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A theoretical investigation of the factors that affect the population dynamics of annual plants growing in deserts was conducted through the use of computer modeling techniques. A series of three models of the yearly life cycle of desert annuals was constructed and their behavior examined. The dissertation centers around the third and most complex model, a computer simulation model with distinguishable seed cohorts in a randomly varying rainfall environment. A typical simulation run was for 80 years and cost $1.00. The five plant functions were (l} seed losses (mainly predation) as a function of seed age, (2) seed dormancy as a function of seed ages (3) percent germination of the non-dormant seeds in response to germinating rainfall, (4) percent survival from the seedling stage to maturity as a function of total rainfall over the growing season and seedling density, and (5) seeds produced per p 1 ant as a function of total rainfall over the growing season and density of mature plants. The stochasitc rainfall generator used historical rainfall probabilities from US Weather Bureau stations at Las Vegas, Nevada and Tucson, Arizona. The literature on desert annuals was carefully searched to provide supporting data for the plant functions used in the simulation model. Most of the data is for winter annuals growing on the Nevada Test Site near Las Vegas. Single species data are rare, so the model functions reflected the average plant responses for winter annuals as a group. This base run set of functions reproduced the observed data quite well. Sensitivity analysis of the simulation model indicated that in order to persist in the Las Vegas area, the seeds of annuals should have at least a one-year period of dormancy and a minimum threshold of about 15 mm of germinating rainfall. The age distribution of the seed reserves in the soil and the percent germinable is strongly influenced by the recent rainfall history of the site and the seed loss rate. The optimum balance is when the losses of older seeds from the seed reserves due to germination is the same size as the sum of the non-productive losses (e.g., predation). Several experiments are suggested -- some to cover gaps in the published data and some that became evident through the sensitivity analysis of the model itself.

A simple stochastic game (SSG) is a game defined on a directed multigraph and played between players MAX and MIN. Both players have control over disjoint subsets of vertices: player MAX controls a subset VMAX and player MIN controls a subset VMIN of vertices. The remaining vertices fall into either VAVE, a subset of vertices that support stochastic transitions, or SINK, a subset of vertices that have zero outdegree and are associated with a payoff in the range [0, 1]. The game starts by placing a token on a designated start vertex. The token is moved from its current vertex position to a neighboring one according to certain rules. A fixed strategy σ of player MAX determines where to place the token when the token is at a vertex of VMAX. Likewise, a strategy τ of player MIN determines where to place the token when the token is at a vertex of VMIN. When the token is at a vertex of VAVE, the token is moved to a uniformly at random chosen neighbor. The game stops when the token arrives on a SINK vertex; at this point, player MAX gets the payoff associated with the SINK vertex. A fundamental question related to SSGs is the SSG value problem: Given a SSG G, is there a strategy of player MAX that gives him an expected payoff at least 1/2 regardless of the strategy of player MIN? This problem is among the rare natural combinatorial problems that belong to the class NP ∩ coNP but for which there is no known polynomial-time algorithm. In this thesis, we survey known algorithms for the SSG value problem and characterize them into four groups of algorithms: iterative approximation, strategy improvement, mathematical programming, and randomized algorithms. We obtain two new algorithmic results: Our first result is an improved worst-case, upper bound on the number of iterations required by the Homan-Karp strategy improvement algorithm. Our second result is a randomized Las Vegas strategy improvement algorithm whose expected running time is O(20:78n).

In case of a pandemic influenza outbreak, non-pharmaceutical interventions will likely be the only containment measure at the early stages of the pandemic when vaccines are not available. NPIs also oer an option for decreasing the probability of creating antiviral resistant viruses product of a mass prophylaxis campaign. In countries where there are not enough resources for vaccines and antivirals, NPIs may be the only mitigation actions available. NPIs have been increasingly used in preparedness plans. We can see recommendations and guidelines regarding the use of NPIs in countries, health departments and universities. Also, researchers all around the world have study the impact of NPI's in pandemic influenza outbreaks, most of them using simulation as their modeling tool. Our review of the aforementioned plans and literature shows that there is a lack of consensus in how to implement these interventions. They vary widely in the choice of key parameters such as intervention initiation threshold, duration and compliance. We believe that the lack of uniformity in NPI mitigation strategies arise from the uncertainty in the virus epidemiology and the current lack of scientic knowledge about the complex interactions between virus epidemiology with social behavioral factors and mitigation actions. In this dissertation we addressed this problem by modeling pandemic influenza outbreaks using an agent-based simulation approach. The model incorporates detailed popu- lation demographics and dynamics, variety of mixing groups and their contact processes, infection transmission process, and non-pharmaceutical interventions. Using a statistical experimental design approach we examine the influence of characteristic parameters of virus epidemiology, social behavior, and non-pharmaceutical interventions on various measures of pandemic impact such as total number of infections, deaths and contacts. The experimental design approach also yields the knowledge of the extent of interactions among the above parameters. Using this knowledge we develop eective NPI strategies and demonstrate the efficacy of these strategies on large-scale simulated outbreaks involving three dierent scenarios of virus transmissibility. The results show that signicant improvements in the NPI based pandemic mitigation approaches can be attained by the strategies derived from our methodology.

