The first international workshop on the role and impact of mathematics in medicine: a collective account

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for inter- disciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtaining

Confucius, constructivism and the impact of continuing professional development on teachers of English in China

In this article we explore issues around the sustainability and appropriateness of professional development for secondary teachers of English in China offered by overseas providers from the perspective of teachers who completed courses at the University of Reading between 2003 and 2010. We start by offering an overview of English teaching in China. We then describe the collection and analysis of interviews and focus groups discussions involving former participants, their teaching colleagues and senior management, as well as classroom observation. Evidence is presented for changes in teachers’ philosophies of education directly attributable to participation in the courses; for improved teacher competencies (linguistic, cultural and pedagogical) in the classroom; and for the ways in which returnees are undertaking new roles and responsibilities which exploit their new understandings. Finally, we discuss the implications of these findings for both providers and sponsors of CPD for English language teachers. We conclude that the recognition of English as an essential element in the modernisation of China, together with the growing awareness of the weaknesses of traditional approaches to the teaching of the language, has opened up new spaces for dialogue concerning pedagogy and professional practice. It is clearly important, however, that new approaches to the teaching of English are presented in a way which allows teachers to decide which elements should be incorporated into their teaching and how.

Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Transition of pupils from Key Stage 2 to 3 deemed gifted and talented in mathematics: an initial study

In this article Geoff Tennant and Dave Harries report on the early stages of a research project looking to examine the transition from Key Stage (KS) 2 to 3 of children deemed Gifted and Talented (G&T) in mathematics. An examination of relevant literature points towards variation in definition of key terms and underlying rationale for activities. Preliminary fieldwork points towards a lack of meaningful communication between schools, with primary school teachers in particular left to themselves to decide how to work with children deemed G&T. Some pointers for action are given, along with ideas for future research and a request for colleagues interested in working with us to get in touch.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Assembling novel protein folds from super-secondary structural fragments

The results of applying a fragment-based protein tertiary structure prediction method to the prediction of 14 CASP5 target domains are described. The method is based on the assembly of supersecondary structural fragments taken from highly resolved protein structures using a simulated annealing algorithm. A number of good predictions for proteins with novel folds were produced, although not always as the first model. For two fold recognition targets, FRAGFOLD produced the most accurate model in both cases, despite the fact that the predictions were not based on a template structure. Although clear progress has been made in improving FRAGFOLD since CASP4, the ranking of final models still seems to be the main problem that needs to be addressed before the next CASP experiment

Secondary structure prediction with support vector machines

Motivation: A new method that uses support vector machines (SVMs) to predict protein secondary structure is described and evaluated. The study is designed to develop a reliable prediction method using an alternative technique and to investigate the applicability of SVMs to this type of bioinformatics problem. Methods: Binary SVMs are trained to discriminate between two structural classes. The binary classifiers are combined in several ways to predict multi-class secondary structure. Results: The average three-state prediction accuracy per protein (Q3) is estimated by cross-validation to be 77.07 ± 0.26% with a segment overlap (Sov) score of 73.32 ± 0.39%. The SVM performs similarly to the 'state-of-the-art' PSIPRED prediction method on a non-homologous test set of 121 proteins despite being trained on substantially fewer examples. A simple consensus of the SVM, PSIPRED and PROFsec achieves significantly higher prediction accuracy than the individual methods. Availability: The SVM classifier is available from the authors. Work is in progress to make the method available on-line and to integrate the SVM predictions into the PSIPRED server.