Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2008. / Nemhauser,George, Committee Member ; Gu, Zonghao, Committee Member ; Ergun, Ozlem, Committee Member ; Sokol, Joel, Committee Co-Chair ; Ahmed, Shabbir, Committee Chair.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (M.S.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaf 39).

by Robert M. Freund. / "April 1984." / Bibliography: leaf i.

Ph.D.

In this dissertation we treat three tiling problems and three problems in combinatorial geometry, extremal graph theory and sparse Ramsey theory. We first consider tilings of $\mathbb{Z}^n$. In this setting a tile $T$ is just a finite subset of $\mathbb{Z}^n$. We say that $T$ tiles $\mathbb{Z}^n$ if the latter set admits a partition into isometric copies of $T$. Chalcraft observed that there exist $T$ that do not tile $\mathbb{Z}^n$ but tile $\mathbb{Z}^{d}$ for some $d > n$. He conjectured that such $d$ exists for any given tile. We prove this conjecture in Chapter 2. In Chapter 3 we prove a conjecture of Lonc, stating that for any poset $P$ of size a power of $2$, if $P$ has a greatest and a least element, then there is a positive integer $k$ such that $[2]^k$ can be partitioned into copies of $P$. The third tiling problem is about vertex-partitions of the hypercube graph $Q_n$. Offner asked: if $G$ is a subgraph of $Q_n$ such $|G|$ is a power of $2$, must $V(Q_d)$, for some $d$, admit a partition into isomorphic copies of $G$? In Chapter 4 we answer this question in the affirmative. We follow up with a question in combinatorial geometry. A line in a planar set $P$ is a maximal collinear subset of $P$. P\'or and Wood considered colourings of finite $P$ without large lines with a bounded number of colours. In particular, they examined whether monochromatic lines always appear in such colourings provided that $|P|$ is large. They conjectured that for all $k,l \ge 2$ there exists an $n \ge 2$ such that if $|P| \ge n$ and $P$ does not contain a line of cardinality larger than $l$, then every colouring of $P$ with $k$ colours produces a monochromatic line. In Chapter 5 we construct arbitrarily large counterexamples for the case $k=l=3$. We follow up with a problem in extremal graph theory. For any graph, we say that a given edge is triangular if it forms a triangle with two other edges. How few triangular edges can there be in a graph with $n$ vertices and $m$ edges? For sufficiently large $n$ we prove a conjecture of F\"uredi and Maleki that gives an exact formula for this minimum. This proof is given in Chapter 6. Finally, Chapter 7 is concerned with degrees of vertices in directed hypergraphs. One way to prescribe an orientation to an $r$-uniform graph $H$ is to assign for each of its edges one of the $r!$ possible orderings of its elements. Then, for any $p$-set of vertices $A$ and any $p$-set of indices $I \subset [r]$, we define the $I$-degree of $A$ to be the number of edges containing vertices $A$ in precisely the positions labelled by $I$. Caro and Hansberg were interested in determining whether a given $r$-uniform hypergraph admits an orientation where every set of $p$ vertices has some $I$-degree equal to $0$. They conjectured that a certain Hall-type condition is sufficient. We show that this is true for $r$ large, but false in general.

Este trabalho trata de uma aplicação de programação estocástica para administração de passivos e ativos. Inicialmente, um modelo de administração de ativos e passivos utilizando valores de retorno de ativos determinísticos é formalizado, constatando-se as suas limitações, justificando-se a necessidade de abranger formalmente a incerteza inerente aos mercados financeiros. Para isso, um modelo para administração de ativos e passivos que utiliza otimização e programação estocástica baseado em uma árvore de cenários multiestágio balanceada é apresentado, descrito, e implementado. Os seus resultados determinam uma política de investimento de ativos para o instante inicial do período considerado, definindo-se também uma regra que possibilita, a partir do equilíbrio entre o patrimônio inicial e total de passivo a ser pago ao final do período considerado, estimar a probabilidade de insolvência do fundo de pensão. Além disso, realiza-se o estudo do impacto da redução de uma proxy da taxa de juros básico na composição do portfólio administrado por essas empresas. / This work discusses an application of stochastic programming for asset-liability management. Initially, a deterministic asset-liability model is formalized. Its limitations become clear which justify the need to include uncertainty in the model. Then, a stochastic programming model based on a balanced multistage scenario tree is presented, described and implemented for an asset-liability environment. The main results are: (i) an investment policy for the fund, and, (ii) the pension’s fund insolvency probability considering an initial relation between the current assets and the present value of the future liabilities. The impact of a possible reduction in interested rate on the pension’s fund optimal portfolio is also presented.

