The sectional curvature remains positive when taking quotients by certain nonfree actions

We study some cases when the sectional curvature remains positive under the taking of quotients by certain nonfree isometric actions of Lie groups. We consider the actions of the groups $S^1$ and $S^3$ such that the quotient space can be endowed with a smooth structure using the fibrations $S^3/S^1{\simeq}S^2$ and $S^7/S^3\simeq S^4$. We prove that the quotient space carries a metric of positive sectional curvature, provided that the original metric has positive sectional curvature on all 2-planes orthogonal to the orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam

The random phase approximation applied to ice

Standard density functionals without van der Waals interactions yield an unsatisfactory description of ice phases, specifically, high density phases occurring under pressure are too unstable compared to the common low density phase I$_h$ observed at ambient conditions. Although the description is improved by using functionals that include van der Waals interactions, the errors in relative volumes remain sizable. Here we assess the random phase approximation (RPA) for the correlation energy and compare our results to experimental data as well as diffusion Monte Carlo data for ice. The RPA yields a very balanced description for all considered phases, approaching the accuracy of diffusion Monte Carlo in relative energies and volumes. This opens a route towards a concise description of molecular water phases on surfaces and in cavities

Mapped Null Hypersurfaces and Legendrian Maps

For an $(m+1)$-dimensional space-time $(X^{m+1}, g),$ define a mapped null hypersurface to be a smooth map $\nu:N^{m}\to X^{m+1}$ (that is not necessarily an immersion) such that there exists a smooth field of null lines along $\nu$ that are both tangent and $g$-orthogonal to $\nu.$ We study relations between mapped null hypersurfaces and Legendrian maps to the spherical cotangent bundle $ST^*M$ of an immersed spacelike hypersurface $\mu:M^m\to X^{m+1}.$ We show that a Legendrian map \wt \lambda: L^{m-1}\to (ST^*M)^{2m-1} defines a mapped null hypersurface in $X.$ On the other hand, the intersection of a mapped null hypersurface $\nu:N^m\to X^{m+1}$ with an immersed spacelike hypersurface $\mu':M'^m\to X^{m+1}$ defines a Legendrian map to the spherical cotangent bundle $ST^*M'.$ This map is a Legendrian immersion if $\nu$ came from a Legendrian immersion to $ST^*M$ for some immersed spacelike hypersurface $\mu:M^m\to X^{m+1}.$Comment: 13 pages, 1 figur

Wave-number Selection by Target Patterns and Side Walls in Rayleigh-Benard Convection

We present experimental results for Rayleigh-Benard convection patterns in a cylindrical container with static side-wall forcing induced by a heater. This forcing stabilized a pattern of concentric rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell after a jump from the conduction to the convection state. A quasi-static increase of the control parameter (epsilon) beyond 0.8 caused the umbilicus of the pattern to move off center. As observed by others, a further quasi-static increase of epsilon up to 15.6 caused a sequence of transitions. Each transition began with the displacement of the umbilicus and then proceeded with the loss of one convection roll at the umbilicus and the return of the umbilicus to a location near the center of the cell. Alternatively, with decreasing epsilon new rolls formed at the umbilicus but large umbilicus displacements did not occur. In addition to quantitative measurements of the umbilicus displacement, we determined and analyzed the entire wave-director field of each image. The wave numbers varied in the axial direction, with minima at the umbilicus and at the cell wall and a maximum at a radial position close to 2/3 Gamma. The wave numbers at the maximum showed hysteretic jumps at the transitions, but on average agreed well with the theoretical predictions for the wave numbers selected in the far field of an infinitely extended target pattern.Comment: ReVTeX, 11 pages, 16 eps figures include

Rational adversaries? evidence from randomised trials in one day cricket

In cricket, the right to make an important decision (bat first or field first) is assigned via a coin toss. These "randomised trials" allow us to examine the consistency of choices made by teams with strictly opposed preferences, and the effects of these choices upon game outcomes. Random assignment allows us to consistently aggregate across matches, ensuring that our tests have power. We find significant evidence of inconsistency, with teams often agreeing on who is to bat first. Choices are often poorly made and reduce the probability of the team winning, a surprising finding given the intense competition and learning opportunities. Keywords: interactive decision theory, zero sum situation, randomised trial, treatment effects

Demography and disorders of the French Bulldog population under primary veterinary care in the UK in 2013

