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.

Rational modification of the hierarchy of intermolecular interactions in molecular crystal structures by using tunable halogen bonds

A family of 16 isomolecular salts (3-XpyH)(2)[MX'(4)] (3-XpyH=3-halopyridinium; M=Co, Zn; X=(F), Cl, Br, (I); X'=Cl, Br, I) each containing rigid organic cations and tetrahedral halometallate anions has been prepared and characterized by X-ray single crystal and/or powder diffraction. Their crystal structures reflect the competition and cooperation between non-covalent interactions: N-H center dot center dot center dot X'-M hydrogen bonds, C-X center dot center dot center dot X'-M halogen bonds and pi-pi stacking. The latter are essentially unchanged in strength across the series, but both halogen bonds and hydrogen bonds are modified in strength upon changing the halogens involved. Changing the organic halogen (X) from F to I strengthens the C-X center dot center dot center dot X'-M halogen bonds, whereas an analogous change of the inorganic halogen (X') weakens both halogen bonds and N-H center dot center dot center dot X'-M hydrogen bonds. By so tuning the strength of the putative halogen bonds from repulsive to weak to moderately strong attractive interactions, the hierarchy of the interactions has been modified rationally leading to systematic changes in crystal packing. Three classes of crystal structure are obtained. In type A (C-F center dot center dot center dot X'-M) halogen bonds are absent. The structure is directed by N-H center dot center dot center dot X'-M hydrogen bonds and pi-stacking interactions. In type B structures, involving small organic halogens (X) and large inorganic halogens (X'), long (weak) C-X center dot center dot center dot X'-M interactions are observed with type I halogen-halogen interaction geometries (C-X center dot center dot center dot X' approximate to X center dot center dot center dot X'-M approximate to 155 degrees), but hydrogen bonds still dominate. Thus, minor but quite significant perturbations from the type A structure arise. In type C, involving larger organic halogens (X) and smaller inorganic halogens (X'), stronger halogen bonds are formed with a type II halogen-halogen interaction geometry (C-X center dot center dot center dot X' approximate to 180 degrees; X center dot center dot center dot X'-M approximate to 110 degrees) that is electrostatically attractive. The halogen bonds play a major role alongside hydrogen bonds in directing the type C structures, which as a result are quite different from type A and B.

Exploring the spatial variation of take-all (Gaeumannomyces graminis var. tritici) for site-specific management

The fungus Gaeumannomyces graminis var. tritici (Ggt), commonly known as the take-all fungus, causes damage to roots of wheat and barley that limits crop growth and causes loss of yield. There was little knowledge on the within-field spatial variation of take-all and relations with features in the growing crop, selected soil properties and spectral information from remotely sensed imagery. Geostatistical analyses showed that take-all, chlorosis and leaf area index had similar patchy distributions. Many of the spectral bands from a hyperspectral image also had similar spatial patterns to take-all and chlorosis. Relations between take-all and mineral nitrogen, elevation and pH were generally weaker.

Pollination and other ecosystem services produced by mobile organisms: a conceptual framework for the effects of land-use change

Many ecosystem services are delivered by organisms that depend on habitats that are segregated spatially or temporally from the location where services are provided. Management of mobile organisms contributing to ecosystem services requires consideration not only of the local scale where services are delivered, but also the distribution of resources at the landscape scale, and the foraging ranges and dispersal movements of the mobile agents. We develop a conceptual model for exploring how one such mobile-agent-based ecosystem service (MABES), pollination, is affected by land-use change, and then generalize the model to other MABES. The model includes interactions and feedbacks among policies affecting land use, market forces and the biology of the organisms involved. Animal-mediated pollination contributes to the production of goods of value to humans such as crops; it also bolsters reproduction of wild plants on which other services or service-providing organisms depend. About one-third of crop production depends on animal pollinators, while 60-90% of plant species require an animal pollinator. The sensitivity of mobile organisms to ecological factors that operate across spatial scales makes the services provided by a given community of mobile agents highly contextual. Services vary, depending on the spatial and temporal distribution of resources surrounding the site, and on biotic interactions occurring locally, such as competition among pollinators for resources, and among plants for pollinators. The value of the resulting goods or services may feed back via market-based forces to influence land-use policies, which in turn influence land management practices that alter local habitat conditions and landscape structure. Developing conceptual models for MABES aids in identifying knowledge gaps, determining research priorities, and targeting interventions that can be applied in an adaptive management context.

Solid-state interconversions of coordination networks and hydrogen-bonded salts

Thermal or chemical treatment of crystalline 4,4-bipyridinium salts of [MCl4]2- (M=Co, Zn, Fe, or Pt) leads to HCl loss and formation of coordination network solids [{MCl2(4,4-bipy)}n]. For M=Co, Zn, and Fe, these solids can also be prepared by mechanochemical means. Their exposure to HCl vapor or the mechanochemical reaction of metal dichlorides with [4,4-H2bipy]Cl2 gives [4,4-H2bipy]2+ salts of [CoCl4]2-, [ZnCl4]2-, and, for the first time, [FeCl4]2-.

