Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (M.S.) in Forestry--University of Maine, 2004. / Includes vita. Includes bibliographical references (leaves 34-39).

Thesis (M.F.)--Oregon State University, 1982. / Includes bibliographical references (p. 69-70). Also available on the World Wide Web.

Thesis (Ph. D.)--Oregon State University, 1985. / Typescript (photocopy). Includes bibliographical references (leaves 72-79). Also available on the World Wide Web.

The purpose of this thesis is to add to the structure theory of Aronszajn orderings. We shall focus essentially in four topics. The first topic of discussion is about the relation between Lipschitz and coherent trees. I will demonstrate that the tree $T(\rho_0)$ is coherent without any extra set theoretic hypothesis. The second topic presents an application of Todorcevic's $\rho$ functions to provide some partial answers to an old question of Juhaz asking whether a standard weakening of Jensen's diamond principle implies the existence of Suslin trees. In the third topic we focus on providing a satisfactory rough classification result of the class of Aronszajn lines. Our main result is that, assuming PFA, the class of Aronszajn lines is well-quasi-ordered by embeddability. The last topic is an investigation of the gap structure of the class of coherent Aronszajn trees. I will show that, assuming PFA, the class of coherent Aronszajn trees quasi-ordered by embeddability is the unique saturated linear order of cardinality $\aleph_2$.

The purpose of this thesis is to add to the structure theory of Aronszajn orderings. We shall focus essentially in four topics. The first topic of discussion is about the relation between Lipschitz and coherent trees. I will demonstrate that the tree $T(\rho_0)$ is coherent without any extra set theoretic hypothesis. The second topic presents an application of Todorcevic's $\rho$ functions to provide some partial answers to an old question of Juhaz asking whether a standard weakening of Jensen's diamond principle implies the existence of Suslin trees. In the third topic we focus on providing a satisfactory rough classification result of the class of Aronszajn lines. Our main result is that, assuming PFA, the class of Aronszajn lines is well-quasi-ordered by embeddability. The last topic is an investigation of the gap structure of the class of coherent Aronszajn trees. I will show that, assuming PFA, the class of coherent Aronszajn trees quasi-ordered by embeddability is the unique saturated linear order of cardinality $\aleph_2$.

Phylogenetic analysis is used in all branches of biology by inferring evolutionary trees. Applications include designing more effective drugs, tracing the transmission of deadly viruses, and guiding conservation and biodiversity efforts. Most analyses rely on effective heuristics for obtaining accurate trees. However, relatively little work has been done to analyze quantitatively the behavior of phylogenetic heuristics in tree space. This is important, because a better understanding of local search behavior can facilitate the design of better heuristics, which ultimately leads to more accurate depictions of the true evolutionary relationships. In order to access and analyze the tree search space, we implement an effec- tive local search heuristic. Having an effective heuristic that can open the space is important, since no search heuristic in this field can effectively provide data collec- tion control. So we have implemented and estimated a search heuristic, Simple Local Search or SLS, that works reasonably well in the space. Our investigations led to several interesting observations about the behavior of a search heuristic and the tree search space. We studied the correlation of tree features of search path trees, where tree features refer to the parsimony score, the Robinson- Foulds distance and the homoplasy measure. Most importantly from the results, parsimony score was highly correlated with Robinson-Foulds distance only in trees that lie on the search path to a local optimum. We also note that the scores of neighborhoods along search paths improve together, as a local search progresses. Correlations of tree features of search path trees are particularly useful in char- acterizing and controlling a search path. This paper proposes one possible stopping criterion to maximize the tree search results while minimizing computational time tested on three biological datasets using the correlation between the parsimony score and the RF distance value of search path trees. Also, the observation that scores of a neighborhood on a search path improve together gives us a significant amount of flexibility in selecting the next pivot of a search without losing performance. Eventually, our long-term goal is developing an effective search heuristic that can deal with large scale tree space in reasonable time. Improved knowledge about the tree search space and the search heuristic can provide a reasonable starting point toward the goal.

Thesis (Ph. D.)--Oregon State University, 2001. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Ecology and Evolution." Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 327-363).