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 enhancement of ferromagnetism in uniaxially stressed diluted magnetic semiconductors

We predict a new mechanism of enhancement of ferromagnetic phase transition temperature $T_c$ in uniaxially stressed diluted magnetic semiconductors (DMS) of p-type. Our prediction is based on comparative studies of both Heisenberg (inherent to undistorted DMS with cubic lattice) and Ising (which can be applied to strongly enough stressed DMS) models in a random field approximation permitting to take into account the spatial inhomogeneity of spin-spin interaction. Our calculations of phase diagrams show that area of parameters for existence of DMS-ferromagnetism in Ising model is much larger than that in Heisenberg model.Comment: 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

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

Suppression of carrier induced ferromagnetism by composition and spin fluctuations in diluted magnetic semiconductors

We suggest an approach to account for spatial (composition) and thermal fluctuations in "disordered" magnetic models (e.g. Heisenberg, Ising) with given spatial dependence of magnetic spin-spin interaction. Our approach is based on introduction of fluctuating molecular field (rather than mean field) acting between the spins. The distribution function of the above field is derived self-consistently. In general case this function is not Gaussian, latter asymptotics occurs only at sufficiently large spins (magnetic ions) concentrations $n_i$. Our approach permits to derive the equation for a critical temperature $T_c$ of ferromagnetic phase transition with respect to the above fluctuations. We apply our theory to the analysis of influence of composition fluctuations on $T_c$ in diluted magnetic semiconductors (DMS) with RKKY indirect spin-spin interaction.Comment: 6 pages, 2 figure