Neighbouring plants can interact strongly, competing for resources including light, water, animal mutualists, and local germination sites. From an evolutionary perspective, this implies that a plant’s best resource acquisition strategy will usually depend on the traits of its neighbours, and for plants in particular, neighbours are often genealogical relatives. Here, I use a combination of theory and experiments to expose some important consequences of social interactions among plants. The first model analyzes selection on traits used to attract pollinators, showing that competitive interactions (in the absence of local relatedness) can select for exaggerated secondary sexual characters. To complement this model, I performed experiments that confirm the mechanisms by which adaptive pollinator foraging naturally leads to interactions among plants. The observed foraging behaviour (of bumble bees) also provides unique evidence for ‘Bayesian foraging’, a sophisticated type of resource assessment that depends on prior experience in a particular environment. A second model considers how selection on the sex allocation of cosexual, animal-dispersed plants leads to competition and cooperation over local germination sites, sometimes leading to the origin of gender dimorphism. The model reveals novel ecological contexts in which disruptive selection on sex allocation can arise, and in general, illustrates how selection for cooperation can facilitate or inhibit evolutionary diversification. In the models considered here, cooperation is indiscriminant, but plants might also assess the relatedness of neighbours and cooperate with kin over non-kin. In the final chapter, I present experimental evidence that is consistent with preferential cooperation over soil resources among sibling plants. This study is the first to link a potentially cooperative resource allocation strategy with an increase in the mean fitness of related plants.

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The following thesis is a project in mathematical biology building upon the so-called "error minimization hypothesis" of the genetic code. After introducing the biological context of this hypothesis, I proceed to develop some relevant information-theoretic ideas, with the overall goal of studying the structure of the genetic code. I then apply the newfound understanding to an important question in the debate about the origin of life, namely, the question of the temperatures in which the genetic code, and life in general, underwent their early evolution. <br /><br /> The main advance in this thesis is a set of methods for calculating the primordial evolutionary pressures that shaped the genetic code. These pressures are due to genetic errors, and hence the statistical properties of the errors and of the genome are imprinted in the statistical properties of the code. Thus, by studying the code it is possible to reconstruct, to some extent, the primordial error rates and the composition of the primordial genome. In this way, I find evidence that the fixation of the genetic code occurred in organisms which were not thermophiles.

Image registration is widely used in different areas nowadays. Usually, the efficiency, accuracy, and robustness in the registration process are concerned in applications. This thesis studies these issues by presenting an efficient intensity-based mono-modality rigid 2D-3D image registration method and constructing a novel mathematical model for intensity-based multi-modality rigid image registration. For mono-modality image registration, an algorithm is developed using RapidMind Multi-core Development Platform (RapidMind) to exploit the highly parallel multi-core architecture of graphics processing units (GPUs). A parallel ray casting algorithm is used to generate the digitally reconstructed radiographs (DRRs) to efficiently reduce the complexity of DRR construction. The optimization problem in the registration process is solved by the Gauss-Newton method. To fully exploit the multi-core parallelism, almost the entire registration process is implemented in parallel by RapidMind on GPUs. The implementation of the major computation steps is discussed. Numerical results are presented to demonstrate the efficiency of the new method. For multi-modality image registration, a new model for computing mutual information functions is devised in order to remove the artifacts in the functions and in turn smooth the functions so that optimization methods can converge to the optimal solutions accurately and efficiently. With the motivation originating from the objective to harmonize the discrepancy between the image presentation and the mutual information definition in previous models, the new model computes the mutual information function using both the continuous image function representation and the mutual information definition for continuous random variables. Its implementation and complexity are discussed and compared with other models. The mutual information computed using the new model appears quite smooth compared with the functions computed by others. Numerical experiments demonstrate the accuracy and efficiency of optimization methods in the case that the new model is used. Furthermore, the robustness of the new model is also verified.

