Spherically Symmetric Solutions to Fourth-Order Theories of Gravity

Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild solution. The asymptotic form of solutions is described, as is the lack of validity of Birkhoff's theorem. Exact solutions are presented which illustrate these points and their stability and geodesics are investigated.Comment: 10 pages, published versio

Fusing Continuous-valued Medical Labels using a Bayesian Model

With the rapid increase in volume of time series medical data available through wearable devices, there is a need to employ automated algorithms to label data. Examples of labels include interventions, changes in activity (e.g. sleep) and changes in physiology (e.g. arrhythmias). However, automated algorithms tend to be unreliable resulting in lower quality care. Expert annotations are scarce, expensive, and prone to significant inter- and intra-observer variance. To address these problems, a Bayesian Continuous-valued Label Aggregator(BCLA) is proposed to provide a reliable estimation of label aggregation while accurately infer the precision and bias of each algorithm. The BCLA was applied to QT interval (pro-arrhythmic indicator) estimation from the electrocardiogram using labels from the 2006 PhysioNet/Computing in Cardiology Challenge database. It was compared to the mean, median, and a previously proposed Expectation Maximization (EM) label aggregation approaches. While accurately predicting each labelling algorithm's bias and precision, the root-mean-square error of the BCLA was 11.78$\pm$0.63ms, significantly outperforming the best Challenge entry (15.37$\pm$2.13ms) as well as the EM, mean, and median voting strategies (14.76$\pm$0.52ms, 17.61$\pm$0.55ms, and 14.43$\pm$0.57ms respectively with $p<0.0001$)

Cepheid Parallaxes and the Hubble Constant

Revised Hipparcos parallaxes for classical Cepheids are analysed together with 10 HST-based parallaxes (Benedict et al.). In a reddening-free V,I relation we find that the coefficient of logP is the same within the uncertainties in our Galaxy as in the LMC, contrary to some previous suggestions. Cepheids in the inner region of NGC4258 with near solar metallicities (Macri et al.) confirm this result. We obtain a zero-point for the reddening-free relation and apply it to Cepheids in galaxies used by Sandage et al. to calibrate the absolute magnitudes of SNIa and to derive the Hubble constant. We revise their result from 62 to 70+/-5 km/s/Mpc. The Freedman et al. 2001 value is revised from 72 to 76+/-8 km/s/Mpc. These results are insensitive to Cepheid metallicity corrections. The Cepheids in the inner region of NGC4258 yield a modulus of 29.22+/-0.03(int) compared with a maser-based modulus of 29.29+/-0.15. Distance moduli for the LMC, uncorrected for any metallicity effects, are; 18.52+/-0.03 from a reddening-free relation in V,I; 18.47+/-0.03 from a period-luminosity relation at K; 18.45+/-0.04 from a period-luminosity-colour relation in J,K. Adopting a metallicity correction in V,I from Marci et al. leads to a true LMC modulus of 18.39+/-0.05.Comment: 9 pages, 1 figure, on-line material from [email protected]. Accepted for MNRA

Volume Weighted Measures of Eternal Inflation in the Bousso-Polchinski Landscape

We consider the cosmological dynamics associated with volume weighted measures of eternal inflation, in the Bousso-Polchinski model of the string theory landscape. We find that this measure predicts that observers are most likely to find themselves in low energy vacua with one flux considerably larger than the rest. Furthermore, it allows for a satisfactory anthropic explanation of the cosmological constant problem by producing a smooth, and approximately constant, distribution of potentially observable values of Lambda. The low energy vacua selected by this measure are often short lived. If we require anthropically acceptable vacua to have a minimum life-time of 10 billion years, then for reasonable parameters a typical observer should expect their vacuum to have a life-time of approximately 12 billion years. This prediction is model dependent, but may point toward a solution to the coincidence problem of cosmology.Comment: 35 pages, 8 figure

Long-term weight maintenance and cardiovascular risk factors are not different following weight loss on carbohydrate-restricted diets high in either monounsaturated fat or protein in obese hyperinsulinaemic men and women

