Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Ahmet Vecdet Arslan. / Ph.D.

Mathematical modeling is a central component of operations research. Most of the academic research in our field focuses on developing algorithmic tools for solving various mathematical problems arising from our models. However, our procedure for selecting the best model to use in any particular application is ad hoc. This dissertation seeks to rigorously quantify the trade-offs between various design criteria in model construction through a series of case studies. The hope is that a better understanding of the pros and cons of different models (for the same application) can guide and improve the model selection process. In this dissertation, we focus on two broad types of trade-offs. The first type arises naturally in mechanism or market design, a discipline that focuses on developing optimization models for complex multi-agent systems. Such systems may require satisfying multiple objectives that are potentially in conflict with one another. Hence, finding a solution that simultaneously satisfies several design requirements is challenging. The second type addresses the dynamics between model complexity and computational tractability in the context of approximation algorithms for some discrete optimization problems. The need to study this type of trade-offs is motivated by certain industry problems where the goal is to obtain the best solution within a reasonable time frame. Hence, being able to quantify and compare the degree of sub-optimality of the solution obtained under different models is helpful. Chapters 2-5 of the dissertation focus on trade-offs of the first type and Chapters 6-7 the second type.

Law Chi Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 86-91). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Contents --- p.v / List of Figures --- p.viii / List of Tables --- p.x / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.4 / Chapter 1.2 --- Thesis Organization --- p.7 / Chapter 2 --- Literature Review --- p.9 / Chapter 2.1 --- Logical Time --- p.9 / Chapter 2.1.1 --- Event Model --- p.9 / Chapter 2.1.2 --- Lamport's Logical Clock --- p.10 / Chapter 2.1.3 --- Mattern's Vector Time --- p.14 / Chapter 2.2 --- Snapshot Algorithms --- p.18 / Chapter 2.2.1 --- Preliminaries --- p.19 / Chapter 2.2.2 --- Chandy-Lamport --- p.22 / Chapter 2.2.3 --- Lai-Yang and Mattern --- p.24 / Chapter 2.2.4 --- Sato --- p.25 / Chapter 3 --- Ad-hoc Network System --- p.29 / Chapter 3.1 --- Event Model --- p.30 / Chapter 3.2 --- Snapshot Problem --- p.32 / Chapter 4 --- Time Approximation in Distributed Systems --- p.37 / Chapter 4.1 --- Definitions --- p.38 / Chapter 4.1.1 --- Preliminary --- p.38 / Chapter 4.1.2 --- Event Ordering --- p.39 / Chapter 4.1.3 --- Clock --- p.40 / Chapter 4.1.4 --- Time Approximation Levels --- p.41 / Chapter 4.1.5 --- Offline Algorithm --- p.41 / Chapter 4.2 --- Time Approximation in Static Network Systems --- p.42 / Chapter 4.2.1 --- Stable Snapshot --- p.43 / Chapter 4.2.2 --- Snapshot --- p.50 / Chapter 4.2.3 --- Latest Snapshot --- p.52 / Chapter 4.2.4 --- Time Approximation Levels --- p.54 / Chapter 4.3 --- Time Approximation in Ad-hoc Network Systems --- p.54 / Chapter 4.3.1 --- Snapshot --- p.56 / Chapter 4.3.2 --- Latest Snapshot --- p.61 / Chapter 4.3.3 --- Time Approximation Levels --- p.61 / Chapter 4.3.4 --- Bi-vector Clock --- p.63 / Chapter 4.3.5 --- Strong Snapshot Problem --- p.67 / Chapter 5 --- Snapshot Algorithm for Ad-hoc Network Systems --- p.69 / Chapter 5.1 --- Algorithm --- p.70 / Chapter 5.1.1 --- Notations --- p.70 / Chapter 5.1.2 --- Rules of Maintaining Si and Ti in Pi --- p.72 / Chapter 5.1.3 --- The Properties --- p.73 / Chapter 5.1.4 --- Algorithm --- p.78 / Chapter 5.2 --- Enhancements --- p.82 / Chapter 5.2.1 --- Reduction of Stored States and Exchanged Logs --- p.82 / Chapter 5.2.2 --- LCC Synchronization --- p.82 / Chapter 6 --- Conclusion --- p.84 / Bibliography --- p.86 / Publications --- p.91

