>Magister Scientiae - MSc / For integers n, k 2:: 1, and k ~ n, the graph r~has vertices the 2n vectors of lF2 and adjacency defined by two vectors being adjacent if they differ in k coordinate positions. In particular, r~is the classical n-cube, usually denoted by Hl (n, 2). This study examines the codes (both binary and p-ary for p an odd prime) of the row span of adjacency and incidence matrices of these graphs. We first examine codes of the adjacency matrices of the n-cube. These have been considered in [14]. We then consider codes generated by both incidence and adjacency matrices of the Hamming graphs Hl(n,3) [12]. We will also consider codes of the line graphs of the n-cube as in [13]. Further, the automorphism groups of the codes, designs and graphs will be examined, highlighting where there is an interplay. Where possible, suitable permutation decoding sets will be given.

The purpose of this research is to identify whether synoptic patterns and variables were statistically significantly different between East Coast United States track bomb and ordinary cyclogenesis. The differentiation of East Coast track bomb and ordinary cyclogenesis was completed through the utility of the principal component analysis, a K-means cluster analysis, a subjective composite analysis, and permutation tests. The principal component analysis determined that there were three leading modes of variability within the bomb and ordinary composites. The K-means cluster analysis was used to cluster these leading patterns of variability into three distinct clusters for the bomb and ordinary cyclones. The subjective composite analysis, created by averaging all the variables from each cyclone in each cluster, identified several synoptic variables and patterns to be objectively compared through permutation tests. The permutation tests revealed that synoptic variables and patterns associated with bomb cyclogenesis statistically significantly differ from ordinary cyclogenesis.

Testing the homogeneity of variances is an important problem in many applications since statistical methods of frequent use, such as ANOVA, assume equal variances for two or more groups of data. However, testing the equality of variances is a difficult problem due to the fact that many of the tests are not robust against non-normality. It is known that the kurtosis of the distribution of the source data can affect the performance of the tests for variance. We review the classical tests and their latest, more robust modifications, some other tests that have recently appeared in the literature, and use bootstrap and permutation techniques to test for equal variances. We compare the performance of these tests under different types of distributions, sample sizes and true ratios of variances of the populations. Monte-Carlo methods are used in this study to calculate empirical powers and type I errors under different settings.

After becoming interested in the beauty of numbers and the intricate patterns of their behavior, the author concluded that it would be a good idea to make the subject available for students earlier in their educational experience. In this thesis, the author developed four units in combinatorics, namely Fundamental Principles, Permutations, Combinations, and Pascal's Triangle, which are appropriate for third grade level.

Ice core records from Greenland have shown times of rapid warming during the most recent glacial period, called Dansgaard-Oeschger (D-O) events. D-O events are important to our understanding of both past climate systems and modern climate volatility. In this paper, we present new approaches for statistically evaluating the existence of cyclicity in D-O events and the possible lagged correlation between the Greenland and Antarctica temperature records. Specifically, we consider permutation testing and bootstrapping methodologies for assessing the cyclicity of D-O events and the correlation between the Greenland and Antarctica records. We find that there is not enough evidence to conclude that D-O events are cyclical; however, the Antarctica record leads the Greenland record by 545 years with a statistically significant correlation of 0.455.

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

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