Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

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.     

Excimer Laser Processing of Grey Cast Iron: Microstructural and Tribological Characterization

Pearlitic grey iron was treated by means of a XeCl laser to remelt only a shallow layer. This process allows to modify the heteregeneous surfaces of cast irons in order to improve their tribological behaviour. The energy density ranged from 0.3 to 3 J/cm² and the number of shots from 4 to 40. It is shown that after laser irradiation austenite is formed in the melted layer; compressive stresses at the surface were exhibited as well as the deposition of graphite and the formation of carbides. It is shown that excimer laser processing highly decreases the coefficient of friction and the wear rate. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.