List Edge‐Coloring and Total Coloring in Graphs of Low Treewidth

We prove that the list chromatic index of a graph of maximum degree Δ and treewidth is Δ; and that the total chromatic number of a graph of maximum degree Δ and treewidth is . This improves results by Meeks and Scott.     

A Heuristic for Moment-Matching Scenario Generation

In stochastic programming models we always face the problem of how to represent the random variables. This is particularly difficult with multidimensional distributions. We present an algorithm that produces a discrete joint distribution consistent with specified values of the first four marginal moments and correlations. The joint distribution is constructed by decomposing the multivariate problem into univariate ones, and using an iterative procedure that combines simulation, Cholesky decomposition and various transformations to achieve the correct correlations without changing the marginal moments.With the algorithm, we can generate 1000 one-period scenarios for 12 random variables in 16 seconds, and for 20 random variables in 48 seconds, on a Pentium III machine.     

Depth profile investigations of metallic layer contacts to GaAs(100) and InP(100) by means of Auger Electron Spectroscopy and sputter technique

Summary The present technological development in the field of opto-electronics requires a sufficiently high stability of the applied metal-semiconductor contacts because of the thermal and electrical cross-section loading. Au/Pt/Ti layer contacts to GaAs(100) and InP(100) substrates annealed under various conditions were investigated by means of Auger Electron Spectroscopy (AES) in conjunction with ion sputtering. The diffusion and reaction behavior are discussed based on intensity-depth profiles and chemical shifts. As the main result we found that the GaAs contact is more stable. It reacts strongly at a temperature of about 450°C. On the other hand Au/Pt/Ti/InP contact reacts already above 300°C. The principal reason for the difference in the behavior of InP and GaAs contacts is the In segregation.     

Forcing highly connected subgraphs

A theorem of Mader states that highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. We extend this result to infinite graphs. Here, it is necessary to require not only high degree for the vertices but also high vertex‐degree (or multiplicity) for the ends of the graph, that is, a large number of disjoint rays in each end. We give a lower bound on the degree of vertices and the vertex‐degree of the ends which is quadratic in k, the connectedness of the desired subgraph. In fact, this is not far from best possible: we exhibit a family of graphs with a degree of order 2^k at the vertices and a vertex‐degree of order k log k at the ends which have no k‐connected subgraphs. Furthermore, if in addition to the high degrees at the vertices, we only require high edge‐degree for the ends (which is defined as the maximum number of edge‐disjoint rays in an end), Mader's theorem does not extend to infinite graphs, not even to locally finite ones. We give a counterexample in this respect. But, assuming a lower bound of at least 2k for the edge‐degree at the ends and the degree at the vertices does suffice to ensure the existence (k + 1)‐edge‐connected subgraphs in arbitrary graphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 331–349, 2007     

Maturation of the lantibiotic subtilin: matrix-assisted laser desorption/ionization time-of-flight mass spectrometry to monitor precursors and their proteolytic processing in crude bacterial cultures.

Bacillus subtilis synthesizes the lanthionine containing 32-amino-acid peptide antibiotic (lanti-biotic) subtilin from a ribosomally generated 56-amino-acid precursor pre-propeptide by extensive posttranslational modifications. Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) was used to monitor the production of matured subtilin within crude samples taken from B. subtilis culture media without prior fractionation. The processing reaction of subtilin was blocked with the serine protease inhibitor phenylmethylsulfonyl fluoride and different subtilin precursor peptides in the molecular mass range up to 6220 were observed. Two of these species were isolated by reversed-phase high-performance liquid chromatography (HPLC) and structurally analyzed by post-source decay MALDI-TOFMS. We provide evidence that the precursor species comprise the posttranslational modified C-terminal part of subtilin to which leader peptide moieties with different chain lengths are attached. These antimicrobial-inactive species could be processed to antibiotic-active subtilin by incubation with culture media of different subtilin-nonproducing B. subtilis strains as indicated by a combination of antimicrobial growth assays and MALDI-TOFMS analyses. These achievements are strong evidence for the sensitivity of MALDI-TOFMS methodology that allows straightforward investigations of analytes even in complex mixtures without time-consuming sample preparations.