published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

The process of soft tissue injury repair at the cellular lew I can be decomposed into three phases: acute inflammation including coagulation, proliferation and remodelling. While the later phases are well understood the early phase is less so. We produce a series of new mathematical models for the early phases coagulation and inflammation. The models produced are relevant not only to soft tissue injury repair but also to the many disease states in which coagulation and inflammation play a role. The coagulation cascade and the subsequent formation of the enzyme thrombin are central to the creation of blood clots. By focusing on a subset of reactions that occur within the coagulation cascade, we develop a model that exhibits a rich asymptotic structure. Using singular perturbation theory we produce a sequence of simpler time-dependent model which enable us to elucidate the physical mechanisms that underlie the cascade and the formation of thrombin. There is considerable interest in identifying new therapeutic targets within the coagulation cascade, as current drugs for treating pathological coagulation (thrombosis) target multiple factors and cause the unwelcome side effect of excessive bleeding. Factor XI is thought to be a potential therapeutic target, as it is implicated in pathological coagulation but not in haemostasis (the stopping of bleeding), but its mechanism of activation is controversial. By extending our previous model of the coagulation cascade to include the whole cascade (albeit in a simplistic way) we use numerical methods to simulate experimental data of the coagulation cascade under normal as well as specific-factor-deficient conditions. We then provide simulations supporting the hypothesis that thrombin activates factor XI. The interest in inflammation is now increasing due to it being implicated in such diverse conditions as Alzmeimer's disease, cancer and heart disease. Inflammation can either resolve or settle into a self-perpetuating condition which in the context of soft tissue repair is termed chronic inflammation. Inflammation has traditionally been thought gradualIy to subside but new biological interest centres on the anti-inflammatory processes (relating to macrophages) that are thought to promote resolution and the pro-inflammatory role that neutrophils can provide by causing damage to healthy tissue. We develop a new ordinary differential equation model of the inflammatory process that accounts for populations of neutrophils and macrophages. We use numerical techniques and bifurcation theory to characterise and elucidate the physiological mechanisms that are dominant during the inflammatory phase and the roles they play in the healing process. There is therapeutic interest in modifying the rate of neutrophil apoptosis but we find that increased apoptosis is dependent on macrophage removal to be anti-inflammatory. We develop a simplified version of the model of inflammation reducing a system of nine ordinary equations to six while retaining the physical processes of neutrophil apoptosis and macrophage driven anti-inflammatory mechanisms. The simplified model reproduces the key outcomes that we relate to resolution or chronic inflammation. We then present preliminary work on the inclusion of the spatial effects of chemotaxis and diffusion.

This thesis seeks to identify factors affecting the probability of selection of a Surface Warfare Officer (SWO) to Executive Officer (XO) in the U.S. Navy. Selections to XO are made by a board that meets annually. Because a candidate is considered for selection in up to three consecutive boards, the possible outcomes in this process are selection to XO in one of three annual boards, failure to be selected to XO in the third board, or attrition from the process between boards. Using data on the board's selections over a three-year period (2002-2004) a hazards-based logistic regression model is developed to estimate the probabilities associated with a candidate's disposition based on his or her career profile. The model confirms that a candidate's recent fitness and evaluation report (FITREP) is the single-most-important factor affecting selection. Additionally, officers who have completed a tour in Washington D.C. or at the Bureau of Naval Personnel have higher probabilities of selection than do those who have completed other shore tours. But when an officer receives a poor FITREP, the probability of selection is low, regardless of other factors. A nonparametric statistical analysis is used to confirm these findings.

How do infants segment objects from the complex visual environment? Investigations of figure-ground perception have been dominated by studies assessing infants' sensitivity to depth and figure cues; few studies have assessed what information infants' use to perceive figures as separate from grounds. Research examining word segmentation suggests that statistical learning might aid segmentation in visual scenes. Despite the numerous studies investigating figure-ground segmentation, none have investigated the role of spatial transitional probabilities as a means for segmentation. To examine this question, we used a habituation/familiarity-preference procedure to assess whether background variability enables 5.5-month-old infants' perception of figures as separate from the background. The results of Experiments 1 and 2 indicated that statistical learning extends to scene segmentation, scene contexts allowed extraction of statistical distribution. Experiment 3 demonstrated that matching the configuration of visual arrays during training and test is essential; mismatched stimuli impede the measurement of segmentation.

