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.

Calcrete profile development in quaternary alluvial sequences, southeast Spain: Implications for using calcretes as a basis for landform chronologies

A detailed study of the morphology and micro-morphology of Quaternary alluvial calcrete profiles from the Sorbas Basin shows that calcretes may be morphologically simple or complex. The 'simple' profiles reflect pedogenesis occurring after alluvial terrace formation and consist of a single pedogenic horizon near the land surface. The 'complex' profiles reflect the occurrence of multiple calcrete events during terrace sediment aggradation and further periods of pedogenesis after terrace formation. These 'complex' calcrete profiles are consequently described as composite profiles. The exact morphology of the composite profiles depends upon: (1) the number of calcrete-forming events occurring during terrace sediment aggradation; (2) the amount of sediment accretion that occurs between each period of calcrete formation; and (3) the degree of pedogenesis after terrace formation. Simple calcrete profiles are most useful in establishing landform chronologies because they represent a single phase of pedogenesis after terrace formation. Composite profiles are more problematic. Pedogenic calcretes that form within them may inherit carbonate from calcrete horizons occurring lower down in the terrace sediments. In addition erosion may lead to the exhumation of older calcretes within the terrace sediment. Calcrete 'inheritance' may make pedogenic horizons appear more mature than they actually are and produce horizons containing carbonate embracing a range of ages. Calcrete exhumation exposes calcrete horizons whose morphology and radiometric ages are wholly unrelated to terrace surface age. Composite profiles are, therefore, only suitable for chronological studies if the pedogenic horizon capping the terrace sequence can be clearly distinguished from earlier calcrete-forming events. Thus, a detailed morphological/micro-morphological study is required before any chronological study is undertaken. This is the only way to establish whether particular calcrete profiles are suitable for dating purposes. Copyright (C) 2003 John Wiley Sons, Ltd.

Producing Inequalities: Regional Sequences in Later Prehistoric Southern Spain

This paper presents regional sequences of production, consumption and Social relations ill Southern Spain from the beginning of the Neolithic to the Early Bronze Age (c. 5600-1550 BC). The regions Studied are southeast Spain, Valencia, the southern Meseta and central/western Andalucia. The details presented for each region and period vary in quality but Show how Much our knowledge of the archaeological record of southern Spain has changed during the last four decades. Among the Surprises are the rapidity of agricultural adoption. the emergence of regional centres of aggregated population in enclosed/fortified settlements of up to 400 hectares in the fourth and third millennia BC. the use of copper objects as instruments of production, rather than as items With 11 purely symbolic of 'prestige' value, large-scale copper production in western Andalucia in the third millennium BC (as opposed to the usual domestic production model), and the inference of societies based oil relations of class.

Wiggle-match dating of tree-ring sequences

Given the non-monotonic form of the radiocarbon calibration curve, the precision of single C-14 dates on the calendar timescale will always be limited. One way around this limitation is through comparison of time-series, which should exhibit the same irregular patterning as the calibration curve. This approach can be employed most directly in the case of wood samples with many years growth present (but not able to be dated by dendrochronology), where the tree-ring series of unknown date can be compared against the similarly constructed C-14 calibration curve built from known-age wood. This process of curve-fitting has come to be called "wiggle-matching." In this paper, we look at the requirements for getting good precision by this method: sequence length, sampling frequency, and measurement precision. We also look at 3 case studies: one a piece of wood which has been independently dendrochronologically dated, and two others of unknown age relating to archaeological activity at Silchester, UK (Roman) and Miletos, Anatolia (relating to the volcanic eruption at Thera).

Pleistocene geochronologies for fluvial sedimentary sequences: an archaeologist's perspective

Current models of Pleistocene fluvial system development and dynamics are assessed from the perspective of European Lower and Middle Palaeolithic stone tool assemblages recovered from fluvial secondary contexts. Fluvial activity is reviewed both in terms of Milankovitch-scale processes across the glacial/interglacial cycles of the Middle and Late Pleistocene, and in response to sub-Milankovitch scale, high-frequency, low-magnitude climatic oscillations. The chronological magnitude of individual phases of fluvial activity is explored in terms of radiocarbon-dated sequences from the Late Glacial and early Holocene periods. It is apparent that fluvial activity is associated with periods of climatic transition, both high and low magnitude, although system response is far more universal in the case of the high magnitude glacial/ interglacial transitions. Current geochronological tools do not permit the development of high-resolution sequences for Middle Pleistocene sediments, while localised erosion and variable system responses do not facilitate direct comparison with the ice core records. However, Late Glacial and early Holocene sequences indicate that individual fluvial activity phases are relatively brief in duration (e.g. 10(2) and 10(3) yr). From an archaeological perspective, secondary context assemblages can only be interpreted in terms of a floating geochronology, although the data also permit a reinvestigation of the problems of artefact reworking. Copyright (c) 2005 John Wiley I Sons, Ltd.

Aligning sequences to structures

Most newly sequenced proteins are likely to adopt a similar structure to one which has already been experimentally determined. For this reason, the most successful approaches to protein structure prediction have been template-based methods. Such prediction methods attempt to identify and model the folds of unknown structures by aligning the target sequences to a set of representative template structures within a fold library. In this chapter, I discuss the development of template-based approaches to fold prediction, from the traditional techniques to the recent state-of-the-art methods. I also discuss the recent development of structural annotation databases, which contain models built by aligning the sequences from entire proteomes against known structures. Finally, I run through a practical step-by-step guide for aligning target sequences to known structures and contemplate the future direction of template-based structure prediction.

A test of the master gene hypothesis for interspersed repetitive DNA sequences

Many families of interspersed repetitive DNA elements, including human Alu and LINE (Long Interspersed Element) elements, have been proposed to have accumulated through repeated copying from a single source locus: the "master gene." The extent to which a master gene model is applicable has implications for the origin, evolution, and function of such sequences. One repetitive element family for which a convincing case for a master gene has been made is the rodent ID (identifier) elements. Here we devise a new test of the master gene model and use it to show that mouse ID element sequences are not compatible with a strict master gene model. We suggest that a single master gene is rarely, if ever, likely to be responsible for the accumulation of any repeat family.