This research is motivated by our collaborations with a large French university teaching hospital in order to reduce the Length of Stay (LoS) of stroke patients treated in the neurovascular department. Quick diagnosis is critical for stroke patients but relies on expensive and heavily used imaging facilities such as MRI (Magnetic Resonance Imaging) scanners. Therefore, it is very important for the neurovascular department to reduce the patient LoS by reducing their waiting time of imaging examinations. From the neurovascular department perspective, this thesis proposes a new MRI examinations reservation process in order to reduce patient waiting times without degrading the utilization of MRI. The service provider, i.e., the imaging department, reserves each week a certain number of appropriately distributed contracted time slots (CTS) for the neurovascular department to ensure quick MRI examination of stroke patients. In addition to CTS, it is still possible for stroke patients to get MRI time slots through regular reservation (RTS). This thesis first proposes a stochastic programming model to simultaneously determine the contract decision, i.e., the number of CTS and its distribution, and the patient assignment policy to assign patients to either CTS or RTS. To solve this problem, structure properties of the optimal patient assignment policy for a given contract are proved by an average cost Markov decision process (MDP) approach. The contract is determined by a Monte Carlo approximation approach and then improved by local search. Computational experiments show that the proposed algorithms can efficiently solve the model. The new reservation process greatly reduces the average waiting time of stroke patients. At the same time, some CTS cannot be used for the lack of patients.To reduce the unused CTS, we further explore the possibility of the advance cancellation of CTS. Structure properties of optimal control policies for one-day and two-day advance cancellation are established separately via an average-cost MDP approach with appropriate modeling and advanced convexity concepts used in control of queueing systems. Computational experiments show that appropriate advance cancellations of CTS greatly reduce the unused CTS with nearly the same waiting times.

Cette thèse propose un nouveau processus de réservation d'examens IRM (Imagerie par Résonance Magnétique) afin de réduire les temps d’attente d’examens d'imagerie des patients atteint d'un AVC (Accident Vasculaire Cérébral) soignés dans une unité neurovasculaire. Le service d’imagerie réserve chaque semaine pour l'unité neurovasculaire un nombre donné de créneaux d'examens IRM appelés CTS afin d’assurer un diagnostic rapide aux patients. L'unité neurovasculaire garde la possibilité de réservations régulières appelées RTS pour pallier les variations des flux de patients.Nous donnons d'abord une formulation mathématique du problème d'optimisation pour déterminer le nombre et la répartition des créneaux CTS appelée contrat et une politique d'affectation des patients entre les créneaux CTS ou les réservations RTS. L'objectif est de trouver le meilleur compromis entre le délai d'examens et le nombre de créneaux CTS non utilisés. Pour un contrat donné, nous avons mis en évidence les propriétés et la forme des politiques d'affectation optimales à l'aide d'une approche de processus de décision markovien à coût moyen et coût actualisé. Le contrat est ensuite déterminé par une approche d'approximation Monté Carlo et amélioré par des recherches locales. Les expérimentations numériques montrent que la nouvelle méthode de réservation permet de réduire de manière importante les délais d'examens au prix des créneaux inutilisés.Afin de réduire le nombre de CTS inutilisé, nous explorons ensuite la possibilité d’annuler des créneaux CTS un ou deux jours en avance. Une approche de processus de décision markovien est de nouveau utilisée pour prouver les propriétés et la forme de la politique optimale d’annulation. Les expérimentations numériques montrent que l'annulation avancée des créneaux CTS permet de réduire de manière importante les créneaux CTS inutilisés avec une augmentation légère des délais d'attente. / This research is motivated by our collaborations with a large French university teaching hospital in order to reduce the Length of Stay (LoS) of stroke patients treated in the neurovascular department. Quick diagnosis is critical for stroke patients but relies on expensive and heavily used imaging facilities such as MRI (Magnetic Resonance Imaging) scanners. Therefore, it is very important for the neurovascular department to reduce the patient LoS by reducing their waiting time of imaging examinations. From the neurovascular department perspective, this thesis proposes a new MRI examinations reservation process in order to reduce patient waiting times without degrading the utilization of MRI. The service provider, i.e., the imaging department, reserves each week a certain number of appropriately distributed contracted time slots (CTS) for the neurovascular department to ensure quick MRI examination of stroke patients. In addition to CTS, it is still possible for stroke patients to get MRI time slots through regular reservation (RTS). This thesis first proposes a stochastic programming model to simultaneously determine the contract decision, i.e., the number of CTS and its distribution, and the patient assignment policy to assign patients to either CTS or RTS. To solve this problem, structure properties of the optimal patient assignment policy for a given contract are proved by an average cost Markov decision process (MDP) approach. The contract is determined by a Monte Carlo approximation approach and then improved by local search. Computational experiments show that the proposed algorithms can efficiently solve the model. The new reservation process greatly reduces the average waiting time of stroke patients. At the same time, some CTS cannot be used for the lack of patients.To reduce the unused CTS, we further explore the possibility of the advance cancellation of CTS. Structure properties of optimal control policies for one-day and two-day advance cancellation are established separately via an average-cost MDP approach with appropriate modeling and advanced convexity concepts used in control of queueing systems. Computational experiments show that appropriate advance cancellations of CTS greatly reduce the unused CTS with nearly the same waiting times.

