The past two decades have seen a surge in the number of applications requiring precise positioning data. Modern cellular networks offer many services based on the user's location, such as emergency services (e.g., E911), and emerging wireless sensor networks are being used in applications spanning environmental monitoring, precision agriculture, warehouse and manufacturing logistics, and traffic monitoring, just to name a few. In these sensor networks in particular, obtaining precise positioning data of the sensors gives vital context to the measurements being reported. While the Global Positioning System (GPS) has traditionally been used to obtain this positioning data, the deployment locations of these cellular and sensor networks in GPS-constrained environments (e.g., cities, indoors, etc.), along with the need for reliable positioning, requires a localization scheme that does not rely solely on GPS. This has lead to localization being performed entirely by the network infrastructure itself, or by the network infrastructure aided, in part, by GPS. In the literature, benchmarking localization performance in these networks has traditionally been done in a deterministic manner. That is, for a fixed setup of anchors (nodes with known location) and a target (a node with unknown location) a commonly used benchmark for localization error, such as the Cramer-Rao lower bound (CRLB), can be calculated for a given localization strategy, e.g., time-of-arrival (TOA), angle-of-arrival (AOA), etc. While this CRLB calculation provides excellent insight into expected localization performance, its traditional treatment as a deterministic value for a specific setup is limited. Rather than trying to gain insight into a specific setup, network designers are more often interested in aggregate localization error statistics within the network as a whole. Questions such as: "What percentage of the time is localization error less than x meters in the network?" are commonplace. In order to answer these types of questions, network designers often turn to simulations; however, these come with many drawbacks, such as lengthy execution times and the inability to provide fundamental insights due to their inherent ``block box'' nature. Thus, this dissertation presents the first analytical solution with which to answer these questions. By leveraging tools from stochastic geometry, anchor positions and potential target positions can be modeled by Poisson point processes (PPPs). This allows for the CRLB of position error to be characterized over all setups of anchor positions and potential target positions realizable within the network. This leads to a distribution of the CRLB, which can completely characterize localization error experienced by a target within the network, and can consequently be used to answer questions regarding network-wide localization performance. The particular CRLB distribution derived in this dissertation is for fourth-generation (4G) and fifth-generation (5G) sub-6GHz networks employing a TOA localization strategy. Recognizing the tremendous potential that stochastic geometry has in gaining new insight into localization, this dissertation continues by further exploring the union of these two fields. First, the concept of localizability, which is the probability that a mobile is able to obtain an unambiguous position estimate, is explored in a 5G, millimeter wave (mm-wave) framework. In this framework, unambiguous single-anchor localization is possible with either a line-of-sight (LOS) path between the anchor and mobile or, if blocked, then via at least two NLOS paths. Thus, for a single anchor-mobile pair in a 5G, mm-wave network, this dissertation derives the mobile's localizability over all environmental realizations this anchor-mobile pair is likely to experience in the network. This is done by: (1) utilizing the Boolean model from stochastic geometry, which statistically characterizes the random positions, sizes, and orientations of reflectors (e.g., buildings) in the environment, (2) considering the availability of first-order (i.e., single-bounce) reflections as well as the LOS path, and (3) considering the possibility that reflectors can either facilitate or block reflections. In addition to the derivation of the mobile's localizability, this analysis also reveals that unambiguous localization, via reflected NLOS signals exclusively, is a relatively small contributor to the mobile's overall localizability. Lastly, using this first-order reflection framework developed under the Boolean model, this dissertation then statistically characterizes the NLOS bias present on range measurements. This NLOS bias is a common phenomenon that arises when trying to measure the distance between two nodes via the time delay of a transmitted signal. If the