The two-dimensional Kolmogorov-Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical 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 2d −1 independent ways of defining a cumulative distribution function when d dimensions are involved. In this paper three variations on the Kolmogorov-Smirnov test for multi-dimensional data sets are surveyed: Peacock’s test [1] that computes in O(n3); Fasano and Franceschini’s test [2] that computes in O(n2); Cooke’s test that computes in O(n2). We prove that Cooke’s algorithm runs in O(n2), contrary to his claims that it runs in O(nlgn). We also compare these algorithms with ROOT’s version of the Kolmogorov-Smirnov test

Tree Contraction, Connected Components, Minimum Spanning Trees: a GPU Path to Vertex Fitting

Standard parallel computing operations are considered in the context of algorithms for solving 3D graph problems which have applications, e.g., in vertex finding in HEP. Exploiting GPUs for tree-accumulation and graph algorithms is challenging: GPUs offer extreme computational power and high memory-access bandwidth, combined with a model of fine-grained parallelism perhaps not suiting the irregular distribution of linked representations of graph data structures. Achieving data-race free computations may demand serialization through atomic transactions, inevitably producing poor parallel performance. A Minimum Spanning Tree algorithm for GPUs is presented, its implementation discussed, and its efficiency evaluated on GPU and multicore architectures

Comparison of two-dimensional binned data distributions using the energy test

For the purposes of monitoring HEP experiments, comparison is often made between regularly acquired histograms of data and reference histograms which represent the ideal state of the equipment. With the larger experiments now starting up, there is a need for automation of this task since the volume of comparisons would overwhelm human operators. However, the two-dimensional histogram comparison tools currently available in ROOT have noticeable shortcomings. We present a new comparison test for 2D histograms, based on the Energy Test of Aslan and Zech, which provides more decisive discrimination between histograms of data coming from different distributions

Bmp7 Functions via a Polarity Mechanism to Promote Cloacal Septation

During normal development in human and other placental mammals, the embryonic cloacal cavity separates along the axial longitudinal plane to give rise to the urethral system, ventrally, and the rectum, dorsally. Defects in cloacal development are very common and present clinically as a rectourethral fistula in about 1 in 5,000 live human births. Yet, the cellular mechanisms of cloacal septation remain poorly understood.We previously detected Bone morphogenetic protein 7 (Bmp7) expression in the urorectal mesenchyme (URM), and have shown that loss of Bmp7 function results in the arrest of cloacal septation. Here, we present evidence that cloacal partitioning is driven by Bmp7 signaling in the cloacal endoderm. We performed TUNEL and immunofluorescent analysis on cloacal sections from Bmp7 null and control littermate embryos. We found that loss of Bmp7 results in a dramatic decrease in the endoderm survival and a delay in differentiation. We used immunological methods to show that Bmp7 functions by activating the c-Jun N-terminal kinase (JNK) pathway. We carried out confocal and 3D imaging analysis of mitotic chromosome bundles to show that during normal septation cells in the cloacal endoderm divide predominantly in the apical-basal direction. Loss of Bmp7/JNK signaling results in randomization of mitotic angles in the cloacal endoderm. We also conducted immunohistochemical analysis of human fetal sections to show that BMP/phospho-SMAD and JNK pathways function in the human cloacal region similar as in the mouse.Our results strongly indicate that Bmp7/JNK signaling regulates remodeling of the cloacal endoderm resulting in a topological separation of the urinary and digestive systems. Our study points to the importance of Bmp and JNK signaling in cloacal development and rectourethral malformations