Thesis (M.Sc.). / Written for the School of Computer Science. Title from title page of PDF (viewed 2009/06/23). Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Dept. of Astronomy and Astrophysics, August 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--Tohoku University, 2004. / "June 2004." Includes bibliographical references (p. 69-72).

Thesis (M.S.)--University of Wisconsin--Madison, 1968. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 49-51). Also available in electronic version.

For beta > 0, the beta-ensemble corresponds to the joint probability density on the real line proportional to prod_{n > m}^N abs{x_n - x_m}^beta prod_{n = 1}^N w(x_n) where w is the weight of the system. It has the application of being the Boltzmann factor for the configuration of N charge-one particles interacting logarithmically on an infinite wire inside an external field Q = -log w at inverse temperature beta. Similarly, the circular beta-ensemble has joint probability density proportional to prod_{n > m}^N abs{e^{itheta_n} - e^{itheta_m}}^beta prod_{n = 1}^N w(x_n) quad for theta_n in [- pi, pi) and can be interpreted as N charge-one particles on the unit circle interacting logarithmically with no external field. When beta = 1, 2, and 4, both ensembles are said to be solvable in that their correlation functions can be expressed in a form which allows for asymptotic calculations. It is not known, however, whether the general beta-ensemble is solvable. We present four families of particle models which are solvable point processes related to the beta-ensemble. Two of the examples interpolate between the circular beta-ensembles for beta = 1, 2, and 4. These give alternate ways of connecting the classical beta-ensembles besides simply changing the values of beta. The other two examples are "mirrored" particle models, where each particle has a paired particle reflected about some point or axis of symmetry.

We give overcrowding estimates for the Sine(beta) process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having exactly n points in a fixed interval is given by e(-beta/2n2) log(n)+O(n(2)) as n -> infinity. We also identify the next order term in the exponent if the size of the interval goes to zero.

A method of integrating over difficult sets in Eⁿ by replacing the characteristic function of the set with a discontinuous integral has been used by Markov, Chandrasekhar, Melzak, and others. This thesis employs this method in some problems arising from random walks. A discussion of the difficulties encountered and suggestions for further study are included. / Science, Faculty of / Mathematics, Department of / Graduate

A stock market speculation scheme proposed by Sidney S. Alexander was tested and was found to be more profitable than would be predicted on the assumption that stock prices perform a random walk with a Gaussian distribution and linear trend. The difference between empirical and theoretical gains was found to be statistically significant. By means of an F-ratio, it was demonstrated that the statistical estimate of the variance of the population of price fluctuations tends to increase as the size of sample is increased. This is consistent with the assumption that the population actually has an infinite variance, but is not consistent with the behavior which would be predicted by any variety of Gaussian random walk. The sophisticated quantity theory of money was found to be unable to account for any non-random movements in stock market price indices. / Business, Sauder School of / Graduate

This paper discusses about the data obtained from gene chips and methods of their analysis. Analyzes some methods for analyzing these data and focus on the method of "Random Forests". Shows dataset that is used for specific experiments. Methods are realized in R language environment. Than they are tested, and the results are presented and compared. Results with method "Random Forests" are compared with other experiments on same dataset.