Fast rates in statistical and online learning

The speed with which a learning algorithm converges as it is presented with more data is a central problem in machine learning --- a fast rate of convergence means less data is needed for the same level of performance. The pursuit of fast rates in online and statistical learning has led to the discovery of many conditions in learning theory under which fast learning is possible. We show that most of these conditions are special cases of a single, unifying condition, that comes in two forms: the central condition for 'proper' learning algorithms that always output a hypothesis in the given model, and stochastic mixability for online algorithms that may make predictions outside of the model. We show that under surprisingly weak assumptions both conditions are, in a certain sense, equivalent. The central condition has a re-interpretation in terms of convexity of a set of pseudoprobabilities, linking it to density estimation under misspecification. For bounded losses, we show how the central condition enables a direct proof of fast rates and we prove its equivalence to the Bernstein condition, itself a generalization of the Tsybakov margin condition, both of which have played a central role in obtaining fast rates in statistical learning. Yet, while the Bernstein condition is two-sided, the central condition is one-sided, making it more suitable to deal with unbounded losses. In its stochastic mixability form, our condition generalizes both a stochastic exp-concavity condition identified by Juditsky, Rigollet and Tsybakov and Vovk's notion of mixability. Our unifying conditions thus provide a substantial step towards a characterization of fast rates in statistical learning, similar to how classical mixability characterizes constant regret in the sequential prediction with expert advice setting.Comment: 69 pages, 3 figure

Flux calibration of the AAO/UKST SuperCOSMOS H-alpha Survey

The AAO/UKST SuperCOSMOS H$\alpha$ Survey (SHS) was, when completed in 2003, a powerful addition to extant wide-field surveys. The combination of areal coverage, spatial resolution and sensitivity in a narrow imaging band, still marks it out today as an excellent resource for the astronomical community. The 233 separate fields are available online in digital form, with each field covering 25 square degrees. The SHS has been the motivation for equivalent surveys in the north, and new digital H$\alpha$ surveys now beginning in the south such as VPHAS+. It has been the foundation of many important discovery projects with the Macquarie/AAO/Strasbourg H$\alpha$ planetary nebula project being a particularly successful example. However, the full potential of the SHS has been hampered by lack of a clear route to acceptable flux calibration from the base photographic data. We have determined the calibration factors for 170 individual SHS fields, and present a direct pathway to the measurement of integrated H$\alpha$ fluxes and surface brightnesses for resolved nebulae detected in the SHS. We also include a catalogue of integrated H$\alpha$ fluxes for $>$100 planetary and other nebulae measured from the SHS, and use these data to show that fluxes, accurate to $\pm$ 0.10 - 0.14 dex ($\sim$25-35 per cent), can be obtained from these fields. For the remaining 63 fields, a mean calibration factor of 12.0 counts pix$^{-1}$ R$^{-1}$ can be used, allowing the determination of reasonable integrated fluxes accurate to better than $\pm$0.2 dex ($\sim$50 per cent). We outline the procedures involved and the caveats that need to be appreciated in achieving such flux measurements. This paper forms a handy reference source that will significantly increase the scientific utility of the SHS.Comment: 14 pages, 12 figures, 2 tables (plus 7 pp. of supplementary online information). Version to appear in MNRA

The Mass of the Black Hole in Cygnus X-1

Cygnus X-1 is a binary star system that is comprised of a black hole and a massive giant companion star in a tight orbit. Building on our accurate distance measurement reported in the preceding paper, we first determine the radius of the companion star, thereby constraining the scale of the binary system. To obtain a full dynamical model of the binary, we use an extensive collection of optical photometric and spectroscopic data taken from the literature. By using all of the available observational constraints, we show that the orbit is slightly eccentric (both the radial velocity and photometric data independently confirm this result) and that the companion star rotates roughly 1.4 times its pseudosynchronous value. We find a black hole mass of M =14.8\pm1.0 M_{\sun}, a companion mass of M_{opt}=19.2\pm1.9 M_{\sun}, and the angle of inclination of the orbital plane to our line of sight of i=27.1\pm0.8 deg.Comment: Paper II of three papers on Cygnus X-1; 27 pages including 5 figures and 3 tables, ApJ in pres

