abundance) of each of these tumor tissue types to the profile of each spectrum. The problem is formulated as a non‐negative source separation problem. Non‐negative matrix factorization, convex analysis of non‐negative sources and non‐negative independent component analysis methods are considered. The results are in agreement with the pathology obtained by the histopathological examination that succeeded the HR‐MAS measurements. Furthermore, an analysis to verify to which extent the dimension of the input space, the input features and the number of sources to be extracted from the HR‐MAS data could influence the performance of the source separation is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Bilateral comparisons and consistent fair division rules in the context of bankruptcy problems

We analyze the problem of extending a given bilateral principle of justice to a consistentn-creditor bankruptcy rule. Based on the bilateral principle, we build a family of binary relations on the set of creditors in order to make bilateral comparisons between them. We find that the possibility of extending a specific bilateral principle of justice in a consistent way is closely related to the quasi-transitivity of the binary relations mentioned above.     

Lipase-catalyzed kinetic resolution of racemic 1-(10-alkyl-10H-phenothiazin-3-yl)ethanols and their butanoates

The synthesis of both enantiomers of 1-(10-alkyl-10H-phenothiazin-3-yl)ethanols and their butanoates by enantiomer-selective acylation of racemic alcohols with the lipase from Pseudomonas fluorescens (L-AK) or/and by methanolysis of the corresponding racemic esters with lipase B from Candida antarctica (CaL-B) is described. The absolute configuration of the enantiomerically pure enantiomers was determined by X-ray crystallography.