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 the (un)-ambiguity of adjectival modification in Spanish determiner phrases: informing debates on the mental representations of L2 syntax.

This study contributes to a central debate within contemporary generative second language (L2) theorizing: the extent to which adult learners are (un)able to acquire new functional features that result in a L2 grammar that is mentally structured like the native target (see White, 2003). The adult acquisition of L2 nominal phi-features is explored, with focus on the syntactic and semantic reflexes in the related domain of adjective placement in two experimental groups: English-speaking intermediate (n = 21) and advanced (n = 24) learners of Spanish, as compared to a native-speaker control group (n = 15). Results show that, on some of the tasks, the intermediate L2 learners appear to have acquired the syntactic properties of the Spanish determiner phrase but, on other tasks, to show some delay with the semantic reflexes of prenominal and postnominal adjectives. Crucially, however, our data demonstrate full convergence by all advanced learners and thus provide evidence in contra the predictions of representational deficit accounts (e.g., Hawkins & Chan, 1997; Hawkins & Franceschina, 2004; Hawkins & Hattori, 2006).

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.

The Liberal Way of War? French representations of the Allies, 1944-2008

This chapter looks at the ways in which Anglo-American participants in the Liberation of France have been represented in French narratives in the decades since the Second World War, through the developing French historiography of Allied participation in the War, and through the various roles assigned to the Allies in key postwar memorialisation ceremonies in France.

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

Terrorist transgressions: gendered representations of the terrorist in visual culture

The aim of Terrorist Transgressions is to analyse the myths inscribed in images of the terrorist and identify how agency is attributed to representation through invocations and inversions of gender stereotypes. In modern discourses on the terrorist the horror experienced in Western societies was the appearance of a new sense of the vulnerability of the body politic, and therefore of the modern self with its direct dependency on security and property. The terrorist has been constructed as the epitome of transgression against economic resources and moral, physical and political boundaries. Although terrorism has been the focus of intense academic activity, cultural representations of the terrorist have received less attention. Yet terrorism is dependent on spectacle and the topic is subject to forceful exposure in popular media. While the terrorist is predominantly aligned with masculinity, women have been active in terrorist organisations since the late 19th century and in suicidal terrorist attacks since the 1980s. Such attacks have confounded constructions of femininity and masculinity, with profound implications for the gendering of violence and horror. The publication arises from an AHRC networking grant, 2011-12, with Birkbeck, and includes collaboration with the army at Sandhurst RMA. The project relates to a wider investigation into feminism, violence and contemporary art.

Socially anxious mothers’ narratives to their children, and their relation to child representations and adjustment

Anxious mothers’ parenting, particularly transfer of threat information, has been considered important in their children’s risk for social anxiety disorder (SAnxD), and maternal narratives concerning potential social threat could elucidate this contribution. Maternal narratives to their pre-school 4-5 year-old children, via a picture book about starting school, were assessed in socially anxious (N=73), and non-anxious (N=63) mothers. Child representations of school were assessed via Doll Play (DP). After one school term, mothers (CBCL) and teachers (TRF) reported on child internalizing problems, and child SAnxD was assessed via maternal interview. Relations between these variables, infant behavioral inhibition, and attachment, were examined. Socially anxious mothers showed more negative (higher threat attribution), and less supportive (lower encouragement) narratives, than controls, and their children’s DP representations, SAnxD and CBCL scores were more adverse. High narrative threat predicted child SAnxD; lower encouragement predicted negative child CBCL scores and, particularly for behaviorally inhibited children, TRF scores and DP representations. In securely attached children, CBCL scores and risk for SAnxD were affected by maternal anxiety and threat attributions, respectively. Low encouragement mediated the effects of maternal anxiety on child DP representations, and CBCL scores. Maternal narratives are affected by social anxiety, and contribute to adverse child outcome.