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Harrington Sound, located in east central Bermuda, is almost entirely enclosed by land except for a 26.4 m wide channel called Flatts Inlet. This limited connection to the open ocean restricts Harrington Sound’s tides, resulting in a near 3 hour delay and dampening the tidal range to 35% of those on the coast. By comparing the tidal amplitude and surface area of Harrington Sound, tidal exchange can be determined. Past research has shown Flatts Inlet only supplies the Sound with about half of its tidal water. The remaining tidal exchange enters and leaves the Sound either via groundwater influx through pores in the rock or through the traversable passageways of limestone cave systems in the land that encloses the Sound. The aim of this study was to model hydrodynamic tidal flux and current through marine caves into Harrington Sound. One of the goals of Bermuda’s cave habitat protection plan is to track tidal circulation of water through these cave systems. Information on such cave water transport would facilitate future pollution and nutrient exchange studies. This research was initiated during a six week trip to Bermuda by Jonathan Stoffer as he obtained tidal and water quality data from caves along the perimeter of Harrington Sound. Additional flow data was collected with instruments placed by local cave divers. A YSI 600XLM water quality sonde, Norteck Vector Current Meter, and an in-situ level Aqua TROLL were used to monitor tidal amplitude, periodicity, current velocity, and water quality in cave pools and submerged passages. Profiles of the top 1-2 meters of water at each pool were taken at 56 sites. Tidal gauges were placed in 27 major cave pools surrounding Harrington Sound, as well as Harrington Sound itself, for 48 hours, to monitor tidal propagation through the island. The vector current meter was placed for six weeks to measure water flow in and out of Harrington Sound in six cave passageways known to have high flow rates. The resulting data have been compared to atmospheric data obtained from the Bermuda Weather Service and analyzed using Microsoft Excel, MATLAB and ArcGIS. The final goal of this project was to create a hydrological model able to predict flow rate and water depth in Bermudian caves with water depth data from the ocean and Harrington Sound. In constructing a water budget for Harrington Sound, I was able to account for 72.3% of all tidal inflow and 43.3% of all tidal outflow from the Sound as passing through either Flatt’s Inlet or one of the six tested caves. In creating my tidal models, I was able to achieve an averaged sum of squared deviation (SSD) normalized against count ranging from 5.1x10^-4 to 8.4x10^-4 m^2. The flow model achieved a SSD of 3.8x10^-3 m^2. My data also suggest that exchange between Harrington Sound and other inland waters, through cave systems, does exist.

The diffusion approximation to the equation of transfer (Boltzmann transport equation) is usually applied to media where scattering dominates the interactions. Diffusion approximation helps in significant savings in terms of code complexity and computational time. However, this approximation often has significant error. Error due to the inherent nature of a physics model is called model error. Information about the model error associated with the diffusion approximation is clearly desirable. An indirect measure of model error is a quantity that is related in some way to the error but not equal to the error. In general, indirect measures of error are expected to be less costly than direct measures. Perhaps the most well-known indirect measure of the diffusion model error is the variable-Eddington tensor. This tensor provides a great deal of information about the angular dependence of the angular intensity solution, but it is not always simple to interpret. We define a new indirect measure of the diffusion model error called the diffusion model error source (DME source). When this DME source is added to the diffusion equation, the transport solution for the angular-integrated intensity is obtained. In contrast to the variable-Eddington tensor, our DME source is a scalar that is conceptually easy to interpret. In addition to defining the DME source analytically, we show how to generate this source numerically relative to the Sn radiative transfer equations with linear-discontinuous spatial discretization. This numerical source is computationally tested and shown to reproduce the Sn solution for a number of problems. Our radiative transfer model solves a coupled, time dependent, multi-frequency, 1-D slab equation and material heat transfer equation. We then use diffusion approximation to solve the same problem. The difference due to this approximation can be modelled by a “diffusion source”. The diffusion source is defined as an amount of inhomogeneous source that, when added to a diffusion calculation, gives a solution for the angle-integrated intensity that is equal to the transport solution.

