Computationally efficient algorithms for the two-dimensional Kolmogorov-Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2^d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n^2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Omega(n^2.lg(n)), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test

Exploring the inner region of Type 1 AGNs with the Keck interferometer

The exploration of extragalactic objects with long-baseline interferometers in the near-infrared has been very limited. Here we report successful observations with the Keck interferometer at K-band (2.2 um) for four Type 1 AGNs, namely NGC4151, Mrk231, NGC4051, and the QSO IRAS13349+2438 at z=0.108. For the latter three objects, these are the first long-baseline interferometric measurements in the infrared. We detect high visibilities (V^2 ~ 0.8-0.9) for all the four objects, including NGC4151 for which we confirm the high V^2 level measured by Swain et al.(2003). We marginally detect a decrease of V^2 with increasing baseline lengths for NGC4151, although over a very limited range, where the decrease and absolute V^2 are well fitted with a ring model of radius 0.45+/-0.04 mas (0.039+/-0.003 pc). Strikingly, this matches independent radius measurements from optical--infrared reverberations that are thought to be probing the dust sublimation radius. We also show that the effective radius of the other objects, obtained from the same ring model, is either roughly equal to or slightly larger than the reverberation radius as a function of AGN luminosity. This suggests that we are indeed partially resolving the dust sublimation region. The ratio of the effective ring radius to the reverberation radius might also give us an approximate probe for the radial structure of the inner accreting material in each object. This should be scrutinized with further observations.Comment: accepted for publication in A&A Letter

Direct evaporative cooling of 41K into a Bose-Einstein condensate

We have investigated the collisional properties of 41K atoms at ultracold temperature. To show the possibility to use 41K as a coolant, a Bose-Einstein condensate of 41K atoms in the stretched state (F=2, m_F=2) was created for the first time by direct evaporation in a magnetic trap. An upper bound of three body loss coefficient for atoms in the condensate was determined to be 4(2) 10^{-29} cm -6 s-1. A Feshbach resonance in the F=1, m_F=-1 state was observed at 51.42(5) G, which is in good agreement with theoretical prediction.Comment: 4 pages, 4 figure

Statistical description of turbulent transport for flux driven toroidal plasmas

A novel methodology to analyze non-Gaussian probability distribution functions (PDFs) of intermittent turbulent transport in global full-f gyrokinetic simulations is presented. In this work, the Auto-Regressive Integrated Moving Average (ARIMA) model is applied to time series data of intermittent turbulent heat transport to separate noise and oscillatory trends, allowing for the extraction of non-Gaussian features of the PDFs. It was shown that non-Gaussian tails of the PDFs from first principles based gyrokinetic simulations agree with an analytical estimation based on a two fluid model.Comment: arXiv admin note: text overlap with arXiv:1008.321

Mapping the radial structure of AGN tori

We present mid-IR interferometric observations of 6 type 1 AGNs at multiple baseline lengths of 27--130m, reaching high angular resolutions up to lambda/B~0.02 arcseconds. For two of the targets, we have simultaneous near-IR interferometric measurements as well. The multiple baseline data directly probe the radial distribution of the material on sub-pc scales. Within our sample, which is small but spans over ~2.5 orders of magnitudes in the UV/optical luminosity L of the central engine, the radial distribution clearly and systematically changes with luminosity. First, we show that the brightness distribution at a given mid-IR wavelength seems to be rather well described by a power law, which makes a simple Gaussian or ring size estimation quite inadequate. Here we instead use a half-light radius R_1/2 as a representative size. We then find that the higher luminosity objects become more compact in normalized half-light radii R_1/2 /R_in in the mid-IR, where R_in is the dust sublimation radius empirically given by the L^1/2 fit of the near-IR reverberation radii. This means that, contrary to previous studies, the physical mid-IR emission size (e.g. in pc) is not proportional to L^1/2, but increases with L much more slowly, or in fact, nearly constant at 13 micron. Combining the size information with the total flux specta, we infer that the radial surface density distribution of the heated dust grains changes from a steep ~r^-1 structure in high luminosity objects to a shallower ~r^0 structure in those of lower luminosity. The inward dust temperature distribution does not seem to smoothly reach the sublimation temperature -- on the innermost scale of ~R_in, a relatively low temperature core seems to co-exist with a slightly distinct brightness concentration emitting roughly at the sublimation temperature.Comment: accepted for publication in A&