Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 57-59).

Thesis (Ph. D.)--Drexel University, 2004. / Includes abstract and vita.

Thesis (Ph. D.)--University of Wyoming, 2005. / Title from PDF title page (viewed on Feb. 22, 2008). Includes bibliographical references (p. 136-139).

Thesis(B.Sc.(Hons. ))--University of Adelaide, dept. of Mathematics, 1968.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 114-117).

Thesis (doctoral)--Rheinischen-Friedrich-Wilhelms-Universität. / "August 1999." Includes bibliographical references (p. 106-109) and index.

Thesis (M. Sc.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 57-59). Also available via the World Wide Web.

An acyclic orientation of a graph is an assignment of a direction to each edge in a way that does not form any directed cycles. Acyclic orientations of a complete bipartite graph are in bijection with a class of matrices called lonesum matrices, which can be uniquely reconstructed from their row and column sums. We utilize this connection and other properties of lonesum matrices to determine an analytic form of the generating function for the length of the longest path in an acyclic orientation on a complete bipartite graph, and then study the distribution of the length of the longest path when the acyclic orientation is random. We use methods of analytic combinatorics, including analytic combinatorics in several variables (ACSV), to determine asymptotics for lonesum matrices and other related classes. / Includes bibliography. / Dissertation (PhD)--Florida Atlantic University, 2021. / FAU Electronic Theses and Dissertations Collection

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After that, strip sum and orthogonal Haar transform are proposed. The sum of pixels in a rectangle can be computed by one addition using the strip sum. Then this thesis proposes to use the orthogonal Haar transform (OHT) for pattern matching. Applied for pattern matching, the fast OHT algorithm using strip sum requires O(log u) additions per pixel to project input data of size N1 x N2 onto u 2-D OHT bases. Experimental results show the efficiency of pattern matching using OHT. / Firstly, this thesis proposes a fast algorithm for Walsh Hadamard Transform (WHT) on sliding windows which can be used to implement pattern matching efficiently. / Support vector machine (SVM) is a widely used classification approach. Direct computation of SVM is not desirable in applications requiring computationally efficient classification. To relieve the burden of high computational time required for computing SVM, this thesis proposes a transform domain SVM (TDSVM) using pruning that computes SVM much faster. Experimental results show the efficiency in applying the proposed method for human detection. / Then this thesis analyzes and compares state-of-the-art algorithms for full search equivalent pattern matching. Inspired by the analysis, this thesis develops a new family of transforms called the Kronecker-Hadamard Transform (KHT) of which the GCK family is a subset and WHT is a member. Thus, KHT provides more choices of transforms for representing images. Then this thesis proposes a new fast algorithm that is more efficient than the GCK algorithm. All KHTs can be computed efficiently using the fast KHT algorithm. Based on the KHT, this thesis then proposes the segmented KHT (SegKHT). By segmenting input data into Ls parts, the SegKHT requires 1/Ls the computation required by the KHT algorithm in computing basis vectors. Experimental results show that the proposed algorithm can significantly accelerate the pattern matching process and outperforms state-of-the-art methods. / This thesis aims at improving the computational efficiency in pattern matching. / Ouyang, Wanli. / Adviser: Wai Kuen Cham. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 143-147). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.