The Singular Value Decomposition is one of the most useful matrix factorizations in applied linear algebra, the Principal Component Analysis has been called one of the most valuable results of applied linear algebra. How and why principal component analysis is intimately related to the technique of singular value decomposition is shown. Their properties and applications are described. Assumptions behind this techniques as well as possible extensions to overcome these limitations are considered. This understanding leads to the real world applications, in particular, image processing of neurons. Noise reduction, and edge detection of neuron images are investigated.

This research addresses sizing and dimensioning of a forward-reserve warehouse, a strategic design problem that has important implications on warehouse life cycle costs including construction, inventory holding and replenishment, and material handling. Large mixed integer nonlinear models are developed that capture the complex tradeoffs among the different costs in order to achieve a global optimal design satisfying throughput requirements. We first consider the situation where the forward area includes all SKUs so that order picking is performed only in the forward area. In this case, the problem can be decomposed. The resulting sub-problem is convex and can be solved very efficiently based on the Karush-Kuhn-Tucker (KKT) conditions. This property enables the use of a Generalized Benders Decomposition (GBD) method to solve the sizing and dimensioning problem exactly. We then extend the problem to more general situations where the forward area contains a subset of SKUs. This requires integrating the sizing and dimensioning decisions with the decision to assign SKUs to the forward area based on their flow characteristics (i.e., the forward reserve allocation). A similar decomposition strategy can be employed, but the sub-problem (incorporating the forward reserve allocation) is no longer convex. A bi-level hierarchical heuristic approach is proposed that integrates a pattern search method for the master problem and optimal and heuristic algorithms for the sub-problems. Numerical results demonstrate that the proposed solution methods can efficiently find optimal or near optimal solutions for the sizing and dimensioning problem, and the resulting solutions are robust with regards to possible forecasting errors in design parameters.

In this thesis, a novel technique based on the empirical mode decomposition (EMD) methodology is proposed and examined for the noise-robustness of automatic speech recognition systems. The EMD analysis is a generalization of the Fourier analysis for processing nonlinear and non-stationary time functions, in our case, the speech feature sequences. We use the intrinsic mode functions (IMF), which include the sinusoidal functions as special cases, obtained from the EMD analysis in the post-processing of the log energy feature. We evaluate the proposed method on Aurora 2.0 and Aurora 3.0 databases. On Aurora 2.0, we obtain a 44.9% overall relative improvement over the baseline for the mismatched (clean-training) tasks. The results show an overall improvement of 49.5% over the baseline for Aurora 3.0 on the high-mismatch tasks. It shows that our proposed method leads to significant improvement.

This dissertation, which consists of four parts, is to (i) present a mixed integer programming model for the strategic design of an assembly system in the international business environment established by the North American Free Trade Agreement (NAFTA) with the focus on modeling the material flow network with assembly operations, (ii) compare different decomposition schemes and acceleration techniques to devise an effective branch-and-price solution approach, (iii) introduce a generalization of Dantzig-Wolf Decomposition (DWD), and (iv) propose a combination of dual-ascent and primal drop heuristics. The model deals with a broad set of design issues (bill-of-materials restrictions, international financial considerations, and material flows through the entire supply chain) using effective modeling devices. The first part especially focuses on modeling material flows in such an assembly system. The second part is to study several schemes for applying DWD to the productionassembly- distribution system design problem (PADSDP). Each scheme exploits selected embedded structures. The research objective is to enhance the rate of DWD convergence in application to PADSDP through formulating a rationale for decomposition by analyzing potential schemes, adopting acceleration techniques, and assessing the impacts of schemes and techniques computationally. Test results provide insights that may be relevant to other applications of DWD. The third part proposes a generalization of column generation, reformulating the master problem with fewer variables at the expense of adding more constraints; the subproblem structure does not change. It shows both analytically and computationally that the reformulation promotes faster convergence to an optimal solution in application to a linear program and to the relaxation of an integer program at each node in the branchand- bound tree. Further, it shows that this reformulation subsumes and generalizes prior approaches that have been shown to improve the rate of convergence in special cases. The last part proposes two dual-ascent algorithms and uses each in combination with a primal drop heuristic to solve the uncapacitated PADSDP, which is formulated as a mixed integer program. Computational results indicate that one combined heuristic finds solutions within 0.15% of optimality in most cases and within reasonable time, an efficacy suiting it well for actual large-scale applications.

