Globe-hopping.

We consider versions of the grasshopper problem (Goulko & Kent 2017 Proc. R. Soc. A 473, 20170494) on the circle and the sphere, which are relevant to Bell inequalities. For a circle of circumference 2π, we show that for unconstrained lawns of any length and arbitrary jump lengths, the supremum of the probability for the grasshopper's jump to stay on the lawn is one. For antipodal lawns, which by definition contain precisely one of each pair of opposite points and have length π, we show this is true except when the jump length ϕ is of the form π(p/q) with p, q coprime and p odd. For these jump lengths, we show the optimal probability is 1 - 1/q and construct optimal lawns. For a pair of antipodal lawns, we show that the optimal probability of jumping from one onto the other is 1 - 1/q for p, q coprime, p odd and q even, and one in all other cases. For an antipodal lawn on the sphere, it is known (Kent & Pitalúa-García 2014 Phys. Rev. A 90, 062124) that if ϕ = π/q, where q ∈ N , then the optimal retention probability of 1 - 1/q for the grasshopper's jump is provided by a hemispherical lawn. We show that in all other cases where 0 < ϕ < π/2, hemispherical lawns are not optimal, disproving the hemispherical colouring maximality hypotheses (Kent & Pitalúa-García 2014 Phys. Rev. A 90, 062124). We discuss the implications for Bell experiments and related cryptographic tests.

Construct validity of RT3 accelerometer: a comparison of level-ground and treadmill walking at self-selected speeds.

This study examined differences in accelerometer output when subjects walked on level ground and on a treadmill. We asked 25 nondisabled participants to wear an RT3 triaxial accelerometer (StayHealthy, Inc; Monrovia, California) and walk at their "normal" and "brisk" walking speeds for 10 minutes. These activities were repeated on a treadmill using the individual speeds from level-ground walking on two occasions 1 week apart. Paired t-tests found a difference in RT3 accelerometer vector magnitude (VM) counts/min between the two walking speeds on both surfaces on days 1 and 2 (p < 0.001). Although we found no significant differences between VM counts/min on the two surfaces at normal and brisk speeds on days 1 and 2 (p > 0.05), we found wide limits of agreement between level ground and treadmill walking at both speeds. Measurement and discrimination of walking intensity employing RT3 accelerometer VM counts/min on the treadmill demonstrated reasonable validity and stability over two time points compared with level-ground walking.

Serous ovarian carcinoma in pregnancy.

The diagnosis of ovarian carcinoma in pregnancy is rare (incidence of 0.018-0.073/1000 pregnancies). Its rarity is reflected by a paucity of cases reported in the literature. The present report concerns a case of advanced serous ovarian carcinoma in a full-term pregnancy. This was an incidental finding discovered during an emergency caesarean section for presumed fetal distress. The majority of ovarian carcinomas diagnosed in pregnancy present at early stages, are associated with a good prognosis and are non-epithelial type tumours. Advanced epithelial ovarian carcinoma diagnosed in pregnancy however is associated with a poor prognosis. Case reporting should certainly contain detailed information on clinicopathological variables and treatment regimens. Longer-term maternal and neonatal outcomes are more difficult to substantiate in case reporting. The authors therefore feel that data centralisation would be beneficial in identifying optimal management strategies in these rare tumours and in other malignant tumours diagnosed and treated during pregnancy.