Stiffness of ODEs

It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudospectra instead of spectra. Numerical experiments with an adaptive ODE solver illustrate these findings.Supported by a Dundee University Research Initiatives Grant.Supported by NSF Grant DMS-9116110.     

Applications of Mössbauer Spectroscopy in Industry

Hyperfine Interactions - The demand by industrial researchers to characterize commercial materials with high precision has seen the growth of many spectroscopic techniques in the broad area of...     

A new approach for the formation of fused cyclooctane or cyclohexane rings

The intramolecular regioselective addition of unsymmetrical allylsilanes to conjugated dienones is shown to permit facile entry into 5-6, 6-6, 5-8, and 6-8 bicyclic ring systems.     

An efficient chemoenzymatic approach to (S)-gamma-fluoroleucine ethyl ester

[reaction: see text] An asymmetric synthesis of (S)-gamma-fluoroleucine ethyl ester 1 is described. The key transformation involves a lipase-catalyzed dynamic ring-opening of 2-(3-butenyl)azlactone 7b with EtOH to give amide ester (S)-6b in 84% enantiomeric excess. Removal of the N-pentenoyl group with N,N'-dibromodimethylhydantoin in the presence of trifluoroacetic acid afforded the titled compound, which was isolated as its hydrogen sulfate salt in 75% yield and >97% ee.     

Oligomeric proanthocyanidins: naturally occurring O-heterocycles

This review covers the flavan-3-ols (catechins), flavan-4-ols/flavan-3,4-diols (leucoanthocyanidins), A-type proanthocyanidins, B-type proanthocyanidins including the procyanidins, prodelphinidins, propelargonidins, proteracacinidins, promelacacinidins, procassinidins, probutinidins, and non-proanthocyanidins with flavan-3-ol constituent units. Newly isolated proanthocyanidins, structure elucidation, syntheses, HPLC/MS analysis, NMR/ conformational analysis, and the effects of proanthocyanidins on human nutrition and health are reported. The literature from January 1999 to December 2001 is reviewed, and 130 references are cited.     

Asymmetry through time dependency

Given a single network of interactions, asymmetry arises when the links aredirected. For example, if protein A upregulates protein B and protein Bupregulates protein C, then (in the absence of any further relationships between them) Amay affect C but not vice versa. This type of imbalance is reflected in the associatedadjacency matrix, which will lack symmetry. A different type of imbalance can arise wheninteractions appear and disappear over time. If A meets B today and B meets C tomorrow,then (in the absence of any further relationships between them) A may pass a message ordisease to C, but not vice versa. Hence, even when each interaction is a two-way exchange,the effect of time ordering can introduce asymmetry. This observation is very closelyrelated to the fact that matrix multiplication is not commutative. In this work, wedescribe a method that has been designed to reveal asymmetry in static networks and showhow it may be combined with a measure that summarizes the potential information flowbetween nodes in the temporal case. This results in a new method that quantifies theasymmetry arising through time ordering. We show by example that the new tool can be usedto visualize and quantify the amount of asymmetry caused by the arrow of time.     

Synthesis of a tertiary carbinamide via a novel Rh-catalyzed asymmetric hydrogenation

Asymmetric hydrogenation of allylic dimethylcarbinamide 2 with 1 mol % of cationic Rh(I)-Josiphos complex in THF under 500 psi of H2 generated the corresponding tertiary carbinamide 1 in 98.5% assay yield and a 94:6 enantiomeric ratio. Upon crystallization, the product was isolated in 91% isolated yield and 95:5 enantiomeric ratio.     

Accelerated throughput metabolic route screening in early drug discovery using high-resolution liquid chromatography/quadrupole time-of-flight mass spectrometry and automated data analysis

The resource investment required to characterise the metabolic fate of a compound is relatively large, meaning that within a drug discovery environment relatively few compounds are characterised in depth. Rate-limiting steps include the setting up of a complex array of mass spectrometry experiments and the subsequent analysis of the large data sets produced. We describe here a strategy for the evaluation of metabolic routes using full-scan high-resolution liquid chromatography/quadrupole time-of-flight mass spectrometry (LC/QToFMS) with automated data analysis using Metabolynx, a commercially available software package. Data from several structurally diverse compounds taken from the literature illustrate that, with careful setting of key parameters, this approach is able to indicate the presence of a wide range of metabolites with only a limited requirement for manual intervention.     

Spectral reordering of a range-dependent weighted random graph

^** Email: aas96106{at}maths.strath.ac.uk Grindrod (2002. Phys. Rev. E, 66, 0667021–0667027) posedthe problem of reordering a range-dependent random graph andshowed that it is relevant to the analysis of data sets frombioinformatics. Reordering under a random graph hypothesis canbe regarded as an extension of clustering and fits into thegeneral area of data mining. Here, we consider a generalizationof Grindrod's model and show how an existing spectral reorderingalgorithm that has arisen in a number of areas may be interpretedfrom a maximum likelihood range-dependent random graph viewpoint.Looked at this way, the spectral algorithm, which uses eigenvectorinformation from the graph Laplacian, is found to be automaticallytuned to an exponential edge density. The connection is precisefor optimal reorderings, but is weaker when approximate reorderingsare computed via relaxation. We illustrate the performance ofthe spectral algorithm in the weighted random graph contextand give experimental evidence that it can be successful forother edge densities. We conclude by applying the algorithmto a data set from the biological literature that describescortical connectivity in the cat brain.