On s’intéresse au problème de contrôle impulsionnel à horizon infini avec facteur d’oubli pour les processus de Markov déterministes par morceaux (PDMP). Dans un premier temps, on modélise l’évolution d’un système opto-électronique par des PDMP. Afin d’optimiser la maintenance du système, on met en place un problème de contrôle impulsionnel tenant compte à la fois du coût de maintenance et du coût lié à l’indisponibilité du matériel auprès du client.On applique ensuite une méthode d’approximation numérique de la fonction valeur associée au problème, faisant intervenir la quantification de PDMP. On discute alors de l’influence des paramètres sur le résultat obtenu. Dans un second temps, on prolonge l’étude théorique du problème de contrôle impulsionnel en construisant de manière explicite une famille de stratégies є-optimales. Cette construction se base sur l’itération d’un opérateur dit de simple-saut-ou-intervention associé au PDMP, dont l’idée repose sur le procédé utilisé par U.S. Gugerli pour la construction de temps d’arrêt є-optimaux. Néanmoins, déterminer la meilleure position après chaque intervention complique significativement la construction de telles stratégies et nécessite l’introduction d’un nouvel opérateur. L’originalité de la construction de stratégies є-optimales présentée ici est d’être explicite, au sens où elle ne nécessite pas la résolution préalable de problèmes complexes. / We are interested in a discounted impulse control problem with infinite horizon forpiecewise deterministic Markov processes (PDMPs). In the first part, we model the evolutionof an optronic system by PDMPs. To optimize the maintenance of this equipment, we study animpulse control problem where both maintenance costs and the unavailability cost for the clientare considered. We next apply a numerical method for the approximation of the value function associated with the impulse control problem, which relies on quantization of PDMPs. The influence of the parameters on the numerical results is discussed. In the second part, we extendthe theoretical study of the impulse control problem by explicitly building a family of є-optimalstrategies. This approach is based on the iteration of a single-jump-or-intervention operator associatedto the PDMP and relies on the theory for optimal stopping of a piecewise-deterministic Markov process by U.S. Gugerli. In the present situation, the main difficulty consists in approximating the best position after the interventions, which is done by introducing a new operator.The originality of the proposed approach is the construction of є-optimal strategies that areexplicit, since they do not require preliminary resolutions of complex problems.

The work is devoted to the analytic construction of solvability sets (the maximal stable bridges) in two examples of antagonistic differential games. In the first example, the control system is described by the dynamics of simple motions. The sections of the solvability sets at given time are defined on the basis of the terminal set and sets restricting the players' controls by means of the algebraic sum and the geometric difference. In the proof, we construct optimal strategies of the players explicitly. In the second example, we consider the system with modified dynamics, in which the possibilities capabilities of the second player depend on the phase position of the system. The investigation is carried out by means of the characteristic system of the Hamilton–Jacobi–Isaacs equation. We found conditions on the parameters of the problem under which the boundary of the solvability set is smooth. For the remaining values of the parameters, we found a qualitative picture of the, which is similar to the solution in the first example and has a scattering line. The obtained results can be used as a basis for further analytical studies of differential games with the dependence of the players' possibilities on the phase position of the system as well as for the development of numerical methods for solving such problems. / Работа посвящена аналитическому построению множеств разрешимости (максимальных стабильных мостов) в двух примерах антагонистических дифференциальных игр. В первом примере управляемая система описывается динамикой простых движений. Сечения множеств разрешимости в заданный момент времени определяются на основе терминального множества и множеств, ограничивающих управления игроков, с помощью операций алгебраической суммы и геометрической разности. Доказательство проводится при помощи явного построения оптимальных стратегий игроков. Во втором примере рассматривается система с модифицированной динамикой, при которой возможности второго игрока зависят от фазового положения системы. Исследование проводится при помощи характеристической системы уравнения Гамильтона – Якоби – Айзекса. Выделены условия на параметры задачи, при которых граница множества разрешимости является гладкой. Для остальных значений параметров найдена качественная картина решения, которая аналогична решению в первом примере и обладает рассеивающей линией. Полученные результаты могут быть использованы как основа для дальнейших аналитических исследований дифференциальных игр с зависимостью возможностей игроков от фазового положения системы, а также для разработки численных методов решения таких задач.