Personalised medicine describes the practice of tailoring medical care to the individual characteristics of each patient. Fundamental to this practice is the identification of markers associated with differential treatment response. Such markers can be identified through the assessment of treatment effect modification using statistical methods. Randomised controlled trials provide the optimal setting for evaluating differential response to treatment. Due to restrictions regarding sample size, study length and ethics, observational studies are more appropriate in many circumstances, particularly for the identification of markers associated with adverse side-effects and long term response to treatments. However, the analysis of observational data raises some additional challenges. The overall aim of this thesis was to develop statistical methodology for the analysis of observational data, specifically primary care databases, to identify and evaluate markers associated with differential treatment response. Three aspects of the assessment of treatment effect modification in an observational setting were addressed. The first aspect related to the assessment of treatment effect modification on the additive measurement scale which corresponds to a comparison of absolute treatment effects across patient subgroups. Various ways in which this can be assessed in an observational setting were reviewed and a novel measure, the ratio of absolute effects, which can be calculated from certain multiplicative regression models, was proposed. The second aspect regarded the confounding adjustment and it was investigated how the presence of interactions between the moderator and confounders on both treatment receipt and outcome can bias estimates of treatment effect modification if unaccounted for using Monte Carlo simulations. It was determined that the presence of bias differed across different confounding adjustment methods and, in the majority of settings, the bias was reduced when the interactions between the moderator and confounders were accounted for in the confounding adjustment model. Thirdly, it has been proposed that patient data in observational studies be organised into and analysed as series of nested nonrandomised trials. This thesis extended this study design to evaluate predictive markers of differential treatment response and explored the benefits of this methodology for this purpose. It was suggested how absolute treatment effect estimates can be estimated and compared across patient subgroups in this setting. A dataset comprising primary care medical records of adults with rheumatoid arthritis was used throughout this thesis. Interest lay in the identification of characteristics predictive of the onset of type II diabetes associated with steroid (glucocorticoid) therapy. The analysis in this thesis suggested older age may be associated with a higher risk of steroid-associated type II diabetes, but this warrants further investigation. Overall, this thesis demonstrates how observational studies can be analysed such that accurate and meaningful conclusions are made within personalised medicine research.

The baroclinic and surface-frictional contributions to stratified wake formation are considered as a function of the non-dimensional height ( = Nho/U) and aspect-ratio ( = ho/L) of the barrier. Numerical simulations are computed for a wide range of the - parameter space, including both unstratified ( = 0) and highly stratified ( = 4) flows and for terrain slopes characteristic of both geophysical ( = 0.1) and laboratory scale ( = 2.0) obstacles. Simulations both with and without applied surface stresses are compared to gain insight into the baroclinic and surface-frictional contributions to each flow. Particular emphasis is given to the changes in kinematic wake structure, the relative contributions of skin and pressure drag, and the vertical momentum flux observed as the mountain height and terrain slope are varied. We also examine several cases from the parameter-space study in more detail using a method for decomposing the flow into baroclinic and viscous parts. The decompositions show that for large- and small- flows, wake generation is primarily baroclinic in nature, while at smaller- and/or larger-, the wake becomes increasingly surface frictional.

In the early 70's Parshin introduced his notion of the multidimensional residues of meromorphic top-forms on algebraic varieties. Parshin's theory is a generalization of the classical one-dimensional residue theory. The main difference between the Parshin's definition and the one-dimensional case is that in higher dimensions one computes the residue not at a point but at a complete flag of irreducible subvarieties. Parshin, Beilinson, and Lomadze also proved the Reciprocity Law for residues: if one fixes all elements of the flag, except for one, and consider all possible choices of the missing element, then only finitely many of these choices give non-zero residues, and the sum of these residues is zero. Parshin's constructions are completely algebraic. In fact, they work in very general settings, not only over complex numbers. However, in the complex case one would expect a more geometric variant of the theory. In my thesis I study Parshin residues from the geometric point of view. In particular, the residue is expressed in terms of the integral over a smooth cycle. Parshin-Lomadze Reciprocity Law for residues in the complex case is proved via a homological relation on these cycles. The thesis consists of two parts. In the first part the theory of Leray coboundary operators for stratified spaces is developed. These operators are used to construct the cycle and prove the homological relation. In the second part resolution of singularities techniques are applied to study the local geometry near a complete flag of subvarieties.

In the early 70's Parshin introduced his notion of the multidimensional residues of meromorphic top-forms on algebraic varieties. Parshin's theory is a generalization of the classical one-dimensional residue theory. The main difference between the Parshin's definition and the one-dimensional case is that in higher dimensions one computes the residue not at a point but at a complete flag of irreducible subvarieties. Parshin, Beilinson, and Lomadze also proved the Reciprocity Law for residues: if one fixes all elements of the flag, except for one, and consider all possible choices of the missing element, then only finitely many of these choices give non-zero residues, and the sum of these residues is zero. Parshin's constructions are completely algebraic. In fact, they work in very general settings, not only over complex numbers. However, in the complex case one would expect a more geometric variant of the theory. In my thesis I study Parshin residues from the geometric point of view. In particular, the residue is expressed in terms of the integral over a smooth cycle. Parshin-Lomadze Reciprocity Law for residues in the complex case is proved via a homological relation on these cycles. The thesis consists of two parts. In the first part the theory of Leray coboundary operators for stratified spaces is developed. These operators are used to construct the cycle and prove the homological relation. In the second part resolution of singularities techniques are applied to study the local geometry near a complete flag of subvarieties.

