Moments of Moments and Branching Random Walks

We calculate, for a branching random walk $X_n(l)$ to a leaf $l$ at depth $n$ on a binary tree, the positive integer moments of the random variable $\frac{1}{2^{n}}\sum_{l=1}^{2^n}e^{2\beta X_n(l)}$, for $\beta\in\mathbb{R}$. We obtain explicit formulae for the first few moments for finite $n$. In the limit $n\to\infty$, our expression coincides with recent conjectures and results concerning the moments of moments of characteristic polynomials of random unitary matrices, supporting the idea that these two problems, which both fall into the class of logarithmically correlated Gaussian random fields, are related to each other.Comment: 26 pages, version published in Journal of Statistical Physic

On the moments of the moments of ζ(1/2+it)\zeta(1/2+it)

Taking $t$ at random, uniformly from $[0,T]$, we consider the $k$th moment, with respect to $t$, of the random variable corresponding to the $2\beta$th moment of $\zeta(1/2+ix)$ over the interval $x\in(t, t+1]$, where $\zeta(s)$ is the Riemann zeta function. We call these the `moments of moments' of the Riemann zeta function, and present a conjecture for their asymptotics, when $T\to\infty$, for integer $k,\beta$. This is motivated by comparisons with results for the moments of moments of the characteristic polynomials of random unitary matrices and is shown to follow from a conjecture for the shifted moments of $\zeta(s)$ due to Conrey, Farmer, Keating, Rubinstein, and Snaith \cite{cfkrs2}. Specifically, we prove that a function which, the shifted-moment conjecture of \cite{cfkrs2} implies, is a close approximation to the moments of moments of the zeta function does satisfy the asymptotic formula that we conjecture. We motivate as well similar conjectures for the moments of moments for other families of primitive $L$-functions.Comment: 18 pages, final version to appear in Journal of Number Theor

Effect of Cluster Formation on Isospin Asymmetry in the Liquid-Gas Phase Transition Region

Nuclear matter within the liquid-gas phase transition region is investigated in a mean-field two-component Fermi-gas model. Following largely analytic considerations, it is shown that: (1) Due to density dependence of asymmetry energy, some of the neutron excess from the high-density phase could be expelled into the low-density region. (2) Formation of clusters in the gas phase tends to counteract this trend, making the gas phase more liquid-like and reducing the asymmetry in the gas phase. Flow of asymmetry between the spectator and midrapidity region in reactions is discussed and a possible inversion of the flow direction is indicated.Comment: 9 pages,3 figures, RevTe

Patient safety in dentistry: development of a candidate 'never event' list for primary care

Introduction The 'never event' concept is often used in secondary care and refers to an agreed list of patient safety incidents that 'should not happen if the necessary preventative measures are in place'. Such an intervention may raise awareness of patient safety issues and inform team learning and system improvements in primary care dentistry. Objective To identify and develop a candidate never event list for primary care dentistry. Methods A literature review, eight workshops with dental practitioners and a modified Delphi with 'expert' groups were used to identify and agree candidate never events. Results Two-hundred and fifty dental practitioners suggested 507 never events, reduced to 27 distinct possibilities grouped across seven themes. Most frequently occurring themes were: 'checking medical history and prescribing' (119, 23.5%) and 'infection control and decontamination' (71, 14%). 'Experts' endorsed nine candidate never event statements with one graded as 'extreme risk' (failure to check past medical history) and four as 'high risk' (for example, extracting wrong tooth). Conclusion Consensus on a preliminary list of never events was developed. This is the first known attempt to develop this approach and an important step in determining its value to patient safety. Further work is necessary to develop the utility of this method

Understanding responses to a UK high-voltage powerline proposal: the role of place and project-based social representations

In going beyond the NIMBY (Not In My Backyard) concept, Devine-Wright (2009) posited a place-based approach highlighting the role of social representations of place for understanding responses to energy infrastructure projects. Existing studies (Devine- Wright & Howes, 2010; Anderson, 2013) have investigated the ways in which representations of diverse forms of place change are anchored and objectified symbolically based on existing social representations of place. These studies have shown that the degree of fit between representations of place and proposed place change can be seen to inform community responses to different developments. There is however, a dearth of research investigating the symbolic fit of power line projects amongst existing representations of the English countryside, despite the fact that such projects are both highly controversial and key to ensuring delivery of low-carbon energy policy targets. This paper thus sought to explore social representations of a proposed power line development in Southwest England and their symbolic fit with representations of nearby countryside areas, given the increased deployment of lowcarbon energy infrastructure in this locale. Five focus groups were conducted with residents of a town in North Somerset, to highlight residents' co-constructed place and project-based social representations. Findings from thematic data analysis suggest that those representing the nearby countryside as replete with existing grid infrastructure objectified the power line proposal as an acceptable and 'familiar' form of place change. Conversely, those representing the countryside as 'natural' tended to objectify the proposal as industrialising this locale, objecting to it on this basis. This study reveals the utility of adopting Social Representations Theory to understand responses to proposed energy infrastructure developments given the UK low carbon transition, and suggests that grid companies could enhance acceptance by seeking to minimise the 'industrial' nature of such projects.info:eu-repo/semantics/publishedVersio

