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Optimal experimental designs for generalized linear models have received increasing attention in recent years. Yet, most of the current research focuses on binary data models especially the one-variable first-order logistic regression model. This research extends this topic to count data models. The primary goal of this research is to develop efficient and robust experimental designs for the Poisson regression model in toxicity studies. D-optimal designs for both the one-toxicant second-order model and the two-toxicant interaction model are developed and their dependence upon the model parameters is investigated. Application of the D-optimal designs is very limited due to the fact that these optimal designs, in terms of ED levels, depend upon the unknown parameters. Thus, some practical designs like equally spaced designs and conditional D-optimal designs, which, in terms of ED levels, are independent of the parameters, are studied. It turns out that these practical designs are quite efficient when the design space is restricted. Designs found in terms of ED levels like D-optimal designs are not robust to parameters misspecification. To deal with this problem, sequential designs are proposed for Poisson regression models. Both fully sequential designs and two-stage designs are studied and they are found to be efficient and robust to parameter misspecification. For experiments that involve two or more toxicants, restrictions on the survival proportion lead to restricted design regions dependent on the unknown parameters. It is found that sequential designs perform very well under such restrictions. In most of this research, the log link is assumed to be the true link function for the model. However, in some applications, more than one link functions fit the data very well. To help identify the link function that generates the data, experimental designs for discrimination between two competing link functions are investigated. T-optimal designs for discrimination between the log link and other link functions such as the square root link and the identity link are developed. To relax the dependence of T-optimal designs on the model truth, sequential designs are studied, which are found to converge to T-optimal designs for large experiments. / Ph. D.

A mixture experiment is an experiment in which the q-ingredients {x_i,i=1,2,...,q} are nonnegative and ubject to the simplex restriction £Ux_i=1 on the (q-1)-dimensional probability simplex S^{q-1}. It is usually assumed that the observations are uncorrelated, although in many applications the observations are correlated. We study the difference between the ordinary least square estimator and the Gauss Markov estimator under correlated observations. It is shown that for certain models and a special covariance structure for the mixture experiments, the unknown parameter vector for the ordinary least square estimators and the Gauss Markov estimators are the same. Moreover, we also show that the corresponding optimal designs may be obtained from previous D- and A-optimal designs for uncorrelated observations. The models studied here includ Scheff'e models, log contrast models, models containing homogeneous functions, and models containing inverse terms.

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Tato diplomová práce se zabývá problematikou spojitého optimálního řízení, což je jedna z nejvýznamnějších aplikací teorie diferenciálních rovnic. Cílem této práce bylo jak nastudování matematické teorie optimálního řízení, tak především ukázat užití Pontrjaginova principu maxima a Bellmanova principu optimality při řešení vybraných úloh optimálního řízení. Důraz byl kladen především na problematiku časově a energeticky optimálního řízení elektrického vlaku, při zahrnutí kvadratické odporové funkce.

Recent works show that, by incorporating queue length information, CSMA/CA multiple access protocols can achieve maximum throughput in general ad-hoc wireless networks. In all of these protocols, the aggressiveness with which a link attempts to grab the channel is governed solely by its own queue, and is independent of the queues of other interfering links. While this independence allows for minimal control signaling, it results in schedules that change very slowly. This causes starvation and delays - especially at moderate to high loads. In this work we add a very small amount of signaling - an occasional few bits between interfering links. These bits allow us a new functionality: switching - a link can now turn off its interfering links with a certain probability. The challenge is ensuring maximum throughput and lower delay via the use of this new functionality. We develop a new protocol - Switch-enabled Queue-based CSMA (SQ-CSMA) - that uses switching to achieve both of these objectives. This simple additional functionality, and our protocol to leverage it, can be “added on'' to every existing CSMA/CA protocol that uses queue lengths. Interestingly, we see that in every case it has a significant positive impact on delay, universally furthering the performance of existing protocols. / text