Cancer morbidity and mortality is greatly reduced when the disease is diagnosed and treated early in its development. Tissue biopsies are the gold standard for cancer diagnosis, and an accurate diagnosis requires a biopsy from the malignant portion of an organ. Light, guided through a fiber optic probe, could be used to inspect regions of interest and provide real-time feedback to determine the optimal tissue site for biopsy. This approach could increase the diagnostic accuracy of current biopsy procedures. The studies in this thesis have characterized changes in tissue optical signals with carcinogenesis, increasing our understanding of the sensitivity of optical techniques for cancer detection. All in vivo studies were conducted on the dimethylbenz[alpha]anthracene treated hamster cheek pouch model of epithelial carcinogenesis. Multiphoton microscopy studies in the near infrared wavelength region quantified changes in tissue morphology and fluorescence with carcinogenesis in vivo. Statistically significant morphological changes with precancer included increased epithelial thickness, loss of stratification in the epithelium, and increased nuclear diameter. Fluorescence changes included a statistically significant decrease in the epithelial fluorescence intensity per voxel at 780 nm excitation, a decrease in the fluorescence lifetime of protein-bound nicotinamide adenine dinucleotide (NADH, an electron donor in oxidative phosphorylation), and an increase in the fluorescence lifetime of protein-bound flavin adenine dinucleotide (FAD, an electron acceptor in oxidative phosphorylation) with precancer. The redox ratio (fluorescence intensity of FAD/NADH, a measure of the cellular oxidation-reduction state) did not significantly change with precancer. Cell culture experiments (MCF10A cells) indicated that the decrease in protein-bound NADH with precancer could be due to increased levels of glycolysis. Point measurements of diffuse reflectance and fluorescence spectra in the ultraviolet to visible wavelength range indicated that the most diagnostic optical signals originate from sub-surface tissue layers. Optical properties extracted from these spectroscopy measurements showed a significant decrease in the hemoglobin saturation, absorption coefficient, reduced scattering coefficient and fluorescence intensity (at 400 nm excitation) in neoplastic compared to normal tissues. The results from these studies indicate that multiphoton microscopy and optical spectroscopy can non-invasively provide information on tissue structure and function in vivo that is related to tissue pathology. / Dissertation

The Big Thicket National Preserve (BTNP) is a unit of the National Park Service whose mission prioritizes conservation of its wildlands in the United States. One threat to natural resources of the BTNP has been impacts associated with feral hog (Sus scrofa) activities. Population numbers of this non-native game species have increased throughout Texas, including areas within the preserve. Recreational hunting permitted by the BTNP has served as a means of controlling hog numbers, although the reported amounts of hog damage to park resources appear to have increased in recent years. Population reduction of feral hogs and mitigation of their impacts require research that documents and validates feral hog impacts on park resources. Here, I evaluated (1) population trends of feral hogs for the past 20 years via data from hunter-card surveys and track-counts, and (2) feral hog impacts on native vegetation for 3 management units of the BTNP. Results from my analysis suggest a nearly 3-fold increase in hog numbers throughout the preserve since 1981. The overall damage to vegetation from hog rooting or wallowing averaged to 28% among the 3 units of the BTNP. Landscape features such as topography, soil moisture, soil type, and dominant vegetative cover types were used to predict hog damage. Floodplains had the most damage in the Big Sandy unit (45%), while flatlands were mostly impacted in the Turkey Creek unit (46%), and uplands in the Lance Rosier unit (32%). Vegetative cover was an important variable in explaining variation in hog damage throughout the 3 units of the preserve. Impacts were more widespread across different vegetative strata than previously believed. Study results also support the premise that hog damage in the BTNP parallels the increase in hog abundance over the past 20 years. A more aggressive program for population reduction of feral hogs and mitigation of their impacts is recommended for the BTNP to continue to meet its legal mandates for conservation.

The baroclinic and surface-frictional contributions to stratified wake formation are considered as a function of the non-dimensional height ( = Nho/U) and aspect-ratio ( = ho/L) of the barrier. Numerical simulations are computed for a wide range of the - parameter space, including both unstratified ( = 0) and highly stratified ( = 4) flows and for terrain slopes characteristic of both geophysical ( = 0.1) and laboratory scale ( = 2.0) obstacles. Simulations both with and without applied surface stresses are compared to gain insight into the baroclinic and surface-frictional contributions to each flow. Particular emphasis is given to the changes in kinematic wake structure, the relative contributions of skin and pressure drag, and the vertical momentum flux observed as the mountain height and terrain slope are varied. We also examine several cases from the parameter-space study in more detail using a method for decomposing the flow into baroclinic and viscous parts. The decompositions show that for large- and small- flows, wake generation is primarily baroclinic in nature, while at smaller- and/or larger-, the wake becomes increasingly surface frictional.