The purpose of this project is to reexamine established free-radical polymerization theories and build a mechanistic reactor model for multi-component (up to six monomers) bulk and solution polymerizations under batch/semi-batch reactor configurations. The six-monomer system of interest is: Styrene (Sty), n-Butyl acrylate (BA), Butyl methacrylate (BMA), Hydroxyethyl acrylate (HEA), Hydroxybutyl acrylate (HBA), and Acrylic acid (AA). In order to develop a flexible, comprehensive, and user-friendly model, not only a physical/kinetic database of individual monomers and ingredients such as solvents, initiators, and chain transfer agents, but also a co-polymer database of reactivity ratios, and glass transition temperatures were built and combined with the modeling steps. Through an extensive literature search for polymerization models and kinetics, the simulation model was developed in a general way to cover the range from homo- to hexa-polymerization at both regular and elevated temperature levels, and explain various polymerization kinetics and characteristics. Model testing was conducted with experimental data as much as possible to check the model’s reliability. Due to limited experimental data for higher multi-component polymerizations, the simulation model was tested with homo-polymerizations and other available cases of combinations of two to four monomers. Very reasonable agreement was found between model predictions and experimental data on rate of polymerization, molecular weight, polymer composition, sequence length, etc. through the entire conversion. This multi-component modeling study continuously requires experimental checkups and parameter fine-tuning for better predictions. Further literature search or experimental studies still remain necessary for the hydroxyalkyl acrylate kinetic database and model testing of the depropagation feature. Sensitivity analysis also could be performed to locate critical parameters. This model should find use in industry for analyzing and optimizing reactor conditions as well as in the academic field as a research and educational tool.

The following thesis is a project in mathematical biology building upon the so-called "error minimization hypothesis" of the genetic code. After introducing the biological context of this hypothesis, I proceed to develop some relevant information-theoretic ideas, with the overall goal of studying the structure of the genetic code. I then apply the newfound understanding to an important question in the debate about the origin of life, namely, the question of the temperatures in which the genetic code, and life in general, underwent their early evolution. <br /><br /> The main advance in this thesis is a set of methods for calculating the primordial evolutionary pressures that shaped the genetic code. These pressures are due to genetic errors, and hence the statistical properties of the errors and of the genome are imprinted in the statistical properties of the code. Thus, by studying the code it is possible to reconstruct, to some extent, the primordial error rates and the composition of the primordial genome. In this way, I find evidence that the fixation of the genetic code occurred in organisms which were not thermophiles.

Image registration is widely used in different areas nowadays. Usually, the efficiency, accuracy, and robustness in the registration process are concerned in applications. This thesis studies these issues by presenting an efficient intensity-based mono-modality rigid 2D-3D image registration method and constructing a novel mathematical model for intensity-based multi-modality rigid image registration. For mono-modality image registration, an algorithm is developed using RapidMind Multi-core Development Platform (RapidMind) to exploit the highly parallel multi-core architecture of graphics processing units (GPUs). A parallel ray casting algorithm is used to generate the digitally reconstructed radiographs (DRRs) to efficiently reduce the complexity of DRR construction. The optimization problem in the registration process is solved by the Gauss-Newton method. To fully exploit the multi-core parallelism, almost the entire registration process is implemented in parallel by RapidMind on GPUs. The implementation of the major computation steps is discussed. Numerical results are presented to demonstrate the efficiency of the new method. For multi-modality image registration, a new model for computing mutual information functions is devised in order to remove the artifacts in the functions and in turn smooth the functions so that optimization methods can converge to the optimal solutions accurately and efficiently. With the motivation originating from the objective to harmonize the discrepancy between the image presentation and the mutual information definition in previous models, the new model computes the mutual information function using both the continuous image function representation and the mutual information definition for continuous random variables. Its implementation and complexity are discussed and compared with other models. The mutual information computed using the new model appears quite smooth compared with the functions computed by others. Numerical experiments demonstrate the accuracy and efficiency of optimization methods in the case that the new model is used. Furthermore, the robustness of the new model is also verified.

The purpose of this project is to reexamine established free-radical polymerization theories and build a mechanistic reactor model for multi-component (up to six monomers) bulk and solution polymerizations under batch/semi-batch reactor configurations. The six-monomer system of interest is: Styrene (Sty), n-Butyl acrylate (BA), Butyl methacrylate (BMA), Hydroxyethyl acrylate (HEA), Hydroxybutyl acrylate (HBA), and Acrylic acid (AA). In order to develop a flexible, comprehensive, and user-friendly model, not only a physical/kinetic database of individual monomers and ingredients such as solvents, initiators, and chain transfer agents, but also a co-polymer database of reactivity ratios, and glass transition temperatures were built and combined with the modeling steps. Through an extensive literature search for polymerization models and kinetics, the simulation model was developed in a general way to cover the range from homo- to hexa-polymerization at both regular and elevated temperature levels, and explain various polymerization kinetics and characteristics. Model testing was conducted with experimental data as much as possible to check the model’s reliability. Due to limited experimental data for higher multi-component polymerizations, the simulation model was tested with homo-polymerizations and other available cases of combinations of two to four monomers. Very reasonable agreement was found between model predictions and experimental data on rate of polymerization, molecular weight, polymer composition, sequence length, etc. through the entire conversion. This multi-component modeling study continuously requires experimental checkups and parameter fine-tuning for better predictions. Further literature search or experimental studies still remain necessary for the hydroxyalkyl acrylate kinetic database and model testing of the depropagation feature. Sensitivity analysis also could be performed to locate critical parameters. This model should find use in industry for analyzing and optimizing reactor conditions as well as in the academic field as a research and educational tool.

