Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Combinatorial peptide ligand libraries and plant proteomics: a winning strategy at a price

The mechanism of action and properties of a solid-phase ligand library made of hexapeptides (combinatorial peptide ligand libraries or CPLL), for capturing the "hidden proteome", i.e. the low- and very low-abundance proteins constituting the vast majority of species in any proteome, as applied to plant tissues, are reviewed here. Plant tissues are notoriously recalcitrant to protein extraction and to proteome analysis. Firstly, rigid plant cell walls need to be mechanically disrupted to release the cell content and, in addition to their poor protein yield, plant tissues are rich in proteases and oxidative enzymes, contain phenolic compounds, starches, oils, pigments and secondary metabolites that massively contaminate protein extracts. In addition, complex matrices of polysaccharides, including large amount of anionic pectins, are present. All these species compete with the binding of proteins to the CPLL beads, impeding proper capture and identification / detection of low-abundance species. When properly pre-treated, plant tissue extracts are amenable to capture by the CPLL beads revealing thus many new species among them low-abundance proteins. Examples are given on the treatment of leaf proteins, of corn seed extracts and of exudate proteins (latex from Hevea brasiliensis). In all cases, the detection of unique gene products via CPLL capture is at least twice that of control, untreated sample.

Combinatorial peptide ligand libraries and plant proteomics: a winning strategy at a price

The mechanism of action and properties of a solid-phase ligand library made of hexapeptides (combinatorial peptide ligand libraries or CPLL, for capturing the "hidden proteome", i.e. the low- and very low-abundance proteins Constituting the vast majority of species in any proteome. as applied to plant tissues, are reviewed here. Plant tissues are notoriously recalcitrant to protein extraction and to proteome analysis, Firstly, rigid plant cell walls need to be mechanically disrupted to release the cell content and, in addition to their poor protein yield, plant tissues are rich in proteases and oxidative enzymes, contain phenolic Compounds, starches, oils, pigments and secondary metabolites that massively contaminate protein extracts. In addition, complex matrices of polysaccharides, including large amount of anionic pectins, are present. All these species compete with the binding of proteins to the CPLL beads, impeding proper capture and identification I detection of low-abundance species. When properly pre-treated, plant tissue extracts are amenable to capture by the CPLL beads revealing thus many new species among them low-abundance proteins. Examples are given on the treatment of leaf proteins, of corn seed extracts and of exudate proteins (latex from Hevea brasiliensis). In all cases, the detection of unique gene products via CPLL Capture is at least twice that of control, untreated sample. (c) 2008 Elsevier B.V. All rights reserved.

Models, mathematics and meaning in interdisciplinary research

Interdisciplinary research presents particular challenges for unambiguous communication. Frequently, the meanings of words differ markedly between disciplines, leading to apparent consensus masking fundamental misunderstandings. Researchers can agree on the need for models, but conceive of models fundamentally differently. While mathematics is frequently seen as an elitist language reinforcing disciplinary distinctions, both mathematics and modelling can also offer scope to bridge disciplinary epistemological divisions and create common ground on which very different disciplines can meet. This paper reflects on the role and scope for mathematics and modelling to present a common epistemological space in interdisciplinary research spanning the social, natural and engineering sciences.