Abstract Background Despite its Gallic name, the French Bulldog is a breed of both British and French origin that was first recognised by The Kennel Club in 1906. The French Bulldog has demonstrated recent rapid rises in Kennel Club registrations and is now (2017) the second most commonly registered pedigree breed in the UK. However, the breed has been reported to be predisposed to several disorders including ocular, respiratory, neurological and dermatological problems. The VetCompass™ Programme collates de-identified clinical data from primary-care veterinary practices in the UK for epidemiological research. Using VetCompass™ clinical data, this study aimed to characterise the demography and common disorders of the general population of French Bulldogs under veterinary care in the UK. Results French Bulldogs comprised 2228 (0.49%) of 445,557 study dogs under veterinary care during 2013. Annual proportional birth rates showed that the proportional ownership of French Bulldog puppies rose steeply from 0.02% of the annual birth cohort attending VetCompass™ practices in 2003 to 1.46% in 2013. The median age of the French Bulldogs overall was 1.3 years (IQR 0.6–2.5, range 0.0–13.0). The most common colours of French Bulldogs were brindle (solid or main) (32.36%) and fawn (solid or main) (29.9%). Of the 2228 French Bulldogs under veterinary care during 2013, 1612 (72.4%) had at least one disorder recorded. The most prevalent fine-level precision disorders recorded were otitis externa (14.0%, 95% CI: 12.6–15.5), diarrhoea (7.5%, 95% CI: 6.4–8.7), conjunctivitis (3.2%, 95% CI: 2.5–4.0), nails overlong (3.1%, 95% CI% 2.4–3.9) and skin fold dermatitis (3.0%, 95% CI% 2.3–3.8). The most prevalent disorder groups were cutaneous (17.9%, 95% CI: 16.3–19.6), enteropathy (16.7%, 95% CI: 15.2–18.3), aural (16.3%, 95% CI: 14.8–17.9), upper respiratory tract (12.7%, 95% CI: 11.3–14.1) and ophthalmological (10.5%, 95% CI: 9.3–11.9). Conclusions Ownership of French Bulldogs in the UK is rising steeply. This means that the disorder profiles reported in this study reflect a current young UK population and are likely to shift as this cohort ages. Otitis externa, diarrhoea and conjunctivitis were the most common disorders in French Bulldogs. Identification of health priorities based on VetCompass™ data can support evidence–based reforms to improve health and welfare within the breed

Program trace optimization

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.Paper to be presented at the Fifteenth International Conference on Parallel Problem Solving from Nature (PPSN XV), Coimbra, Portugal on 8-12 September 2018.We introduce Program Trace Optimization (PTO), a system for `universal heuristic optimization made easy'. This is achieved by strictly separating the problem from the search algorithm. New problem definitions and new generic search algorithms can be added to PTO easily and independently, and any algorithm can be used on any problem. PTO automatically extracts knowledge from the problem specifi cation and designs search operators for the problem. The operators designed by PTO for standard representations coincide with existing ones, but PTO automatically designs operators for arbitrary representations

Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-times

The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, zeta, and sigma functions as well as hyperelliptic Kleinian sigma functions restricted to the one-dimensional theta-divisor. We analyze the dependency of timelike geodesics on the parameters of the space-time metric and the test-particle and compare the results with the situation in Kerr space-time with vanishing cosmological constant. Furthermore, we systematically can find all last stable spherical and circular orbits and derive the expressions of the deflection angle of flyby orbits, the orbital frequencies of bound orbits, the periastron shift, and the Lense-Thirring effect.Comment: 18 pages, 11 figure

Reducing alcohol use during pregnancy: Listening to women who drink as an intervention starting point

Objectives: This study assesses factors that contribute to alcohol consumption during pregnancy and identifies potential intervention strategies to reduce consumption. Methods: The study sample includes 142 pregnant women who attended a public hospital for prenatal health care in Perth, Western Australia. All participants returned a self-completion survey. Results: Women who discontinued drinking during pregnancy were significantly more likely to be engaged in full time home duties and had completed less formal education. Women who continued to drink were more likely to have drunk in previous pregnancies and during the preconception period. Nearly 40% of high risk women reported a negative comment in response to their drinking. One-third of women in the risky group were advised by a health professional not to drink alcohol. Women were most likely to drink in their own home or at the home of a friend. Conclusions: Participatory research with women who drink while pregnant can assist in identifying potential intervention strategies that have resonance with this group and therefore more potential for creating behaviour change. Implications: The World Health Organization recognises, and has done for over 10 years, that alcohol use during pregnancy which results in Foetal Alcohol Spectrum Disorder is the leading cause of environmental related birth defects and mental retardation in the Western world

Spin Frustration and Magnetic Exchange in Cobalt Aluminum Oxide Spinels

We report on x-ray diffraction, magnetic susceptibility, electron- spin resonance and heat- capacity studies of Co[Al_1-xCo_x]_2O_4 for Co concentrations 0<x<1. In this spinel system only the A-site Co^2+ cation is magnetic, while the non-magnetic B-site Al^3+ is substituted by the low-spin non-magnetic Co^3+, and it is possible to investigate the complete phase diagram from Co^2+Al^3+_2O_4 to Co^2+Co^3+_2O_4. All samples reveal large negative Curie-Weiss temperatures Theta_CW of the order of -110 K independent of concentration, which is attributed to a high multiplicity of the superexchange interactions between the A-site Co^2+ cations. A pure antiferromagnetic state is found for x = 1.0 and 0.9 with Neel temperatures T_N = 29.5 K and 21.2 K, respectively, as evidenced by lambda-like anomalies in the specific heat. Compositions with 0.3<x<0.75 show smeared out strongly reduced magnetic ordering temperatures. At low temperatures, a T^2.5 dependence of the specific heat is indicative of a spin-liquid state. For x < 0.2 a T^2 dependence of the specific heat and a spin-glass like behavior of the susceptibility below T_f = 4.7 K are observed. The high value of the frustration parameter f = |Theta_CW|/T_f > 10 indicates the presence of strong spin frustration at least for x < 0.6. The frustration mechanism is attributed to competing nearest neighbor and next-nearest neighbor superexchange interactions between the A-site Co^2+ ions.Comment: 19 pages, 9 figures, 46 reference