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.

Assessment of the presence of Salmonella spp. in Egyptian dairy products using various detection media

Aims: To make a preliminary assessment of the incidence of Salmonella in Egyptian dairy products, and to investigate the effectiveness of various protocols for the detection of the pathogen in these products. Methods and Results: Samples of milk and related dairy products were randomly collected from local markets and examined for the presence of Salmonella. While most samples were free of the organism, isolates of Salmonella enterica subsp. enterica serovar Typhimurium PT 8 could be recovered from 'matared' cream specimens. These isolates were susceptible to antibiotics usually used to challenge infections caused by Salmonella. A combination of buffered peptone water, Muller-Kauffman tetrathionate broth, and brilliant green phenol red agar gave the best results for the detection of the pathogen. Selenite-cystine broth and Hektoen enteric agar were ineffective as an enrichment and a plating medium, respectively, in the isolation of Salmonella. A modified identification strategy that reduces the burden of serological testing of presumptive isolates is proposed. Conclusions, Significance and Impact of the Study: 'Matared' cream could be a vehicle for transmitting Salmonella. Using the above combination of media, beside the suggested modified confirmatory procedure, should increase the effectiveness and ease of the detection of Salmonella in milk and dairy products.

Viability of Salmonella enterica subsp. enterica during the preparation and cold storage of Egyptian soft cheeses and ice-cream

Changes occurring in the viability of Salmonella enterica subsp. enterica during the preparation and cold storage of Domiati cheese, Kariesh cheese and ice-cream were examined. A significant decrease in numbers was observed after whey drainage during the manufacture of Domiati cheese, but Salmonella remained viable for 13 weeks in cheeses prepared from milks with between 60 and 100 g/L NaCl; the viability declined in Domiati cheese made from highly salted milk during the later stages of storage. The method of coagulation used in the preparation of Kariesh cheese affected the survival time of the pathogen, and it varied from 2 to 3 weeks in cheeses made with a slow-acid coagulation method to 4-5 weeks for an acid-rennet coagulation method. This difference was attributed to the higher salt-in-moisture levels and lower pH values of Kariesh cheese prepared by the slow-acid coagulation method. A slight decrease in the numbers of Salmonella resulted from ageing ice-cream mix for 24 h at 0degreesC, but a greater reduction was evident after one day of frozen storage at -20degreesC. The pathogen survived further frozen storage for four months without any substantial change in numbers.

Reading Derrida on mathematics

This article engages with the claims of Anne Brubaker that “[n]ow that the dust has settled after the so-called ‘Science Wars’ […] it is an opportune time to reassess the ways in which poststructural theory both argues persuasively for mathematics as a culturally embedded practice – a method as opposed to a metaphysics – and, at the same time, reinscribes realist notions of mathematics as a noise-free description of a mind independent reality.” Through a close re-reading of Jacques Derrida’s work I argue, in alliance with Vicki Kirby’s critique of the work of Brian Rotman, not only that Brubaker misunderstands Derrida’s “writing” but also that her argument constitutes a typical instance of much wider misreadings of Derrida and “poststructuralism” across a range of disciplines in terms of the ways in which her text re-institutes the very stabilities it itself attributes to Derrida’s texts.