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.

Degree of oxidation of low density lipoprotein affects expression of CD36 and PPAR gamma, but not cytokine production, by human monocyte-macrophages

Oxidized low-density lipoprotein (oxLDL) exhibits many atherogenic effects, including the promotion of monocyte recruitment to the arterial endothelium and the induction of scavenger receptor expression. However, while atherosclerosis involves chronic inflammation within the arterial intima, it is unclear whether oxLDL alone provides a direct inflammatory stimulus for monocyte-macrophages. Furthermore, oxLDL is not a single, well-defined entity, but has structural and physical properties which vary according to the degree of oxidation. We tested the hypothesis that the biological effects of oxLDL will vary according to its degree of oxidation and that some species of oxLDL will have atherogenic properties, while other species may be responsible for its inflammatory activity. The atherogenic and inflammatory properties of LDL oxidized to predetermined degrees (mild, moderate and extensive oxidation) were investigated in a single system using human monocyte-derived macrophages. Expression of CD36 mRNA was up-regulated by mildly- and moderately-oxLDL, but not highly-oxLDL. The expression of the transcription factor, proliferator-activated receptor-gamma (PPARgamma), which has been proposed to positively regulate the expression of CD36, was increased to the greatest degree by highly-oxLDL. However, the DNA binding activity of PPARgamma was increased only by mildly- and moderately-oxLDL. None of the oxLDL species appeared to be pro-inflammatory towards monocytes, either directly or indirectly through mediators derived from lymphocytes, regardless of the degree of oxidation. (C) 2003 Published by Elsevier Science Ireland Ltd.

Diameter of parallelogramic honeycomb torus

The determination of the diameter of an interconnection network is essential in evaluating the performance of the network. Parallelogramic honeycomb torus is an attractive alternative to classical torus network due to smaller vertex degree, and hence, lower implementation cost. In this paper, we present the expression for the diameter of a parallelogramic, honeycomb torus, which extends a known result about rhombic: honeycomb torus. (c) 2005 Elsevier Ltd. All rights reserved.

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.