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.     

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.     

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.     

FeGa3 and RuGa3: Semiconducting Intermetallic Compounds

The intermetallic compounds FeGa₃ and RuGa₃ were prepared from the elements using a Ga flux and their structures were refined from single-crystal X-ray data. Both compounds crystallize with the FeGa₃ structure type (tetragonal, space group P4₂/mnm, Z=4). Electrical resistivity measurements revealed a semiconducting behavior for FeGa₃ and RuGa₃, which is in contrast to the good metallic conductivity observed for the isotypic compound CoGa₃. The origin of the different electronic properties of these materials was investigated by first-principle calculations. It was found that in compounds adopting the FeGa₃ structure type the transition metal atoms and Ga atoms interact strongly. This opens a d-p hybridization bandgap with a size of about 0.31 eV in the density of states at the Fermi level for 17-electron compounds (i.e., FeGa₃ and RuGa₃). The electronic structure of CoGa₃ (an 18-electron compound) displays rigid band behavior with respect to FeGa₃. As a consequence, the Fermi level in CoGa₃ becomes located above the d-p hybridization gap which explains its metallic conductivity.     

Influence of structure and solubility of chain transfer agents on the RAFT control of dispersion polymerisation in scCO2

Reversible addition–fragmentation chain transfer (RAFT) dispersion polymerisation of methyl methacrylate (MMA) is performed in supercritical carbon dioxide (scCO₂) with 2-(dodecylthiocarbonothioylthio)-2-methylpropionic acid (DDMAT) present as chain transfer agent (CTA) and surprisingly shows good control over PMMA molecular weight. Kinetic studies of the polymerisation in scCO₂ also confirm these data. By contrast, only poor control of MMA polymerisation is obtained in toluene solution, as would be expected for this CTA which is better suited for acrylates. In this regard, we select a range of CTAs and use them to determine the parameters that must be considered for good control in dispersion polymerisation in scCO₂. A thorough investigation of the nucleation stage during the dispersion polymerisation reveals an unexpected “in situ two-stage” mechanism that strongly determines how the CTA works. Finally, using a novel computational solvation model, we identify a correlation between polymerisation control and degree of solubility of the CTAs. All of this ultimately gives rise to a simple, elegant and counterintuitive guideline to select the best CTA for RAFT dispersion polymerisation in scCO₂.

RAFT dispersion polymerisation of methyl methacrylate is performed in scCO₂ with 2-(dodecylthiocarbonothioylthio)-2-methylpropionic acid (DDMAT) present as chain transfer agent (CTA) and surprisingly shows good control over PMMA molecular weight.     

Asymmetric base-mediated epoxide isomerisation

The base-mediated rearrangement of epoxides into allylic alcohols is a well-known synthetic transformation. The first enantioselective version of the reaction using a chiral base was reported in 1980. Since then, the reaction has received a lot of attention mostly due to the great usefulness of chiral allylic alcohols in organic synthesis. Major breakthroughs in the area were the first report on using a sub-stoichiometric amount of chiral base, and the development of chiral bases for a true catalytic reaction protocol. The present review covers the time from when the first asymmetric epoxide isomerisation reaction was reported (1980) up to now, focusing on the period 1997-2001.