A random variable that is defined as the absorption time of an evanescent finite-state continuous-time Markov chain is said to have a phase-type distribution. A phase-type distribution is said to have a representation (α,T ) where α is the initial state probability distribution and T is the infinitesimal generator of the Markov chain. The distribution function of a phase-type distribution can be expressed in terms of this representation. The wider class of matrix-exponential distributions have distribution functions of the same form as phase-type distributions, but their representations do not need to have a simple probabilistic interpretation. This class can be equivalently defined as the class of all distributions that have rational Laplace-Stieltjes transform. There exists a one-to-one correspondence between the Laplace-Stieltjes transform of a matrix- exponential distribution and a representation (β,S) for it where S is a companion matrix. In order to use matrix-exponential distributions to fit data or approximate probability distributions the following question needs to be answered: “Given a rational Laplace-Stieltjes transform, or a pair (β,S) where S is a companion matrix, when do they correspond to a matrix-exponential distribution?” In this thesis we address this problem and demonstrate how its solution can be applied to the abovementioned fitting or approximation problem. / Thesis (Ph.D.)--School of Applied Mathematics, 2003.

The investigation of this paper is introduced by describing an important collection of classes arising from a class which forms the domain of an abstract measure. Characterizations of the different types of classes will be formulated in order to facilitate the construction and the identification of the various classes considered.

Over the past few years, a considerable number of studies have been made on Support Vector Machines (SVMs) in many domains to improve classification or prediction. However, SVMs request high computational time and memory when the datasets are large. Although incremental learning techniques are viewed as one possible solution developed to reduce the computation complexity of the scalability problem, few studies have considered that some examples close to the decision hyperplane other than support vectors (SVs) might contribute to the learning process. Consequently, we propose three novel algorithms, named Mixed Incremental learning (MIL), Half-Mixed Incremental learning (HMIL), and Partition Incremental learning (PIL), by improving Syed¡¦s incremental learning method based on fuzzy set theory. We expect to achieve better accuracy than other methods. In the experiments, the proposed algorithms are investigated on five standard machine learning benchmark datasets to demonstrate the effectiveness of the method. Experimental results show that HIL have superior classification accuracy than the other incremental or active learning algorithms. Especially, for the datasets that might have high accuracy in other research reports, HMIL and PIL could even improve the performance.

Thesis (Ph. D.)--York University, 1999. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 87-93). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ43427.

Thesis (M.S.)--University of Alabama at Birmingham, 2009. / Title from PDF title page (viewed Jan. 21, 2010). Additional advisors: Yulia Karpeshina, Ian Knowles, Rudi Weikard. Includes bibliographical references (p. 19).

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 99-101). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 99-101). Also available on the Internet.

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Given two set systems $\mathscr{A}$ and $\mathscr{B}$ over an $n$-element set, we say that $(\mathscr{A,B})$ forms a recovering pair if the following conditions hold: \\ $ \forall A, A' \in \mathscr{A}$ and $ \forall B, B' \in \mathscr{B}$, $A \setminus B = A' \setminus B' \Rightarrow A=A'$ \\ $ \forall A, A' \in \mathscr{A}$ and $ \forall B, B' \in \mathscr {B}$, $B \setminus A = B' \setminus A' \Rightarrow B=B'$ \\ In 1989, G\'bor Simonyi conjectured that if $(\mathscr)$ forms a recovering pair, then $|\mathscr||\mathscr|\leq 2^n$. This conjecture is the focus of this thesis. This thesis contains a collection of proofs of special cases that together form a complete proof that the conjecture holds for all values of $n$ up to 8. Many of these special cases also verify the conjecture for certain recovering pairs when $n>8$. We also present a result describing the nature of the set of numbers over which the conjecture in fact holds. Lastly, we present a new problem in graph theory, and discuss a few cases of this problem.

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