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.

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.

Fine root biomass and turnover in southern taiga estimated by root inclusion nets

Fine roots play an important part in forest carbon, nutrient and water cycles. The turnover of fine roots constitutes a major carbon input to soils. Estimation of fine root turnover is difficult, labour intensive and is often compounded by artefacts created by soil disturbance. In this work, an alternative approach of using inclusion nets installed in an undisturbed soil profile was used to measure fine root production and was compared to the in-growth core method. There was no difference between fine root production estimated by the two methods in three southern taiga sites with contrasting soil conditions and tree species composition in the Central Forest State Biosphere Reserve, Russia. Expressed as annual production over standing biomass, Norway spruce fine root turnover was in the region of 0.10 to 0.24 y-1. The inclusion net technique is suitable for field based assessment of fine root production. There are several advantages over the in-growth core method, due to non-disturbance of the soil profile and its potential for very high rate of replication.

Weightless neural nets for face recognition: a comparison

This paper considers the application of weightless neural networks (WNNs) to the problem of face recognition and compares the results with those provided using a more complicated multiple neural network approach. WNNs have significant advantages over the more common forms of neural networks, in particular in term of speed of operation and learning. A major difficulty when applying neural networks to face recognition problems is the high degree of variability in expression, pose and facial details: the generalisation properties of a WNN can be crucial. In the light of this problem a software simulator of a WNN has been built and the results of some initial tests are presented and compared with other techniques

Pattern separation in digital learning nets

Pattern separation is a new technique in digital learning networks which can be used to detect state conflicts. This letter describes pattern separation in a simple single-layer network, and an application of the technique in networks with feedback.