T. E. Harris's contributions to recurrent Markov processes and stochastic flows

This is a brief survey of T. E. Harris's work on recurrent Markov processes and on stochastic flows, and of some more recent work in these fields.Comment: Published in at http://dx.doi.org/10.1214/10-AOP594 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Renewal theory and computable convergence rates for geometrically ergodic Markov chains

We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and Tweedie, and from estimates using coupling, although we start from essentially the same assumptions of a drift condition toward a ``small set.'' The estimates show a noticeable improvement on existing results if the Markov chain is reversible with respect to its stationary distribution, and especially so if the chain is also positive. The method of proof uses the first-entrance-last-exit decomposition, together with new quantitative versions of a result of Kendall from discrete renewal theory.Comment: Published at http://dx.doi.org/10.1214/105051604000000710 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning Design and Service Oriented Architectures:a mutual dependency?

This paper looks at how the concept of reusability has gained currency in e-learning. Initial attention was focused on reuse of content, but recently attention has focused on reusable software tools and reusable activity structures. The former has led to the proposal of service-oriented architectures, and the latter has seen the development of the Learning Design specification. The authors suggest that there is a mutual dependency between the success of these two approaches, as complex Learning Designs require the ability to call on a range of tools, while remaining technology neutral. The paper describes a project at the UK Open University, SLeD, which sought to develop a Learning Design player that would utilise the service-oriented approach. This acted both as a means of exploring some of the issues implicit within both approaches and also provided a practical tool. The SLeD system was successfully implemented in a different university, Liverpool Hope, demonstrating some of the principles of re-use

The impact of different touchpoints on brand consideration

Marketers face the challenge of resource allocation across a range of touchpoints. Hence understanding their relative impact is important, but previous research tends to examine brand advertising, retailer touchpoints, word-of-mouth, and traditional earned touchpoints separately. This article presents an approach to understanding the relative impact of multiple touchpoints. It exemplifies this approach with six touchpoint types: brand advertising, retailer advertising, in-store communications, word-of-mouth, peer observation (seeing other customers), and traditional earned media such as editorial. Using the real-time experience tracking (RET) method by which respondents report on touchpoints by contemporaneous text message, the impact of touchpoints on change in brand consideration is studied in four consumer categories: electrical goods, technology products, mobile handsets, and soft drinks. Both touchpoint frequency and touchpoint positivity, the valence of the customer's affective response to the touchpoint, are modeled. While relative touchpoint effects vary somewhat by category, a pooled model suggests the positivity of in-store communication is in general more influential than that of other touchpoints including brand advertising. An almost entirely neglected touchpoint, peer observation, is consistently significant. Overall, findings evidence the relative impact of retailers, social effects and third party endorsement in addition to brand advertising. Touchpoint positivity adds explanatory power to the prediction of change in consideration as compared with touchpoint frequency alone. This suggests the importance of methods that track touchpoint perceptual response as well as frequency, to complement current analytic approaches such as media mix modeling based on media spend or exposure alone

Studies on the measurement and significance of androgens in saliva

Imperial Users onl

Uniform shrinking and expansion under isotropic Brownian flows

We study some finite time transport properties of isotropic Brownian flows. Under a certain nondegeneracy condition on the potential spectral measure, we prove that uniform shrinking or expansion of balls under the flow over some bounded time interval can happen with positive probability. We also provide a control theorem for isotropic Brownian flows with drift. Finally, we apply the above results to show that under the nondegeneracy condition the length of a rectifiable curve evolving in an isotropic Brownian flow with strictly negative top Lyapunov exponent converges to zero as $t\to \infty$ with positive probability

The pandemic has left us in a state of flux at work. How can we manage the unknown?

With COVID-19, uncertainty and a state of transition are creating and increasing individual, team, and organisational risk. Feelings of impending change affect recruitment, team development and career ambitions. Catherine Baxendale discusses how leaders can deal with these different levels of risk