LOS path is blocked, then the extra distance that the signal must travel to the receiver, in excess of the LOS path, is termed the NLOS bias. Due to the random nature of the propagation environment, the NLOS bias is a random variable, and as such, its distribution is sought. As before, assuming NLOS propagation is due to first-order reflections, and that reflectors can either facilitate or block reflections, the distribution of the path length (i.e., absolute time delay) of the first-arriving multipath component (MPC) is derived. This result is then used to obtain the first NLOS bias distribution in the localization literature that is based on the absolute delay of the first-arriving MPC for outdoor time-of-flight (TOF) range measurements. This distribution is shown to match exceptionally well with commonly assumed gamma and exponential NLOS bias models in the literature, which were only attained previously through heuristic or indirect methods. Finally, the flexibility of this analytical framework is utilized by further deriving the angle-of-arrival (AOA) distribution of the first-arriving MPC at the mobile. This distribution gives novel insight into how environmental obstacles affect the AOA and also represents the first AOA distribution, of any kind, derived under the Boolean model. In summary, this dissertation uses the analytical tools offered by stochastic geometry to gain new insights into localization metrics by performing analyses over the entire ensemble of infrastructure or environmental realizations that a target is likely to experience in a network. / Doctor of Philosophy / The past two decades have seen a surge in the number of applications requiring precise positioning data. Modern cellular networks offer many services based on the user's location, such as emergency services (e.g., E911), and emerging wireless sensor networks are being used in applications spanning environmental monitoring, precision agriculture, warehouse and manufacturing logistics, and traffic monitoring, just to name a few. In these sensor networks in particular, obtaining precise positioning data of the sensors gives vital context to the measurements being reported. While the Global Positioning System (GPS) has traditionally been used to obtain this positioning data, the deployment locations of these cellular and sensor networks in GPS-constrained environments (e.g., cities, indoors, etc.), along with the need for reliable positioning, requires a localization scheme that does not rely solely on GPS. This has lead to localization being performed entirely by the network infrastructure itself, or by the network infrastructure aided, in part, by GPS. When speaking in terms of localization, the network infrastructure consists of what are called anchors, which are simply nodes (points) with a known location. These can be base stations, WiFi access points, or designated sensor nodes, depending on the network. In trying to determine the position of a target (i.e., a user, or a mobile), various measurements can be made between this target and the anchor nodes in close proximity. These measurements are typically distance (range) measurements or angle (bearing) measurements. Localization algorithms then process these measurements to obtain an estimate of the target position. The performance of a given localization algorithm (i.e., estimator) is typically evaluated by examining the distance, in meters, between the position estimates it produces vs. the actual (true) target position. This is called the positioning error of the estimator. There are various benchmarks that bound the best (lowest) error that these algorithms can hope to achieve; however, these benchmarks depend on the particular setup of anchors and the target. The benchmark of localization error considered in this dissertation is the Cramer-Rao lower bound (CRLB). To determine how this benchmark of localization error behaves over the entire network, all of the various setups of anchors and the target that would arise in the network must be considered. Thus, this dissertation uses a field of statistics called stochastic geometry} to model all of these random placements of anchors and the target, which represent all the setups that can be experienced in the network. Under this model, the probability distribution of this localization error benchmark across the entirety of the network is then derived. This distribution allows network designers to examine localization performance in the network as a whole, rather than just for a specific setup, and allows one to obtain answers to questions such as: "What percentage of the time is localization error less than x meters in the network?" Next, this dissertation examines a concept called localizability, which is the probability that a target can obtain a unique