Doctor of Philosophy / Department of Agricultural Economics / Nathan P. Hendricks / Risk averse farmers face a substantial challenge managing irrigation water when they face limited water availability. The two primary reasons for limited water availability in the High Plains Aquifer region of the United States are limited well capacity (i.e., the rate at which groundwater can be extracted) or a constraint imposed by a policy. In this dissertation, I study how risk averse farmers optimally manage limited water availability in the face of weather uncertainty and also the impact of limited water availability on farmer welfare. I use AquaCrop, a daily biophysical crop simulation model, to predict corn yield under alternative irrigation scenarios with historical weather. Since no simple functional form exists for the crop production function, I use discrete optimization and consider 234,256 potential irrigation strategies. I also account for risk preferences by using expected utility analysis to determine the optimal irrigation strategy. Using a daily biophysical model is important because water stress in a short period of the growing season can impact crop yield (even if average water availability throughout the growing season is sufficient) and well capacity is a constraint on daily water use. The daily biophysical crop simulation model accounts for the dynamic response of crop production to water availability. First, I examine how optimal irrigation strategies change due to limited water availability. I find that it is never optimal for irrigators to apply less than a particular minimum instantaneous rate per irrigated acre. An optimal required instantaneous rate implies that a farmer with a low well capacity focuses on adjustment at the extensive margin. On the other hand, farmers who initially have a high well capacity should adjust at the intensive margin in response to well capacity declining. I also find that total water use increases as the degree of risk aversion increases. More risk averse farmers increase water use by increasing irrigation intensity to reduce the variance in corn yields. Another important finding is that a higher well capacity could actually promote less water use because the higher well capacity allows a greater instantaneous rate of application that allows the farmer to decrease irrigation intensity while still maintaining or increasing corn yield. This finding may imply an accelerated rate of groundwater extraction when the groundwater depletion reaches a particular threshold. Second, I analyze the welfare loss due to limited water availability. The relationship between welfare loss and well capacity due to a policy constraint differs by soil type. I found the welfare loss from a water constraint policy does not always increase as well capacity increases. Farmers with very high well capacity may make small or no adjustment at the extensive margin due to a higher instantaneous rate and higher soil water holding capacity. However, that is not the case for a farmer with land that has lower soil water holding capacity as the increase in well capacity results in greater welfare loss. I also investigate the effect of risk averse behavior on the magnitude of welfare loss. I found that the welfare loss per unit of reduced water use is lower for the farmer with more risk aversion. Thus, economic models that ignore risk aversion misestimate the cost of reducing water use. Finally, I investigate the incentive for adopting drip irrigation and its effect on water use. I find that a decrease in well capacity increases the benefits of adopting drip irrigation but is not sufficient to overcome the high initial investment cost without government support. While subsidies of the magnitude offered by current U.S. programs are sufficient to induce drip irrigation adoption, I find that such subsidies have the unintended consequence of increasing total water use, particularly for small well capacities.

Motivated by primality and integer factorization, this thesis introduces generalizations of standard binary multiplication to commutative n-ary operations based upon geometric construction and representation. This class of operations are constructed to preserve commutativity and identity so that binary multiplication is included as a special case, in order to preserve relationships with ordinary multiplicative number theory. This leads to a study of their expression in terms of elementary symmetric polynomials, and connections are made to results from the theory of polyadic (n-ary) groups. Higher order operations yield wider factorization and representation possibilities which correspond to reductions in the set of primes as well as tiered notions of primality. This comes at the expense of familiar algebraic properties such as associativity, and unique factorization. Criteria for primality and a naive testing algorithm are given for the ternary arithmetic, drawing heavily upon modular arithmetic. Finally, connections with the theory of partitions of integers and quadratic forms are discussed in relation to questions about cardinality of primes.

This paper develops a data structure based on preimage sets of functions on a finite set. This structure, called the sigma matrix, is shown to be particularly well-suited for exploring the structural characteristics of recursive functions relevant to investigations of complexity. The matrix is easy to compute by hand, defined for any finite function, reflects intrinsic properties of its generating function, and the map taking functions to sigma matrices admits a simple polynomial-time algorithm . Finally, we develop a flexible measure of preimage complexity using the aforementioned matrix. This measure naturally partitions all functions on a finite set by characteristics inherent in each function's preimage structure.