Aircraft are dynamic systems that naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems are becoming increasingly important as the performance and complexity of the controlled systems is constantly increasing. It is especially important in the design of control systems for fighter aircraft. These require maximum control performance in order to have the upper hand in a dogfight or when they have to outmaneuver an enemy missile. Therefore pilots often maneuver the aircraft very close to the limit of what it is capable of, and an automatic system (called flight envelope protection system) against violating the restrictions is a necessity. In other application areas, nonlinear optimal control methods have been successfully used to solve this but in the aeronautical industry, these methods have not yet been established. One of the more popular methods that are well suited to handle constraints is Model Predictive Control (MPC) and it is used extensively in areas such as the process industry and the refinery industry. Model predictive control means in practice that the control system iteratively solves an advanced optimization problem based on a prediction of the aircraft's future movements in order to calculate the optimal control signal. The aircraft's operating limitations will then be constraints in the optimization problem. In this thesis, we explore model predictive control and derive two fast, low complexity algorithms, one for guaranteed stability and feasibility of nonlinear systems and one for reference tracking for linear systems. In reference tracking model predictive control for linear systems we build on the dual mode formulation of MPC and our goal is to make minimal changes to this framework, in order to develop a reference tracking algorithm with guaranteed stability and low complexity suitable for implementation in real time safety critical systems. To reduce the computational burden of nonlinear model predictive control several methods to approximate the nonlinear constraints have been proposed in the literature, many working in an ad hoc fashion, resulting in conservatism, or worse, inability to guarantee recursive feasibility. Also several methods work in an iterative manner which can be quit time consuming making them inappropriate for fast real time applications. In this thesis we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefits of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence. / <p>The series name "<em>Linköping studies in science and technology. Licentiate Thesis</em>" is incorrect. The correct series name is "<em>Linköping studies in science and technology. Thesis</em>".</p>

Using a multiple stage age of infection model, we derive an expression for the basic reproduction number, Ro. We apply this method to find Ro in analogous treatment models. We find, in the model without treatment, Ro depends only on the mean infective period, and not on the infective distribution. In treatment models, Ro depends on the mean infective and mean treatment period, as well as the distribution of the infective period, but not on the distribution of the treatment period. With an explicit formula for Ro and the final size relation, we provide a practical alternative to evaluating the effect of treatment and other control measures. We compare our models to previous models of SARS and TB.

Cross validation (CV) is widely used for model assessment and comparison. In this thesis, we first review and compare three v-fold CV strategies: best single CV, repeated and averaged CV and double CV. The mean squared errors of the CV strategies in estimating the best predictive performance are illustrated by using simulated and real data examples. The results show that repeated and averaged CV is a good strategy and outperforms the other two CV strategies for finite samples in terms of the mean squared error in estimating prediction accuracy and the probability of choosing an optimal model. In practice, when we need to compare many models, conducting repeated and averaged CV strategy is not computational feasible. We develop an efficient sequential methodology for model comparison based on CV. It also takes into account the randomness in CV. The number of models is reduced via an adaptive, multiplicity-adjusted sequential algorithm, where poor performers are quickly eliminated. By exploiting matching of individual observations, it is sometimes even possible to establish the statistically significant inferiority of some models with just one execution of CV. This adaptive and computationally efficient methodology is demonstrated on a large cheminformatics data set from PubChem. Cross validated mean squared error (CVMSE) is widely used to estimate the prediction mean squared error (MSE) of statistical methods. For linear models, we show how CVMSE depends on the number of folds, v, used in cross validation, the number of observations, and the number of model parameters. We establish that the bias of CVMSE in estimating the true MSE decreases with v and increases with model complexity. In particular, the bias may be very substantial for models with many parameters relative to the number of observations, even if v is large. These results are used to correct CVMSE for its bias. We compare our proposed bias correction with that of Burman (1989), through simulated and real examples. We also illustrate that our method of correcting for the bias of CVMSE may change the results of model selection.

