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

Screening for resistance to ripe rot caused by Colletotrichum acutatum in grape germplasm

We screened 235 Vitis and six Muscadinia grapevine cultivars and selections conserved at the National Institute of Fruit Tree Science in Japan for resistance to grape ripe rot, caused by Colletotrichum acutatum Simmonds ex Simmonds. This fungus is insensitive to fungicides such as benomyl, diethofencarb, and iminoctadine-triacetate. We evaluated the disease resistance of nearly ripe berries from each cultivar and selection by artificial inoculation with C. acutatum. Analysis of variance of 20 cultivars and selections indicated that the genotype had a significant effect but that the year had no significant effect on the percentage of diseased berries. Genetic variance explained 85 % of total variance. Each cultivar or selection was classified into one of the following four classes based on its level of resistance to ripe rot: 50 highly resistant (≤ 20 % affected), 37 resistant (21- 40 %), 48 susceptible (41- 60 %), and 106 highly susceptible (≥ 61 %). Of the highly resistant cultivars and selections, we consider a diploid named 676-64 to be promising material for ripe rot resistant table grape breeding.

The FEBEX benchmark test: case definition and comparison of modelling approaches

The FEBEX (Full-scale Engineered Barriers Experiment in Crystalline Host Rock) ‘‘in situ’’ test was installed at the Grimsel Test Site underground laboratory (Switzerland) and is a near-to-real scale simulation of the Spanish reference concept of deep geological storage in crystalline host rock. A modelling exercise, aimed at predicting field behaviour, was divided in three parts. In Part A, predictions for both the total water inflow to the tunnel as well as the water pressure changes induced by the boring of the tunnel were required. In Part B, predictions for local field variables, such as temperature, relative humidity, stresses and displacements at selected points in the bentonite barrier, and global variables, such as the total input power to the heaters were required. In Part C, predictions for temperature, stresses, water pressures and displacements in selected points of the host rock were required. Ten Modelling Teams from Europe, North America and Japan were involved in the analysis of the test. Differences among approaches may be found in the constitutive models used, in the simplifications made to the balance equations and in the geometric symmetries considered. Several aspects are addressed in the paper: the basic THM physical phenomena which dominate the test response are discussed, a comparison of different modelling results with actual measurements is presented and a discussion is given to explain the performance of the various predictions.Peer Reviewe