Geometric computations are essential in many real-world problems. One important issue in geometric computations is that the geometric models in these problems can be so large that computations on them have infeasible storage or computation time requirements. Decomposition is a technique commonly used to partition complex models into simpler components. Whereas decomposition into convex components results in pieces that are easy to process, such decompositions can be costly to construct and can result in representations with an unmanageable number of components. In this work, we have developed an approximate technique, called Approximate Convex Decomposition (ACD), which decomposes a given polygon or polyhedron into "approximately convex" pieces that may provide similar benefits as convex components, while the resulting decomposition is both significantly smaller (typically by orders of magnitude) and can be computed more efficently. Indeed, for many applications, an ACD can represent the important structural features of the model more accurately by providing a mechanism for ignoring less significant features, such as wrinkles and surface texture. Our study of a wide range of applications shows that in addition to providing computational efficiency, ACD also provides natural multi-resolution or hierarchical representations. In this dissertation, we provide some examples of ACD's many potential applications, such as particle simulation, mesh generation, motion planning, and skeleton extraction.

Cholesky Decomposition is usually used to deal with the correlation problem among a financial product's underlying assets. However, Cholesky Decomposition inherently suffers from the requirement that all eigenvalues must be positive. Therefore, Cholesky Decomposition can't work very well when the number of the underlying assets is high. The report takes a diffrent approach called spectral Decomposition in attempt to solve the problem. But it turns out that although Spectral Decomposition can meet the requirement of all-positive eigenvalue, the decomposision error will be larger as the number of underlying asset getting larger. Thus, although Spectral Decomposition does offer some help, it works better when the number of underlying assets is not very large.

A thermal catalytic decomposition process has been developed to recycle used tire rubber. This process enables the recovery of useful products, such as hydrocarbons and carbon blacks. During the catalytic decomposition process, the tire rubber is decomposed into smaller hydrocarbons, which are collected in the process. The solid reaction residue, which normally consists of carbon black, catalysts, other inorganic rubber compound components, and organic carbonaceous deposits, was subjected to a series of treatments with the intention to recover the valuable carbon black and catalyst. The process economics depend strongly on the commercial value of the recovered carbon black and the ability to recover and recycle the catalysts used in the process. Some of the important properties of the recovered carbon black product have been characterized and compared with that of commercial-grade carbon blacks. The composition of the recovered carbon black was analyzed by TGA and EDX, the structure and morphology were studied through transmission electron microscopy (TEM), and the specific surface area was measured by BET nitrogen adsorption. The recovered products possess qualities at least comparable to (or even better than) that of the commercial-grade carbon black N660. Methods for increasing the market value of this recovered carbon black product are discussed. Anhydrous aluminum chloride (AlCl3) was used as the primary catalyst in the process. A catalyst recovery method based on the AlCl3 sublimation and recondensation was studied and found to be non-feasible. It is believed that the catalyst forms an organometallic complex with the decomposed hydrocarbons, such that it becomes chemically bonded to the residue material and hence not removable by evaporation. A scheme for the further study of the catalyst recovery is suggested.

This paper surveys the method of beta decomposition and the evolution of different type betas in Taiwan stock market. We break the unexpected market return into two different types of news term, which are the discount-rate news about the expected change of discount rate and the cash-flow news about the expected change of future cash dividends, and then, estimate the relationship between these two market news and the return of different cross-section industries. The traditional beta used in financial market is broken into two different betas with different risk price. Our study finds out some evidence about the change in the attitude of investors for our two news term that affect market return.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 56-59).

Thesis (Ph. D.)--School of Chemistry and Biochemistry, Georgia Institute of Technology, 2004. Directed by Jiri Janata. / Vita. Includes bibliographical references.