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.     

Realizing the analytic surgery group of Higson and Roe geometrically part III: higher invariants

We construct an isomorphism between the geometric model and Higson-Roe’s analytic surgery group, reconciling the constructions in the previous papers in the series on “Realizing the analytic surgery group of Higson and Roe geometrically” with their analytic counterparts. Following work of Lott and Wahl, we construct a Chern character on the geometric model for the surgery group; it is a “delocalized Chern character”, from which Lott’s higher delocalized \(\rho \)-invariants can be retrieved. Following work of Piazza and Schick, we construct a geometric map from Stolz’ positive scalar curvature sequence to the geometric model of Higson-Roe’s analytic surgery exact sequence.     

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     

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.     

Weighted proximity search

Journal of Heuristics - Proximity search is an iterative method to solve complex mathematical programming problems. At each iteration, the objective function of the problem at hand is replaced by...     

(E,E,E)‐1,3,5‐Tris[4‐(acetyl­sulfan­yl)­styr­yl]­benzene toluene hemisolvate

The first crystal structure of a three‐terminal sulfur end‐capped oligo­phenyl­ene­vinyl­ene, C₃₆H₃₀O₃S₃·0.5C₇H₈, has been determined at 122 (1) K. The mol­ecular threefold symmetry is not utilized in the crystal structure. It is confirmed that the double bonds have been fully transformed into a trans configuration by iodine treatment.     

One-pot three-component reaction for the synthesis of alpha-(aminoethyl)-alpha,beta-enones

[reaction: see text] The synthesis of alpha-substituted alpha,beta-enones by a new metal iodide-promoted one-pot three-component reaction involving commercially available cyclopropyl ketones, aldehydes, and secondary amines followed by base treatment is described.