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 .

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.

Diet and lifestyle in Bronze Age Northwest Spain: the collective burial of Cova do Santo

A multidisciplinary investigation of the collective burial of Cova do Santo is presented as a novel approach to understand daily life during the Bronze Age in Northwest Iberia. The research is focused on three main aspects: i) taphonomy and patterns of disposal, ii) paleopathology and -demography as indicators of health status and lifestyle, and iii) stable isotope analysis to reconstruct paleodiet and to investigate the timing of the introduction of millet to the Iberian Peninsula. Osteological analyses were performed on 64 bones (61 human and 3 animal); additionally, bone collagen was extracted from 15 samples (13 human and 2 animal) and analyzed for its carbon and nitrogen stable isotopes composition. The radiocarbon age of the human remains is consistent with the Middle Bronze Age (c. 1890 to 1600 cal BC). The recovered remains belonged to a minimum number of 14 individuals with an estimated age at death of forty years or younger. This relatively young age is in contrast to a high prevalence of degenerative joint disease in the group. The isotopic results suggest a very homogeneous diet, which was almost exclusively based on C3 plants and terrestrial animal products. Overall, the data suggest that the studied population belonged to a period prior to the introduction of spring or summer-grown crops such as millets. The collective burial from the cave of Cova de Santo, Galicia, currently represents the largest assemblage of prehistoric human remains from Northwest Spain and the relatively good preservation of the bones offers a unique opportunity to investigate daily life in Northern Iberia during the Bronze Age.

Effect of pair interactions on transition probabilities between inactive and active states: achieving collective behaviour via pair interactions in social insects

To understand the evolution of well-organized social behaviour, we must first understand the mechanism by which collective behaviour establishes. In this study, the mechanisms of collective behaviour in a colony of social insects were studied in terms of the transition probability between active and inactive states, which is linked to mutual interactions. The active and inactive states of the social insects were statistically extracted from the velocity profiles. From the duration distributions of the two states, we found that 1) the durations of active and inactive states follow an exponential law, and 2) pair interactions increase the transition probability from inactive to active states. The regulation of the transition probability by paired interactions suggests that such interactions control the populations of active and inactive workers in the colony.

Capturing and sharing our collective expertise on climate data: the CHARMe project

For users of climate services, the ability to quickly determine the datasets that best fit one's needs would be invaluable. The volume, variety and complexity of climate data makes this judgment difficult. The ambition of CHARMe ("Characterization of metadata to enable high-quality climate services") is to give a wider interdisciplinary community access to a range of supporting information, such as journal articles, technical reports or feedback on previous applications of the data. The capture and discovery of this "commentary" information, often created by data users rather than data providers, and currently not linked to the data themselves, has not been significantly addressed previously. CHARMe applies the principles of Linked Data and open web standards to associate, record, search and publish user-derived annotations in a way that can be read both by users and automated systems. Tools have been developed within the CHARMe project that enable annotation capability for data delivery systems already in wide use for discovering climate data. In addition, the project has developed advanced tools for exploring data and commentary in innovative ways, including an interactive data explorer and comparator ("CHARMe Maps") and a tool for correlating climate time series with external "significant events" (e.g. instrument failures or large volcanic eruptions) that affect the data quality. Although the project focuses on climate science, the concepts are general and could be applied to other fields. All CHARMe system software is open-source, released under a liberal licence, permitting future projects to re-use the source code as they wish.