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 structural and functional integrity of peripheral nerves depends on the glial-derived signal desert hedgehog

We show that desert hedgehog ( dhh), a signaling molecule expressed by Schwann cells, is essential for the structural and functional integrity of the peripheral nerve. Dhh-null nerves display multiple abnormalities that affect myelinating and nonmyelinating Schwann cells, axons, and vasculature and immune cells. Myelinated fibers of these mice have a significantly increased ( more than two times) number of Schmidt-Lanterman incisures ( SLIs), and connexin 29, a molecular component of SLIs, is strongly upregulated. Crossing dhh-null mice with myelin basic protein ( MBP)-deficient shiverer mice, which also have increased SLI numbers, results in further increased SLIs, suggesting that Dhh and MBP control SLIs by different mechanisms. Unmyelinated fibers are also affected, containing many fewer axons per Schwann cell in transverse profiles, whereas the total number of unmyelinated axons is reduced by approximately one-third. In dhh-null mice, the blood-nerve barrier is permeable and neutrophils and macrophage numbers are elevated, even in uninjured nerves. Dhh-null nerves also lack the largest-diameter myelinated fibers, have elevated numbers of degenerating myelinated axons, and contain regenerating fibers. Transected dhh nerves degenerate faster than wild-type controls. This demonstrates that a single identified glial signal, Dhh, plays a critical role in controlling the integrity of peripheral nervous tissue, in line with its critical role in nerve sheath development ( Parmantier et al., 1999). The complexity of the defects raises a number of important questions about the Dhh-dependent cell-cell signaling network in peripheral nerves

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

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

Band Calculations for Ce Compounds with AuCu3_{3}-type Crystal Structure on the basis of Dynamical Mean Field Theory I. CePd3_{3} and CeRh3_{3}

Band calculations for Ce compounds with the AuCu$_{3}$-type crystal structure were carried out on the basis of dynamical mean field theory (DMFT). The auxiliary impurity problem was solved by a method named NCA$f^{2}$vc (noncrossing approximation including the $f^{2}$ state as a vertex correction). The calculations take into account the crystal-field splitting, the spin-orbit interaction, and the correct exchange process of the $f^{1} \rightarrow f^{0},f^{2}$ virtual excitation. These are necessary features in the quantitative band theory for Ce compounds and in the calculation of their excitation spectra. The results of applying the calculation to CePd$_{3}$ and CeRh$_{3}$ are presented as the first in a series of papers. The experimental results of the photoemission spectrum (PES), the inverse PES, the angle-resolved PES, and the magnetic excitation spectra were reasonably reproduced by the first-principles DMFT band calculation. At low temperatures, the Fermi surface (FS) structure of CePd$_{3}$ is similar to that of the band obtained by the local density approximation. It gradually changes into a form that is similar to the FS of LaPd$_{3}$ as the temperature increases, since the $4f$ band shifts to the high-energy side and the lifetime broadening becomes large.}Comment: 12 pasges, 13 figure

Double Beta Decay: Historical Review of 75 Years of Research

Main achievements during 75 years of research on double beta decay have been reviewed. The existing experimental data have been presented and the capabilities of the next-generation detectors have been demonstrated.Comment: 25 pages, typos adde

The Cherenkov Telescope Array Large Size Telescope

The two arrays of the Very High Energy gamma-ray observatory Cherenkov Telescope Array (CTA) will include four Large Size Telescopes (LSTs) each with a 23 m diameter dish and 28 m focal distance. These telescopes will enable CTA to achieve a low-energy threshold of 20 GeV, which is critical for important studies in astrophysics, astroparticle physics and cosmology. This work presents the key specifications and performance of the current LST design in the light of the CTA scientific objectives.Comment: 4 pages, 5 figures, In Proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), Rio de Janeiro (Brazil). All CTA contributions at arXiv:1307.223