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.     

Laser ablation lithography on thermoelectric semiconductor

In this paper, experimental results of the investigation of the periodic structure on thermoelectric semiconductor Cu₂Se are presented. Periodic structures were formed on surfaces of semiconductors due to multi-beam interaction of Q-switched Nd:YAG laser, which was operated in the lowest order of Gaussian mode and pulse duration 7 ns. Surface temperature evolution and transient reflectivity are studied during laser treatment. Creation of Cu islands in the maximal intensity of interference pattern was found.     

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.     

Structural properties of the condensate in two-dimensional mesoscopic systems of strongly correlated excitons

A two-dimensional mesoscopic Bose system of dipoles in a 2D trap is considered using computer simulation by the quantum path-integral Monte Carlo method. The model describes a rarefied system of spatially indirect excitons in a confining potential. Bose condensation in the system and its superfluid and structural properties are studied over a wide range of interparticle spatial correlations, from an almost ideal Bose gas to the regime of a strongly correlated system. It is found that, at strong interparticle spatial correlations, particles in the condensate form a crystal-like structure. In this case, the spatial correlations of particles in the condensate are less pronounced than the correlations of noncondensed particles. The effect of recurrent crystallization is observed in the regime of strong interparticle correlations.     

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.