Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure

This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible → infected → removed) model for the spread of an epidemic amongst a population of individuals with a random network of social contacts that is also partitioned into households. Under various vaccine action models, we consider both household-based vaccination schemes, in which the way in which individuals are chosen for vaccination depends on the size of the households in which they reside, and acquaintance vaccination, which targets individuals of high degree in the social network. For both types of vaccination scheme, assuming a large population with few initial infectives, we derive a threshold parameter which determines whether or not a large outbreak can occur and also the probability and fraction of the population infected by such an outbreak. The performance of these schemes is studied numerically, focusing on the influence of the household size distribution and the degree distribution of the social network. We find that acquaintance vaccination can significantly outperform the best household-based scheme if the degree distribution of the social network is heavy-tailed. For household-based schemes, when the vaccine coverage is insufficient to prevent a major outbreak and the vaccine is imperfect, we find situations in which both the probability and size of a major outbreak under the scheme which minimises the threshold parameter are \emph{larger} than in the scheme which maximises the threshold parameter

The treatment of the infrared region in perturbative QCD

We discuss the contribution coming from the infrared region to NLO matrix elements and/or coefficient functions of hard QCD processes. Strictly speaking, this contribution is not known theoretically, since it is beyond perturbative QCD. For DGLAP evolution all the infrared contributions are collected in the phenomenological input parton distribution functions (PDFs), at some relatively low scale Q_0; functions which are obtained from a fit to the `global' data. However dimensional regularization sometimes produces a non-zero result coming from the infrared region. Instead of this conventional regularization treatment, we argue that the proper procedure is to first subtract from the NLO matrix element the contribution already generated at the same order in \alpha_s by the LO DGLAP splitting function convoluted with the LO matrix element. This prescription eliminates the logarithmic infrared divergence, giving a well-defined result which is consistent with the original idea that everything below Q_0 is collected in the PDF input. We quantify the difference between the proposed treatment and the conventional approach using low-mass Drell-Yan production and deep inelastic electron-proton scattering as examples; and discuss the potential impact on the `global' PDF analyses. We present arguments to show that the difference cannot be regarded as simply the use of an alternative factorization scheme.Comment: 15 pages, 5 figures, title changed, text considerably modified to improve presentation, and discussion section enlarge

Most vital segment barriers

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

b-Initiated processes at the LHC: a reappraisal

Several key processes at the LHC in the standard model and beyond that involve $b$ quarks, such as single-top, Higgs, and weak vector boson associated production, can be described in QCD either in a 4-flavor or 5-flavor scheme. In the former, $b$ quarks appear only in the final state and are typically considered massive. In 5-flavor schemes, calculations include $b$ quarks in the initial state, are simpler and allow the resummation of possibly large initial state logarithms of the type $\log \frac{{\cal Q}^2}{m_b^2}$ into the $b$ parton distribution function (PDF), ${\cal Q}$ being the typical scale of the hard process. In this work we critically reconsider the rationale for using 5-flavor improved schemes at the LHC. Our motivation stems from the observation that the effects of initial state logs are rarely very large in hadron collisions: 4-flavor computations are pertubatively well behaved and a substantial agreement between predictions in the two schemes is found. We identify two distinct reasons that explain this behaviour, i.e., the resummation of the initial state logarithms into the $b$-PDF is relevant only at large Bjorken $x$ and the possibly large ratios ${\cal Q}^2/m_b^2$'s are always accompanied by universal phase space suppression factors. Our study paves the way to using both schemes for the same process so to exploit their complementary advantages for different observables, such as employing a 5-flavor scheme to accurately predict the total cross section at NNLO and the corresponding 4-flavor computation at NLO for fully exclusive studies.Comment: Fixed typo in Eq. (A.10) and few typos in Eq. (C.2) and (C.3

Leading school networks, hybrid leadership in action?

A range of different constructs are used to describe and define the way that leadership operates in education settings. This range can be presented as binary categories of leadership, in which either one, or the other form of leadership is preferred, but not both. An example of this is the contrast made between solo and distributed leadership. A more sophisticated alternative has been proposed, which is to consider leadership as a hybrid activity, one which entails a range of approaches inspired by varying ideals. Taking this ‘hybrid’ notion of leadership this article explores the nature of leadership in networks of schools. Illustrated with data from three case studies of school networks this article highlights some of the issues and tensions in the enactment of the hybrid forms of leadership encountered in these networks. This article concludes with some reflections on the adoption of hybrid notions of leadership in researching and enacting educational leadership and specifically on the place of school networks in that consideration

