Non-local dispersal

We consider a model of spatial spread that has applications in both material science and biology. The classical models are based upon partial differential equations, in particular reaction-diffusion equations. Here the dispersal term is given in terms of an integral operator and we restrict ourselves to the scalar case

Tom Vickers, Gary Craig and Karl Atkin (2013), ‘Addressing Ethnicity in Social Care Research’, Social Policy and Administration, 47 (3), June, 310–26

This article surveys recent developments in relation to the dimensions of ethnicity and ethnic disadvantage in social policy research and practice, with a focus on social care. While there has been limited increase in attention to ethnicity within general policy discussion and increasing sophistication within specialist debates, advances in theory and methodology have largely failed to penetrate the mainstream of research, let alone policy or practice. We argue for a more focussed consideration of ethnicity and ethnic disadvantage at all levels. Failure to do so creates the risk of social policy research being left behind in understanding rapid changes in ethnic minority demographics and patterns of migration, and increasing disadvantage to minorities

A topos for algebraic quantum theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible only through classical physics, we show how a C*-algebra of observables A induces a topos T(A) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum S(A) in T(A), which in our approach plays the role of a quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on S(A), and self-adjoint elements of A define continuous functions (more precisely, locale maps) from S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical Physic

Naked Singularity and Thunderbolt

We consider quantum theoretical effects of the sudden change of the boundary conditions which mimics the occurrence of naked singularities. For a simple demonstration, we study a massless scalar field in $(1 + 1)$-dimensional Minkowski spacetime with finite spatial interval. We calculate the vacuum expectation value of the energy-momentum tensor and explicitly show that singular wave or {\em thunderbolt} appears along the Cauchy horizon. The thunderbolt possibly destroys the Cauchy horizon if its backreaction on the geometry is taken into account, leading to quantum restoration of the global hyperbolicity. The result of the present work may also apply to the situation that a closed string freely oscillating is traveling to a brane and changes itself to an open string pinned-down by the ends satisfying the Dirichlet boundary conditions on the brane.Comment: 12 pages, 1 figure, references added, to appear in Phys. Rev.

ESS Patterns: Adding Pairs to an ESS

ABSTRACT The notion of a pattern of evolutionarily stable strategies was introduced by Cannings and Vickers in 1988 (J. Theor. Biol. 132:387-420)

Feasibility study of a clinically-integrated randomized trial of modifications to radical prostatectomy

<p>Abstract</p> <p>Background</p> <p>Numerous technical modifications to radical prostatectomy have been proposed. Such modifications are likely to lead to only slight improvements in outcomes. Although small differences would be worthwhile, an appropriately powered randomized trial would need to be very large, and thus of doubtful feasibility given the expense, complexity and regulatory burden of contemporary clinical trials. We have proposed a novel methodology, the clinically-integrated randomized trial, which dramatically streamlines trial procedures in order to reduce the marginal cost of an additional patient towards zero. We aimed to determine the feasibility of implementing such a trial for radical prostatectomy.</p> <p>Methods</p> <p>Patients undergoing radical prostatectomy as initial treatment for prostate cancer were randomized in a factorial design to involvement of the fascia during placement of the anastomotic sutures, urethral irrigation, both or neither. Endpoint data were obtained from routine clinical documentation. Accrual and compliance rates were monitored to determine the feasibility of the trial.</p> <p>Results</p> <p>From a total of 260 eligible patients, 154 (59%) consented; 56 patients declined to participate, 20 were not approached on recommendation of the treating surgeon, and 30 were not approached for logistical reasons. Although recording by surgeons of the procedure used was incomplete (~80%), compliance with randomization was excellent when it was recorded, with only 6% of procedures inconsistent with allocation. Outcomes data was received from 71% of patients at one year. This improved to 83% as the trial progressed.</p> <p>Conclusions</p> <p>A clinically-integrated randomized trial was conducted at low cost, with excellent accrual, and acceptable compliance with treatment allocation and outcomes reporting. This demonstrates the feasibility of the methodology. Improved methods to ensure documentation of surgical procedures would be required before wider implementation.</p> <p>Trial registration</p> <p>ClinicalTrials.gov <a href="http://www.clinicaltrials.gov/ct2/show/NCT00928850">NCT00928850</a></p