The Duffin-Schaeffer Conjecture with extra divergence II

This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.Comment: 7 page

Initiation of Psychotropic Medication after Partner Bereavement: A Matched Cohort Study

Background Recent changes to diagnostic criteria for depression in DSM-5 remove the bereavement exclusion, allowing earlier diagnosis following bereavement. Evaluation of the potential effect of this change requires an understanding of existing psychotropic medication prescribing by non-specialists after bereavement. Aims To describe initiation of psychotropic medication in the first year after partner bereavement. Methods In a UK primary care database, we identified 21,122 individuals aged 60 and over with partner bereavement and no psychotropic drug use in the previous year. Prescribing (anxiolytic/hypnotic, antidepressant, antipsychotic) after bereavement was compared to age, sex and practice matched controls. Results The risks of receiving a new psychotropic prescription within two and twelve months of bereavement were 9.5% (95% CI 9.1 to 9.9%) and 17.9% (17.3 to 18.4%) respectively; an excess risk of initiation in the first year of 12.4% compared to non-bereaved controls. Anxiolytic/hypnotic and antidepressant initiation rates were highest in the first two months. In this period, the hazard ratio for initiation of anxiolytics/hypnotics was 16.7 (95% CI 14.7 to 18.9) and for antidepressants was 5.6 (4.7 to 6.7) compared to non-bereaved controls. 13.3% of those started on anxiolytics/hypnotics within two months continued to receive this drug class at one year. The marked variation in background family practice prescribing of anxiolytics/hypnotics was the strongest determinant of their initiation in the first two months after bereavement. Conclusion Almost one in five older people received a new psychotropic drug prescription in the year after bereavement. The early increase and trend in antidepressant use after bereavement suggests some clinicians did not adhere to the bereavement exclusion, with implications for its recent removal in DSM-5. Family practice variation in use of anxiolytics/hypnotics suggests uncertainty over their role in bereavement with the potential for inappropriate long term use

Visualizing landscapes of the superconducting gap in heterogeneous superconductor thin films: geometric influences on proximity effects

The proximity effect is a central feature of superconducting junctions as it underlies many important applications in devices and can be exploited in the design of new systems with novel quantum functionality. Recently, exotic proximity effects have been observed in various systems, such as superconductor-metallic nanowires and graphene-superconductor structures. However, it is still not clear how superconducting order propagates spatially in a heterogeneous superconductor system. Here we report intriguing influences of junction geometry on the proximity effect for a 2D heterogeneous superconductor system comprised of 2D superconducting islands on top of a surface metal. Depending on the local geometry, the superconducting gap induced in the surface metal region can either be confined to the boundary of the superconductor, in which the gap decays within a short distance (~ 15 nm), or can be observed nearly uniformly over a distance of many coherence lengths due to non-local proximity effects.Comment: 17 pages, 4 figure

Consequences of converting graded to action potentials upon neural information coding and energy efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ~50% in generator potentials, to ~3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation

Weakened magnetic braking as the origin of anomalously rapid rotation in old field stars

A knowledge of stellar ages is crucial for our understanding of many astrophysical phenomena, and yet ages can be difficult to determine. As they become older, stars lose mass and angular momentum, resulting in an observed slowdown in surface rotation. The technique of 'gyrochronology' uses the rotation period of a star to calculate its age. However, stars of known age must be used for calibration, and, until recently, the approach was untested for old stars (older than 1 gigayear, Gyr). Rotation periods are now known for stars in an open cluster of intermediate age (NGC 6819; 2.5 Gyr old), and for old field stars whose ages have been determined with asteroseismology. The data for the cluster agree with previous period-age relations, but these relations fail to describe the asteroseismic sample. Here we report stellar evolutionary modelling, and confirm the presence of unexpectedly rapid rotation in stars that are more evolved than the Sun. We demonstrate that models that incorporate dramatically weakened magnetic braking for old stars can---unlike existing models---reproduce both the asteroseismic and the cluster data. Our findings might suggest a fundamental change in the nature of ageing stellar dynamos, with the Sun being close to the critical transition to much weaker magnetized winds. This weakened braking limits the diagnostic power of gyrochronology for those stars that are more than halfway through their main-sequence lifetimes.Comment: 25 pages, 3 figures in main paper, 6 extended data figures, 1 table. Published in Nature, January 2016. Please see https://youtu.be/O6HzYgP5uyc for a video description of the resul