This thesis examines finite dimensional representability of Forward Rate and LIBOR models. A new approach is examined. This approach is more general, elementary, and relevant to finance when compared with existing approaches. This new approach is applied to the following infinite dimensional equations used in finance: ?Gaussian Heath, Jarrow and Morton model; ?Free 1 Heath, Jarrow and Morton model; ?Brace, G?atarek and Musiela???s LIBOR model. Stronger results have been achieved using this approach. The results are as follows: ?The Gaussian HJM model can be represented in finite dimensions if and only if the volatility satisfies a particular differential equation. In which case the finite dimensional representation can be explicitly written; ?The Brace, G?atarek and Musiela???s LIBOR model with one dimensional Wiener process cannot be represented in finite dimensions (other than in a trivial case); ?The Brace, G?atarek and Musiela???s LIBOR model with multidimen-sional Wiener process, and Free HJM have a finite dimensional repre-sentation only if the initial yield curves satisfy a restrictive differential equation. This thesis is arranged as follows ?Chapter 1 is an introduction to this thesis and derivative pricing in general. The reader is referred to section 1.4 titled ???This Thesis?for a more detailed description of the approach of this thesis and its results. ?Chapter 2 contains a brief summary of results from the theory of stochastic processes, stochastic calculus and stochastic equations in infinite dimensions ?Chapter 3 contains an overview of spot market pricing models including the Cox, Ross and Rubinstein and Black and Scholes models. ?Chapter 4 contains an overview of the fixed income market pricing models including the Heath, Jarrow and Morton model; Musiela???s re-formulation of the HJM model; the Goldys, Musiela and Sondermann model; and the Brace, G?atarek and Musiela LIBOR model. ?Chapter 5 contains the primary results of this thesis. Finite Dimen-sional Representability is defined formally and applied to the Musiela reformulated Gaussian HJM model; Musiela reformulated free HJM model; and the Brace, G?atarek and Musiela LIBOR model. This ap-proach and results are compared with the literature.

Title page, table of contents and abstract only. The complete thesis in print form is available from the University of Adelaide Library. / The enzyme 25-hydroxyvitamin D la-hydroxylase or CYP27Bl is the key enzyme in the two-step activation process by which vitamin D is converted to its biologically active form 1,25-dihydroxyvitamin D (1,25D). The actions of a number of regulators on the renal CYP27B1 enzyme activity have been recognized for some years, although the underlying molecular mechanisms remain largely unknown and the DNA regions involved in the in vivo regulation of gene expression by these factors have not been delineated as yet. In order to identify the regulatory regions through which these factors control CYP27B1 expression in the kidney in vivo and to study the spatial and temporal expression of the CYP27B1 gene during development, a transgenic mouse model was established. This model was developed using pro-nuclear injection of a DNA construct containing the firefly luciferase reporter gene under the control of the 1541 bp region of the human CYP27B1 promoter. Following pro-nuclear injection, three transgenic founders were obtained and bred to establish three independent transgenic lines. In all three lines, a very similar expression pattern of the luciferase reporter gene was detected. High levels of luciferase activity were detected in the kidney, brain, testis, skin and bone. Lower levels of luciferase activity were detected in heart, lung, liver, distal small intestine, skeletal muscle and spleen extracts. No reporter gene expression could be detected in the proximal small intestine. This animal model was used to identify the ability of the 1541 bp promoter region of the CYP27B1 gene to respond in the kidney to a number of physiological challenges including dietary calcium, vitamin D and the immunomodulator LPS. In addition, the temporal expression of the reporter gene was studied by sacrificing animals at 6 different time points (2, 4, 6, 8, 12 and 64 weeks of age). The functionality of the CYP27B1 promoter was verified by comparing the regulation of the expression of the reporter gene with that of the endogenous CYP27B1 gene. The expression of endogenous CYP27B1 mRNA levels was therefore determined using Real-Time RT-PCR. The expression of the reporter gene and the endogenous CYP27B1 mRNA levels in the kidney were increased during early development (2 week old animals) and fell with increasing age. Reporter gene expression and CYP27BI mRNA levels were down-regulated in response to increasing amounts of dietary calcium in a dosedependent manner. Vitamin D-deficiency resulted in an increase in both the reporter gene and CYP27B1 expression. However, the increase in CYP27B1 mRNA levels was substantially higher than the increase in reporter gene expression, suggesting that other regulatory elements are required to maximize the effect of vitamin D-deficiency. LPS administration did not affect the expression of either luciferase or the endogenous CYP27B1 gene in the kidney. Immunohistochemistry was used to identify the cell-specific location of the luciferase and the endogenous CYP27B1 protein in the kidney in kidney sections of vitamin D-deficient animals. Both luciferase protein and the endogenous CYP27B1 protein were identified in the proximal tubular cells of the kidney. The regulation of the expression of the reporter gene was also studied in the transgenic mouse model in a number of extra-renal tissues that have been shown to express CYP27Bl and to be responsive to 1,25D. These tissues include heart, liver, lung, femora, bone marrow, skeletal muscle, testis, skin, brain, spleen and proximal and distal small intestine. Although in most tissues, the expression of luciferase was highest in the 2 week old animals and fell with increasing age, in the testis, the expression levels were low in the developing animals and increased with increasing age. No physiological significant effects were detected in any of the extra-renal tissues examined in response to dietary calcium and vitamin D, suggesting that these factors control CYP27Bl expression in a kidney-specific manner. In addition, no physiologically significant effect of the LPS administration could be detected in these tissues. Future studies employing transgenic animals which express transgenic constructs containing both the CYP27Bl promoter and upstream and/or intronic sequences are required to identify the factors that regulate CYP27Bl expression in the different tissues and to delineate the DNA regulatory regions through which these factors exert their effects in vivo. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1140412 / Thesis (Ph.D.) -- University of Adelaide, School of Molecular and Biomedical Science, 2004

