On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance

The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore, we show that this distance is fixed parameter tractable when parameterised by the distance between the two trees.Received March 16, 2004     

Sodium trichloro­methane­sulfonate monohydrate

Sodium trichloro­methane­sulfonate monohydrate, Na⁺·CCl₃SO₃⁻·H₂O, crystallizes in P2₁/a with all the atoms located in general positions. The trichloro­methane­sulfonate (trichlate) anion consists of pyramidal SO₃ and CCl₃ groups connected via an S—C bond in a staggered conformation with approximate C_3v symmetry. The water mol­ecule is hydrogen bonded to the sulfonate O atoms, with one water H atom forming weak bifurcated O—H⋯O hydrogen bonds to two different trichlate ions. Two water O atoms and three O atoms from different SO₃ groups form a square‐pyramidal arrangement around the sodium ion.     

Capabilities and limits of ICP-MS for direct determination of element traces in saline solutions

An ICP-MS method for the determination of ultra-traces of 24 Elements (Li, Be, Mg, Al, Cr, Mn, Co, Zn, Cu, Ga, As, Se, Rb, Sr, Mo, Ag, Cd, Sn, Sb, Ba, Tl, Pb, Bi, U) at ng/L to μg/L levels in highly saline solutions (up to 30 g/L NaCl) was developed. Calculated to the salt content of the samples, limits of detection at the sub-μg/kg level were obtained. This allows the measurement of samples like sea water, or clinical samples like urine, serum and whole blood, with few or without sample preparation and a drastic improvement to the limits of detection. Compared to the determination in solutions of 1 g/L NaCl the limits of detection in the original sample were improved by one order of magnitude. Improvements in instrumental stability are achieved by the use of an additional gas, that is introduced to the aerosol stream and avoids salt deposition in the aerosol tube of the torch, the use of High Matrix Content (HMC) cones, that show no clogging even at NaCl-concentrations up to 50 g/L. With this setup the long term stability for measurements with changing matrix concentrations is < 10% without and < 5% with use of an internal standard for the individual samples. Cleaning up is necessary after 2 days of operation. The direct analysis of the Nearshore Seawater Reference Material NRC-CNRC CASS3 showed a good agreement with the certified and measured concentrations. Elements, that do not suffer from an isobaric overlap of matrix compounds can be determined clearly at ng/L levels. Measurement of different matrix concentrations showed, that acceptable results can be achieved with a single calibration for concentrations from 5 g/L NaCl to 30 g/L NaCl, though matrix matching shows the best results.     

Traces on Noncommutative Homogeneous Spaces

We study properties of C*-algebraic deformations of homogeneous spaces G/Γ which are equivariant in the sense that they preserve the natural action of G by left translation. The center is shown to be isomorphic to C(G/G⁰_ρ) for a certain subgroup G⁰_ρ of G, and there is a 1-1 correspondence between normalised traces and probability measures on G/G⁰_ρ. This makes it possible to represent the deformed algebra as operators over L²(G/Γ). Applications to K-theory are also mentioned.     

Monitoring photopolymerization reactions with optical pyrometry

This article describes the development of optical pyrometry (OP) as a new analytical technique for the continuous monitoring of the progress of both free‐radical and cationic photopolymerizations. The method is rapid, reproducible, and very easy to implement. A temperature profile of a photopolymerization can be obtained. Preliminary studies have shown that the temperatures of some polymerizing monomers can easily reach temperatures in excess of 250 °C. The effects of the mass and reactivity of the monomer, light intensity, structures, and concentrations of the photoinitiators and monomers as well as the presence or absence of oxygen on various free‐radical and cationic photopolymerizations were examined with this method. Coupling of real‐time infrared spectroscopy with OP provides a convenient method for simultaneously monitoring both the chemical conversion and the temperature of a photopolymerization. This combined technique affords new insights into the effects of temperature‐induced autoacceleration on the course of photopolymerizations. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 579–596, 2003     

Identifying phylogenetic trees

A central problem that arises in evolutionary biology is that of displaying partitions of subsets of a finite set X on a tree whose vertices are partially labelled with the elements of X. Such a tree is called an X-tree and, for a collection of partitions of subsets of X, characterisations for the existence and uniqueness of an X-tree that displays have been previously given in terms of chordal graphs. In this paper, we obtain two closely related characterisations also in terms of chordal graphs. The first describes when identifies an X-tree, and the second describes when a compatible subset of is of maximum size.     

The synthesis of N-substituted ureas II: Nucleophilic substitution of ureas at the carbonyl group

Summary N-Arylsubstituted ureas undergo exchange of the N-residue upon reaction with amines. Using kinetic measurements, investigation of product distribution, regioselectivity, catalysis, and substrate influences, it was shown that this reaction proceeds via a second order nucleophilic substitution at the urea carbonyl center. By means of semiempirical calculations using the MNDO method the alternative mechanism of fragmentation was investigated.

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Zur Synthese N-substituierter Harnstoffe II: Nucleophile Substitution von Harnstoffen an der Carbonylgruppe

Zusammenfassung N-Arylsubstituierte Harnstoffe erleiden bei der Reaktion mit Aminen einen Austausch des N-Restes. Durch kinetische Messungen, Untersuchung der Produktverteilung, Regioselektivität, Katalyse und des Einflusses des Edukts konnte abgeleitet werden, daß es sich hiebei um eine nucleophile Substitution zweiter Ordnung am Carbonylzentrum des Harnstoffs handelt. Durch semiempirische Rechnungen mit Hilfe der MNDO Methode wurde der alternative Reaktionsmechanismus einer Fragmentierung untersucht.