Are superhumps good measures of the mass ratio for AM CVn systems?

We extend recent work that included the effect of pressure forces to derive the precession rate of eccentric accretion discs in cataclysmic variables to the case of double degenerate systems. We find that the logical scaling of the pressure force in such systems results in predictions of unrealistically high primary masses. Using the prototype AM CVn as a calibrator for the magnitude of the effect, we find that there is no scaling that applies consistently to all the systems in the class. We discuss the reasons for the lack of a superhump period to mass ratio relationship analogous to that known for SU UMa systems and suggest that this is because these secondaries do not have a single valued mass-radius relationship. We highlight the unreliability of mass-ratios derived by applying the SU UMa expression to the AM CVn binaries.

Superhumps, magnetic fields and the mass ratio in AM Canum Venaticorum

We show that the observed K velocities and periodicities of AM CVn can be reconciled given a mass ratio q~0.22 and a secondary star with a modest magnetic field of surface strength B~1 T. We see that the new mass ratio implies that the secondary is most likely semidegenerate. The effect of the field on the accretion disc structure is examined. The theory of precessing discs and resonant orbits is generalized to encompass higher order resonances than 3:2 and shown to retain consistency with the new mass ratio.

The trading profitability of forecasts of the gilt–equity yield ratio

Research has highlighted the usefulness of the Gilt–Equity Yield Ratio (GEYR) as a predictor of UK stock returns. This paper extends recent studies by endogenising the threshold at which the GEYR switches from being low to being high or vice versa, thus improving the arbitrary nature of the determination of the threshold employed in the extant literature. It is observed that a decision rule for investing in equities or bonds, based on the forecasts from a regime switching model, yields higher average returns with lower variability than a static portfolio containing any combinations of equities and bonds. A closer inspection of the results reveals that the model has power to forecast when investors should steer clear of equities, although the trading profits generated are insufficient to outweigh the associated transaction costs.

Sample size considerations in active-control non-inferiority trials with binary data based on the odds ratio

This paper presents an approximate closed form sample size formula for determining non-inferiority in active-control trials with binary data. We use the odds-ratio as the measure of the relative treatment effect, derive the sample size formula based on the score test and compare it with a second, well-known formula based on the Wald test. Both closed form formulae are compared with simulations based on the likelihood ratio test. Within the range of parameter values investigated, the score test closed form formula is reasonably accurate when non-inferiority margins are based on odds-ratios of about 0.5 or above and when the magnitude of the odds ratio under the alternative hypothesis lies between about 1 and 2.5. The accuracy generally decreases as the odds ratio under the alternative hypothesis moves upwards from 1. As the non-inferiority margin odds ratio decreases from 0.5, the score test closed form formula increasingly overestimates the sample size irrespective of the magnitude of the odds ratio under the alternative hypothesis. The Wald test closed form formula is also reasonably accurate in the cases where the score test closed form formula works well. Outside these scenarios, the Wald test closed form formula can either underestimate or overestimate the sample size, depending on the magnitude of the non-inferiority margin odds ratio and the odds ratio under the alternative hypothesis. Although neither approximation is accurate for all cases, both approaches lead to satisfactory sample size calculation for non-inferiority trials with binary data where the odds ratio is the parameter of interest.

Soil phosphorus supply affects nodulation and N:P ratio in 11 perennial legume seedlings

Developing new perennial pasture legumes for low-P soils is a priority for Australian Mediterranean agro-ecosystems, where soil P availability is naturally low. As legumes tend to require higher P inputs than non-legumes, the ability of these plants to fix N2 under varying soil P levels must be determined. Therefore, the objective of this study was to investigate the influence of soil P supply on plant N status and nodule formation in 11 perennial legumes, including some novel pasture species. We investigated the effect of applying soil P, ranging from 0 to 384 μg P/g dry soil, on plant N status and nodulation in a glasshouse. Without exogenous P supply, shoot N concentration and N : P ratio were higher than at 6 μg P/g soil. Shoot N concentration and N : P ratio then changed little with further increase in P supply. There was a close positive correlation between the number of nodules and shoot P concentration in 7 of the 11 species. Total nodule dry weight and the percentage of plant dry weight that consisted of nodules increased when P supply increased from 6 to 48 μg P/g. Without exogenous P addition, N : P ratios partitioned into a two-group distribution, with species having a N : P ratio of either >70 or <50 g/g. We suggest that plants with a high N : P ratio may take up N from the soil constitutively, while those with a low N : P ratio may regulate their N uptake in relation to internal P concentration. The flexibility of the novel pasture legumes in this study to adjust their leaf N concentrations under different levels of soil P supplements other published evidence of good growth and high P uptake and P-use efficiency under low soil P supply and suggests their potential as pasture plants in low-P soils in Australian Mediterranean agro-ecosystems warrants further attention.

The ratio bias phenomenon: fact or artifact?

The ratio bias—according to which individuals prefer to bet on probabilities expressed as a ratio of large numbers to normatively equivalent or superior probabilities expressed as a ratio of small numbers—has recently gained momentum, with researchers especially in health economics emphasizing the policy importance of the phenomenon. Although the bias has been replicated several times, some doubts remain about its economic significance. Our two experiments show that the bias disappears once order effects are excluded, and once salient and dominant incentives are provided. This holds true for both choice and valuation tasks. Also, adding context to the decision problem does not alter this finding. No ratio bias could be found in between-subject tests either, which leads us to the conclusion that the policy relevance of the phenomenon is doubtful at best.

Arnold v. Britton: a ratio and two sets of obiter dicta

Arnold v Britton marks the final stage of the longstanding dispute as to the correct interpretation of a number of 99-year leases of chalets on a leisure park at Oxwich, in the Gower peninsula, near Swansea. The aspect of the case which has attracted most discussion has, understandably, been its main ratio: the proper way to construe a provision of a lease which arguably has an absurd result. This will be considered in this case-note. The judgment of the Supreme Court – particularly the judgment of Lord Neuberger PSC – does, however contain some observations on the possible reform of the law on service charges which are of interest to those engaged in this field. It also contains some obiter comments on ‘letting schemes’ which are – in the view of the present author – highly unorthodox. These three rather disparate issues which are raised by this case will be considered in turn. As they have little in common with each other, they will be considered as separate sections.