Lunar soil, defined as the finest part of the lunar regolith which covers the entire surface of the Moon, has shown to have remarkable shear strength properties, highlighted by the clearly visible effects of soil cohesion. The main objective of this thesis is to unveil the physical explanations causing this unusual soil behaviour in a waterless, airless, lunar environment. Ultra-High Vacuum (UHV), in particular, is considered responsible for increasing the strength of surface energy forces due to lunar soil outgassing. In turn, the presence of surface energy forces, arising from van der Waals intermolecular forces, is thought to alter the mechanical properties of lunar soil. A particle-based microscopic approach by means of the Discrete Element Method (DEM) was utilised to investigate the effects of surface energy forces on the macroscopic soil be- haviour. A micro-mechanical contact model, based on the JKR theory, was selected to describe the inter-granular behaviour between lunar soil particles. Physical and geometrical parameters typical of lunar soil were employed. Several triaxial tests were run to identify a link, if any, between the microscopic surface energy parameter and the macroscopic soil cohesion, which was interpreted as a true soil cohesion. In addition, very low stress levels and high soil densities were simulated in order to take into account the low gravitational field and the high state of soil compaction caused by continuous meteorite impacts on the Moon. Results from triaxial tests were analysed at both the peak and critical state. It was found that in the ideal case of perfectly spherical grains, the presence of adhesion is a source of noticeable macroscopic soil cohesion. However, no influence was observed in terms of macroscopic friction angle. Furthermore, a brittle macroscopic soil behaviour was revealed, owing to the simulated inter-granular chemical bonds and the very low stress conditions applied. Finally, similar to the behaviour of cemented sands, very little cohesion was recorded at the critical state. Subsequently, particle shape effects were investigated by complementing the numerical model with a simple form of inter-particle rolling resistance. Simulations were also run with non-convex grains of increasing geometrical complexity in order to simulate more realistically the irregular shapes of lunar soil grains. In both cases, the interplay of surface energy forces with particle shape effects resulted in even higher shear strength, with predictions similar to the estimates of shear strength for real lunar soil. Once again, the peak strength was dominated by macroscopic cohesion which, on the other hand, was hardly observable at the critical state, confirming the tendency observed from spherical grains. Finally, the practical implications of the above findings were discussed in terms of bearing capacity, trafficability and slope stability on the lunar surface. In particular an analytical approach, based on the bearing capacity problem, was devised to study the performance of a rigid wheel rotating on a lunar terrain and operating under different dynamic conditions.

This thesis deals with solving a real case from one specific part of Operations Research -- Discrete Models. The case can be classified as Vehicle Routing Problem (VRP) which is a subset of classical Travelling Salesman Problem (TSP). The VRP is modified TSP when requirements of customers and capacities of trucks play role. The data needed for calculations were taken from the real situation of Pivovar Svijany a.s. The problem can be defined as VRP with cars with different capacities and split delivery. Even though the mathematic model of the problem is known and described in the thesis, the size of the problem is too big to be optimized. Therefore heuristic was used to solve it. Because of the good computational results in the past the savings algorithm was chosen. Its model was set using Visual Basic for Applications (VBA). The thesis (among others) analyses the sensitivity of the output on the values of the factors that can be chosen by the analyst. At the end of the thesis the best found solution is presented and the initial and the new scheme of the circles are compared.

