Construction of inverses with prescribed zero minors and applications to decentralized stabilization

We examine the following question: Suppose R is a principal ideal domain, and that F is an n × m matrix with elements in R, with n>m. When does there exist an m × n matrix G such that GF = Im, and such that certain prescribed minors of G equal zero? We show that there is a simple necessary condition for the existence of such a G, but that this condition is not sufficient in general. However, if the set of minors of G that are required to be zero has a certain pattern, then the condition is necessary as well as sufficient. We then show that the pattern mentioned above arises naturally in connection with the question of the existence of decentralized stabilizing controllers for a given plant. Hence our result allows us to derive an extremely simple proof of the fact that a necessary and sufficient condition for the existence of decentralized stabilizing controllers is the absence of unstable decentralized fixed modes, as well as to derive a very clean expression for these fixed modes. In addition to the application to decentralized stabilization, we believe that the result is of independent interest.

Mechanism of foetal wastage following immunoneutralization of riboflavin carrier protein in the pregnant rat: disturbances in flavin coenzyme levels

Immunoneutralization of maternal RCP results in a >90% decrease in the content and the incorporation of [2-14C]riboflavin into embryonic FAD as well as a percentage redistribution of both embryonic FMN and riboflavin. This is unaccompanied by any discernible changes in flavin distribution pattern in the maternal liver. Embryonic α-glycerophosphate dehydrogenase and NADPH-cytochrome c reductase register significant decreases in activities in the RCP antiserum-treated rats. These alterations readily explain the arrest of foetal growth culminating in pregnancy termination in the antiserum-treated animals.

Stabilizing trench's algorithm to invert symmetric toeplitz matrices

Presented here is a stable algorithm that uses Zohar's formulation of Trench's algorithm and computes the inverse of a symmetric Toeplitz matrix including those with vanishing or nearvanishing leading minors. The algorithm is based on a diagonal modification of the matrix, and exploits symmetry and persymmetry properties of the inverse matrix.

Identification of mycobacterial lectins from genomic data

Sixty-four sequences containing lectin domains with homologs of known three-dimensional structure were identified through a search of mycobacterial genomes. They appear to belong to the -prism II, the C-type, the Microcystis virdis (MV), and the -trefoil lectin folds. The first three always occur in conjunction with the LysM, the PI-PLC, and the -grasp domains, respectively while mycobacterial -trefoil lectins are unaccompanied by any other domain. Thirty heparin binding hemagglutinins (HBHA), already annotated, have also been included in the study although they have no homologs of known three-dimensional structure. The biological role of HBHA has been well characterized. A comparison between the sequences of the lectin from pathogenic and nonpathogenic mycobacteria provides insights into the carbohydrate binding region of the molecule, but the structure of the molecule is yet to be determined. A reasonable picture of the structural features of other mycobacterial proteins containing one or the other of the four lectin domains can be gleaned through the examination of homologs proteins, although the structure of none of them is available. Their biological role is also yet to be elucidated. The work presented here is among the first steps towards exploring the almost unexplored area of the structural biology of mycobacterial lectins. Proteins 2013. (c) 2012 Wiley Periodicals, Inc.