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.

Incorporating Legacy Soil pH Databases into Digital Soil Maps

Soil data and reliable soil maps are imperative for environmental management. conservation and policy. Data from historical point surveys, e.g. experiment site data and farmers fields can serve this purpose. However, legacy soil information is not necessarily collected for spatial analysis and mapping such that the data may not have immediately useful geo-references. Methods are required to utilise these historical soil databases so that we can produce quantitative maps of soil propel-ties to assess spatial and temporal trends but also to assess where future sampling is required. This paper discusses two such databases: the Representative Soil Sampling Scheme which has monitored the agricultural soil in England and Wales from 1969 to 2003 (between 400 and 900 bulked soil samples were taken annually from different agricultural fields); and the former State Chemistry Laboratory, Victoria, Australia where between 1973 and 1994 approximately 80,000 soil samples were submitted for analysis by farmers. Previous statistical analyses have been performed using administrative regions (with sharp boundaries) for both databases, which are largely unrelated to natural features. For a more detailed spatial analysis that call be linked to climate and terrain attributes, gradual variation of these soil properties should be described. Geostatistical techniques such as ordinary kriging are suited to this. This paper describes the format of the databases and initial approaches as to how they can be used for digital soil mapping. For this paper we have selected soil pH to illustrate the analyses for both databases.

Ibergirhynchia contraria (F. A. Roemer, 1850), an Early Carboniferous seep-related rhynchonellide brachiopod from the Harz Mountains, Germany - A possible successor to Dzieduszyckia?

A new genus Ibergirhynchia, a member of the rhynchonellide superfamily Dimerelloidea, is described for the species Terebratula contraria Roemer, 1850, from Early Carboniferous deposits of the Harz Mountains, Germany. Ibergirhynchia contraria is from a monospecific brachiopod limestone that formed on top of the drowned Devonian Iberg Reef which persisted as a seamount during Famennian and Early Carboniferous times. Ibergirhynchia contraria is considered a cold seep-related brachiopod based on this locality. Such seep associations have been observed for Mesozoic representatives of the rhynchonellide superfamily Dimerelloidea. Ibergirhynchia is considered the first Paleozoic representative of the family Rhynchonellinidae. Ibergirhynchia resembles Dzieduszyckia externally and may be derived from this dimerelloid.

Conservation strategy maps: a tool to facilitate biodiversity action planning illustrated using the heath fritillary butterfly

1. The UK Biodiversity Action Plan (UKBAP) identifies invertebrate species in danger of national extinction. For many of these species, targets for recovery specify the number of populations that should exist by a specific future date but offer no procedure to plan strategically to achieve the target for any species. 2. Here we describe techniques based upon geographic information systems (GIS) that produce conservation strategy maps (CSM) to assist with achieving recovery targets based on all available and relevant information. 3. The heath fritillary Mellicta athalia is a UKBAP species used here to illustrate the use of CSM. A phase 1 habitat survey was used to identify habitat polygons across the county of Kent, UK. These were systematically filtered using relevant habitat, botanical and autecological data to identify seven types of polygon, including those with extant colonies or in the vicinity of extant colonies, areas managed for conservation but without colonies, and polygons that had the appropriate habitat structure and may therefore be suitable for reintroduction. 4. Five clusters of polygons of interest were found across the study area. The CSM of two of them are illustrated here: the Blean Wood complex, which contains the existing colonies of heath fritillary in Kent, and the Orlestone Forest complex, which offers opportunities for reintroduction. 5. Synthesis and applications. Although the CSM concept is illustrated here for the UK, we suggest that CSM could be part of species conservation programmes throughout the world. CSM are dynamic and should be stored in electronic format, preferably on the world-wide web, so that they can be easily viewed and updated. CSM can be used to illustrate opportunities and to develop strategies with scientists and non-scientists, enabling the engagement of all communities in a conservation programme. CSM for different years can be presented to illustrate the progress of a plan or to provide continuous feedback on how a field scenario develops.

Fast training of self organizing maps for the visual exploration of molecular compounds

Visual exploration of scientific data in life science area is a growing research field due to the large amount of available data. The Kohonen’s Self Organizing Map (SOM) is a widely used tool for visualization of multidimensional data. In this paper we present a fast learning algorithm for SOMs that uses a simulated annealing method to adapt the learning parameters. The algorithm has been adopted in a data analysis framework for the generation of similarity maps. Such maps provide an effective tool for the visual exploration of large and multi-dimensional input spaces. The approach has been applied to data generated during the High Throughput Screening of molecular compounds; the generated maps allow a visual exploration of molecules with similar topological properties. The experimental analysis on real world data from the National Cancer Institute shows the speed up of the proposed SOM training process in comparison to a traditional approach. The resulting visual landscape groups molecules with similar chemical properties in densely connected regions.

Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.

Intercomparison of aircraft instruments on board the C-130 and Falcon-20 over southern Germany during EXPORT2000

In the summer 2000 EXPORT aircraft campaign (European eXport of Precursors and Ozone by long-Range Transport), two comprehensively instrumented research aircraft measuring a variety of chemical species flew wing tip to wing tip for a period of one and a quarter hours. During this interval a comparison was undertaken of the measurements of nitrogen oxide (NO), odd nitrogen species (NOy), carbon monoxide (CO) and ozone (O3). The comparison was performed at two different flight levels, which provided a 10-fold variation in the concentrations of both NO (10 to 1000 parts per trillion by volume (pptv)) and NOy (200 to over 2500 pptv). Large peaks of NO and NOy observed from the Falcon 20, which were at first thought to be from the exhaust of the C-130, were also detected on the 4 channel NOxy instrument aboard the C-130. These peaks were a good indication that both aircraft were in the same air mass and that the Falcon 20 was not in the exhaust plume of the C-130. Correlations and statistical analysis are presented between the instruments used on the two separate aircraft platforms. These were found to be in good agreement giving a high degree of correlation for the ambient air studied. Any deviations from the correlations are accounted for in the estimated inaccuracies of the instruments. These results help to establish that the instruments aboard the separate aircraft are reliably able to measure the corresponding chemical species in the range of conditions sampled and that data collected by both aircraft can be co-ordinated for purposes of interpretation.