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

The Location of the Nucleus of NGC 1068 and the Three-dimensional Structure of Its Nuclear Region

The HST archival UV imaging polarimetry data of NGC 1068 is re-examined. Through an extensive estimation of the observational errors, we discuss whether the distribution of the position angles (PAs) of polarization is simply centrosymmetric or not. Taking into account the effect of a bad focus at the time of the observation, we conclude that, within the accuracy of HST/FOC polarimetry, the PA distribution is completely centrosymmetric. This means that the UV polarization originates only from scattering of the radiation from a central point-like source. However, our analysis shows that the most probable location of the nucleus is only ~0.''08 (~6pc) south from the brightest cloud called ``cloud B''. The error circle of 99% confidence level extends to cloud B and to ``cloud A'' which is about 0.''2 south of cloud B. By this FOC observation, Cloud B is only marginally rejected as the nucleus. Assuming that the UV flux is dominated by electron-scattered light, we have also derived a three-dimensional structure of the nuclear region. The inferred distribution suggests a linear structure which could be related to the radio jet.Comment: 19 pages, 14 figures, to be published in the Astrophysical Journa

In--Flight (K−,pK^-,p) Reactions for the Formation of Kaonic Atoms and Kaonic Nuclei in Green function method

We study theoretically the kaonic atom and kaonic nucleus formations in the in--flight ($K^-,p$) reactions using the Green function method, which is suited to evaluate formation rates both of stable and unstable bound systems. We consider $^{12}$C and $^{16}$O as the targets and calculate the spectra of the ($K^-,p$) reactions. We conclude that a no peak structure due to kaonic nucleus formation is expected in the reaction spectra calculated with the chiral unitary kaon--nucleus optical potential. In the spectra with the phenomenological deep kaon--nucleus potential, we may have possibilities to observe some structures due to kaonic nucleus states. For all cases, we have peaks due to the kaonic atom formations in the reaction spectra.Comment: 10 pages, 9 figures, newly calculated results added, revisions and updated references, to appear in Physical Review

Regularization of identity based solution in string field theory

We demonstrate that an Erler-Schnabl type solution in cubic string field theory can be naturally interpreted as a gauge invariant regularization of an identity based solution. We consider a solution which interpolates between an identity based solution and ordinary Erler-Schnabl one. Two gauge invariant quantities, the classical action and the closed string tadpole, are evaluated for finite value of the gauge parameter. It is explicitly checked that both of them are independent of the gauge parameter.Comment: 9 pages, minor typos corrected and references adde

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