Global consensus Monte Carlo

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

A note on heat and mass transfer from a sphere in Stokes\ud flow at low Péclet number

We consider the low Péclet number, Pe ≪ 1, asymptotic solution for steady-state heat and mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of van Dyke’s rule up to terms of O(Pe3) shows that the O(Pe3 log Pe) terms in the expression for the average Nusselt/Sherwood number are double those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase significantly the range of validity of the expansion

Britain Says NO: Voting in the AV Ballot Referendum

The purpose of this paper is to explain why voters made the choices that they did in Britains Alternative Vote (AV) referendum on 5 May 2011. The paper utilises four alternative theoretical models to analyse individual voting behaviour. They are described as the cost-benefit, cognitive engagement, heuristics and mobilisation models. The explanatory power of these models is investigated using a large survey data set gathered in the AV referendum study conducted in conjunction with the British Election Study. Multivariate analyses show that all four models contribute to explaining why some people voted in favour of electoral reform, with the cost-benefit model exhibiting particularly strong effects. The conclusion discusses public reactions to the referendum and possible implications of the decisive rejection of electoral reform after a campaign characterised by disaffection and disengagement. © 2011 The Author Published by Oxford University Press on behalf of the Hansard Society. All rights reserved

Nonuniqueness in a minimal model for cell motility

Two–phase flow models have been used previously to model cell motility, however these have rapidly become very complicated, including many physical processes, and are opaque. Here we demonstrate that even the simplest one–dimensional, two–phase, poroviscous, reactive flow model displays a number of behaviours relevant to cell crawling. We present stability analyses that show that an asymmetric perturbation is required to cause a spatially uniform, stationary strip of cytoplasm to move, which is relevant to cell polarization. Our numerical simulations identify qualitatively distinct families of travelling–wave solution that co–exist at certain parameter values. Within each family, the crawling speed of the strip has a bell–shaped dependence on the adhesion strength. The model captures the experimentally observed behaviour that cells crawl quickest at intermediate adhesion strengths, when the substrate is neither too sticky nor too slippy

Critical thinking/questioning skills a meta-model for cognitive development in management education

The paper presents a model for the critical questioning of organisational practices and theories. P.A.T.P. represents PHILOSOPHY, ASSUMPTIONS, THEORY AND PRACTICES. The aim is to develop skills of questioning through three levels. The first level is Interesting. The second level is Important. The third level is Critical. The paper presents the model using two contrasting philosophies of organisation, as expounded by F W Taylor and Stephen Covey. The paper presents the educational setting of MBA seminar, a series of presentations by international and professional experts. Following each presented seminar is the Critical Questioning Session. The student co-author presents the student learning process through two case examples. He applies the approach outside of the MBA seminar setting, showing an extension of his learning. As a meta-model, the application should span cultures and disciplines with the aim of making sense of rather than adding on

On the deflection of a liquid jet by an air-cushioning layer

A hierarchy of models is formulated for the deflection of a thin two-dimensional liquid jet as it passes over a thin air-cushioning layer above a rigid flat impermeable substrate. We perform a systematic derivation of the leading-order equations of motion for the jet in the distinguished limit in which the air pressure jump, surface tension and gravity affect the displacement of the centreline of the jet, but not its thickness or velocity. We identify thereby the axial length scales for centreline deflection in regimes in which the air layer is dominated by viscous or inertial effects. The derived length scales and reduced equations aim to expand the suite of tools available for future analyses of the evolution of lamellae and ejecta in impact problems. Assuming that the jet is sufficiently long that tip and entry effects can be neglected, we demonstrate that the centreline of a constant-thickness jet moving with constant axial speed is destabilised by the air layer for sufficiently small surface tension. Expressions for the fastest-growing modes are obtained in both the viscous-dominated air and inertia-dominated air regimes. For a finite-length jet emanating from a nozzle, we show that, in one particular asymptotic limit, the evolution of the jet centreline is akin to the flapping of an unfurling flag above a thin air layer. We discuss the distinguished limit in which tip retraction can be neglected and perform numerical investigations into the resulting model. We show that the cushioning layer causes the jet centreline to bend, leading to rupture of the air layer. We discuss how our toolbox of models can be adapted and utilised in the context of recent experimental and numerical studies of splash dynamics