Cardiovascular disease is one of the leading causes of the mortality in the western world. Many imaging modalities have been used to diagnose cardiovascular diseases. However, each has different forms of noise and artifacts that make the medical image analysis field important and challenging. This thesis is concerned with developing fully automatic segmentation methods for cross-sectional coronary arterial imaging in particular, intra-vascular ultrasound and optical coherence tomography, by incorporating prior and tracking information without any user intervention, to effectively overcome various image artifacts and occlusions. Combinatorial optimisation methods are proposed to solve the segmentation problem in polynomial time. A node-weighted directed graph is constructed so that the vessel border delineation is considered as computing a minimum closed set. A set of complementary edge and texture features is extracted. Single and double interface segmentation methods are introduced. Novel optimisation of the boundary energy function is proposed based on a supervised classification method. Shape prior model is incorporated into the segmentation framework based on global and local information through the energy function design and graph construction. A combination of cross-sectional segmentation and longitudinal tracking is proposed using the Kalman filter and the hidden Markov model. The border is parameterised using the radial basis functions. The Kalman filter is used to adapt the inter-frame constraints between every two consecutive frames to obtain coherent temporal segmentation. An HMM-based border tracking method is also proposed in which the emission probability is derived from both the classification-based cost function and the shape prior model. The optimal sequence of the hidden states is computed using the Viterbi algorithm. Both qualitative and quantitative results on thousands of images show superior performance of the proposed methods compared to a number of state-of-the-art segmentation methods.

This dissertation shows that the autocorrelation of switching functions can be effectively utilized in combinational logic optimization and synthesis. The procedures developed exploit information contained in the autocorrelation of switching functions to perform optimization of Programmable Logic Arrays (PLAs) and to aid in a multi-level logic synthesis approach called two-place decomposition. A new optimization technique is presented, based on the autocorrelation of switching functions, to find near-optimal variable pairings for decoded PLAs. The results of this approach compare favourably to those of other researchers’ techniques. The key advantages of the new approach are its simplicity and its efficiency. The basic two-place decomposition approach is augmented with various enhancements. These include an improved decomposition merge procedure, the addition of alternate mapping functions for complex disjunctive decompositions, and the incorporation of linearization using the autocorrelation to handle functions that are non-two-place decomposable. A robust implementation of the enhanced method is presented and is used to generate function realizations for comparison with other synthesis methods. The enhanced two-place decomposition method is shown to perform particularly well for functions exhibiting high degrees of symmetry. The dissertation also presents a new synthesis technique that utilizes a particular representation of a switching function called a Reduced Ordered Binary Decision Diagram (ROBDD) and is targeted to two-place decomposition. This new technique allows the two-place decomposition approach to synthesize a much broader range of functions. Although, in comparison to one other synthesis method, the new approach does not perform as well in most cases, it has considerable promise and several enhancements are proposed for improvement. This dissertation also shows that there is a strong connection among autocorrelation, two-place decomposition, and good variable orders in an ROBDD. A first attempt to formally analyze the relationship between autocorrelation and two-place decomposition is presented. Relationships are identified between certain autocorrelation coefficients when particular two-place decompositions exist in a function. These relationships are also connected to the heuristics used in the above mentioned PLA optimization technique. Variable order can have a substantial impact on the size of an ROBDD. This dissertation shows that a good variable order is related to the two-place decompositions that are exhibited in a function. Thus, variable order is also related to the autocorrelation and this relationship can lead to an autocorrelation-based technique for determining good variable orders for ROBDDs. / Graduate

abstract: A new algebraic system, Test Algebra (TA), is proposed for identifying faults in combinatorial testing for SaaS (Software-as-a-Service) applications. In the context of cloud computing, SaaS is a new software delivery model, in which mission-critical applications are composed, deployed, and executed on cloud platforms. Testing SaaS applications is challenging because new applications need to be tested once they are composed, and prior to their deployment. A composition of components providing services yields a configuration providing a SaaS application. While individual components in the configuration may have been thoroughly tested, faults still arise due to interactions among the components composed, making the configuration faulty. When there are k components, combinatorial testing algorithms can be used to identify faulty interactions for t or fewer components, for some threshold 2 <= t <= k on the size of interactions considered. In general these methods do not identify specific faults, but rather indicate the presence or absence of some fault. To identify specific faults, an adaptive testing regime repeatedly constructs and tests configurations in order to determine, for each interaction of interest, whether it is faulty or not. In order to perform such testing in a loosely coupled distributed environment such as the cloud, it is imperative that testing results can be combined from many different servers. The TA defines rules to permit results to be combined, and to identify the faulty interactions. Using the TA, configurations can be tested concurrently on different servers and in any order. The results, using the TA, remain the same. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2014