Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation

We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural smoothness parameters of an associated Riemannian manifold. We then apply the method with the manifold defined by the log barrier function to the problems of (1) uniformly sampling a polytope and (2) computing its volume, the latter by extending Gaussian cooling to the manifold setting. In both cases, the total number of steps needed is O^{*}(mn^{\frac{2}{3}}), improving the state of the art. A key ingredient of our analysis is a proof of an analog of the KLS conjecture for Gibbs distributions over manifolds

Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox

Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between Parrondo's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.Comment: 17 pages, 5 figure

Approximate Near Neighbors for General Symmetric Norms

We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every $n$, $d = n^{o(1)}$, and every $d$-dimensional symmetric norm $\|\cdot\|$, there exists a data structure for $\mathrm{poly}(\log \log n)$-approximate nearest neighbor search over $\|\cdot\|$ for $n$-point datasets achieving $n^{o(1)}$ query time and $n^{1+o(1)}$ space. The main technical ingredient of the algorithm is a low-distortion embedding of a symmetric norm into a low-dimensional iterated product of top-$k$ norms. We also show that our techniques cannot be extended to general norms.Comment: 27 pages, 1 figur

Constructing local bulk observables in interacting AdS/CFT

Local operators in the bulk of AdS can be represented as smeared operators in the dual CFT. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. Large-N factorization plays a key role in the construction. We show diagrammatically how this procedure is related to bulk Feynman diagrams.Comment: 41 pages, LaTeX. v2: reference correcte

Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra

We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the usual Hamiltonian constraint by alternative combinations of the gravitational constraints (scalar densities of arbitrary weight), whose Poisson brackets strongly vanish and cast the standard constraint-system for vacuum gravity into a form that generates a true Lie algebra. It is shown that any such combination---that satisfies certain reality conditions---may be derived from an action principle involving a single scalar field and a single Lagrange multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE

Seventy years of sex education in Health Education Journal: a critical review

This paper examines key debates and perspectives on sex education in Health Education Journal (HEJ), from the date of the journal’s first publication in March 1943 to the present day. Matters relating to sexuality and sexual health are revealed to be integral to HEJ’s history. First published as Health and Empire (1921 – 1942), a key purpose of the journal since its inception has been to share information on venereal disease and its prevention within the UK and across the former British Empire. From 1943 to the present day, discussions on sex education in the newly-christened HEJ both reflect and respond to evolving socio-cultural attitudes towards sexuality in the UK. Changing definitions of sex education across the decades are examined, from the prevention of venereal disease and moral decline in war-time Britain in the 1940s, to a range of responses to sexual liberation in the 1960s and 1970s; from a focus on preventing sexually-transmitted infections, teenage pregnancy and HIV in the 1980s, to the provision of sexual health services alongside sex education in the 2000s. Over the past 70 years, a shift from prevention of pre-marital sexual activity to the management of its outcomes is apparent; however, while these changes over time are notable, perhaps the most striking findings of this review are the continuities in arguments for and against the discussion of sexual issues. After more than 70 years of debate, it would seem that there is little consensus concerning motivations for and the content of sex education

Syndromic surveillance: two decades experience of sustainable systems – its people not just data!

Syndromic surveillance is a form of surveillance that generates information for public health action by collecting, analysing and interpreting routine health-related data on symptoms and clinical signs reported by patients and clinicians rather than being based on microbiologically or clinically confirmed cases. In England, a suite of national real-time syndromic surveillance systems (SSS) have been developed over the last 20 years, utilising data from a variety of health care settings (a telehealth triage system, general practice and emergency departments). The real-time systems in England have been used for early detection (e.g. seasonal influenza), for situational awareness (e.g. describing the size and demographics of the impact of a heatwave) and for reassurance of lack of impact on population health of mass gatherings (e.g. the London 2012 Olympic and Paralympic Games).We highlight the lessons learnt from running SSS, for nearly two decades, and propose questions and issues still to be addressed. We feel that syndromic surveillance is an example of the use of ‘big data’, but contend that the focus for sustainable and useful systems should be on the added value of such systems and the importance of people working together to maximise the value for the public health of syndromic surveillance services