Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

The potential for competitive and healthy food chains of benefit to the countryside

Agricultural policy liberalisation, concern about unhealthy diets and growing recognition of the importance of sustainable land use have fostered interest in the development of competitive food chains based around products that are beneficial to the rural environment. We review the potential for foods with enhanced health attributes based on alternative varieties/breeds and production systems to traditional agriculture which has been predominantly motivated by yields. We concentrate on soft fruit, which is an important source of polyphenols, and grazing livestock systems that have the potential for improving fatty acid profiles in meat products and find there to be clear scientific potential, but limited research to date. Consumer research suggests considerable acceptance of such products and willingness to pay sufficient to cover additional production costs. Purchase of such foods could have major implications for agricultural land use and the rural environment. There is little research to date on specific healthier food products, but spatially explicit models are being developed to assess land use and environmental implications of changing demand and husbandry methods.

Genomic and genetic analyses of diversity and plant interactions of Pseudomonas fluorescens

Background: Pseudomonas fluorescens are common soil bacteria that can improve plant health through nutrient cycling, pathogen antagonism and induction of plant defenses. The genome sequences of strains SBW25 and Pf0-1 were determined and compared to each other and with P. fluorescens Pf-5. A functional genomic in vivo expression technology (IVET) screen provided insight into genes used by P. fluorescens in its natural environment and an improved understanding of the ecological significance of diversity within this species. Results: Comparisons of three P. fluorescens genomes (SBW25, Pf0-1, Pf-5) revealed considerable divergence: 61% of genes are shared, the majority located near the replication origin. Phylogenetic and average amino acid identity analyses showed a low overall relationship. A functional screen of SBW25 defined 125 plant-induced genes including a range of functions specific to the plant environment. Orthologues of 83 of these exist in Pf0-1 and Pf-5, with 73 shared by both strains. The P. fluorescens genomes carry numerous complex repetitive DNA sequences, some resembling Miniature Inverted-repeat Transposable Elements (MITEs). In SBW25, repeat density and distribution revealed 'repeat deserts' lacking repeats, covering approximately 40% of the genome. Conclusions: P. fluorescens genomes are highly diverse. Strain-specific regions around the replication terminus suggest genome compartmentalization. The genomic heterogeneity among the three strains is reminiscent of a species complex rather than a single species. That 42% of plant-inducible genes were not shared by all strains reinforces this conclusion and shows that ecological success requires specialized and core functions. The diversity also indicates the significant size of genetic information within the Pseudomonas pan genome.

Characterization of protein-polyphenol interactions

Dietary polyphenols have received attention for their biologically significant functions as antioxidants, anticarcinogens or antimutagens, which have led to their recognition as potential nutraceuticals. Polyphenols also characteristically possess a significant binding affinity for proteins, which can lead to the formation of soluble and insoluble protein-polyphenol complexes. Questions remain concerning whether and to what extent the protein-polyphenol interaction influences functionality. For example, is the formation of protein-polyphenol complexes an obstacle to the nutritional bioavailability of either species? This article discusses the development of suitable methodologies to investigate the physicochemical basis of protein-polyphenol interactions and the influence of structure-activity relationships on binding affinities. (C) 2003 Elsevier Ltd. All rights reserved.