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

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

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

Mapping the three-body system - decay time and reversibility

In this paper we carry out a quantitative analysis of the three-body systems and map them as a function of decaying time and intial conguration, look at this problem as an example of a simple deterministic system, and ask to what extent the orbits are really predictable. We have investigated the behavior of about 200 000 general Newtonian three body systems using the simplest initial conditions. Within our resolution these cover all the possible states where the objects are initially at rest and have no angular momentum. We have determined the decay time-scales of the triple systems and show that the distribution of this parameter is fractal in appearance. Some areas that appear stable on large scales exhibit very narrow strips of instability and the overall pattern, dominated by resonances, reminds us of a traditional Maasai warrior shield. Also an attempt is made to recover the original starting conguration of the three bodies by backward integration. We find there are instances where the evolution to the future and to the past lead to different orbits, in spite of time symmetric initial conditions. This implies that even in simple deterministic systems there exists an Arrow of Time.Comment: 8 pages, 9 figures. Accepted for publication in MNRAS. Includes low-resolution figures. High-resolution figures are available as PNG