position estimate. Oftentimes localization algorithms can produce position estimates that congregate around different potential target positions, and thus, it is important to know when algorithms will produce estimates that congregate around a unique (single) potential target position; hence the importance of localizability. In fifth generation (5G), millimeter wave (mm-wave) networks, only one anchor is needed to produce a unique target position estimate if the line-of-sight (LOS) path between the anchor and the target is unimpeded. If the LOS path is impeded, then a unique target position can still be obtained if two or more non-line-of-sight (NLOS) paths are available. Thus, over all possible environmental realizations likely to be experienced in the network by this single anchor-mobile pair, this dissertation derives the mobile's localizability, or in this case, the probability the LOS path or at least two NLOS paths are available. This is done by utilizing another analytical tool from stochastic geometry known as the Boolean model, which statistically characterizes the random positions, sizes, and orientations of reflectors (e.g., buildings) in the environment. Under this model, considering the availability of first-order (i.e., single-bounce) reflections as well as the LOS path, and considering the possibility that reflectors can either facilitate or block reflections, the mobile's localizability is derived. This result reveals the roles that the LOS path and the NLOS paths play in obtaining a unique position estimate of the target. Using this first-order reflection framework developed under the Boolean model, this dissertation then statistically characterizes the NLOS bias present on range measurements. This NLOS bias is a common phenomenon that arises when trying to measure the distance between two nodes via the time-of-flight (TOF) of a transmitted signal. If the LOS path is blocked, then the extra distance that the signal must travel to the receiver, in excess of the LOS path, is termed the NLOS bias. As before, assuming NLOS propagation is due to first-order reflections and that reflectors can either facilitate or block reflections, the distribution of the path length (i.e., absolute time delay) of the first-arriving multipath component (MPC) (or first-arriving ``reflection path'') is derived. This result is then used to obtain the first NLOS bias distribution in the localization literature that is based on the absolute delay of the first-arriving MPC for outdoor TOF range measurements. This distribution is shown to match exceptionally well with commonly assumed NLOS bias distributions in the literature, which were only attained previously through heuristic or indirect methods. Finally, the flexibility of this analytical framework is utilized by further deriving angle-of-arrival (AOA) distribution of the first-arriving MPC at the mobile. This distribution yields the probability that, for a specific angle, the first-arriving reflection path arrives at the mobile at this angle. This distribution gives novel insight into how environmental obstacles affect the AOA and also represents the first AOA distribution, of any kind, derived under the Boolean model. In summary, this dissertation uses the analytical tools offered by stochastic geometry to gain new insights into localization metrics by performing analyses over all of the possible infrastructure or environmental realizations that a target is likely to experience in a network.

Today's commercial rapid prototyping systems (i.e., solid freeform fabrication, layered manufacturing) rely on human intervention to load and unload build jobs. Hence, jobs are processed subject to both the machine's and the operator's schedules. In particular, first-in-first-out (FIFO) queuing of such systems will result in machine idle time whenever a build job has been completed and an operator is not available to unload that build job and start up the next one. These machine idle times can significantly affect the system throughput, and, hence, the effective cost rate. This thesis addresses this problem by rearranging the job queue to minimizing the machine idle time, subject to the machine's and operator's schedules. This is achieved by employing a general branch-and-bound search method, that, for efficiency, reduces the search space by identifying contiguous sequences and avoiding reshuffling of those sequences during the branching procedure. The effectiveness of this job scheduling optimization has been demonstrated using a sequence of 30 jobs extracted from the usage log for the FDM 1600 rapid prototyping system in the Department of Mechanical Engineering at Virginia Tech. / Master of Science