Interaction of sulphur-containing aroma compounds with proteins in both model systems and real food systems

Irreversible binding of key flavour disulphides to ovalbumin has been shown previously to occur in model systems. The extent of binding is determined by the availability of the sulphydryl groups to participate in disulphide exchange, influenced either by pH, or the state of the protein (native or heat-denatured). In this study, two further proteins, one with sulphydryl groups available in the native state (beta-lactoglobulin) and one with no sulphydryl groups in the native state (lysozyme) were used to confirm this hypothesis. When the investigation was extended to real food systems, a similar effect was shown when a commercial meat flavouring containing disulphides was added to heat-denatured ovalbumin. Furthermore, comparison of the volatiles generated from onions, cooked either alone, or in the presence of meat, showed a significant reduction of key onion-derived disulphides when cooked in the presence of meat, and an even greater reduction of trisulphides. These findings may have implications for consumer acceptance of food products; where these compounds are used as flavourings or where they occur naturally.

High temperature reduction of metmyoglobin in aqueous muscle extracts

Oxymyoglobin in aqueous extracts of fresh beef longissimus dorsi muscles was initially oxidised to metmyoglobin during heat treatments at temperatures in the range 50-70 degreesC. The metmyoglobin then underwent reduction to a red pigment that was shown spectrally to be identical to oxymyoglobin. The formation of oxymyoglobin involved a heat induced precipitate that when removed from the solution, allowed oxidation to metmyoglobin to occur. However, on re-addition of the precipitate further reduction to oxymyoglobin took place. Dialysis of the muscle extract prior to heating markedly inhibited the reduction but addition of NADH to the dialysate permitted further reduction. The precipitate plus NADH caused oxymyoglobin formation in the presence of metmyoglobin but neither the precipitate nor NADH alone induced this formation. It is concluded that the initial conversion of oxymyoglobin to metmyoglobin on heating fresh beef muscle extracts was reversible and that the reverse reaction depended on the presence of both NADH and a muscle protein.

Heat-inactivated peroxidases and the role of calcium abstraction as a cause of their enhanced lipid oxidation activity: potential effects on the flavour quality of heat-processed vegetables

Cationic swede and anionic turnip peroxidases were partially purified by ion-exchange and gel-filtration chromatography, respectively. Heat treatment of these enzymes and of a commercial high purity horseradish peroxidase (HRP) caused a loss of enzyme activity and a corresponding increase in linoleic acid hydroperoxide formation activity. The hydroperoxide levels in model systems increased only in the early stages of the oxidation reaction and then declined as degradation became more significant. The presence of a dialysed blend of cooked swede markedly lowered the hydroperoxide level formed. Analysis of volatile compounds formed showed that hexanal predominated in a buffer system and in a blend of cooked turnip. In dialysed blends of cooked swede, hexanol was the primary volatile compound generated. After inactivation under mild conditions in the presence of EDTA, the peroxidases showed hydroperoxide formation activity and patterns of volatile compounds from linoleic acid that were similar to those found on heat-inactivation. This suggested that calcium abstraction from the peroxidases was critical for the enhancement of lipid oxidation activity. (C) 2002 Elsevier Science Ltd. All rights reserved.

Socioemotional development in adolescents at risk for depression: the role of maternal depression and attachment style

We examined the impact on adolescent socioemotional functioning of maternal postnatal depression (PND) and attachment style. We also investigated the role of earlier aspects of the child's development-attachment in infancy, and 5-year representations of family relationships. Ninety-one mother-child pairs, recruited in the postnatal period, were followed tip at 13 years. Adolescents were interviewed about their friendships, and their level of emotional sensitivity and maturity were rated. Emotional sensitivity was heightened in girls whose mothers experienced PND; notably, its occurrence was also linked to insecure attachment in infancy and raised awareness of emotional components of family relationships at 5 years. High emotional sensitivity was also associated with adolescent depressed mood. Raised social maturity was predicted by a secure maternal attachment style and, for girls, by exposure to maternal PND. Precursors of adolescent social maturity were evident in the narrative coherence of 5-year family representations. Higher social maturity in the friendship interview was also associated with overall good adjustment.

Requirements analysis for an e-government system to support multi-organisational collaborative groups

We present a conceptual architecture for a Group Support System (GSS) to facilitate Multi-Organisational Collaborative Groups (MOCGs) initiated by local government and including external organisations of various types. Multi-Organisational Collaborative Groups (MOCGs) consist of individuals from several organisations which have agreed to work together to solve a problem. The expectation is that more can be achieved working in harmony than separately. Work is done interdependently, rather than independently in diverse directions. Local government, faced with solving complex social problems, deploy MOCGs to enable solutions across organisational, functional, professional and juridical boundaries, by involving statutory, voluntary, community, not-for-profit and private organisations. This is not a silver bullet as it introduces new pressures. Each member organisation has its own goals, operating context and particular approaches, which can be expressed as their norms and business processes. Organisations working together must find ways of eliminating differences or mitigating their impact in order to reduce the risks of collaborative inertia and conflict. A GSS is an electronic collaboration system that facilitates group working and can offer assistance to MOCGs. Since many existing GSSs have been primarily developed for single organisation collaborative groups, even though there are some common issues, there are some difficulties peculiar to MOCGs, and others that they experience to a greater extent: a diversity of primary organisational goals among members; different funding models and other pressures; more significant differences in other information systems both technologically and in their use than single organisations; greater variation in acceptable approaches to solve problems. In this paper, we analyse the requirements of MOCGs led by local government agencies, leading to a conceptual architecture for an e-government GSS that captures the relationships between 'goal', 'context', 'norm', and 'business process'. Our models capture the dynamics of the circumstances surrounding each individual representing an organisation in a MOCG along with the dynamics of the MOCG itself as a separate community.