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There is a need for the development of models that are able to account for discreteness in data, along with its time series properties and correlation. A review of the application of thinning operators to adapt the ARMA recursion to the integer-valued case is first discussed. A class of integer-valued ARMA (INARMA) models arises from this application. Our focus falls on INteger-valued AutoRegressive (INAR) type models. The INAR type models can be used in conjunction with existing model-based clustering techniques to cluster discrete valued time series data. This approach is then illustrated with the addition of autocorrelations. With the use of a finite mixture model, several existing techniques such as the selection of the number of clusters, estimation using expectation-maximization and model selection are applicable. The proposed model is then demonstrated on real data to illustrate its clustering applications. / Thesis / Master of Science (MSc)

In this thesis, we investigate the problem of fault tolerance in the framework of discrete-event systems (DES). We introduce our setting, and then provide a set of fault-tolerant definitions designed to capture different types of fault scenarios and to ensure that our system remains controllable and nonblocking in each scenario. This is a passive approach that relies upon inherent redundancy in the system being controlled, and focuses on the intermittent occurrence of faults. Our approach provides an easy method for users to add fault events to a system model and is based on user designed supervisors and verification. As synthesis algorithms have higher complexity than verification algorithms, our approach should be applicable to larger systems than existing active fault-recovery methods that are synthesis based. Also, modular supervisors are typically easier to understand and implement than the results of synthesis. Finally, our approach does not require expensive (in terms of algorithm complexity) fault diagnosers to work. Diagnosers are, however, required by existing methods to know when to switch to a recovery supervisor. As a result, the response time of diagnosers is not an issue for us. Our supervisors are designed to handle the original and the faulted system. In this thesis, we next present algorithms to verify these properties followed by complexity analyses and correctness proofs of the algorithms. Finally, examples are provided to illustrate our approach. In the above framework, permanent faults can be modelled, but the current method was onerous. To address this, we then introduce a new modeling approach for permanent faults that is easy to use, as well as a set of new permanent fault-tolerant definitions. These definitions are designed to capture several types of permanent fault scenarios and to ensure that our system remains controllable and nonblocking in each scenario. New definitions and scenarios were required as the previous ones were incompatible with the new permanent fault modeling approach. We then present algorithms to verify these properties followed by complexity analyses and correctness proofs of the algorithms. An example is then provided to illustrate our approach. Finally, we extend the above intermittent and permanent fault-tolerant approach to the timed DES setting. As before, we introduced new fault-tolerant properties and algorithms. We then provide complexity analyses and correctness proofs for the algorithms. An example is then provided to illustrate our approach. / Thesis / Doctor of Philosophy (PhD)

Water, a fundamental human right, impacts human health through its quantity (i.e., physical amount and ability to access it) and quality. Consumption of poor-quality water can lead to a variety of waterborne illnesses, often manifested as diarrhoea. Millions of individuals worldwide lack access to drinking water that is free from contaminants and is available and accessible when needed. In areas where water is not piped to homes, several physical, demographic, socio-economic and health factors affect access to potable water. These factors may also influence which water point an individual fetches water (i.e. their waterpoint choice) from in the presence of multiple alternative waterpoints. Through this study, effects of various physical, health, demographic and socio-economic factors on waterpoint choice were explored. This study, based on datasets from a rural Maasai community in Kenya, implements a multinomial logit model to explore effects of various physical (travel time and water quality), health (aggregate frequency of self-reported diarrhoea stratified by age groups), demographic (average household age, household population, number of children under 5, number of women between 8-45 years of age and ratio of household population to number of women between 8-45) and socio-economic factors (education and income) on waterpoint choice. Travel time to the most probable waterpoint as predicted by the model was compared with the travel time to a household’s chosen waterpoint. Both travel times were calculated using the least-resistance path function incorporating slope and landcover. Results from model optimization showed that combinations of travel time, average household age, diarrhoea among adult women, income, education and number of women between 8-45 years were significant contributors to the three waterpoint choice models. The expected travel time to the most probable waterpoint predicted by these models and actual travel time to chosen waterpoint fit well, showing that the models explain waterpoint choice well. / Thesis / Master of Public Health (MPH)

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Yes / Researchers have used the simulation technique to develop new networks and test, modify, and optimize existing ones. The scientific community has developed a wide range of network simulators to fulfil these objectives and facilitate this creative process. However, selecting a suitable simulator appropriate for a given purpose requires a comprehensive study of network simulators. The current literature on network simulators has limitations. Limited simulators have been included in the studies with functional and performance criteria appropriate for comparison not been considered, and a reasonable selection model for selecting the suitable simulator has not been presented. To overcome these limitations, we studied twenty-three existing network simulators with classifications, additional comparison parameters, system limitations, and comparisons using several criteria. / This work was supported by the Petroleum Technology Development Fund (PTDF) Nigeria with grant number PTDF/ED/PHD/MAS/179/17.

