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     

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.     

Hydrogen bond studies: 80. A deuteron magnetic resonance and infrared spectroscopic study of the water molecule in lithium formate monohydrate,LiHCOO · H2O

A deuteron magnetic resonance and infrared study of the water molecules in lithium formate monohydrate, LiHCOO · H₂O, has been made. The quadrupole coupling constants (e²qQ/h) and asymmetry parameters (η) were found to be 198.7±0.4 and 231.3±0.6 kHz, and 0.060±0.005 and 0.097±0.003, respectively, at 25 ° C.An interpretation is given of the infrared spectra in the OH-stretching region in terms of intra- and intermolecular couplings of the water molecules. It is found that the water molecules are vibrationally distorted by their environments such that the OH-stretching modes consist of independent stretchings of the two O-H bonds.     

Structure and dynamic stability of cyclodextrin inclusion complexes with 1,4-disubstituted bicyclo[2.2.2]octanes

The properties of inclusion complexes of 1,4-di-R-bicyclo[2.2.2]octaves (R = H (1), Me (2), Cl (3), Br (4), and OH (5)) with cyclodextrins have been studied by NMR, microcalorimetry, and force-field computations. The compounds2 and3 (but not the other compounds) give dynamically stable 1:2 guest-host complexes with -cyclodextrin. Microcalorimetry of5 in water indicates a moderately strong 1:1 complex with - but weak complexes with - or -cyclodextrin. The behaviour depends on the subtle interplay size, polarity, hydrophobicity and type of solvent.     

Hydrogen bond studies: Part 118. A deuteron magnetic resonance study of BeSO4· 4D2O and Li2SO4· D2O

The electric field gradient (EFG) tensors at the deuterons in the water molecules in BeSO₄ · 4D₂O at 25°C are reported. The quadrupole coupling constants (e²Q/h) and asymmetry parameters (η) for the two independent deuterons are 181.1(4) and 194.8(3) kHz, and 0.226(4) and 0.123(3), respectively. The EFG tensor corresponding to the smallest e²qQ/h is considerably distorted by the beryllium ion, which causes a high η value as well as a deviation of the y-principal axis by 21.8(6)° from the normal to the water molecule plane. A redetermination of the EFG tensors at the deuterons in the water molecule in Li₂SO₄ · D₂O at 25°C and ?110°C is also reported. The e²Q/h and η values for the two deuterons are 236.6(1.2) and 239.8(1.1) kHz, and 0.091(8) and 0.126(7), respectively, at ?110°C. The corresponding e²qQ/h and η values for the averaged EFG tensor at 25°C are 125.8(1.1) kHz and 0.813(13), respectively. The results are in good agreement with those from the pioneer work by Ketudat and Pound, 20 years ago on the same compound.     

Structure determination of zinc iodide complexes formed in aqueous solution

Structures of the complexes formed in aqueous solutions between zinc(II) and iodide ions have been determined from large-angle X-ray scattering, Raman and far-IR measurements. The coordination in the hydrated Zn²⁺ hexaaqua ion and the first iodide complex, [ZnI]⁺, is octahedral, but is changed into tetrahedral in the higher complexes, [ZnI₂(H₂O)₂], [ZnI₃(H₂O)]^– and [ZnI₄]^2–. The Zn-I bond length is 2.635(4)Å in the [ZnI₄]^2– ion and slightly shorter, 2.592(6)Å, in the two lower tetrahedral complexes. In the octahedral [ZnI(H₂O)₅]⁺ complex the Zn-I bond length is 2.90(1)Å. The Zn-O bonding distances in the complexes are approximately the same as that in the hydrated Zn²⁺ ion, 2.10(1)Å.     

Synthesis of the tetrahydroisoquinoline alkaloid (+/-)-renieramycin G and A (+/-)-lemonomycinone analogue from a common intermediate

The total synthesis of tetrahydroisoquinoline alkaloids (+/-)-renieramycin G (4) and a lemonomycinone analogue (7) is described. A general strategy to synthesize both the mono- and bistetrahydroisoquinoline alkaloids from a common advanced intermediate, 17, is presented.     

The complete matter sector in a three-generation compactification

We consider a Calabi-Yau compactification paradigm with three light generations and anR-symmetry. From a special form of the Tian-Yau manifold, we also construct a new three-generation model with markedly different phenomenology. Thecomplete spectrum of all light matter fields is obtained in a universal way and moreover in a physically suitable basis, allowing a straightforward analysis of all their couplings. Here we discuss all the renormalizable Yukawa couplings. This computation can equally well be repeated for all compactification models based on Calabi-Yau complete intersections in products of homogeneous spaces.