NP-hard problems of higher-dimensional orthogonal packing are considered. We look closer at their logical structure and show that they can be decomposed into problems of a smaller dimension with a special contiguous structure. This decomposition influences the modeling of the packing process, which results in three new solution approaches. Keeping this decomposition in mind, we model the smaller-dimensional problems in a single position-indexed formulation with non-overlapping inequalities serving as binding constraints. Thus, we come up with a new integer linear programming model, which we subject to polyhedral analysis. Furthermore, we establish general non-overlapping and density inequalities and prove under appropriate assumptions their facet-defining property for the convex hull of the integer solutions. Based on the proposed model and the strong inequalities, we develop a new branch-and-cut algorithm. Being a relaxation of the higher-dimensional problem, each of the smaller-dimensional problems is also relevant for different areas, e.g. for scheduling. To tackle any of these smaller-dimensional problems, we use a Gilmore-Gomory model, which is a Dantzig-Wolfe decomposition of the position-indexed formulation. In order to obtain a contiguous structure for the optimal solution, its basis matrix must have a consecutive 1's property. For construction of such matrices, we develop new branch-and-price algorithms which are distinguished by various strategies for the enumeration of partial solutions. We also prove some characteristics of partial solutions, which tighten the slave problem of column generation. For a nonlinear modeling of the higher-dimensional packing problems, we investigate state-of-the-art constraint programming approaches, modify them, and propose new dichotomy and intersection branching strategies. To tighten the constraint propagation, we introduce new pruning rules. For that, we apply 1D relaxation with intervals and forbidden pairs, an advanced bar relaxation, 2D slice relaxation, and 1D slice-bar relaxation with forbidden pairs. The new rules are based on the relaxation by the smaller-dimensional problems which, in turn, are replaced by a linear programming relaxation of the Gilmore-Gomory model. We conclude with a discussion of implementation issues and numerical studies of all proposed approaches. / Es werden NP-schwere höherdimensionale orthogonale Packungsprobleme betrachtet. Wir untersuchen ihre logische Struktur genauer und zeigen, dass sie sich in Probleme kleinerer Dimension mit einer speziellen Nachbarschaftsstruktur zerlegen lassen. Dies beeinflusst die Modellierung des Packungsprozesses, die ihreseits zu drei neuen Lösungsansätzen führt. Unter Beachtung dieser Zerlegung modellieren wir die Probleme kleinerer Dimension in einer einzigen positionsindizierten Formulierung mit Nichtüberlappungsungleichungen, die als Bindungsbedingungen dienen. Damit entwickeln wir ein neues Modell der ganzzahligen linearen Optimierung und unterziehen dies einer Polyederanalyse. Weiterhin geben wir allgemeine Nichtüberlappungs- und Dichtheitsungleichungen an und beweisen unter geeigneten Annahmen ihre facettendefinierende Eigenschaft für die konvexe Hülle der ganzzahligen Lösungen. Basierend auf dem vorgeschlagenen Modell und den starken Ungleichungen entwickeln wir einen neuen Branch-and-Cut-Algorithmus. Jedes Problem kleinerer Dimension ist eine Relaxation des höherdimensionalen Problems. Darüber hinaus besitzt es Anwendungen in verschiedenen Bereichen, wie zum Beispiel im Scheduling. Für die Behandlung der Probleme kleinerer Dimension setzen wir das Gilmore-Gomory-Modell ein, das eine Dantzig-Wolfe-Dekomposition der positionsindizierten Formulierung ist. Um eine Nachbarschaftsstruktur zu erhalten, muss die Basismatrix der optimalen Lösung die consecutive-1’s-Eigenschaft erfüllen. Für die Konstruktion solcher Matrizen entwickeln wir neue Branch-and-Price-Algorithmen, die sich durch Strategien zur Enumeration von partiellen Lösungen unterscheiden. Wir beweisen auch einige Charakteristiken von partiellen Lösungen, die das Hilfsproblem der Spaltengenerierung verschärfen. Für die nichtlineare Modellierung der höherdimensionalen Packungsprobleme untersuchen wir moderne Ansätze des Constraint Programming, modifizieren diese und schlagen neue Dichotomie- und Überschneidungsstrategien für die Verzweigung vor. Für die Verstärkung der Constraint Propagation stellen wir neue Ablehnungskriterien vor. Wir nutzen dabei 1D Relaxationen mit Intervallen und verbotenen Paaren, erweiterte Streifen-Relaxation, 2D Scheiben-Relaxation und 1D Scheiben-Streifen-Relaxation mit verbotenen Paaren. Alle vorgestellten Kriterien basieren auf Relaxationen durch Probleme kleinerer Dimension, die wir weiter durch die LP-Relaxation des Gilmore-Gomory-Modells abschwächen. Wir schließen mit Umsetzungsfragen und numerischen Experimenten aller vorgeschlagenen Ansätze.