The aim of this study was to determine after 52 weeks whether advice to follow a lower carbohydrate diet, either high in monounsaturated fat or low fat, high in protein had differential effects in a free-living community setting. Following weight loss on either a high monounsaturated fat, standard protein (HMF; 50 % fat, 20 % protein (67 g/d), 30 % carbohydrate) or a high protein, moderate fat (HP) (40 % protein (136 g/d), 30 % fat, 30 % carbohydrate) energy-restricted diet (6000 kJ/d) subjects were asked to maintain the same dietary pattern without intensive dietary counselling for the following 36 weeks. Overall weight loss was 6·2 (sd 7·3) kg (P < 0·01 for time with no diet effect, 7·6 (sd 8·1) kg, HMF v. 4·8 (sd 6·6) kg, HP). In a multivariate regression model predictors of weight loss at the end of the study were sex, age and reported percentage energy from protein (R2 0·22, P < 0·05 for the whole model). Fasting plasma insulin decreased (P < 0·01, with no difference between diets), 13·9 (sd 4·6) to 10·2 (sd 5·2) mIU/l, but fasting plasma glucose was not reduced. Neither total cholesterol nor LDL-cholesterol were different but HDL was higher, 1·19 (sd 0·26) v. 1·04 (sd 0·29) (P < 0·001 for time, no diet effect), while TAG was lower, 1·87 (sd 1·23) v. 2·22 (sd 1·15) mmol/l (P < 0·05 for time, no diet effect). C-reactive protein decreased (3·97 (sd 2·84) to 2·43 (sd 2·29) mg/l, P < 0·01). Food records showed that compliance to the prescribed dietary patterns was poor. After 1 year there remained a clinically significant weight loss and improvement in cardiovascular risk factors with no adverse effects of a high monounsaturated fat diet.Jennifer B. Keogh, Natalie D. Luscombe-Marsh, Manny Noakes, Gary A. Wittert and Peter M. Clifto

Greenberger-Horne-Zeilinger paradox for continuous variables

We show how to construct states for which a Greenberger-Horne-Zeilinger type paradox occurs if each party measures either the position or momentum of his particle. The paradox can be ascribed to the anticommutation of certain translation operators in phase space. We then rephrase the paradox in terms of modular and binary variables. The origin of the paradox is then due to the fact that the associativity of addition of modular variables is true only for c-numbers but does not hold for operators.Comment: 4 pages, no figure

On The Existence Of Anisotropic Cosmological Models In Higher-Order Theories Of Gravity

We investigate the behaviour on approach to the initial singularity in higher-order extensions of general relativity by finding exact cosmological solutions for a wide class of models in which the Lagrangian is allowed to depend nonlinearly upon the three possible linear and quadratic scalars built from the Riemann tensor; $R$, $R_{ab}R^{ab}$ and $R_{abcd}R^{abcd}$. We present new anisotropic vacuum solutions analagous to the Kasner solutions of general relativity and extend previous results to a much wider range of fourth order theories of gravity. We discuss the implications of these results for the behaviour of the more general anisotropic Bianchi type VIII and IX cosmologies as the initial singularity is approached. Furthermore, we also consider the existence conditions for some other simple anisotropic Bianchi I vacuum solutions in which the expansion in each direction is of exponential, rather than power-law behaviour and their relevance for cosmic ``no-hair'' theorems.Comment: 24 pages, submitted to CQ

Nonlocality without inequalities has not been proved for maximally entangled states

Two approaches to extend Hardy's proof of nonlocality without inequalities to maximally entangled states of bipartite two-level systems are shown to fail. On one hand, it is shown that Wu and co-workers' proof [Phys. Rev. A 53, R1927 (1996)] uses an effective state which is not maximally entangled. On the other hand, it is demonstrated that Hardy's proof cannot be generalized by the replacement of one of the four von Neumann measurements involved in the original proof by a generalized measurement to unambiguously discriminate between non-orthogonal states.Comment: 7 pages, 2 figures. To appear in Phys. Rev.

Existential Contextuality and the Models of Meyer, Kent and Clifton

It is shown that the models recently proposed by Meyer, Kent and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual existence of an observable which is context dependent. This result confirms the point made elsewhere, that the MKC models do not, as the authors claim, ``nullify'' the Kochen-Specker theorem. It may also be of some independent interest.Comment: Revtex, 7 pages, 1 figure. Replaced with published versio