La fragmentation des matériaux est un phénomène qui entre en jeu dans de nombreux systèmes naturels et industriels, et à différentes échelles. D'un point de vue industriel, la fragmentation est d'une grande importance dans la production de granulats de carrière, qui sont soumis à des critères stricts en termes de tailles et de formes. Néanmoins, les phénomènes à l'origine de la fracture des matériaux restent encore aujourd'hui mal maîtrisés. Les méthodes aux éléments discrets permettent une modélisation des interactions à l'échelle de la microstructure du matériau. Un des avantages de ces méthodes est que la fissure apparaît et se propage dans l'empilement de manière naturelle, sans qu'il soit nécessaire de la décrire par modèles de fissuration.Un modèle aux éléments discrets permettant de représenter la cohésion au sein d'un matériau composé de particules de formes quelconques a été développé durant cette thèse. Des simulations numériques ont été effectuées pour deux types d'empilements représentant soit des matériaux cimentés, soit des matériaux “pleins”. Les résultats obtenus ont permis de confirmer que ce modèle est capable de reproduire le comportement macroscopique de la rupture de matériau fragile. Le modèle a été ensuite appliqué à l'étude de l'influence du positionnement de points de contact externes sur la résistance d'une particule cylindrique. Une étude expérimentale d'impact a été menée et a permis de confirmer ces résultats. Enfin, nous avons appliqué notre approche à la reconstruction de grains issus de données tomographiques. / The fragmentation of materials is a phenomenon which arises in several natural and industrial systems, and for a wide range of scales. From an industrial point of view, the crushing process is very important in the production of aggregates, which are often required to meet high criteria in terms of size and shape. However, the phenomena behind fracture of materials are still not completely understood. The discrete element methods allow to model interactions at the scale of the material micro-structure, by means of simple models. One of the advantages of this kind of methods is the natural way the crack initiates and propagates in the sample, without any need of a crack model. A discrete element model allowing to describe cohesion inside the material composed of particles of arbitrary shapes has been developed in this work. Numerical simulations have been conducted for two kinds of samples describing both cemented and plain materials. The results obtained have shown the ability of the numerical model to reproduce the macroscopic behavior of the fracture of a brittle material. The developed model has been applied to study the influence of the positioning of external contact points on the effective strength of a cylindrical shaped grain. The results have demonstrated an increase of the required force to break the grain depending on the position of the contacts. An experimental study has confirmed the numerical results. Finally, the model has been applied to the building of grains based on tomographic data.

Dans cette thèse, nous nous intéressons à la reconnaissance des primitives discrètes multi-échelles. Nous considérons qu'une primitive discrète multi-échelles est une superposition de primitives discrètes de différentes échelles ; et nous proposons des approches qui permettent de déterminer les caractéristiques d'une primitive discrète ou d'une partie d'une primitive discrète.Nous proposons une nouvelle approche de reconnaissance de sous-segment discret qui se base sur des propriétés portant sur l'ordre des restes arithmétiques de la droite discrète. Nous établissons des liens entre les points d'appuis du sous-segment discret et les points ayant des restes arithmétiques minimaux et maximaux sur la droite discrète. D'après les résultats de nos comparaisons, cette approche se relève être plus efficace que des approches existantes.Nous nous intéressons ensuite à des approches de reconnaissance d'arcs et de cercles discrets par le centre généralisé. Nous étudions le dual de la médiatrice généralisée et proposons de calculer le centre généralisé par des calculs de visibilité dans l'espace dual afin de réduire son temps de calcul. Cette approche est valide aussi bien dans une grille régulière que dans une grille irrégulière isothétique.Finalement, nous nous intéressons à des approches de reconnaissance de droite discrète par la préimage généralisée. Nous utilisons la notion de frontière afin de diminuer le nombre d'éléments rentrant dans le calcul de la préimage généralisée ; ce qui simplifie le calcul et réduit le temps de calcul. Cette approche s'applique aussi dans une grille régulière comme dans une grille irrégulière isothétique. / This thesis is about discrete geometry and particularly recognition of multi-scale discrete primitives. We consider that a multiscale discrete primitive is a superimposition of many discrete primitives of different scales. Then we propose approaches of recognition of discrete primitives or parts of a discrete primitives.Firstly we propose a new approach for the recognition of digital subsegment that is based on properties of the sequence of arithmetic remainders of the digital straight line. We show there are sorne links between the leaning points of the digital subsegment and the points that have the minimal and maximal arithmetic remainders on the digital straight line. Based on the results of comparisons with others approaches, the approach seems more efficient. Secondly we present sorne work on improving digital rings and circles recognition by general circumcenter. We use the dual of the generalized bissector in order to simplify the computation of the intersections of generalized bissectors as a polygon stabbing problem. The dual of the generalized bissector is computed likely for pixels of a regular grid or paves of an irregular isothetic grid. Finaly we present some work on improving digital straight line recogrutlon by generalized preimage. To reduce the number of elements to take into account for the computation of the generalized preimage we introduce the concept of boundary. The approach based on boundary could be used in a regular grid or an irregular isothetic grid.