Learning to comply with parental commands and requests is an important developmental achievement during toddlerhood. Although more responsive parenting often is associated with increases in children's compliance during the toddler years, the role of mothers' and toddlers' language abilities on change in compliance has largely been ignored. The current study addressed this gap using a sample of low-income, primarily African American mothers and toddlers (N = 55). Two models examining the role of receptive vocabulary were evaluated. First, mothers with higher receptive vocabulary scores were hypothesized to display more warm responsive communication in a teaching situation, which would be related to higher children's receptive vocabulary scores, and increased child compliance from age 2 to 3. Conversely, mothers with lower receptive vocabulary scores were expected to use more hostile intrusive communication, or communication patterns that would predict lower receptive vocabulary scores in children and increases in noncompliance over the third year. While direct associations were supported linking mothers' communication style with mothers' receptive vocabulary and change in compliance and noncompliance from age 2 to age 3, mediational hypotheses were not supported. The results of this study, while limited by small sample size, indicate that mothers' use of warm responsive or hostile intrusive communication in teaching situations affects their toddlers' development of compliance and noncompliance during the third year of life.

A research report submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfillment of the requirements for the degree of Master of' Science. / This research report describes the use or the Pearl's algorithm in Bayesian belief networks to induce a belief network from a database. With a solid grounding in probability theory, the Pearl algorithm allows belief updating by propagating likelihoods of leaf nodes (variables) and the prior probabilities. The Pearl algorithm was originally developed for binary variables and a generalization to more states is investigated. The data 'Used to test this new method, in a Portfolio Management context, are the Return and various attributes of companies listed on the Johannesburg Stock Exchange ( JSE ). The results of this model is then compared to a linear regression model. The bayesian method is found to perform better than a linear regression approach. / Andrew Chakane 2018

In this paper we present a simple combinatorial approach for the derivation of zero avoiding transition probabilities in a Markovian r- node series Jackson network. The method we propose offers two advantages: first, it is conceptually simple because it is based on transition counts between the nodes and does not require a tensor representation of the network. Second, the method provides us with a very efficient technique for numerical computation of zero avoiding transition probabilities. / Series: Forschungsberichte / Institut für Statistik

Counting lattice paths where the number of occurrences of a given pattern is monitored requires a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of ! and " steps determine the recursion formula. In the case of ballot paths, that is paths the stay weakly above the line y = x, the solutions to the recursions are typically polynomial sequences. The objects of Finite Operator Calculus are polynomial sequences, thus the theory can be used to solve the recursions. The theory of Finite Operator Calculus is strengthened and extended to the multivariate setting in order to obtain solutions, and to prepare for future applications. / by Shaun Sullivan. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