Using a narrative approach to understand place attachments and responses to power line proposals: the importance of life-place trajectories

Research on people-place relations, incorporating place attachment and place identity, has often adopted a structural approach, overlooking the dynamic nature of these relations over time. More process-oriented research has tended to investigate the impacts of single moments or events, neglecting a broader focus upon people's life course. To address this gap, this study investigated patterns of residential place attachments ('life-place trajectories') and used these to better understand current place relations and responses to change, including disruption to pre-existing place bonds. Narrative interviews (n = 25) were conducted in 2013 with residents living in Nailsea, a UK town affected by proposals to construct a high voltage power line. Three notable findings emerged. First, the study indicated five novel lifeplace trajectories characterised by diverse configurations of residential mobility and continuity of settlement type. Second, the study extends our understanding of varieties of relationship with the current residence place, including identifying a novel variety of 'traditional-active attachment'. Third, the study indicates the relevance of the trajectories for understanding responses to place change proposals, including acceptance and opposition. The findings show the value of the narrative interview method for revealing place relations across the life course, informing understanding of people-place relations and infrastructure siting.info:eu-repo/semantics/acceptedVersio

Strong pressure-energy correlations in van der Waals liquids

Strong correlations between equilibrium fluctuations of the configurational parts of pressure and energy are found in the Lennard-Jones liquid and other simple liquids, but not in hydrogen-bonding liquids like methanol and water. The correlations, that are present also in the crystal and glass phases, reflect an effective inverse power-law repulsive potential dominating fluctuations, even at zero and slightly negative pressure. In experimental data for supercritical Argon, the correlations are found to be approximately 96%. Consequences for viscous liquid dynamics are discussed.Comment: Phys. Rev. Lett., in pres

Prevalence of sulfonamide resistance genes in bacterial isolates from manured agricultural soils and pig slurry in the United Kingdom

Prevalence of three sulfonamide resistance genes, sul1, sul2 and sul3 and sulfachloropyridazine (SCP) resistance was determined in bacteria isolated from UK manured agricultural clay soils and slurry samples, over a two year period. Slurry from tylosin-fed pigs amended with SCP and oxytetracycline (OTC) was used for manuring. Sul gene positive isolates were further screened for the presence of class 1 and 2 integrons. Phenotypic resistance to SCP was significantly higher in pig slurry and post application soil than in pre-application soil. Of 5isolates, 23 % carried sul1, 18 % sul2 and 9 % sul3 only. Two percent of isolates contained all three sul genes. Class 1 and class 2 integrons were identified in 5 % and 11.7 % of sul positive isolates. In previous reports, sul1 was linked to class 1 integrons, but in this study only 8 % of sul1 positive isolates carried the intI1 gene. Sulfonamide resistant pathogens were identified in slurry amended soil and soil leachate, including Shigella flexneri, Aerococcus spp. and Acinetobacter baumanni, suggesting a potential environmental reservoir. Sulfonamide resistance in Psychrobacter, Enterococcus and Bacillus spp. is reported for the first time, and this study also provides the first description of the genotype sul1, sul2 and sul3 outside the Enterobacteriacae, and in the soil environment

On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices

We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the matrix-size tends to infinity in terms of the volumes of certain regions involving continuous Gelfand-Tsetlin patterns with constraints. The results we find differ from those in the unitary case considered previouslyComment: 31 page

Analytic Calculation of Prompt Photon plus Associated Heavy Flavor at Next-to-Leading Order in QCD

Contributions through second order, $O(\alpha ^2_s)$, in perturbative quantum chromodynamics are calculated analytically for inclusive associated production of a prompt photon and a charm quark at large values of transverse momentum in high energy hadron-hadron collisions. Seven partonic subprocesses contribute at order $\alpha^2_s$. We find important corrections to the lowest order, $O(\alpha_s)$, subprocess $c g \rightarrow \gamma c$. We demonstrate to what extent data from $p +\bar{p}\rightarrow \gamma + c + X$ may serve to measure the charm quark density in the nucleon.Comment: 34 pages RevTex plus 9 figures submitted as uuencoded ps files; figures replaced and text revised to include one additional referenc