A comparison of A-level performance in economics and business studies: how much more difficult is economics?

This paper uses ALIS data to compare academic performance in two subjects often viewed as relatively close substitutes for one another at A-level. The important role of GCSE achievement is confirmed for both subjects. There is evidence of strong gender effects and variation in outcomes across Examination Boards. A counterfactual exercise suggests that if the sample of Business Studies candidates had studied Economics nearly 40% of those who obtained a grade C or better in the former subject would not have done so in the latter. The opposite exercise uggests that 12% more Economics candidates would have achieved a grade C or better if they had taken Business Studies. In order to render a Business Studies A-level grade comparable to an Economics one in terms of relative difficulty, we estimate that a downward adjustment of 1.5 UCAS points should be applied to the former subject. This adjustment is lower than that suggested by correction factors based on conventional subject pair analysis for these two subjects

Exponentially growing solutions in homogeneous Rayleigh-Benard convection

It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full non-linear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.Comment: 4 pages, 3 figures, to be published in Phys. Rev. E - rapid communication

Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations

We build on recent developments in the study of fluid turbulence [Gibbon \textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\pm}$, of $\omega^\pm= \omega \pm j$, where $\omega$ and $j$ are, respectively, the vorticity and current density in three-dimensional magnetohydrodynamics (MHD). We show by mathematical analysis, for unit magnetic Prandtl number $P_M$, how these moments can be used to identify three possible regimes for solutions of the MHD equations; these regimes are specified by inequalities for $D_m^{\pm}$ and $D_1^{\pm}$. We then compare our mathematical results with those from our direct numerical simulations (DNSs) and thus demonstrate that 3D MHD turbulence is like its fluid-turbulence counterpart insofar as all solutions, which we have investigated, remain in \textit{only one of these regimes}; this regime has depleted nonlinearity. We examine the implications of our results for the exponents $q^{\pm}$ that characterize the power-law dependences of the energy spectra $\mathcal{E}^{\pm}(k)$ on the wave number $k$, in the inertial range of scales. We also comment on (a) the generalization of our results to the case $P_M \neq 1$ and (b) the relation between $D_m^{\pm}$ and the order-$m$ moments of gradients of hydrodynamic fields, which are used in characterizing intermittency in turbulent flows.Comment: 14 pages, 3 figure

Blocking by fixed and variable stimuli: effects of stimulus distribution on blocking

An experiment with rats compared the ability of fixed and variable duration cues to produce blocking. Rats in Group B (Blocking) were trained that both fixed- (F) and variable- (V) duration cues would be followed by food delivery. In a subsequent training stage F and V continued to be reinforced, but F was accompanied by X, and V by Y. In the test phase responding to X and Y was examined. Control Group O (Overshadowing) received identical treatment, except that F and V were nonreinforced in the first training stage. In Group B there was evidence for blocking, but only of X which had been conditioned in compound with the fixed-duration F; there was no evidence for blocking of Y, which had been conditioned in compound with the variable duration V. It is suggested that this result may occur because fixed cues reach a higher, more stable asymptote of associative strength than their variable equivalents

Evolution of a Primordial Black Hole Population

We reconsider in this work the effects of an energy absorption term in the evolution of primordial black holes (hereafter PBHs) in the several epochs of the Universe. A critical mass is introduced as a boundary between the accreting and evaporating regimes of the PBHs. We show that the growth of PBHs is negligible in the Radiation-dominated Era due to scarcity of energy density supply from the expanding background, in agreement with a previous analysis by Carr and Hawking, but that nevertheless the absorption term is large enough for black holes above the critical mass to preclude their evaporation until the universe has cooled sufficiently. The effects of PBH motion are also discussed: the Doppler effect may give rise to energy accretion in black-holes with large peculiar motions relative to background. We discuss how cosmological constraints are modified by the introduction of the critical mass since that PBHs above it do not disturb the CMBR. We show that there is a large range of admissible masses for PBHs above the critical mass but well below the cosmological horizon. Finally we outline a minimal kinetic formalism, solved in some limiting cases, to deal with more complicated cases of PBH populationsComment: RevTex file, 8 pp., 3 .ps figures available upon request from [email protected]

Is overweight and obesity in 9–10-year-old children in Liverpool

Objectives: To determine whether weight problems in children (overweight, obesity and overweight or obesity) were related to deprivation indices when attributed only according to electoral ward of the school attended. To determine whether children with weight problems were more likely to be found in some wards rather than others, and to compare the distribution for boys and girls. Design: Retrospective, cross-sectional, observational study. Setting: One hundred and six primary schools from all parts of Liverpool city. Subjects: Five cohorts of 9–10-year-old children between 1998 and 2003. Main outcome measures: Body mass index (BMI) for each child to estimate proportions overweight, obese and overweight or obese according to international criteria. Results: Between January 1998 and March 2003, the heights and weights of 7902 boys and 7514 girls were measured and BMI calculated. The prevalence of boys and girls categorised as overweight or obese was very high (1620, 20.6% and 1909, 25.7%, respectively). Prevalence was not related to deprivation and varied between wards only for the girls; some wards had very different prevalence rates for boys and girls (Picton: 59 boys, 23.4%; 106 girls, 36.6%). The most deprived ward did not have a remarkable prevalence of overweight or obesity (Speke: 32 boys, 15.3%; 40 girls, 19.8%). Conclusions: Obesity is a major problem and requires urgent action but targeting intervention on the basis of administrative areas may be very wasteful. Different factors seem to lead to obesity in boys and girls, and attention should be paid to the role of the physical environment