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

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Incorporating creativity into teachers practice and self-concept of professional identity

The study explores what happens to teachers practice and ’ professional identity when they adopt a collaborative action research approach to teaching and involve external creative partners and a university mentor. The teachers aim to nurture and develop the creative potential of their learners through empowering them to make decisions for themselves about their own progress and learning directions. The teachers worked creatively and collaboratively designing creative teaching and learning methods in support of pupils with language and communication difficulties. The respondents are from an English special school, primary school and girls secondary school. A mixed methods methodology is adopted. Gains in teacher confidence and capability were identified in addition to shifts in values that impacted directly on their self-concept of what it is to be an effective teacher promoting effective learning. The development of their professional identities within a team ethos included them being able to make decisions about learning that are based on the educational potential of learners that they proved resulted in elevated standards achieved by this group of learners. They were able to justify their actions on established educational principles. Tensions however were revealed between what they perceived as their normal required professionalism imposed by external agencies and the enhanced professionalism experienced working through the project where they were able to integrate theory and practice.

Creative participation in construction firms: bridging creativity and innovation

An intricate evolution of mainstream theories follows the growing need to explain employees’ commitment and engagement. Our understanding of these work-related phenomena and behaviour has improved but creativity and innovation as desired indicators are still often treated as coexisting constructs with very little attention given to a state of willingness of an individual to even consider contributing ideas. In this research we investigate the influence of knowledge and understanding, perceived radicality, personality dimensions, and favouring of ideas on employee willingness to creatively participate in order to trace its existence in propagation of ideas. A total of 76 construction and non-construction professionals participated in between-subject quasi-experiments. We also proposed IPO-based radicality of ideas construct from the viewpoint of employees involved in the processes of transformation. The research findings show that experts with deep understanding of the work are more likely to contribute highly radical ideas to decision-makers than less knowledgeable employees. Furthermore, personal factors that impact employee willingness to creatively participate have been valued higher than organisational factors. Personality dimensions by The BigFive Inventory have shown no effect on willingness to contribute ideas, while favouring of ideas showed a significant effect. In general, the findings show similarities with some studies of consumer willingness to participate in co-creation processes and thus indicate that firms may be studied as dynamic internal markets of ideas.

Adaptation-induced collective dynamics of a single-cell protozoan

We investigate the behavior of a single-cell protozoan in a narrow tubular ring. This environment forces them to swim under a one-dimensional periodic boundary condition. Above a critical density, single-cell protozoa aggregate spontaneously without external stimulation. The high-density zone of swimming cells exhibits a characteristic collective dynamics including translation and boundary fluctuation. We analyzed the velocity distribution and turn rate of swimming cells and found that the regulation of the turing rate leads to a stable aggregation and that acceleration of velocity triggers instability of aggregation. These two opposing effects may help to explain the spontaneous dynamics of collective behavior. We also propose a stochastic model for the mechanism underlying the collective behavior of swimming cells.

Can valuation factors be prescribed? The case of collective enfranchisement and leasehold extension of flats in England and Wales

Recent concerns over the valuation process in collective leasehold enfranchisement and lease extension cases have culminated in new legislation. To underpin this, the Government (Department of Environment Transport and the Regions (DETR)) commissioned new research, which examined whether the valuation of the freehold in such cases could be simplified through the prescription of either yield or marriage value/relativity. This paper, which is based on that research, examines whether it is possible or desirable to prescribe such factors in the valuation process. Market, settlement and Local Valuation Tribunal (LVT) decisions are analysed, and the basis of 'relativity charts' used in practice is critically examined. Ultimately the imperfect nature of the market in freehold investment sales and leasehold vacant possession sales means that recommendations must rest on an analysis of LVT data. New relativity curves are developed from this data and used in conjunction with an alternative approach to valuation yields (based on other investment assets). However, the paper concludes that although the prescription of yields and relativity is possible, it is not fully defensible because of problems in determining risk premia; that the evidential basis for relativity consists of LVT decisions; and that a formula approach would tend to 'lead' the market as a whole.

On collective intentions: collective action in economics and philosophy

Philosophers and economists write about collective action from distinct but related points of view. This paper aims to bridge these perspectives. Economists have been concerned with rationality in a strategic context. There, problems posed by “coordination games” seem to point to a form of rational action, “team thinking,” which is not individualistic. Philosophers’ analyses of collective intention, however, sometimes reduce collective action to a set of individually instrumental actions. They do not, therefore, capture the first person plural perspective characteristic of team thinking. Other analyses, problematically, depict intentions ranging over others’ actions. I offer an analysis of collective intention which avoids these problems. A collective intention aims only at causing an individual action, but its propositional content stipulates its mirroring in other minds.