NP-hard problems of higher-dimensional orthogonal packing are considered. We look closer at their logical structure and show that they can be decomposed into problems of a smaller dimension with a special contiguous structure. This decomposition influences the modeling of the packing process, which results in three new solution approaches. Keeping this decomposition in mind, we model the smaller-dimensional problems in a single position-indexed formulation with non-overlapping inequalities serving as binding constraints. Thus, we come up with a new integer linear programming model, which we subject to polyhedral analysis. Furthermore, we establish general non-overlapping and density inequalities and prove under appropriate assumptions their facet-defining property for the convex hull of the integer solutions. Based on the proposed model and the strong inequalities, we develop a new branch-and-cut algorithm. Being a relaxation of the higher-dimensional problem, each of the smaller-dimensional problems is also relevant for different areas, e.g. for scheduling. To tackle any of these smaller-dimensional problems, we use a Gilmore-Gomory model, which is a Dantzig-Wolfe decomposition of the position-indexed formulation. In order to obtain a contiguous structure for the optimal solution, its basis matrix must have a consecutive 1's property. For construction of such matrices, we develop new branch-and-price algorithms which are distinguished by various strategies for the enumeration of partial solutions. We also prove some characteristics of partial solutions, which tighten the slave problem of column generation. For a nonlinear modeling of the higher-dimensional packing problems, we investigate state-of-the-art constraint programming approaches, modify them, and propose new dichotomy and intersection branching strategies. To tighten the constraint propagation, we introduce new pruning rules. For that, we apply 1D relaxation with intervals and forbidden pairs, an advanced bar relaxation, 2D slice relaxation, and 1D slice-bar relaxation with forbidden pairs. The new rules are based on the relaxation by the smaller-dimensional problems which, in turn, are replaced by a linear programming relaxation of the Gilmore-Gomory model. We conclude with a discussion of implementation issues and numerical studies of all proposed approaches. / Es werden NP-schwere höherdimensionale orthogonale Packungsprobleme betrachtet. Wir untersuchen ihre logische Struktur genauer und zeigen, dass sie sich in Probleme kleinerer Dimension mit einer speziellen Nachbarschaftsstruktur zerlegen lassen. Dies beeinflusst die Modellierung des Packungsprozesses, die ihreseits zu drei neuen Lösungsansätzen führt. Unter Beachtung dieser Zerlegung modellieren wir die Probleme kleinerer Dimension in einer einzigen positionsindizierten Formulierung mit Nichtüberlappungsungleichungen, die als Bindungsbedingungen dienen. Damit entwickeln wir ein neues Modell der ganzzahligen linearen Optimierung und unterziehen dies einer Polyederanalyse. Weiterhin geben wir allgemeine Nichtüberlappungs- und Dichtheitsungleichungen an und beweisen unter geeigneten Annahmen ihre facettendefinierende Eigenschaft für die konvexe Hülle der ganzzahligen Lösungen. Basierend auf dem vorgeschlagenen Modell und den starken Ungleichungen entwickeln wir einen neuen Branch-and-Cut-Algorithmus. Jedes Problem kleinerer Dimension ist eine Relaxation des höherdimensionalen Problems. Darüber hinaus besitzt es Anwendungen in verschiedenen Bereichen, wie zum Beispiel im Scheduling. Für die Behandlung der Probleme kleinerer Dimension setzen wir das Gilmore-Gomory-Modell ein, das eine Dantzig-Wolfe-Dekomposition der positionsindizierten Formulierung ist. Um eine Nachbarschaftsstruktur zu erhalten, muss die Basismatrix der optimalen Lösung die consecutive-1’s-Eigenschaft erfüllen. Für die Konstruktion solcher Matrizen entwickeln wir neue Branch-and-Price-Algorithmen, die sich durch Strategien zur Enumeration von partiellen Lösungen unterscheiden. Wir beweisen auch einige Charakteristiken von partiellen Lösungen, die das Hilfsproblem der Spaltengenerierung verschärfen. Für die nichtlineare Modellierung der höherdimensionalen Packungsprobleme untersuchen wir moderne Ansätze des Constraint Programming, modifizieren diese und schlagen neue Dichotomie- und Überschneidungsstrategien für die Verzweigung vor. Für die Verstärkung der Constraint Propagation stellen wir neue Ablehnungskriterien vor. Wir nutzen dabei 1D Relaxationen mit Intervallen und verbotenen Paaren, erweiterte Streifen-Relaxation, 2D Scheiben-Relaxation und 1D Scheiben-Streifen-Relaxation mit verbotenen Paaren. Alle vorgestellten Kriterien basieren auf Relaxationen durch Probleme kleinerer Dimension, die wir weiter durch die LP-Relaxation des Gilmore-Gomory-Modells abschwächen. Wir schließen mit Umsetzungsfragen und numerischen Experimenten aller vorgeschlagenen Ansätze.