Mechanical pressing of soybean is highly desirable as it provides, at low cost, non-contaminated, protein-rich, low-fat soyflour which can be further processed into nutritious edible foods. Unfortunately, mechanical pressing of this low-fat oilseed ($<$20%) yields only 50-70% of the available oil, in contrast to the solvent extraction method which recovers over 98% of the oil. The main focus of the study was to maximize the oil recovery from soybean using mechanical oil expression by applying two pretreatments, enzymatic hydrolysis and extrusion cooking of soybeans, and by varying the pressing conditions including three applied pressures (20, 40 and 60 MPa), three pressing temperatures (22, 60 and 90°C) and two sample sizes (10 and 20 g). To characterize the material properties affecting mechanical oil expression from soybean a mathematical simulation of uniaxial compression was developed which incorporated the time dependent variation of soybean properties. The mathematical simulation was based on Terznaghi's theory of consolidation for soils and was solved using measured values of the coefficients of permeability, volume change and consolidation. A compression-permeability test cell was specifically developed for these measurements. For validation of the model, in addition to extruded soy, sunflower seeds (oil content ca. 45%) were also compressed under the same pressing conditions. Improvements in oil recovery due to enzymatic pretreatment of soybean were small, while the extrusion pretreatment increased the oil recovery from only a trace for raw soybean to 90.6%. Such oil recovery using mechanical pressing of soybean has not been reported in the past. The measured values of oil recovery, coefficients of permeability, volume change and consolidation for soybean and sunflower seeds were found to vary significantly $(P<0.05)$ with time of pressing, applied pressure, pressing temperature and the size of the sample. For extruded soy samples, the developed model predicted the values of oil recovery versus pressing time with an average error of 15%, while for sunflower seed samples the average prediction error was 40%. The high error values were attributed to the presence of hulls in the sunflower seed samples, as well as error during measurement of the coefficient of permeability. The coefficient of consolidation was found to have the greatest influence on oil recovery. The incorporation of time dependent material properties in the developed simulation was demonstrated to give more accurate and consistent prediction in trends of oil recovery as compared to using constant material properties. The correlationship developed between the oilseed material properties and the oil recovery obtained from uniaxially compressed oilseeds would help researchers and designers to better evaluate the mechanical oil expression equipment and systems. To the extent that the developed model adequately predicted oil recoveries from both sunflower and soybean oilseeds, the model is expected to be applicable to other oilseeds as well.

The purpose of this thesis was to determine how shaft stiffness affects clubhead speed and how it alters clubhead orientation at impact. For the first time, a 3D, six-segment forward dynamics model of a golfer and club was developed and optimized to answer these questions. A range of shaft stiffness levels from flexible to stiff were evaluated at three levels of swing speed (38, 45 and 53 m/s). At any level of swing speed, the difference in clubhead speed did not exceed 0.1 m/s across levels of shaft stiffness. Therefore, it was concluded that customizing the stiffness of a golf club shaft to perfectly suit a particular swing will not increase clubhead speed sufficiently to have any meaningful effect on performance. The magnitude of lead deflection at impact increased as shaft stiffness decreased. The magnitude of lead deflection at impact also increased as swing speed increased. For an optimized swing that generated a clubhead speed of 45 m/s, with a shaft of regular stiffness, lead deflection of the shaft at impact was 6.25 cm. The same simulation resulted in a toe-down shaft deflection of 2.27 cm at impact. Using the model, it was estimated that for each centimeter of lead deflection of the shaft, dynamic loft increased by approximately 0.8 degrees. Toe-down shaft deflection had relatively no influence on dynamic loft. For every centimeter increase in lead deflection of the shaft, dynamic closing of the clubface increased by approximately 0.7 degrees. For every centimeter increase in toe-down shaft deflection, dynamic closing of the clubface decreased by approximately 0.5 degrees. The results from this thesis indicate that improvements in driving distance brought about by altering shaft stiffness are the result of altered clubhead orientation at impact and not increased clubhead speed.