Introduction A literature review of the evidence regarding aetiology, classification, epidemiology and treatment of depressive disorders was conducted. All of the domains that constitute the biopychosocial model were investigated as a basis for testing the hypothesis that a biomedical approach, or any domain in isolation, is inadequate for fully understanding depression. An integrative, explanatory, conceptual model was developed, based on supportive evidence that can better inform the clinical encounter. Methods A combination of manual and electronic searches were conducted. Medline, Psychlit, Sociofile and the Social Science index databases were accessed with multiple key words. The University of Queensland library catalogue was also searched. Part A - Historical and Philosophical Basis The limitations and challenges of the biomedical model are followed by suggested responses, in particular a biopsychosocial model applied within a patient-centred consultation style. Various methods of scientific enquiry are needed to develop a more complete understanding of depression. Part B - Assessing the Evidence Evidence from epidemiological, biological and psychosocial research is reviewed. Depressive illness tends to be a chronic or recurrent condition with multifactorial causation, and occurs on a complex spectrum of severity. There is emerging evidence for a chronic stress response being the initial biological dysfunction, This is consistent with the frequency of stressful life events that precipitate depressive episodes. There is convincing evidence for predisposing factors such as low self-esteem, poor interpersonal skills and deficiency of social support. A range of treatment modalities, for example pharmacotherapy and various psychotherapies, appear to have similar effectiveness, which suggests that recovery occurs when the perpetuating cycle is broken at different sites. Part C - Integrative Models. Available schematic integrative models are reviewed and most fall short of integrating the three domains of the biopsychosocial, or fail to illustrate the circular nature of causation. A model is proposed, based on the evidence reviewed in Part B, that addresses both considerations. Conclusion Some causal factors for depression are supported by evidence. Models that integrate these findings are necessary to more fully explain depression. When applied in conjunction with patient-centred consultation styles, improved clinical outcomes could be expected. There is the potential for further research to test out the benefit of such a biopsychosocial approach, and to better elucidate component causes and reversible risk factors. There is a need for narrative approaches to receive considerably greater attention.

Techn. Univ., Diss--Darmstadt, 2006.