Wireless communications are important in our highly connected world. The amount of data being transferred in cellular networks is steadily growing, and consequently more capacity is needed. This thesis considers the problem of downlink capacity improvement from the perspective of multicell coordination. By employing multiple antennas at the transmitters and receivers of a multicell network, the inherent spatial selectivity of the users can be exploited in order to increase the capacity through linear precoding and receive filtering. For the coordination between cells, distributed algorithms are often sought due to their low implementation complexity and robustness. In this context, the thesis considers two problem domains: base station clustering and coordinated precoding. Base station clustering corresponds to grouping the cell base stations into disjoint clusters in order to reduce the coordination overhead. This is needed in intermediate-sized to large networks, where the overhead otherwise would be overwhelmingly high. Two solution methods for the clustering problem are proposed: an optimal centralized method, as well as a heuristic distributed method. The optimal method applies to a family of throughput models and exploits the structure of the model to find bounds that can be used to focus the search for the optimal clustering into promising territories. The distributed method instead uses notions from coalitional game theory, where the base stations are modelled as rational and intelligent players in a game. By letting the players make individual deviations that benefit them in the game, i.e.\@ switching clusters, a distributed coalition formation algorithm is obtained. Coordinated precoding is the act of finding the linear precoders and receive filters that maximize the network performance, given a base station clustering. Four specific challenges are studied in this problem domain. First, coordinated precoding under intercluster interference is considered. The channels of the intercluster links are not explicitly estimated due to overhead reasons, and these links thus lead to intercluster interference. By exploiting the known statistics of the intercluster channels, a robust and distributed coordinated precoding algorithm is developed. Second, coordinated precoding under imperfect channel state information is considered. Relying on the channel reciprocity under time-division duplex operation, a distributed estimation framework is proposed. Given the estimated channels, a robust and distributed coordinated precoding algorithm is then derived. Third, coordinated precoding under imperfect radio hardware is considered. By modelling the radio frequency distortion noises, a distributed coordinated precoding method that accounts for the imperfections is proposed. Fourth, joint coordinated precoding and discrete rate selection is considered. By bounding and linearizing an originally intractable optimization problem, a heuristic algorithm is derived which selects the transmit rate from a finite set and simultaneously forms the linear precoders and receive filters. / Trådlös kommunikation är ett viktigt verktyg i dagens ständigt uppkopplade värld. Datamängden som överförs i mobilnätverk ökar stadigt och därmed behovet av mer kapacitet. För att öka kapaciteten i nedlänken så utvecklar denna avhandling nya metoder för koordinering av multicellnätverk. Med flerantenniga sändare och mottagare så kan den spatiala selektiviteten hos mottagarna utnyttjas för att separera dem, vilket ger en ökad kapacitet. För denna koordinering är distribuerade algoritmer ofta att föredra eftersom de är robusta och har låg implementeringskomplexitet. I detta sammanhang undersöker denna avhandling två problemområden: basstationsgruppering och samordnad förkodning. Basstationsgruppering innebär att basstationerna delas in i disjunkta grupper, vilket minskar overheadkostnaden för samordningen. Detta är framför allt nödvändigt i medelstora till stora nätverk, eftersom overheadkostnaden för koordineringen av dessa annars skulle bli för stor. Två lösningar för basstationsgruppering presenteras: dels en optimal och centraliserad metod samt dels en