Approved for public release; distribution is unlimited / Reissued 30 May 2017 with Second Reader’s non-NPS affiliation added to title page. / The scalar reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. That method, however, does not work when calculating the orthogonal components of the velocity field measured by a fixed receiver. This thesis derives a vector-scalar reciprocity equation that accounts for both monopole and dipole sources. This equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each received field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-independent and a range-dependent environment using a parabolic equation model. / Electronics Engineer, Naval Undersea Warfare Center

This dissertation focuses on the novel learning strategy based on geometric support vector machines to address the difficulties of processing immense data set. Support vector machines find the hyper-plane that maximizes the margin between two classes, and the decision boundary is represented with a few training samples it becomes a favorable choice for incremental learning. The dissertation presents a novel method Geometric Incremental Support Vector Machines (GISVMs) to address both efficiency and accuracy issues in handling massive data sets. In GISVM, skin of convex hulls is defined and an efficient method is designed to find the best skin approximation given available examples. The set of extreme points are found by recursively searching along the direction defined by a pair of known extreme points. By identifying the skin of the convex hulls, the incremental learning will only employ a much smaller number of samples with comparable or even better accuracy. When additional samples are provided, they will be used together with the skin of the convex hull constructed from previous dataset. This results in a small number of instances used in incremental steps of the training process. Based on the experimental results with synthetic data sets, public benchmark data sets from UCI and endoscopy videos, it is evident that the GISVM achieved satisfactory classifiers that closely model the underlying data distribution. GISVM improves the performance in sensitivity in the incremental steps, significantly reduced the demand for memory space, and demonstrates the ability of recovery from temporary performance degradation.

In the modern geographic information systems, COTS software has been playing a major role. However, deploying heterogeneous GIS software has the tendency to form fragmented data sets and to cause inconsistency. To accomplish data consolidation, we must achieve interoperability between different GIS tools. In my thesis project, I developed Vector and Raster Data Adapters to implement the spatial data consolidation. I deployed ArcIMS to publish the spatial data and metadata onto Internet. Furthermore, the SOAP-Based GIS Web services are implemented to achieve the enterprise information system integration. The contribution of ours in this project is we have streamlined the COTS GIS server, the J2EE coordinator server, the web service provider components, and the COTS web publishing tools into a hybrid web service architecture, in which the enterprise information system integration, the web publishing, and the business-to business online services are uniformed.

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.

by Leung Wai-Man Raymond. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves [1]-[3] (2nd gp.)). / Chapter CHAPTER 0 --- Introduction --- p.1 / Chapter CHAPTER 1 --- Einstein-Hermitian Vector Bundles / Chapter 1.1 --- Preliminaries on Einstein-Hermitian structures --- p.4 / Chapter 1.2 --- Conformal invariance --- p.7 / Chapter 1.3 --- A Chern number inequality --- p.9 / Chapter CHAPTER 2 --- Stable Vector Bundles / Chapter 2.1 --- Coherent analytic sheaves --- p.12 / Chapter 2.2 --- "Torsion-free, reflexive and normal coherent analytic sheaves" --- p.18 / Chapter 2.3 --- Determinant bundles --- p.22 / Chapter 2.4 --- Stable vector bundles --- p.27 / Chapter 2.5 --- Stability of Einstein-Hermitian vector bundles --- p.32 / Chapter CHAPTER 3 --- Existence of Einstein-Hermitian connection on stable vector bundle over a compact Riemann Surface --- p.34 / Chapter CHAPTER 4 --- Existence of Einstein-Hermitian metric on stable vector bundle over a projective algebraic manifold / Chapter 4.1 --- Solution of the evolution equation for finite time --- p.45 / Chapter 4.2 --- Convergence of solution for infinite time --- p.53 / APPENDIX / Chapter I. --- A vanishing theorem of Bochner type and its consequences --- p.67 / Chapter II. --- Uhlenbeck's results on connections with Lp bounds on curvature --- p.69 / REFERENCE

by Kin-Ming Liu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 66-67. / Chapter §0 --- Introduction / Chapter §1 --- Preliminaries and notations / Chapter §2 --- A summary on ultra-(DF)-spaces and order-ultra-（DF)-spaces / Chapter §3 --- " ""Dual"" properties between projective and inductive topologies in topological vector spaces" / Chapter §4 --- Application of barrelledness on continuity of bilinear mappings and projective tensor product / Chapter §5 --- Countably order-quasiultrabarrelled spaces

Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf. 29.