Healthcare industry in United States of America is facing a big paradox. Although US is a leader in the industry of medical devices, medical practices and medical researches, however there isnt enough satisfaction and quality in performance of US healthcare operations. Despite the big investments and budgets associated with US healthcare, there are big threats to US healthcare operational side, that reduces the quality of care. In this research study, a step by step Systems Engineering approach is applied to improve healthcare delivery process in an Emergency Department of a hospital located in Indianapolis, Indiana. In this study, different type of systems engineering tools and techniques are used to improve the quality of care and patients satisfaction in ED of Eskenazi hospital. Having a simulation model will help to have a better understanding of the ED process and learn more about the bottlenecks of the process. Simulation model is verified and validated using different techniques like applying extreme and moderate conditions and comparing model results with historical data. 4 different what if scenarios are proposed and tested to find out about possible LOS improvements. Additionally, those scenarios are tested in both regular and an increased patient arrival rate. The optimal selected what-if scenario can reduce the LOS by 37 minutes compared to current ED setting. Additionally, by increasing the patient arrival rate patients may stay in the ED up to 6 hours. However, with the proposed ED setting, patients will only spend an additional 106 minutes compared to the regular patient arrival rate.<br>

Thesis advisor: Frank Gollop / My doctoral dissertation consists of three essays in the field of Industrial Organization. The first two consider exclusive dealing contracts between upstream and downstream firms theoretically, while the third measures consumer substitution among geographically differentiated air travel products empirically. In the first chapter I study the ability of an incumbent seller to use exclusive dealing contracts to foreclose efficient entry when there are n downstream buyers, where n can be viewed as a measure of the degree of downstream competition. The effect of downstream competition on the ability of the upstream incumbent to use exclusive contracts anticompetitively depends on whether upstream firms compete over linear or two-part prices. The model also highlights an interesting effect of the sunk cost of upstream entry that is ignored in models with exactly two buyers. In the second chapter I investigate the ability of an incumbent monopolist to exclude a potential entrant via exclusive dealing contracts when these contracts include an agreement over price. I find that a simple entry game yields both exclusionary and entry equilibria. The exclusionary equilibrium is unique, however, under most reasonable assumptions; for example if buyers are downstream competitors, if entry or the marginal cost of the potential entrant are uncertain, or if the incumbent can commit not to compete for unsigned buyers. When buyers compete with one another downstream, the optimal guaranteed price is above (below) the marginal cost of the incumbent when downstream buyers compete over strategic complements (substitutes). In the third and final chapter (co-authored with Kyle Buika) I study the question of geographic market definition in the US airline industry. Though an accurate definition of an economic market is important for any study of industry, there is no rule governing what exactly constitutes a market. To define a market we must ask the question "between which products do consumers substitute,'' knowing that the answer to this question will depend on how "close'' products are to one another in product space, as well as how close they are to one another, and to consumers, in geographic space. We estimate a discrete choice model of air travel demand that uses known information about the locations of products and consumers, which allows us to study substitution patterns among air travel products at different airports. We evaluate the commonly used city-pair and airport-pair definitions of a market for air travel, and conclude that a city-pair is the appropriate definition. We also employ the Hypothetical Monopolist test for antitrust market definition, as defined by the Department of Justice and Federal Trade Commission, and conclude that the relevant geographic market for antitrust analysis is, according to this test, frequently more narrowly defined as an airport-pair. Finally we conduct merger simulations under different market definitions and compare the results to those obtained using our own results, and conclude that accounting for geography is important when studying mergers. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

Thesis advisor: Arthur Lewbel / The thesis includes two essays. The first essay, Inequality Moments in Estimation of Discrete Games with Incomplete Information and Multiple Equilibria, develops a method for estimation of static discrete games with incomplete information, which delivers consistent estimates of parameters even when games have multiple equilibria. Every Bayes-Nash equilibrium in a discrete game of incomplete information is associated with a set of choice probabilities. I use maximum and minimum equilibrium choice probabilities as upper and lower bounds on empirical choice probabilities to construct moment inequalities. In general, estimation with moment inequalities results in partial identification. I show that point identification is achievable if the payoffs are functions of a sufficient number of explanatory variables with a real line domain and outcome-specific coefficients associated with them. The second essay, Tenancy Rent Control and Credible Commitment in Maintenance, co-authored with Richard Arnott, investigates the effect of tenancy rent control on maintenance and welfare. Under tenancy rent control, rents are regulated within a tenancy but not between tenancies. The essay analyzes the effects of tenancy rent control on housing quality, maintenance, and rehabilitation. Since the discounted revenue received over a fixed-duration tenancy depends only on the starting rent, intuitively the landlord has an incentive to spruce up the unit between tenancies in order to show it well, but little incentive to maintain the unit well during the tenancy. The essay formalizes this intuition, and presents numerical examples illustrating the efficiency loss from this effect. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.