Ordering a sparse graph to minimize the sum of right ends of edges

Motivated by a warehouse logistics problem we study mappings of the vertices of a graph onto prescribed points on the real line that minimize the sum (or equivalently, the average) of the coordinates of the right ends of all edges. We focus on graphs whose edge numbers do not exceed the vertex numbers too much, that is, graphs with few cycles. Intuitively, dense subgraphs should be placed early in the ordering, in order to finish many edges soon. However, our main “calculation trick” is to compare the objective function with the case when (almost) every vertex is the right end of exactly one edge. The deviations from this case are described by “charges” that can form “dipoles”. This reformulation enables us to derive polynomial algorithms and NP-completeness results for relevant special cases, and FPT results

Effects of the Histone Deacetylase Inhibitor Valproic Acid on Human Pericytes In Vitro

Microvascular pericytes are of key importance in neoformation of blood vessels, in stabilization of newly formed vessels as well as maintenance of angiostasis in resting tissues. Furthermore, pericytes are capable of differentiating into pro-fibrotic collagen type I producing fibroblasts. The present study investigates the effects of the histone deacetylase (HDAC) inhibitor valproic acid (VPA) on pericyte proliferation, cell viability, migration and differentiation. The results show that HDAC inhibition through exposure of pericytes to VPA in vitro causes the inhibition of pericyte proliferation and migration with no effect on cell viability. Pericyte exposure to the potent HDAC inhibitor Trichostatin A caused similar effects on pericyte proliferation, migration and cell viability. HDAC inhibition also inhibited pericyte differentiation into collagen type I producing fibroblasts. Given the importance of pericytes in blood vessel biology a qPCR array focusing on the expression of mRNAs coding for proteins that regulate angiogenesis was performed. The results showed that HDAC inhibition promoted transcription of genes involved in vessel stabilization/maturation in human microvascular pericytes. The present in vitro study demonstrates that VPA influences several aspects of microvascular pericyte biology and suggests an alternative mechanism by which HDAC inhibition affects blood vessels. The results raise the possibility that HDAC inhibition inhibits angiogenesis partly through promoting a pericyte phenotype associated with stabilization/maturation of blood vessels

Untersuchungen zur Betriebsicherheit katalytischer Wasserstoffrekombinatoren

The present report describes safety aspects of catalytic recombiners. These devices are used for hydrogen removal from containments of Light Water Reactors. Hydrogen is generated after the reaction of steam with the zirconium of the cladding of the fuel rods in case of the cooling failure of the core. The burnable mixture of hydrogen and air may flagrate or detonate. In a recombiner hydrogen is converted an catalytic surfaces in an exothermic reaction. For developing effective recombiner systems a lot of theoretical and experimental work has been carried out. During the experiments undesirable ignitions were observed, which must be avoided in any case with respect of safety reasons. There is a lack of detailed analyses concerning the position of ignition sources, ignition temperatures etc.. Despite of these results at present the german reactors are retrofitted with catalytic recombiners. In the Research Centre Jülich experiments are carried out in order to study the reaction kinetics and to determine the reaction temperatures of the catalytic elements. Already at low hydrogen concentration almost ignition temperature is observed. Ignitions are likely to occur at elevated concentrations. Proposals to avoid ignition and to improve recombination devices are mad