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

Pressure-induced changes in the magnetic and valence state of EuFe2As2

We present the results of electrical resistivity, ac specific heat, magnetic susceptibility, X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) of the ternary iron arsenide EuFe2As2 single crystal under pressure. Applying pressure leads to a continuous suppression of the antiferromagnetism associated with Fe moments and the antiferromagnetic transition temperature becomes zero in the vicinity of a critical pressure Pc ~2.5-2.7 GPa. Pressure-induced re-entrant superconductivity, which is highly sensitive to the homogeneity of the pressure, only appears in the narrow pressure region in the vicinity of Pc due to the competition between superconductivity and the antiferromagnetic ordering of Eu2+ moments. The antiferromagnetic state of Eu2+ moments changes to the ferromagnetic state above 6 GPa. We also found that the ferromagnetic order is suppressed with further increasing pressure, which is connected with a valence change of Eu ions.Comment: 7 pages, 7 figures, accepted for publication in Phys. Rev.

The performance of thin NaI(Tl) scintillator plate for dark matter search

A thin (0.05cm) and wide area (5cmX5cm) NaI(Tl) scintillator was developed. The performance of the thin NaI(Tl) plate, energy resolution, single photoelectron energy and position sensitivity were tested. An excellent energy resolution of 20% (FWHM) at 60keV was obtained. The single photoelectron energy was calculated to be approximately 0.42 0.02keV. Position information in the 5cmx5cm area of the detector was also obtained by analyzing the ratio of the number of photons collected at opposite ends of the detector. The position resolution was obtained to be 1cm (FWHM) in the 5cmx5cm area.Comment: 10 pages. Accepted to Journal of Physical Society of Japa

Sharp lines in the absorption edge of EuTe and Pb0.1_{0.1}Eu0.9_{0.9}Te in high magnetic fields

The optical absorption spectra in the region of the \fd transition energies of epitaxial layers of of EuTe and \PbEuTe, grown by molecular beam epitaxy, were studied using circularly polarized light, in the Faraday configuration. Under \sigmam polarization a sharp symmetric absorption line (full width at half-maximum 0.041 eV) emerges at the low energy side of the band-edge absorption, for magnetic fields intensities greater than 6 T. The absorption line shows a huge red shift (35 meV/T) with increasing magnetic fields. The peak position of the absorption line as a function of magnetic field is dominated by the {\em d-f} exchange interaction of the excited electron and the \Euion spins in the lattice. The {\em d-f} exchange interaction energy was estimated to be $J_{df}S=0.15\pm 0.01$ eV. In \PbEuTe the same absorption line is detected, but it is broader, due to alloy disorder, indicating that the excitation is localized within a finite radius. From a comparison of the absorption spectra in EuTe and \PbEuTe the characteristic radius of the excitation is estimated to be $\sim 10$\AA.Comment: Journal of Physics: Condensed Matter (2004, at press

WIMPs search by means of the highly segmented scintillator

The highly sensitive method to search for WIMPs dark matter particles is proposed. An array of thin NaI(Tl) plate has the great selectivity for distinguishing the WIMPs events and background ones. The principle of signal selection for WIMPs is described. The high sensitivity for SD (spin-dependent) type WIMPs is expected by applying multi-layer system of NaI(Tl) detector.Comment: 11 pages, added some sentences to make the arguments clea