The integration of discrete mathematics into the secondary school curriculum (grades 7-12) is an important consideration because the mathematical area is dynamic and interesting, providing students the development of mathematical thinking. Also, it provides for teachers the opportunity to develop innovative mathematics instruction. Since the publication of the document Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), it has been difficult to determine how many schools have integrated discrete mathematics as a separate or as an integrated course in the school mathematics curriculum. Moreover, the mathematics education research community has, for the most part, not focused on teachers' perceptions about teaching and learning discrete mathematics as an area of investigation. Because of the lack of research in this area, the researcher investigated preservice secondary mathematics teachers' perceptions about discrete mathematics and their reactions to the integration of discrete mathematics into the school curriculum. The researcher purposely selected four preservice secondary teachers who were enrolled in a mathematics course in the fall of 2005. Various data sources were used to get a deep understanding of each participant, including selected coursework, an online survey, and interviews. Results indicated that these preservice teachers perceive discrete mathematics as meaningful to students, as it emphasizes processes such as problem solving and mathematical thinking, and it provides opportunities to use innovative instruction. Because of this, the preservice teachers believe that discrete mathematics should be integrated in the school mathematics curriculum. In addition, several factors that affect the integration of discrete mathematics in the school were identified. These factors are the state curriculum and testing, the historical emphasis of algebra and calculus in the school curriculum, the National Council of Teachers of Mathematics (1989, 2000) Standards documents' views of discrete mathematics, teachers' views of discrete mathematics, the lack of knowledge of discrete mathematics, and the lack of materials and guidelines for teaching discrete mathematics. / Ph. D.

The purpose of this research was to apply a discrete-bubble model to predict the performance of several hypolimnetic oxygenators. The model is used to predict the oxygen transfer rate in a hypolimnetic oxygenator based on the initial bubble size formed at the diffuser. The discrete-bubble model is based on fundamental principles, and therefore could also be applied to other mass transfer applications involving the injection of bubbles into a fluid. The discrete-bubble model has been applied to a linear bubble-plume diffuser, a full-lift hypolimnetic aerator and the Speece Cone with promising results. The first step in this research was to investigate the principals of bubble formation at a submerged orifice, bubble rise velocity and bubble mass transfer. The discrete-bubble model is then presented. The model traces a single bubble rising through a fluid, accounting for changes in bubble size due to mass transfer, temperature and hydrostatic pressure. The bubble rise velocity and mass transfer coefficients are given by empirical correlations that depend on the bubble size. Bubble size is therefore recalculated at every increment and the values for the bubble rise velocity and mass transfer coefficients are continually updated. The discrete-bubble model is verified by comparison to experimental data collected in large-scale oxygen transfer tests. Finally, the discrete-bubble model is applied to the three most common hypolimnetic oxygenation systems: the Speece Cone, the bubble-plume diffuser, and the full-lift hypolimnetic oxygenation systems. The latter being presented by Vickie Burris in her thesis, <i>Hypolimnetic Aerators: Predicting Oxygen Transfer and Water Flow Rate</i>. / Master of Science

Almost everything that we do involves a choice. In recent years there has been a growing interest in the development and application of quantitative statistical methods to study choices made by individuals with the purpose of gaining a better understanding of how choices are made and also to predict future choice responses. In many fields, the choices made by individuals will determine the effectiveness of policy. Understanding what drives people's choices and how these choices may change is critical for developing successful policy. Discrete choice modeling provides an analytical framework with which to analyze and predict how people's choices are influenced by their personal characteristics and by the different attributes of the alternatives available to them. In an ideal situation we would build discrete choice models using information from choices that people are observed to make, i.e., revealed preference (RP) information. From these data we can quantify the influence of particular variables in the real choice context; for example, how important is price in the decision to travel by train? There are, however, potential problems with these data. There might not be enough variation of the explanatory attributes; for example little price variation across alternatives. Furthermore, several attributes might be highly correlated e.g. price and quality. But the most important of all is the fact that it is not possible to observe choices for alternatives that do not yet exist; for example new programs and technologies. In cases where the data limits the information provided by real choices it may be appropriate to collect stated preference (SP) data, which is information on preferences provided from hypothetical choice situations. This dissertation provides several applications of discrete choice modeling using both raveled preferences and stated preference. Unlike the last two chapters which deal with the revealed preference, the first Chapter, uses stated preference data. This Chapter evaluates the impact of several attributes of monetary incentives on the decision of patients to participate in a new weight loss program. Since this program does not exist yet, revealed preference data were not available and stated preference data were collected. The attributes of interest in this study include magnitude, timing and form of payment. The goal is to see what level and what combination of these attributes provides greater impact on the reach of the program. We also account for preference heterogeneity by using a random parameter framework. Chapter 2 discusses another application of discrete choice models in event history models (also called survival analysis). In these type of models, the main goal is to use the history of happening an event to learn more about the effect of different factors on the probability of occurrence. The event of interest in our case is the birth. We use the birth history of rural women and try to model their decision to give birth over time. The ultimate goal is to evaluate the effect of health clinics and family planning program on this decision. The final Chapter considers the application of discrete choice modeling in an electoral framework. The 2005 presidential election in Iran is used to model the decisions of Iranian voters. Using this revealed preference data we try to learn more about the main factors evolved in both participation and in the candidate selection. / Ph. D.