Reproductive performance of resident and migrant males, females and pairs in a partially migratory bird

We thank everyone from the Centre for Ecology & Hydrology (CEH) who contributed to data collection, and Scottish Natural Heritage for access to the Isle of May National Nature Reserve. We thank the Scottish Ornithologists’ Club (SOC) for their support, and all volunteer observers, particularly Raymond Duncan, Moray Souter and Bob Swann. HG was funded by a Natural Environment Research Council (NERC) CASE studentship supported by CEH and SOC, FD, SW, MPH, MN and SB were funded by NERC and the Joint Nature Conservation Committee, and JMR was part-funded by the Royal Society. Finally, we thank the Associate Editor and two reviewers for constructive comments on the manuscript. The data are available from the Dryad Digital Repository https://doi.org/10.5061/dryad.532j0 (Grist et al., 2017)Peer reviewedPublisher PD

Effect of calcium supplements on risk of myocardial infarction and cardiovascular events : meta-analysis

Peer reviewedPublisher PD

Is there a Supermassive Black Hole at the Center of the Milky Way?

This review outlines the observations that now provide an overwhelming scientific case that the center of our Milky Way Galaxy harbors a supermassive black hole. Observations at infrared wavelength trace stars that orbit about a common focal position and require a central mass (M) of 4 million solar masses within a radius of 100 Astronomical Units. Orbital speeds have been observed to exceed 5,000 km/s. At the focal position there is an extremely compact radio source (Sgr A*), whose apparent size is near the Schwarzschild radius (2GM/c^2). This radio source is motionless at the ~1 km/s level at the dynamical center of the Galaxy. The mass density required by these observations is now approaching the ultimate limit of a supermassive black hole within the last stable orbit for matter near the event horizon.Comment: Invited review submitted to International Journal of Modern Physics D; 23 pages; 10 figure

What is the Accretion Rate in Sgr A*?

The radio source Sgr A* at the center of our Galaxy is believed to be a 2.6 x 10^6 solar mass black hole which accretes gas from the winds of nearby stars. We show that limits on the X-ray and infrared emission from the Galactic Center provide an upper limit of ~ 8 x 10^{-5} solar masses per year on the mass accretion rate in Sgr A*. The advection-dominated accretion flow (ADAF) model favors a rate < 10^{-5} solar masses per year. In comparison, the Bondi accretion rate onto Sgr A*, estimated using the observed spatial distribution of mass losing stars and assuming non-interacting stellar winds, is ~ 3 x 10^{-5} solar masses per year. There is thus rough agreement between the Bondi, the ADAF, and the X-ray inferred accretion rates for Sgr A*. We discuss uncertainties in these estimates, emphasizing the importance of upcoming observations by the Chandra X-ray observatory (CXO) for tightening the X-ray derived limits.Comment: to appear in ApJ Letter

Effect of microstructural morphology on the mechanical properties of titanium alloys

Different morphologies of α+β microstructures were obtained in a commercial Ti-6Al-4V alloy by cooling at different rates from the single β-phase region into the two phase region. The effect of such morphologies on mechanical properties was studied using hot compression tests in a Gleeble thermomechanical simulator. A variety of complex morphologies could be obtained since the cooling rate has a significant influence on the β to α phase transformation and the resulting morphological development. While most of the β phase transformed to colonies of α at high cooling rates, it was possible to obtain a complex mixture of a colonies, grain boundary a and lamellar structure by decreasing the cooling rate. These complex morphologies each exhibited distinctive mechanical properties and characteristic dynamic phase transformation behaviour during deformation as a function of strain rate