Tao Suyi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 51-53). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.2 / Chapter 1.1.1 --- Mobile Phone Applications --- p.3 / Chapter 1.1.2 --- Location Methods --- p.4 / Chapter 1.1.3 --- Location Algorithms --- p.9 / Chapter 1.2 --- AoA Localization --- p.10 / Chapter 1.3 --- The NLOS Problem --- p.11 / Chapter 2 --- AoA Localization --- p.13 / Chapter 2.1 --- Conventional Approach to AoA Localization --- p.14 / Chapter 2.2 --- Least Squares Approach to AoA Localization --- p.16 / Chapter 2.2.1 --- Ordinary Least Squares Approach (OLS) by Pages-Zamora --- p.16 / Chapter 2.2.2 --- The Weighted Least Squares Approach (WLS) --- p.18 / Chapter 2.3 --- Approximate Maximum Likelihood Method (AML) for AoA Localization --- p.19 / Chapter 2.4 --- Simulations --- p.21 / Chapter 3 --- Analysis and Mitigation of NLoS Effects --- p.26 / Chapter 3.1 --- The Non-Line-of-Sight (NLoS) Effects --- p.26 / Chapter 3.2 --- NLoS Mitigation in AoA Localization --- p.27 / Chapter 3.2.1 --- A Selective Model to Suppress NLOS Errors --- p.27 / Chapter 3.2.2 --- Dimension Determination and LOS Identification --- p.29 / Chapter 3.3 --- Simulations --- p.34 / Chapter 3.3.1 --- Experiment 1 --- p.34 / Chapter 3.3.2 --- Experiment 2 --- p.38 / Chapter 4 --- Conclusions and Suggestions for Future Work --- p.42 / Chapter 4.1 --- Conclusions --- p.42 / Chapter 4.2 --- Suggestions for future work --- p.44 / Chapter A --- Derivation of the Cramer Rao Lower Bound (CRLB) for AoA Localization --- p.45 / Chapter A.1 --- CRLB for all LoS --- p.45 / Chapter A.2 --- CRLB for both LoS and NLoS --- p.46 / Chapter B --- Derivation of the Error Covariance for OLS and WLS Estima- tors --- p.48 / Chapter B.1 --- Error Covariance for OLS Estimator --- p.49 / Chapter B.2 --- Error Covariance for WLS Estimator --- p.50 / Bibliography --- p.51

Cuando encontrar la respuesta exacta a una consulta sobre una base de datos muy grande es intratable, es natural aproximar la consulta por otra más eficiente que pertenezca a una clase con buenas cotas en la complejidad de evaluación de consultas. En esta tesis estudiamos tales aproximaciones para consultas conjuntivas. Estas consultas son de especial interés en base de datos, y además sabemos muy bien qué clases de consultas admiten una evaluación eficiente, como las consultas acíclicas, o las de (hyper)treewidth acotado. Definimos una aproximación a una consulta Q como una consulta de una de esas clases que discrepa con Q lo menos posible. Nos concentramos en aproximaciones que siempre entregan respuestas correctas. Probamos que para las clases tratables de consultas conjuntivas mencionadas anteriormente, siempre existen aproximaciones y sus tamaños son a lo más polinomiales en el tamaño de la consulta original. Esto se sigue de resultados generales obtenidos que relacionan propiedades de clausura de clases de consultas conjuntivas con la existencia de aproximaciones. Además, probamos que en muchos casos el tamaño de la aproximación es a lo más el tamaño de la consulta original. Presentamos una serie de resultados sobre cómo ciertas propiedades combinatoriales de las consultas afectan a sus aproximaciones y estudiamos cotas en la cantidad de aproximaciones, al igual que la complejidad de encontrar e identificar aproximaciones. Finalmente, consideramos aproximaciones que entregan todas las respuestas correctas y estudiamos sus propiedades.