Chan Ka Wo. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 114-118). / Abstracts in English and Chinese. / Introduction --- p.iii / Conventions of This Thesis --- p.vi / Prerequisites --- p.xiii / Chapter 1 --- Cones in Real Vector Spaces --- p.1 / Chapter 1.1 --- The Fundamentals of Cones --- p.2 / Chapter 1.2 --- Enlargements of a Cone --- p.22 / Chapter 1.3 --- Special Cones in Real Vector Spaces --- p.29 / Chapter 1.3.1 --- Positive Cones --- p.29 / Chapter 1.3.2 --- Bishop-Phelps Cones --- p.36 / Chapter 1.3.3 --- Quasi-Bishop-Phelps Cones --- p.42 / Chapter 1.3.4 --- Quasi*-Bishop-Phelps Cones --- p.45 / Chapter 1.3.5 --- Gallagher-Saleh D-cones --- p.47 / Chapter 2 --- Generalizations in Topological Vector Spaces --- p.52 / Chapter 2.1 --- Efficiency and Positive Proper Efficiency --- p.54 / Chapter 2.2 --- Type I Generalizations --- p.71 / Chapter 2.3 --- Type II Generalizations --- p.82 / Chapter 2.4 --- Type III Generalizations --- p.92 / Chapter 3 --- Generalizations in Dual Spaces --- p.97 / Chapter 3.1 --- Weak*-Support Points of a Set --- p.98 / Chapter 3.2 --- Generalizations in the Dual Space of a General Normed Space --- p.100 / Chapter 3.3 --- Generalizations in the Dual Space of a Banach Space --- p.104 / Epilogue: Glimpses Beyond --- p.112 / Bibliography --- p.114

The hard tick Ixodes ricinus is one of the most important species of disease vectors worldwide. It transmits a variety of pathogens, including spirochaetes that are the causative agent of Lyme borreliosis (LB) in humans. This study aimed at analysing different aspects of the ecology, molecular evolution, and microbial associations of I. ricinus. A novel scheme for the phylogenetic analysis and genotyping of I. ricinus was established as part of this study. Phylogeographic clustering of I. ricinus samples fromdifferent European countries was observed, while samples from two different sites inSouthwest England did not show spatial differentiation. The ecology and host abundance in these two habitats was assessed. Differences in the density of questing ticks and in the abundance of rodent hosts were observed. Both sites exhibited low densities of rodents and of ticks infesting them. A blood meal analysis revealed high proportions of mixed feedings and showed artiodactyls to be a main host group for immature I. ricinus ticks from Britain. The prevalence rates of Wolbachia endobacteria in British I. ricinus samples were higher than rates found in samples from other European countries. The unique endosymbiont Midichloria was detected in all female I. ricinus ticks that were screened. A newly developed multi gene analysis of Midichloria samples from six European countries showed a largely coordinated phylogeography with their tick hosts. Taken together, the findings of this thesis demonstrate that British I. ricinus ticks differ from their European counterparts in several ways, which has implications for the epidemiology of infectious diseases transmitted by this vector.

Kirchhoff's laws are well-studied for electrical networks with voltage and current sources, and edges marked by resistors. Kirchhoff's voltage law states that the sum of voltages around any circuit of the network graph is zero, while Kirchhoff's current law states that the sum of the currents along any cutset of the network graph is zero. Given a network, these requirements may be encoded by the circuit matrix and cutset matrix of the network graph. The columns of these matrices are indexed by the edges of the network graph, and their row spaces are orthogonal complements. For (chemical or electrochemical) reaction networks, one must naturally study the opposite problem, beginning with the stoichiometric matrix rather than the network graph. This leads to the following question: given such a matrix, what is a suitable graphic rendering of a network that properly visualizes the underlying chemical reactions? Although we can not expect uniqueness, the goal is to prove existence of such a graph for any matrix. Specifically, we study Kirchhoff graphs, originally introduced by Fehribach. Mathematically, Kirchhoff graphs represent the orthocomplementarity of the row space and null space of integer-valued matrices. After introducing the definition of Kirchhoff graphs, we will survey Kirchhoff graphs in the context of several diverse branches of mathematics. Beginning with combinatorial group theory, we consider Cayley graphs of the additive group of vector spaces, and resolve the existence problem for matrices over finite fields. Moving to linear algebra, we draw a number of conclusions based on a purely matrix-theoretic definition of Kirchhoff graphs, specifically regarding the number of vector edges. Next we observe a geometric approach, reviewing James Clerk Maxwell's theory of reciprocal figures, and presenting a number of results on Kirchhoff duality. We then turn to algebraic combinatorics, where we study equitable partitions, quotients, and graph automorphisms. In addition to classifying the matrices that are the quotient of an equitable partition, we demonstrate that many Kirchhoff graphs arise from equitable edge-partitions of directed graphs. Finally we study matroids, where we review Tutte's algorithm for determining when a binary matroid is graphic, and extend this method to show that every binary matroid is Kirchhoff. The underlying theme throughout each of these investigations is determining new ways to both recognize and construct Kirchhoff graphs.