Co-evolution of density and topology in a simple model of city formation

We study the influence that population density and the road network have on each others' growth and evolution. We use a simple model of formation and evolution of city roads which reproduces the most important empirical features of street networks in cities. Within this framework, we explicitely introduce the topology of the road network and analyze how it evolves and interact with the evolution of population density. We show that accessibility issues -pushing individuals to get closer to high centrality nodes- lead to high density regions and the appearance of densely populated centers. In particular, this model reproduces the empirical fact that the density profile decreases exponentially from a core district. In this simplified model, the size of the core district depends on the relative importance of transportation and rent costs.Comment: 13 pages, 13 figure

W boson production at hadron colliders: the lepton charge asymmetry in NNLO QCD

We consider the production of W bosons in hadron collisions, and the subsequent leptonic decay W->lnu_l. We study the asymmetry between the rapidity distributions of the charged leptons, and we present its computation up to the next-to-next-to-leading order (NNLO) in QCD perturbation theory. Our calculation includes the dependence on the lepton kinematical cuts that are necessarily applied to select W-> lnu_l events in actual experimental analyses at hadron colliders. We illustrate the main differences between the W and lepton charge asymmetry, and we discuss their physical origin and the effect of the QCD radiative corrections. We show detailed numerical results on the charge asymmetry in ppbar collisions at the Tevatron, and we discuss the comparison with some of the available data. Some illustrative results on the lepton charge asymmetry in pp collisions at LHC energies are presented.Comment: 37 pages, 21 figure

New Media and Online Mathematics Learning for Teachers

In this chapter we offer a case study of an online Mathematics for Teachers course through the lens of four affordances of new media: democratization, multimodality, collaboration and performance. Mathematics, perhaps more so than other school subjects, has traditionally been a subject that people do not talk about outside of classroom settings. However, we demonstrate through the case of the Mathematics for Teachers course that this does not have to be the case. Mathematics, even mathematics that traditionally has been seen as abstract or inaccessible, can be talked about in ways that can engage not only adults but also young children. The affordances of new media can help us rethink and disrupt our existing views of mathematics (for teachers and for students) and of how it might be taught and learned, by (1) blurring teacher/student distinctions and crossing hierarchical curriculum boundaries; (2) communicating mathematics in multimodal ways; (3) seeing mathematics as a collaborative enterprise; and (4) helping us learn how to relate good math stories to classmates and family when asked “What did you do in math today?

A randomised controlled trial and cost-effectiveness evaluation of "booster" interventions to sustain increases in physical activity in middle-aged adults in deprived urban neighbourhoods

Background: Systematic reviews have identified a range of brief interventions which increase physical activity in previously sedentary people. There is an absence of evidence about whether follow up beyond three months can maintain long term physical activity. This study assesses whether it is worth providing motivational interviews, three months after giving initial advice, to those who have become more active. Methods/Design: Study candidates (n = 1500) will initially be given an interactive DVD and receive two telephone follow ups at monthly intervals checking on receipt and use of the DVD. Only those that have increased their physical activity after three months (n = 600) will be randomised into the study. These participants will receive either a "mini booster" (n = 200), "full booster" (n = 200) or no booster (n = 200). The "mini booster" consists of two telephone calls one month apart to discuss physical activity and maintenance strategies. The "full booster" consists of a face-to-face meeting with the facilitator at the same intervals. The purpose of these booster sessions is to help the individual maintain their increase in physical activity. Differences in physical activity, quality of life and costs associated with the booster interventions, will be measured three and nine months from randomisation. The research will be conducted in 20 of the most deprived neighbourhoods in Sheffield, which have large, ethnically diverse populations, high levels of economic deprivation, low levels of physical activity, poorer health and shorter life expectancy. Participants will be recruited through general practices and community groups, as well as by postal invitation, to ensure the participation of minority ethnic groups and those with lower levels of literacy. Sheffield City Council and Primary Care Trust fund a range of facilities and activities to promote physical activity and variations in access to these between neighbourhoods will make it possible to examine whether the effectiveness of the intervention is modified by access to community facilities. A one-year integrated feasibility study will confirm that recruitment targets are achievable based on a 10% sample.Discussion: The choice of study population, study interventions, brief intervention preceding the study, and outcome measure are discussed

aMCfast: automation of fast NLO computations for PDF fits

We present the interface between MadGraph5 aMC@NLO, a self-contained program that calculates cross sections up to next-to-leading order accuracy in an automated manner, and APPLgrid, a code that parametrises such cross sections in the form of look-up tables which can be used for the fast computations needed in the context of PDF fits. The main characteristic of this interface, which we dub aMCfast, is its being fully automated as well, which removes the need to extract manually the process-specific information for additional physics processes, as is the case with other matrix-element calculators, and renders it straightforward to include any new process in the PDF fits. We demonstrate this by studying several cases which are easily measured at the LHC, have a good constraining power on PDFs, and some of which were previously unavailable in the form of a fast interface