本论文着重研究了带有Lp模球约束以及二次约束的多项式优化问题的计算复杂度以及关于此类问题的近似算法。在本论文中，利用张量对称化的技巧，我们首次证明了当P∈ [2 ，∞] ，任意高阶的带有Lp模球约束的多项式优化问题均为NP 困难。借助模的对偶性质，我们将这类优化问题转化为求解凸体半径的问题，从而使得我们获得了之前研究所无法使用的算法工具。具体来说，利用计算凸几何的算法工具，对于Lp模球约束的多项式优化问题，我们得到了近似比为[附圖]的确定性多项式时间近似算法，其中d为目标多项式的阶次， n 为问题的维度。使用随机算法，我们将近似比进一步提高为此类问题的己知最优值。[附圖]。此外，我们发展了计算凸几何当中对于凸体半径的计算方法，从而设计出了一种对二次约束多项式优化问题近似比为[附圖]的近似算法，其中m为问题的约束个数。我们的结果涵盖并提高了之前关于此类问题的研究结果。我们相信在本论文中使用的新的算法工具，将在今后的多项式优化问题研究中得到更广泛的应用。 / In this thesis, we present polynomial time approximation algorithms for solving various homogeneous polynomial optimization problems and their multilinear relaxations. Specifically, for the problems with Lp ball constraint, where P∈ [2 ，∞], by reducing them to that of determining the Lq-diameter of certain convex body, we show that they can be approximated to within a factor of [with formula] in deterministic polynomial time, where q = p=(p - 1) is the conjugate of p, n is the number of variables, and d is the degree of the polynomial. We further show that with the help of randomization, the approximation guarantee can be improved to [with formula], which is independent of p and is currently the best for the aforementioned problems. Moreover, we extend the argument of deterministic algorithm mentioned above to solve the quadratically constrained polynomial optimization problems. In particular, for any intersection of ellipsoids K, we can, in polynomial time, construct a random polytope P, which satisfies [with formula]. Then, by reducing the problem to that of evaluating the maximum polytopal norm [with formula] induced by P, over certain convex body, we can approximate the quadratically constrained problem within a factor of [with formula] in polynomial time. Our results unify and generalize those in the literature, which focus either on the quadratic case or the case where [with formula]. We believe that the wide array of tools used in this thesis will have further applications in the study of polynomial optimization problems. / Detailed summary in vernacular field only. / Hou, Ke. / On title page "p" is subscript. / Thesis (Ph.D.) Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 106-111). / Abstracts also in Chinese.

Ng Kin Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 186-189). / Ng Kin Man. / Contents --- p.i / List of Figures --- p.ii / Abstract --- p.iv / Acknowledgement --- p.v / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Objective and Methodology --- p.3 / Chapter Chapter 2. --- Theory of the Jaynes-Cummings model --- p.6 / Chapter 2.1 --- Formulation of the Problem --- p.6 / Chapter 2.1.1 --- Quantization of the Electromagnetic Field --- p.7 / Chapter 2.1.2 --- Quantization of the Matter Field --- p.11 / Chapter 2.1.3 --- The Interaction between the Radiation and the Matter --- p.12 / Chapter 2.1.4 --- Formulation of the one-photon JCM --- p.14 / Chapter 2.2 --- Eenergy eigenstates and Eigenvalue Spectrum --- p.16 / Chapter 2.3 --- Dynamics of the one-photon JCM --- p.18 / Chapter 2.3.1 --- The time evolution of the system --- p.19 / Chapter 2.3.2 --- Atomic Observables --- p.20 / Chapter 2.3.3 --- Field Observables --- p.23 / Chapter 2.4 --- Asymptotic solution of the JCM --- p.27 / Chapter 2.5 --- Discussion of the role of the RWA in the JCM --- p.29 / Chapter 2.6 --- Conclusion --- p.30 / Chapter Chapter 3. --- Numerical Results for the one-photon JCM --- p.40 / Chapter 3.1 --- Eigenstates and Eigenvalue Spectrum --- p.40 / Chapter 3.2 --- Dynamics of the System --- p.44 / Chapter 3.2.1 --- Atomic Observables --- p.44 / Chapter 3.2.2 --- Field Observables --- p.45 / Chapter 3.3 --- Conclusion --- p.47 / Chapter Chapter 4. --- Generalization of the JCM --- p.60 / Chapter 4.1 --- Multiphoton JCM --- p.60 / Chapter 4.2 --- Intensity-dependent JCM --- p.62 / Chapter 4.3 --- Two-mode two-photon JCM --- p.64 / Chapter 4.4 --- Conclusion --- p.66 / Chapter Chapter 5. --- Multiphoton Jaynes-Cummings model --- p.67 / Chapter 5.1 --- Energy Eigenstates and Eigenvalue Spectrum --- p.67 / Chapter 5.1.1 --- Energy Eigenstates and Eigenvalue Spectrum of the two- photon JCM --- p.71 / Chapter 5.1.2 --- Eigenstates and Eigenvalue Spectrum for the k-photon JCM with k>2 --- p.73 / Chapter 5.2 --- Dynamics of the two-photon JCM --- p.75 / Chapter 5.2.1 --- Atomic Observables --- p.75 / Chapter 5.2.2 --- Field Observables --- p.77 / Chapter 5.3 --- Conclusion --- p.84 / Chapter Chapter 6. --- Intensity-dependent Jaynes-Cummings model --- p.107 / Chapter 6.1 --- Eigenstates and Eigenvalue Spectrum --- p.107 / Chapter 6.1.1 --- Energy Eigenstates and Eigenvalue Spectrum of the one- photon intensity-dependent JCM --- p.110 / Chapter 6.1.2 --- "Energy Eigenstates and Eigenvalue Spectrum for the k-photon intensity-dependent, JCM with k > 1" --- p.113 / Chapter 6.2 --- Dynamics of the one-photon intensity-dependent JCM --- p.115 / Chapter 6.2.1 --- Atomic Observables --- p.115 / Chapter 6.2.2 --- Field Observables --- p.116 / Chapter 6.3 --- Conclusion --- p.123 / Chapter Chapter 7. --- Two-mode Two-photon Jaynes- Cummings model --- p.148 / Chapter 7.1 --- Eigenstates and Eigenvalue Spectrum --- p.148 / Chapter 7.2 --- Dynamics of the System --- p.156 / Chapter 7.2.1 --- Atomic Observables --- p.156 / Chapter 7.2.2 --- Field Observables --- p.160 / Chapter 7.3 --- Conclusion --- p.161 / Chapter Chapter 8. --- Conclusion --- p.183 / Bibliography --- p.186