Mixing is a common feature of stratified fluids. In stratified fluids the density varies with the height. This is true for the most fluids in geophysical environments, like lakes, the atmosphere or the ocean. Turbulent mixing plays a crucial role for the overall energy budget of the earth and has therefore an huge impact on the global climate. By introducing the mixing efficiency, it is possible to quantify mixing. It is defined as the ratio of gain of potential energy to the injection of mechanical energy. In the ocean energy provided by tidal forces leads to turbulence and thus highly dense water is lifted up from the deep sea to the surface. For this process, a mixing efficiency of 0.2 is estimated. Until now it is not completely understood how this high value can be achieved. Thus we measured the mixing efficiency by using a Couette-Taylor system, which can produce steady-state homogeneous turbulence. This is similar to what we find in the ocean. The Couette-Taylor system consists of two concentric cylinders that can be rotated independently. In between a stratified fluid is filled using salt as a stratifying agent. In the laboratory experiment, we obtained mixing efficiencies in the order of 0.001 as a result. Moreover we found that the mixing efficiency decreases with decreasing stratification like previous laboratory experiments have shown. As this value is two orders of magnitude smaller than what we find in the ocean, further studies will be necessary. / text

In this thesis we will investigate the role of diapycnal mixing on the ocean general circulation. This thesis is divided into three main parts. In the first part we show that there exists an almost infinite number of pathways to turbulence in oceanic energetic shear zones at high Reynolds number. Such a large number of accessible routes to truly chaotic motion is not typical of most of the existing body of laboratory and numerical experiments of shear-induced diapycnal mixing, but is shown to be of relevance to diapycnal mixing in geophysical flows. A key finding is that the use of generally accepted empirical relations based on laboratory experiments for the quantification of diapycnal mixing leads to large inaccuracies. In the second part we perform high resolution numerical experiments of diapycnal mixing in the oceanographically relevant high Reynolds number parameter range. Through detailed analysis of the flow energetics and mixing properties of these flows, we show that the net buoyancy flux facilitated by turbulence, the efficiency of diapycnal mixing, and the resultant effective diffusivity, all depend in non-trivial ways on the specific route to turbulence for each individual mixing event. This has important implications for practical methods of estimating an effective diapycnal mixing diffusivity from observations as well as for parametrization of mixing in ocean general circulation models. We show quantitatively that such methods can be inaccurate to the extent that they will need to be completely revised or replaced. In the third and final part of the thesis we investigate the sensitivity of the meridional overturning circulation of the abyssal ocean to the intensity and spatial variations of diapycnal mixing. We show that changes in intensity of mixing by factors well within the errors associated with practical estimates (as discussed above) lead to significant changes in ocean circulation. We show that enhanced abyssal mixing, surface winds, and meso-scale eddies play leading roles in driving the abyssal ocean circulation and in setting the stratification. As an example of the application of our analysis we show that proper parametrization of enhanced abyssal mixing leads to realization of the important role of the (often neglected) geothermal heat flux in driving the Antarctic Bottom Water circulation.

Current stoichiometric spark-ignited engine technologies require costly catalytic converters for reductions in tailpipe emissions. Load control is achieved by using a throttle, which is a leading contributor to reductions in efficiency. Spark-ignited lean burn natural gas engines have been proven to be more efficient and emit fewer pollutants than their stoichiometric counterparts. Load reduction in these engines can be achieved by regulating the air/fuel ratio of the intake charge thereby reducing the efficiency penalties inherent to throttling. Partially stratified charge (PSC) can provide further reductions in emissions and improvements in efficiency by extending the lean limit of operation. PSC is achieved by the ignition of a small quantity of natural gas in the vicinity of the spark plug. This creates an easily ignitable mixture at the spark plug electrodes, thereby providing a high energy ignition source for the ultra-lean bulk charge. Stratified charge engine operation using direct injection (DI) has been proposed as a method of bridging the throttleless load reduction gap between idle and ultra-lean conditions. A previous study was conducted to determine if PSC can provide a high-energy ignition source in a direct injected stratified charge engine. Difficulties with igniting the PSC injections in an air-only bulk charge were encountered. This study focuses on a fundamental Schlieren image-based analysis of PSC combustion. Natural gas was injected through a modified spark plug located in an optically accessible combustion bomb. The relationships between PSC injection timing, fuel supply pressure and spark timing were investigated. Spark timing is defined as the duration between commanded start of injection and the time of spark. As the fuel supply pressure was increased, the minimum spark timing that lead to successful combustion also increased. The largest spark timing window that led to successful combustion was determined to be 80 ms wide at an injection fuel supply pressure of 300 psi. The amount of unburned natural gas increased with increasing spark timing. A cold flow study of the PSC injection system was also conducted. The PSC injection solenoid was found to have a consistent average injection delay of 1.95 ms. The slope of the linear response region of observed injection duration to commanded injection duration was 8.4. Due to plenum effects, the average observed injection duration of the entire PSC system was an order of magnitude longer than the commanded injection duration and was found to vary significantly with fuel supply pressure.