Like a hawk among house sparrows: Kauto star, a steeplechasing legend

The concept of ‘icon’ has been applied to numerous athletes as a result of their sporting achievements, likeable public personas, and stories of triumph, resilience and courage. The cultural role of the horse as icon, hero, celebrity and national luminary, however, is lacking within the literature. In this article we extend this human concept to apply to the racehorse Kauto Star, who was heralded by many as the saviour of British racing in the early twenty-first century. We argue that the narrative surrounding Kauto Star had all the essential ingredients for the construction of a heroic storyline around this equine superstar: his sporting talent; his flaws and ability to overcome adversity; his ‘rivalry’ with his stable mate; his ‘connections’ to high profile humans in the racing world; and, the adoration he received from the racing public. Media representations are key elements in the construction of sporting narratives, and the production of heroes and villains within sport. In this paper we construct a narrative of Kauto Star, as produced through media reports and published biographies, to explore how this equine star has been elevated beyond the status of ‘animal’, ‘racehorse’ or even ‘athlete’ to the exalted position of sporting icon

Orthogonal Matching Pursuit: A Brownian Motion Analysis

A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix with a probability that approaches one as n approaches infinity. This work strengthens this result by showing that a lower number of measurements, 2 k log(n - k), is in fact sufficient for asymptotic recovery. More generally, when the sparsity level satisfies kmin <= k <= kmax but is unknown, 2 kmax log(n - kmin) measurements is sufficient. Furthermore, this number of measurements is also sufficient for detection of the sparsity pattern (support) of the vector with measurement errors provided the signal-to-noise ratio (SNR) scales to infinity. The scaling 2 k log(n - k) exactly matches the number of measurements required by the more complex lasso method for signal recovery with a similar SNR scaling.Comment: 11 pages, 2 figure

Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing

The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to study estimators that are maximum a posteriori (MAP) under a postulated prior distribution. It is shown that with random linear measurements and Gaussian noise, the replica-symmetric prediction of the asymptotic behavior of the postulated MAP estimate of an n-dimensional vector "decouples" as n scalar postulated MAP estimators. The result is based on applying a hardening argument to the replica analysis of postulated posterior mean estimators of Tanaka and of Guo and Verdu. The replica-symmetric postulated MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. In the case of lasso estimation the scalar estimator reduces to a soft-thresholding operator, and for zero norm-regularized estimation it reduces to a hard-threshold. Among other benefits, the replica method provides a computationally-tractable method for precisely predicting various performance metrics including mean-squared error and sparsity pattern recovery probability.Comment: 22 pages; added details on the replica symmetry assumptio

A new behavioural intervention for tackling obesity: Do Something Different

Peer reviewe

Aeroacoustic analysis of main rotor and tail rotor interaction

The increased restrictions placed on helicopter noise levels over recent decades have encouraged manufacturers to better understand tail rotor noise and its aerodynamic sources. A generic single main rotor and tail rotor helicopter has been simulated in high speed forward, and quartering, flight using the Vorticity Transport Model. The unsteady loads developed on the tail rotor blades and the resulting acoustic noise propagation have been computed. The sound propagation from isolated tail rotors with top-aft and top-forward senses of rotation in high speed forward flight results in impulsive sound being directed downward from the former and upward from the latter. The principal source of tail rotor noise in high speed forward flight is a periodic blade-vortex interaction between the tail rotor blades. The effect of aerodynamic interaction on tail rotor noise is highly dependent on the flight speed and trajectory, such that the noise produced as a result of interaction is, for the particular helicopter geometry simulated here, greater in quartering flight than in high speed forward flight. The sound pressure produced by periodic impulsive loads in high speed forward flight and the high frequency sound generated in quartering flight is sensitive to the scales to which the vortical features within the wake, and the radial and azimuthal distributions of blade loading, are resolved

Vector Approximate Message Passing for the Generalized Linear Model

The generalized linear model (GLM), where a random vector $\boldsymbol{x}$ is observed through a noisy, possibly nonlinear, function of a linear transform output $\boldsymbol{z}=\boldsymbol{Ax}$, arises in a range of applications such as robust regression, binary classification, quantized compressed sensing, phase retrieval, photon-limited imaging, and inference from neural spike trains. When $\boldsymbol{A}$ is large and i.i.d. Gaussian, the generalized approximate message passing (GAMP) algorithm is an efficient means of MAP or marginal inference, and its performance can be rigorously characterized by a scalar state evolution. For general $\boldsymbol{A}$, though, GAMP can misbehave. Damping and sequential-updating help to robustify GAMP, but their effects are limited. Recently, a "vector AMP" (VAMP) algorithm was proposed for additive white Gaussian noise channels. VAMP extends AMP's guarantees from i.i.d. Gaussian $\boldsymbol{A}$ to the larger class of rotationally invariant $\boldsymbol{A}$. In this paper, we show how VAMP can be extended to the GLM. Numerical experiments show that the proposed GLM-VAMP is much more robust to ill-conditioning in $\boldsymbol{A}$ than damped GAMP