Hereditarily Optimal Realizations of Consistent Metrics

One of the main problems in phylogenetics is to find good approximations of metrics by weighted trees. As an aid to solving this problem, it could be tempting to consider optimal realizations of metrics—the guiding principle being that, the (necessarily unique) optimal realization of a tree metric is the weighted tree that realizes this metric. And, although optimal realizations of arbitrary metrics are, in general, not trees, but rather weighted networks, one could still hope to obtain a phylogenetically informative representation of a given metric, maybe even more informative than the best approximating tree. However, optimal realizations are not only difficult to compute, they may also be non-unique. Here we focus on one possible way out of this dilemma: hereditarily optimal realizations. These are essentially unique, and can be described in a rather explicit way. In this paper, we recall what a hereditarily optimal realization of a metric is and how it is related to the 1-skeleton of the tight span of that metric, and we investigate under what conditions it coincides with this 1-skeleton. As a consequence, we will show that hereditarily optimal realizations for consistent metrics, a large class of phylogentically relevant metrics, can be computed in a straight-forward fashion. Received August 26, 2004     

A comparison between two distinct continuous models in projective cluster theory: The median and the tight-span construction

It is possible to consider two variants of cluster theory: Inaffine cluster theory, one considers collections ofsubsets of a given setX of objects or states, whereas inprojective cluster theory, one considers collections ofsplits (orbipartitions) of that set. In both contexts, it can be desirable to produce acontinuous model, that is, a spaceT encompassing the given setX which represents in a well-specified and more or less parsimonious way all possibleintermediate objects ortransition states compatible with certain restrictions derived from the given collection of subsets or splits. We investigate an interesting and intriguing relationship between two such constructions that appear in the context of projective cluster theory: TheBuneman construction and thetight-span (or justT)construction.     

Possible new phase transitions in hexagonal RbxWO3

Two correlated phase transitions have been observed in hexagonal Rb_xWO₃ in the concentration range 0.16≤x≤0.33. One of these is a concentration-dependent transition which occurs near x=0.25, and precipitously affects the superconducting transition temperature. The other is a temperature-dependent transition which appears as anomalies in the resistivity, Hall coefficient, and Seebeck coefficient between 100K and 280K. The temperature at which the anomalies occur depends strongly on the x-value.     

Anisotropy of Hc2 in Rb0.2WO3

The T_c and H_c2 of hexagonal single crystals Rb_0.2WO₃ were measured. Upper critical field rotation data in the plane perpendicular to the c-axis showed a large anisotropy with a 60° periodicity. Rotation in a plane containing the c-axis showed an even larger anisotropy having 180° symmetry.     

Generating functions for multi-labeled trees

Multi-labeled trees are a generalization of phylogenetic trees that are used, for example, in the study of gene versus species evolution and as the basis for phylogenetic network construction. Unlike phylogenetic trees, in a leaf-multi-labeled tree it is possible to label more than one leaf by the same element of the underlying label set. In this paper we derive formulae for generating functions of leaf-multi-labeled trees and use these to derive recursions for counting such trees. In particular, we prove results which generalize previous theorems by Harding on so-called tree-shapes, and by Otter on relating the number of rooted and unrooted phylogenetic trees.     

Growth of Ni-doped MgF2 crystals in self-sealing graphite crucibles

Large Ni-doped MgF₂ single crystals of excellent optical quality have been grown in self-sealing graphite crucibles by a vertical gradient freeze technique. This relatively simple technique always yields single crystals having excellent optical quality and should be applicable to the melt growth of other crystals that are too volatile to permit the use of open systems.     

Eta(1)-2-pyrone metal carbonyl complexes as CO-releasing molecules (CO-RMs): a delicate balance between stability and CO liberation

An evaluation of the CO releasing ability of iron(II) and molybdenum(II) complexes has facilitated the discovery of the most rapid CO releaser, namely [Mo(CO)(3)(eta(5)-C(5)H(5))(eta(1)-{O}-C{=O}-O-CMe=CH-COMe=CBr)]BF(4) (CORM-F10), reported to date. The rate of CO release is related to the overall solution phase stability of the transition metal carbonyl complex. The cytotoxicity and vasodilatory properties of CORM-F10 have been determined.     

Design,synthesis and structural diversity in coordination polymers

The fundamental precept of crystal engineering is that all the information necessary for the design of a network is already stored in the molecular building blocks used. Coordination polymers represent an example of how crystal engineering has become a paradigm for the synthesis of new architectures and compositions. We report herein ten structures that are supramolecular isomers of one another. The structures are prepared from the same building blocks under mild reaction conditions. The modularity of coordination polymers imparts structural diversity that otherwise would not be possible.