Weiyan Ge. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 64-68). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction of Power Control Problem --- p.2 / Chapter 1.1.1 --- Classification of Power Control Problem --- p.2 / Chapter 1.1.2 --- Previous Works --- p.7 / Chapter 1.2 --- Scope and Contribution of the Thesis --- p.11 / Chapter 1.3 --- Organization of the Thesis --- p.12 / Chapter 2 --- Background --- p.14 / Chapter 2.1 --- Stochastic Approximation --- p.14 / Chapter 2.2 --- Lognormal Distribution --- p.17 / Chapter 2.2.1 --- Definition and Properties --- p.17 / Chapter 2.2.2 --- Application on Radio Propagation --- p.18 / Chapter 3 --- System Model and Centralized Algorithm --- p.21 / Chapter 3.1 --- System Model --- p.21 / Chapter 3.2 --- Problem Statement and the Centralized Algorithm --- p.25 / Chapter 4 --- Proposed Stochastic Power Control Algorithm --- p.30 / Chapter 4.1 --- Proposed Power Control Algorithm --- p.30 / Chapter 4.2 --- Basic Properties of the Algorithm --- p.33 / Chapter 4.3 --- Convergence Property --- p.38 / Chapter 5 --- Numerical Results --- p.44 / Chapter 5.1 --- Simulation Model --- p.44 / Chapter 5.2 --- Numerical Results --- p.47 / Chapter 6 --- Conclusions And Future Works --- p.58 / Chapter 6.1 --- Conclusions --- p.58 / Chapter 6.2 --- Future Works --- p.60 / Chapter A --- Basic Properties of LOG-Distribution --- p.62 / Bibliography --- p.64

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / Ph.D.

Cette thèse s'articule autour de deux thématiques : les méthodes numériques pour la propagation d'ondes acoustiques sous écoulement et les méthodes de réduction de modèles. Dans la première thématique, nous développons une méthode de couplage d'éléments finis et d'éléments de frontière pour résoudre l'équation d'Helmholtz convectée, lorsque l'écoulement est uniforme à l'extérieur d'un domaine borné. En particulier, nous proposons une formulation bien posée à toutes les fréquences de la source. Dans la deuxième thématique, nous proposons une solution au problème classique d'accumulation d'arrondis machine qui survient en calculant l'estimateur d'erreur a posteriori dans la méthode des bases réduites. Par ailleurs, nous proposons une méthode non intrusive pour calculer une approximation sous forme séparée des systèmes linéaires résultant de l'approximation en dimension finie de problèmes aux limites dépendant d'un ou plusieurs paramètres / This thesis has two topics : numerical methods for acoustic wave propagation in a flow and reduced order models. In the first topic, we develop a coupled finite element and boundary element method to solve the convected Helmholtz equation, when the flow is uniform outside a bounded domain. In particular, we propose a formulation that is well-posed at all the frequencies of the source. In the second topic, we propose a solution to the classical problem of round-off error accumulation that occurs when computing the a posteriori error bound in the reduced basis method. Furthermore, we propose a non intrusive method for the approximation, in a separated representation form, of linear systems resulting from the finite-dimensional approximation of boundary-value problems depending on one or several parameters