heuristisk och distribuerad metod. Den optimala och centraliserade metoden kan hantera en familj av modeller för den totala datatakten och utnyttjar strukturen i modellen för att fokusera sökandet efter den optimala grupperingen mot lovande områden. Den heuristiska och distribuerade metoden bygger på spelteori för koalitioner och modellerar basstationerna som rationella och intelligenta spelare i ett spel. En distribuerad algoritm för koalitionsformering härleds genom att låta spelarna göra individuella förflyttningar, dvs. byta grupp, när det gynnar dem under spelets regler. Vid samordnad förkodning använder de flerantenniga sändarna och mottagarna linjära förkodare och mottagningsfilter för att maximera nätverkets prestanda. Inom detta problemområde undersöks fyra olika specifika problem. Först undersöks problemet när det finns störningar mellan basstationsgrupperna. För att hålla nere mängden overhead så skattas inte kanalerna mellan grupperna, vilket ger upphov till störningar hos mottagarna. Genom att utnyttja den kända statistiska informationen för dessa okända kanaler kan en robust och distribuerade samordningsmetod för förkodningen utvecklas. Därnäst undersöks problemet då kanalkännedomen är bristfällig i allmänhet. Reciprociteten som uppstår vid tidsdelningsduplexning utnyttjas och flera distribuerade skattningsmetoder härleds. Givet den skattade kanalkännedomen föreslås en robust metod för samordnad förkodning. Därnäst undersöks problemet med samordnad förkodning då radiohårdvaran är bristfällig. En modell för det distortionsbrus som skapas av den bristfälliga hårdvaran används för att föreslå en robust distribuerad metod för samordnad förkodning för detta scenario. Slutligen undersöks valet av diskret datatakt med simultan samordnad förkodning. En heuristisk algoritm utvecklas som löser ett begränsat optimeringsproblem. Algoritmen väljer sänddatatakten från en ändlig mängd och bestämmer simultant de linjära förkodarna och mottagningsfiltrena. / <p>QC 20160407</p>

This study investigates the promise of using therapeutic adventure as an alternative therapeutic approach to address a public health issue: Veterans reticence towards seeking mental health assistance, despite their rising rates of mental health issues. To examine how the intersection between conformity to traditional masculine norms and Outward Bound for Veterans (OB4V) programming impacted psychosocial development, a quasi-experimental, longitudinal design was implemented on 159 male Veterans. The primary goals were twofold: 1) to determine whether improvement in six therapeutic outcome variables occurred due to the OB4V intervention; 2) to discover whether male Veterans’ level of conformity to traditional masculine norms influenced change in the therapeutic outcome variables. Outcome variables included: 1) mental health status; 2) personal growth initiative; 3) attitudes towards seeking professional psychological help; 4) psychological mindedness; 5) restriction of emotions; 6) subjective wellbeing. Results indicated a significant effect of treatment, suggesting that the OB4V treatment promoted Veterans improvement in all the therapeutic outcome variables, except psychological mindedness. Findings also showed that the significant effect of treatment was associated with Veterans’ improvement in therapeutic outcome variables over all time points irrespective of their level of conformity to traditional masculine norms. / text

機率過程（Stochastic Process）是統計學應用的一個領域，而等候系統模型是機率 過程的一個特例。舉凡能適切劃分顧客及服務者的問題，都可用恰當的等候模型尋求 效益上最佳平衡。 對於M/G/r，GI/M/r及GI/G/r 模型，在分析上不易，且現實生活中，穩定（Stationa ry）及獨立（Independence）的假設均難完全符合，因此在這些假設下所導出的確切 模型（Explicit Model），應算是現實狀況的「概略」模型。對於既複雜又無確切結 果的上述模型，利用運作方便的近似值模型來替代，是本篇論文的主要目的。 全文共六章。第一章緒論；第二章等候理論的幾個基本觀念；第三章確切等候系統模 型，討論M/G/I及GI/M/1 模型，及所遭遇的困難；第四章近似值等候系統模型，討論 GI/G/I模型及由此發展出的近似值與上下界（Bound ）；第五章模擬印證；第六章結 論。