The areas of machine learning, data mining, and knowledge representation have many different formats used to represent information. Decision rules, amongst these formats, are the most expressive and easily-understood by humans. In this thesis, we use dynamic programming to design decision rules and analyze them. The use of dynamic programming allows us to work with decision rules in ways that were previously only possible for brute force methods. Our algorithms allow us to describe the set of all rules for a given decision table. Further, we can perform multi-stage optimization by repeatedly reducing this set to only contain rules that are optimal with respect to selected criteria. One way that we apply this study is to generate small systems with short rules by simulating a greedy algorithm for the set cover problem. We also compare maximum path lengths (depth) of deterministic and non-deterministic decision trees (a non-deterministic decision tree is effectively a complete system of decision rules) with regards to Boolean functions. Another area of advancement is the presentation of algorithms for constructing Pareto optimal points for rules and rule systems. This allows us to study the existence of “totally optimal” decision rules (rules that are simultaneously optimal with regards to multiple criteria). We also utilize Pareto optimal points to compare and rate greedy heuristics with regards to two criteria at once. Another application of Pareto optimal points is the study of trade-offs between cost and uncertainty which allows us to find reasonable systems of decision rules that strike a balance between length and accuracy.

The majority of scholars’ work on code-switching within the sociolinguistic approach of Arabic has been mainly concentrated on the interaction of the Standard variety with other regional dialects in indigenous communities (Albirini, 2011; Bassiouney, 2006; Saeed, 1997; Soliman, 2008). Their work also extends to include the interaction of Arabic with other languages in informal and highly interactional settings (Abalhassan and Alshalawi, 2000; Safi, 1992; Sayahi, 2014). When it comes to the religious settings, their work has been solely devoted to Standard Arabic and Dialectal Arabic in Arabic countries and among Arabic native speakers (Albirini, 2011; Bassiouney, 2006; Saeed, 1997; Soliman, 2008). This thesis, in turn, investigates CS between Arabic and English in highly formal religious settings in the United States and among American Islamic preachers, non-native speakers of Arabic. It aims to enumerate the social functions of CS between English and Arabic and provides the internal optimal bilingual grammar of these speakers. To achieve these goals, two analyses have been conducted, the functional analysis and the optimality-theoretic analysis. The results of the first analysis revealed that preachers chiefly switch from English to Arabic for eight functions: (1) to use formulaic expressions; (2) to introduce direct quotations; (3) to show a level of education in the Islamic studies; (4) to show a level of education in the Arabic language; (5) to evoke Muslimness and Islamic affiliation; (6) to mark emphasis; (7) to stress the importance of a speech segment; and (8) to introduce rhyming stretches. On the other hand, they switch from Arabic to English mainly to fulfill two functions: (1) to translate the previous Arabic stretch; and (2) to simplify, explain, and clarify a segment that was previously mentioned in Arabic. The result of the optimality-theoretic analysis showed that the internal optimal bilingual grammar of American preachers is {FAITH, FACE} >> PERSPECTIVE >> {SOLIDARITY, POWER}.

This thesis deals with sequential and adaptive methods for clinical trials, and how such methods can be used to achieve efficient clinical trial designs. The efficiency gains that can be achieved through non-adaptive group sequential methods are well established, while the newer adaptive methods seek to combine the best of the classical group sequential framework with an approach that gives increased flexibility. Our results show that the adaptive methods can provide some additional efficiency, as well as increased possibilities to respond to new internal and external information. Care is however needed when applying adaptive methods. While sub-optimal rules for adaptation can lead to inefficiencies, the logistical challenges can also be considerable. Efficient non-adaptive group sequential designs are often easier to implement in practice, and have for the cases we have considered been quite competitive in terms of efficiency. The four problems that are presented in this thesis are very relevant to how clinical trials are run in practice. The solutions that we present are either new approaches to problems that have not previously been solved, or methods that are more efficient than the ones currently available in the literature. Several challenging optimisation problems are solved through numerical computations. The optimal designs that are achieved can be used to benchmark new methods proposed in this thesis as well as methods available in the statistical literature. The problem that is solved in Chapter 5 can be viewed as a natural extension to the other problems. It brings together methods that we have used to the design of individual trials, to solve the more complex problem of designing a sequence of trials that are the core part of a clinical development program. The expected utility that is maximised is motivated by how the development of new medicines works in practice.