A note on the algebraic growth rate of Poincar\'e series for Kleinian groups

In this note we employ infinite ergodic theory to derive estimates for the algebraic growth rate of the Poincar\'e series for a Kleinian group at its critical exponent of convergence.Comment: 8 page

Trial to encourage adoption and maintenance of a Mediterranean diet (TEAM-MED): Protocol for a randomised feasibility trial of a peer support intervention for dietary behaviour change in adults at high cardiovascular disease risk

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. Adoption of a Mediterranean diet (MD) reduces cardiovascular disease (CVD) risk. However, interventions to achieve dietary behaviour change are typically resource intensive. Peer support offers a potentially low-cost approach to encourage dietary change. The primary objective of this randomised controlled trial is to explore the feasibility of peer support versus a previously tested dietetic-led intervention to encourageMDbehaviour change, and to test recruitment strategies, retention and attrition in order to inform the design of a definitive trial. A total of 75 overweight adults at high CVD risk who do not follow a MD (Mediterranean Diet Score (MDS ≤3)) will be randomly assigned to either: a minimal intervention (written materials), a proven intervention (dietetic support, written materials and key MD foods), or a peer support intervention (group-based community programme delivered by lay peers) for 12 months. The primary end-point is change in MDS from baseline to 6 months (adoption of MD). Secondary end-points include: change in MDS from 6 to 12 months (maintenance of MD), effects on nutritional biomarkers and CVD risk factors, fidelity of implementation, acceptability and feasibility of the peer support intervention. This study will generate important data regarding the feasibility of peer support for ease of adoption of MD in an ‘at risk’ Northern European population. Data will be used to direct a larger scale trial, where the clinical efficacy and cost-effectiveness of peer support will be tested

The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat

Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states

We study relations between $(H,\beta)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\mathcal{L}_{-\beta H}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,\beta)$--KMS states and eigenmeasures of $\mathcal{L}_{-\beta H}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then these are $\ast$--isomorphic to the given Cuntz--Krieger algebra. Finally, we apply these general results to study multifractal decompositions of limit sets of essentially free Kleinian groups $G$ which may have parabolic elements. We show that for the Cuntz--Krieger algebra arising from $G$ there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen--Series map associated with $G$. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous functions on the limit set of $G$. If $G$ has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with $G$.Comment: 30 pages, minor changes in the proofs of Theorem 3.9 and Fact

The Tiber Valley Project: The Tiber and Rome through Two Millennia

In 1997 a new collaborative research project was initiated by the British School at Rome. This project draws on a variety of sources of archaeological information to explore the regional impact of the City of Rome throughout the period from 1000 BC to AD 1300. The project provides a common collaborative research framework which brings together a range of archaeologists and historians working in various institutions. In this paper those involved in different aspects of this new project outline their work and its overall objectives

Wave decay on convex co-compact hyperbolic manifolds

For convex co-compact hyperbolic quotients X=\Gamma\backslash\hh^{n+1}, we analyze the long-time asymptotic of the solution of the wave equation $u(t)$ with smooth compactly supported initial data $f=(f_0,f_1)$. We show that, if the Hausdorff dimension $\delta$ of the limit set is less than $n/2$, then u(t) = C_\delta(f) e^{(\delta-\ndemi)t} / \Gamma(\delta-n/2+1) + e^{(\delta-\ndemi)t} R(t) where $C_{\delta}(f)\in C^\infty(X)$ and ||R(t)||=\mc{O}(t^{-\infty}). We explain, in terms of conformal theory of the conformal infinity of $X$, the special cases \delta\in n/2-\nn where the leading asymptotic term vanishes. In a second part, we show for all \eps>0 the existence of an infinite number of resonances (and thus zeros of Selberg zeta function) in the strip \{-n\delta-\eps<\Re(\la)<\delta\}. As a byproduct we obtain a lower bound on the remainder $R(t)$ for generic initial data $f$.Comment: 18 page

Individual isotopic specializations predict subsequent inter-individual variation in movement in a freshwater fish

Despite many similarities and intuitive links between individual dietary specialization and behavioral inter-individual variation, these phenomena have been studied in isolation, and empirical data confirming relationships between these intraspecific variance sources are lacking. Here we use stable isotope analysis and acoustic telemetry to test the hypothesis that individual specialization in trophic (d15N) and littoral/pelagic prey reliance (d13C) covary with inter-individual variation in movement in a group of 34 free-swimming burbot (Lota lota). By performing stable isotope analysis on tissues with differing isotopic turnover rates (anal fin and dorsal muscle), in 24 lethally sampled burbot, we demonstrate that individual specialization in trophic niche (d15N) and li

Women, men and coronary heart disease: a review of the qualitative literature

Aim. This paper presents a review of the qualitative literature which examines the experiences of patients with coronary heart disease. The paper also assesses whether the experiences of both female and male patients are reflected in the literature and summarizes key themes. Background. Understanding patients' experiences of their illness is important for coronary heart disease prevention and education. Qualitative methods are particularly suited to eliciting patients' detailed understandings and perceptions of illness. As much previous research has been 'gender neutral', this review pays particular attention to gender. Methods. Published papers from 60 qualitative studies were identified for the review through searches in MEDLINE, EMBASE, CINAHL, PREMEDLINE, PsychINFO, Social Sciences Citation Index and Web of Science using keywords related to coronary heart disease. Findings. Early qualitative studies of patients with coronary heart disease were conducted almost exclusively with men, and tended to generalize from 'male' experience to 'human' experience. By the late 1990s this pattern had changed, with the majority of studies including women and many being conducted with solely female samples. However, many studies that include both male and female coronary heart disease patients still do not have a specific gender focus. Key themes in the literature include interpreting symptoms and seeking help, belief about coronary 'candidates' and relationships with health professionals. The influence of social roles is important: many female patients have difficulties reconciling family responsibilities and medical advice, while male patients worry about being absent from work. Conclusions. There is a need for studies that compare the experiences of men and women. There is also an urgent need for work that takes masculinity and gender roles into account when exploring the experiences of men with coronary heart disease