Wai-shing Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 114). / Abstracts in English and Chinese. / Contents --- p.i / List of Figures --- p.iv / List of Tables --- p.v / Abstract --- p.vi / Acknowledgement --- p.vii / Chapter Chapter 1. --- Layout of the thesis --- p.1 / Chapter Chapter 2. --- Introduction --- p.3 / Chapter 2.1 --- What is the reasoning problem? --- p.3 / Chapter 2.2 --- Fundamental nature of Knowledge --- p.4 / Chapter 2.3 --- Fundamental methodology of Reasoning --- p.7 / Chapter 2.4 --- Our intended approach --- p.9 / Chapter Chapter 3. --- Probabilistic reasoning networks --- p.11 / Chapter 3.1 --- Overview --- p.11 / Chapter 3.2 --- Causality and influence diagrams --- p.11 / Chapter 3.3 --- Bayesian networks - influence diagrams endowed with a probability interpretation --- p.13 / Chapter 3.3.1 --- A detour to the interpretations of probability --- p.13 / Chapter 3.3.2 --- Bayesian networks --- p.15 / Chapter 3.3.3 --- Acyclicity and global probability --- p.17 / Chapter 3.4 --- Reasoning on probabilistic reasoning networks I - local updating formulae --- p.17 / Chapter 3.4.1 --- Rationale of the intended reasoning strategy --- p.18 / Chapter 3.4.2 --- Construction of the local updating formula --- p.19 / Chapter 3.5 --- Cluster graphs - another perspective to reasoning problems --- p.23 / Chapter 3.6 --- Semi-lattices - another representation of Cluster graphs --- p.26 / Chapter 3.6.1 --- Construction of semi-lattices --- p.26 / Chapter 3.7 --- Bayesian networks and semi-lattices --- p.28 / Chapter 3.7.1 --- Bayesian networks to acyclic semi-lattices --- p.29 / Chapter 3.8 --- Reasoning on (acyclic) probabilistic reasoning networks II - global updating schedules --- p.29 / Chapter 3.9 --- Conclusion --- p.30 / Chapter Chapter 4. --- Cyclic reasoning networks - a possibility? --- p.32 / Chapter 4.1 --- Overview --- p.32 / Chapter 4.2 --- A meaningful cyclic structure - derivation of the ideal gas law --- p.32 / Chapter 4.3 --- "What's ""wrong"" to be in a cyclic world" --- p.35 / Chapter 4.4 --- Communication - Dynamics - Complexity --- p.39 / Chapter 4.4.1 --- Communication as dynamics; dynamics to complexity --- p.42 / Chapter 4.5 --- Conclusion --- p.42 / Chapter Chapter 5. --- Cyclic reasoning networks ´ؤ error-control application --- p.43 / Chapter 5.1 --- Overview --- p.43 / Chapter 5.2 --- Communication schemes on cyclic reasoning networks directed to error-control applications --- p.43 / Chapter 5.2.1 --- Part I ´ؤ Local updating formulae --- p.44 / Chapter 5.2.2 --- Part II - Global updating schedules across the network --- p.46 / Chapter 5.3 --- Probabilistic reasoning based error-control schemes --- p.47 / Chapter 5.3.1 --- Local sub-universes and global universe underlying the error- control structure --- p.47 / Chapter 5.4 --- Error-control structure I --- p.48 / Chapter 5.4.1 --- Decoding algorithm - Communication between local sub- universes in compliance with the global topology --- p.51 / Chapter 5.4.2 --- Decoding rationales --- p.55 / Chapter 5.4.3 --- Computational results --- p.55 / Chapter 5.5 --- Error-control structure II --- p.57 / Chapter 5.5.1 --- Structure of the code and the corresponding decoding algorithm --- p.57 / Chapter 5.5.2 --- Computational results --- p.63 / Chapter 5.6 --- Error-control structure III --- p.66 / Chapter 5.6.1 --- Computational results --- p.70 / Chapter 5.7 --- Error-control structure IV --- p.71 / Chapter 5.7.1 --- Computational results --- p.73 / Chapter 5.8 --- Conclusion --- p.74 / Chapter Chapter 6. --- Dynamics on cyclic probabilistic reasoning networks --- p.75 / Chapter 6.1 --- Overview --- p.75 / Chapter 6.2 --- Decoding rationales --- p.76 / Chapter 6.3 --- Error-control structure I - exact solutions --- p.77 / Chapter 6.3.1 --- Dynamical invariant - a key to tackle many dynamical problems --- p.77 / Chapter 6.3.2 --- Dynamical invariant for error-control structure I --- p.78 / Chapter 6.3.3 --- Iteration dynamics --- p.79 / Chapter 6.3.4 --- Structure preserving property and the maximum a posteriori solutions --- p.86 / Chapter 6.4 --- Error-control structures III & IV - exact solutions --- p.92 / Chapter 6.4.1 --- Error-control structure III --- p.92 / Chapter 6.4.1.1 --- Dynamical invariants for error-control structure III --- p.92 / Chapter 6.4.1.2 --- Iteration dynamics --- p.93 / Chapter 6.4.2 --- Error-control structure IV --- p.96 / Chapter 6.4.3 --- Structure preserving property and the maximum a posteriori solutions --- p.98 / Chapter 6.5 --- Error-control structure II - exact solutions --- p.101 / Chapter 6.5.1 --- Iteration dynamics --- p.102 / Chapter 6.5.2 --- Structure preserving property and the maximum a posteriori solutions --- p.105 / Chapter 6.6 --- A comparison on the four error-control structures --- p.106 / Chapter 6.7 --- Conclusion --- p.108 / Chapter Chapter 7. --- Conclusion --- p.109 / Chapter 7.1 --- Our thesis --- p.109 / Chapter 7.2 --- Hind-sights and foresights --- p.110 / Chapter 7.3 --- Concluding remark --- p.111 / Appendix A. An alternative derivation of the local updating formula --- p.112 / Bibliography --- p.114