The n‐ordered graphs: A new graph class

For a positive integer n, we introduce the new graph class of n‐ordered graphs, which generalize partial n‐trees. Several characterizations are given for the finite n‐ordered graphs, including one via a combinatorial game. We introduce new countably infinite graphs R⁽ⁿ⁾, which we name the infinite random n‐ordered graphs. The graphs R⁽ⁿ⁾ play a crucial role in the theory of n‐ordered graphs, and are inspired by recent research on the web graph and the infinite random graph. We characterize R⁽ⁿ⁾ as a limit of a random process, and via an adjacency property and a certain folding operation. We prove that the induced subgraphs of R⁽ⁿ⁾ are exactly the countable n‐ordered graphs. We show that all countable groups embed in the automorphism group of R⁽ⁿ⁾. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 204–218, 2009     

Parameter selection for peak alignment in chromatographic sample profiling: objective quality indicators and use of control samples

In chromatographic profiling applications, peak alignment is often essential as most chromatographic systems exhibit small peak shifts over time. When using currently available alignment algorithms, there are several parameters that determine the outcome of the alignment process. Selecting the optimum set of parameters, however, is not straightforward, and the quality of an alignment result is at least partly determined by subjective decisions. Here, we demonstrate a new strategy to objectively determine the quality of an alignment result. This strategy makes use of a set of control samples that are analysed both spiked and non-spiked. With this set, not only the system and the method can be checked but also the quality of the peak alignment can be evaluated. The developed strategy was tested on a representative metabolomics data set using three software packages, namely Markerlynx™, MZmine and MetAlign. The results indicate that the method was able to assess and define the quality of an alignment process without any subjective interference of the analyst, making the method a valuable contribution to the data handling process of chromatography-based metabolomics data.     

A Missing Reaction Step in Dithiobenzoate-Mediated RAFT Polymerization

The debate on the mechanism of dithiobenzoate-mediated RAFT polymerization may be overcome by taking the so-called “missing step” reaction between a highly reactive propagating radical and the three-arm star-shaped product of the combination reaction of an intermediate RAFT radical and a propagating radical into account. The “missing step” reaction transforms a propagating radical and a not overly stable three-arm star species into a resonance-stabilized RAFT intermediate radical and a stable polymer molecule. The enormous driving force behind the “missing step” reaction is estimated via DFT calculations of reaction enthalpies and reaction free enthalpies.