Depuis une vingtaine d'années, la résolution de problèmes d'optimisation globale non convexes avec contraintes a connu un formidable essor. Les algorithmes de branch and bound basée sur l'analyse d'intervalles ont su trouver leur place, car ils ont l'avantage de prouver l'optimalité de la solution de façon déterministe, avec un niveau de certitude pouvant aller jusqu'à la précision machine. Cependant, la complexité exponentielle en temps et en mémoire de ces algorithmes induit une limite intrinsèque, c'est pourquoi il est toujours nécessaire d'améliorer les techniques actuelles. - Dans cette thèse, nous avons développé de nouvelles arithmétiques basées sur l'arithmétique d'intervalles et l'arithmétique affine, afin de calculer des minorants et des majorants de meilleure qualité de fonctions explicites sur un intervalle. - Nous avons ensuite développé une nouvelle méthode automatique de construction de relaxations linéaires. Cette construction est basée sur l'arithmétique affine et procède par surcharge des opérateurs. Les programmes linéaires ainsi générés ont exactement le même nombre de variables et de contraintes d'inégalité que les problèmes originaux, les contraintes d'égalité étant remplacées par deux inégalités. Cette nouvelle procédure permet de calculer des minorants fiables et des certificats d'infaisabilité pour chaque sous-domaine à chaque itération de notre algorithme de branch and bound par intervalles. De nombreux tests numériques issus du site COCONUT viennent confirmer l'efficacité de cette approche. - Un autre aspect de cette thèse a été l'étude d'une extension de ce type d'algorithmes en introduisant une limite sur mémoire disponible. L'idée principale de cette approche est de proposer un processus inverse de l'optimisation par le biais d'un principe métaheuristique: plutôt que d'améliorer des solutions locales à l'aide de métaheuristiques telles que les algorithmes Taboo ou VNS, nous partons d'une méthode exacte et nous la modifions en une heuristique. De cette façon, la qualité de la solution trouvée peut être évaluée. Une étude de la complexité de ce principe métaheuristique a également été effectuée. - Enfin, pour finir l'étude, nous avons appliqué notre algorithme à la résolution de problème en géométrie plane, ainsi qu'à la résolution d'un problème de dimensionnement de moteur électrique. Les résultats obtenus ont permis de confirmer l'intérêt de ce type d'algorithme, en résolvant des problèmes ouverts sur les polygones convexes et proposant des structures innovantes en génie électrique.

文化公共財無法透過一般市場機制評估其價格，但應如何衡量其經濟價值？本研究以臺北市萬華區糖廍文化園區為案例，以條件評估法為理論模型，並以電話訪問、網路調查及面訪訪問等3種方式獲得1,612份問卷進行分析，結果顯示願付價格會隨著人口統計變量和民眾對文化資產保存的態度而有所不同，得到平均每人每次至少消費文化公共財之願付價格約247元，如以每人平均消費一次計算價值，在95%信賴區間下，臺北市萬華區糖廍公園週邊7里約1,094萬元、臺北市萬華區約4,788萬元、臺北市約6.7億元。在目前政府財政困窘情況下，如何將上開數據轉化成地方財源收入，有效將各古蹟或歷史建築充分活化再利用將是一個值得關注的議題。 / By using the contingent valuation method, this study estimates the value of the Tangbu Cultural Park in Taipei City as the value of cultural public goods cannot be directly observed through the markets. Based on 1,612 samples collected by the phone interview, on-site interview, and internet survey, we explore the factors that influence the willingness to pay (WTP) and estimate the resulting WTP on the cultural public goods. The empirical results show that the WTP are varied with the demographics and attitudes toward the cultural assets and the estimated average individual WTP per year is about 247 NTD. It turns out that the corresponding total WTP per year is 10.94 million NTD in the surrounding area of the Cultural Park, 47.88 million NTD in the Wanhua District of Taipei City, or 670 million NTD in Taipei City. The study can shed some light on the revival plans and budget arrangements of the cultural public goods.

This mixed methods study investigated the influence of a career development program attended by low income, first generation, college bound students. Phase I took place in 2006 and 2007 when the students participated in the Upward Bound summer Bridge program. During Phase II in 2009, follow up interviews were conducted. Phase III was completed in 2014 and also included follow-up interviews. Career Identity (CI) scores from My Vocational Situation and Holland codes from the Self Directed Search were obtained during each phase. Changes in measured career identity scores and codes were interpreted by taking into account the students’ experiences. Interviews examined common themes demonstrating the career development of the participants.