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     

Cyclic permutations and evolutionary trees

Given a tree with leaf set X, there are certain ways of arranging the elements of X in a circular order so that can be embedded in the plane and ‘preserve’ this ordering. We investigate some new combinatorial properties of these ‘circular orderings.’ We then use these properties to establish two results concerning dissimilarity maps on X that are induced by edge-weighted trees with leaf set X.     

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.     

A 1H MRS study of probable Alzheimer's disease and normal aging: implications for longitudinal monitoring of dementia progression

In order to evaluate the capability of 1H MRS to monitor longitudinal changes in subjects with probable Alzheimer's disease (AD), the temporal stability of the metabolite measures N-acetylaspartate and N-acetylaspartylglutamate (NA), total Creatine (Cr), myo-Inositol (mI), total Choline (Chol), NA/Cr, mI/Cr, Chol/Cr and NA/mI were investigated in a cohort of normal older adults. Only the metabolite measures NA, mI, Cr, NA/Cr, mI/Cr, and NA/mI were found to be stable after a mean interval of 260 days. Relative and absolute metabolite measures from a cohort of patients with probable AD were subsequently compared with data from a sample of normal older adult control subjects, and correlated with mental status and the degree of atrophy in the localized voxel. Concentrations of NA, NA/Cr, and NA/mI were significantly reduced in the AD group with concomitant significant increases in mI and mI/Cr. There were no differences between the two groups in measures of Cr, Chol, or Chol/Cr. Significant correlations between mental status as measured by the Mini-Mental State Examination and NA/mI, mI/Cr and NA were found. These metabolite measures were also significantly correlated with the extent of atrophy (as measured by CSF and GM composition) in the spectroscopy voxel.     

New synthetic technology for efficient construction of alpha-hydroxy-beta-amino amides via the Passerini reaction

[reaction: see text] The Passerini reaction of N-protected amino aldehydes, isonitriles, and TFA using pyridine-type bases proceeds under mild conditions and directly affords alpha-hydroxy-beta-amino amide derivatives in moderate to high yields. These adducts are readily hydrolyzed to alpha-hydroxy-beta-amino carboxylic acids. Application of these key intermediates to concise syntheses of P(1)-alpha-ketoamide protease inhibitors is illustrated.     

Radii of Classification Preservation in Data Envelopment Analysis: a Case Study of ‘Program Follow-Through’

Sensitivity and robustness of efficiency classifications for the additive model and its geometric equivalents in Data Envelopment Analysis (DEA) are addressed. The minimum distance (measured by a Tchebycheff norm) separating an organization from reclassification is computed via linear programming formulations and shown to constitute a generalized ‘residual’ for each organization. Without this sensitivity information, findings can be distorted when marginally efficient or inefficient units are distinguished solely on the basis of their classification. Analysis of these residuals from an earlier (inconclusive) DEA study further reveals how substantive differences in a sample's underlying groups can be detected. Properties of group efficiency and group proximity to the efficient frontier are investigated using these new indicators.     

An effective non-Archimedean anti-degeneracy/cycling linear programming method especially for data envelopment analysis and like models

A non-Archimedean effective anti-degeneracy/cycling method for linear programming models, especially Data Envelopment Analysis (DEA), processing networks and advertising media mix models is herein developed. It has given a tenfold speed increase plus elimination of cycling difficulties over conventional Marsden or Kennington/Ali LP software modules in a 1000 LP DEA application.     

Band terminations in valence-space and core-excited configurations in102Pd

The level structure of¹⁰²Pd has been investigated using the Eurogam Phase2 array. Termination of rotational bands has been observed atI=28^? andI=32⁺, and tentatively atI=38⁺ andI=42⁺. Three other bands evolving towards termination have also been identified. These terminating bands are explained in terms of valence-space and core-excited configurations.