Vancomycin is an antibiotic used for the treatment of systemic infections. It is given intravenously usually every twelve or twenty-four hours. This particular drug has a medium level of boundedness, with approximately fty percent of the drug being free and thus physiologically eective. A physiologically-based pharmacokinetic (PBPK) model was used to better understand the absorption, distribution, and elimination of the drug. Using optimal parameters, the model could be used in the future to test how various factors, such as BMI or excretion levels, might aect the concentration of the antibiotic.

Levofloxacin is in a class of antibiotics known as fluoroquinolones, which treat infections by killing the bacteria that cause them. A physiologically-based pharmacokinetic (PBPK) model was developed to investigate the uptake, distribution, and elimination of Levofloxacin after a single dose. PBPK modeling uses parameters such as body weight, blood flow rates, partition coefficients, organ volumes, and several other parameters in order to model the distribution of a particular drug throughout the body. Levofloxacin is only moderately bound in human blood plasma, and, thus, for the purposes of this paper, linear bonding is incorporated into the model because the free or unbound portion of the drug is the only portion that is considered to be medicinally effective. Parameter estimation is then used to estimate the two unknown parameters given clinical data from literature on the total concentration of Levofloxacin in the blood over time. Once an adequate model is generated, the effects of varying Body Mass Index are tested for the absorption and distribution of Levofloxacin throughout the body.

abstract: Mathematical models are important tools for addressing problems that exceed experimental capabilities. In this work, I present ordinary and partial differential equation (ODE, PDE) models for two problems: Vicodin abuse and impact cratering. The prescription opioid Vicodin is the nation's most widely prescribed pain reliever. The majority of Vicodin abusers are first introduced via prescription, distinguishing it from other drugs in which the most common path to abuse begins with experimentation. I develop and analyze two mathematical models of Vicodin use and abuse, considering only those patients with an initial Vicodin prescription. Through adjoint sensitivity analysis, I show that focusing efforts on prevention rather than treatment has greater success at reducing the total population of abusers. I prove that solutions to each model exist, are unique, and are non-negative. I also derive conditions for which these solutions are asymptotically stable. Verification and Validation (V&V) are necessary processes to ensure accuracy of computational methods. Simulations are essential for addressing impact cratering problems, because these problems often exceed experimental capabilities. I show that the Free Lagrange (FLAG) hydrocode, developed and maintained by Los Alamos National Laboratory, can be used for impact cratering simulations by verifying FLAG against two analytical models of aluminum-on-aluminum impacts at different impact velocities and validating FLAG against a glass-into-water laboratory impact experiment. My verification results show good agreement with the theoretical maximum pressures, and my mesh resolution study shows that FLAG converges at resolutions low enough to reduce the required computation time from about 28 hours to about 25 minutes. Asteroid 16 Psyche is the largest M-type (metallic) asteroid in the Main Asteroid Belt. Radar albedo data indicate Psyche's surface is rich in metallic content, but estimates for Psyche's composition vary widely. Psyche has two large impact structures in its Southern hemisphere, with estimated diameters from 50 km to 70 km and estimated depths up to 6.4 km. I use the FLAG hydrocode to model the formation of the largest of these impact structures. My results indicate an oblique angle of impact rather than a vertical impact. These results also support previous claims that Psyche is metallic and porous. / Dissertation/Thesis / Psyche asteroid impact simulation initialization / Psyche asteroid impact simulation video / Doctoral Dissertation Applied Mathematics 2019

Ce travail présente la manière dont le regard d'Elizabeth Bishop appréhende le monde en refusant toute illusion de familiarité. Il étudie les diverses stratégies de défamiliarisation qui invitent le lecteur à redécouvrir les surprises que peuvent réserver l'ordinaire et le quotidien, ainsi que le rapport qui s'instaure entre le sujet lyrique et le monde dans ces conditions. Il s'agit d'analyser comment l'affleurement de l'étrange ou de l'informe dans le familier et l'intime permet d'accéder à une reconnaissance du soi plus ample et plus authentique. L'écriture de Bishop remet inlassablement en question la stabilité de la réalité, y compris celle du sujet, ainsi que toute notion d'acquis, ou d'acquisition dans le temps. C'est ainsi que sa voix – sa signature – se singularise et qu'elle se démarque de ses pairs, mais aussi de la société à laquelle elle appartient. Ce qui s'affirme au travers de son écriture n'est paradoxalement fait que d'incertitude et de vulnérabilité. Le sujet qui s'y forme se construit sur de l'éphémère, sur ses propres limites ; il ne peut s'appuyer que sur la découverte de l'aliénation exogène mais également endogène à laquelle il est confronté. Simultanément, cette écriture cherche des moyens de maintenir le sujet, par la résonance d'échos, par le foisonnement, la prolifération, autant de techniques qui le ramènent incessamment au manque, au vide, à la faille qu'elles sont supposées masquer. Cette thèse propose d'interroger le rapport entre perte et création dans l'œuvre de Bishop, la manière dont la création se nourrit de la perte, et dont elle entraîne le lecteur dans cette transaction, l'incluant par là-même dans le processus créatif. / This study examines the way Elizabeth Bishop's writings probe the world's seeming familiarity, how through various strategies of defamiliarization they reveal to the reader the hidden surprises of the ordinary, and how the lyrical subject relates to the world. As the strange and the shapeless surface within the intimate and the familiar, the persona gains access to a better and more authentic understanding of his-her own self. Bishop's writing relentlessly questions the stability of reality, including that of the self. It seems that the only knowledge available is that of uncertainty and contingency. Her voice is therefore necessarily singular and isolated, being itself in perpetual mutation. In order to maintain itself, her subject is constrained to rely on its own ephemeral and limited nature, as well as on external and internal alienation. Echoes and techniques of proliferation are construed to achieve that aim. Yet those techniques keep ! bringing the subject back to the lack, the absence, the gaps they are meant to bridge and cover up. Finally, this analysis explores the relationship between loss and creation: how creation is fueled by loss and how the reader is drawn into Bishop's writing thus ensuring the persistence of creation.

Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number of practical fields such as equations arising in population dynamics and astrophysics. It includes discussion what are the advantages and disadvantages of implicit methods over explicit methods, the accuracy and stability of methods and how the order of various methods can be approximated numerically. Also, semidiscretization of some partial differential equations and stiff systems which may arise from these semidiscretizations are examined.

The aim of the thesis is to find a method, in conjunction with the ordinary differential equation (ODE) based method of lines (MOL) solution of Richards’ equation, to model the steep wetting front infiltration in very dry soils, accurately and efficiently. Due to the steep pressure head or steep water volumetric content gradients, highly nonlinear soil hydraulic properties and the rapid movement of the wetting front, accurate solutions for infiltration into a dry soil are usually difficult to obtain. Additionally, such problems often require very small time steps and large computation times. As an enhancement to the used ODE/MOL approach, Higher Order Finite Differencing, Varying Order Finite Differencing, Vertical Scaling, Adaptive Schemes and Non-uniform Stretching Techniques have been implemented and tested in this thesis. Success has been found in the ability of Vertical Scaling to simulate very steep moving front solution for the Burgers’ equation. Unfortunately, the results also show that Vertical Scaling needs significant research and improvement before their full potential in routine applications for difficult nonlinear problems, such as Richard’s equation with very steep moving front solution, can be realized. However, we have also shown that the use of the composed form of RE and a 2nd order finite differencing for the first order derivative approximation is conducive for modelling steep moving front problem in a very dry soil. Additionally, with the combination of an optimal influx value at the edges of the inlet, the ODE/MOL approach is able to model a 2-D infiltration in very dry soils, effectively and accurately. Furthermore, one of the strengths of this thesis is the use of a MATLAB PDE template. Implementing the ODE/MOL approach via a MATLAB PDE template has shown to be most suitable for modelling of partial differential equations. The plug and play mode of modifying the PDE template for solving time-dependent partial differential equations is user-friendly and easy, as compared to more conventional approaches using Pascal, Fortran, C or C++. The template offers greater modularity, flexibility, versatility, and efficiency for solving PDE problems in both 1-D and 2-D spatial dimensions. Moreover, the 2-D PDE template has been extended for irregular shaped domains.

The objective of this research is to empirically assess the value and validity of a multi-organization data set in the building of prediction models for several ‘local’ software organizations; that is, smaller organizations that might have a few project records but that are interested in improving their ability to accurately predict software project effort. Evidence to date in the research literature is mixed, due not to problems with the underlying research ideas but with limitations in the analytical processes employed: • the majority of previous studies have used only a single organization as the ‘local’ sample, introducing the potential for bias • the degree to which the conclusions of these studies might apply more generally is unable to be determined because of a lack of transparency in the data analysis processes used. It is the aim of this research to provide a more robust and visible test of the utility of the largest multi-organization data set currently available – that from the ISBSG – in terms of enabling smaller-scale organizations to build relevant and accurate models for project-level effort prediction. Stepwise regression is employed to enable the construction of ‘local’, ‘global’ and ‘refined global’ models of effort that are then validated against actual project data from eight organizations. The results indicate that local data, that is, data collected for a single organization, is almost always more effective as a basis for the construction of a predictive model than data sourced from a global repository. That said, the accuracy of the models produced from the global data set, while worse than that achieved with local data, may be sufficiently accurate in the absence of reliable local data – an issue that could be investigated in future research. The study concludes with recommendations for both software engineering practice – in setting out a more dynamic scenario for the management of software development – and research – in terms of implications for the collection and analysis of software engineering data.

In qualitative theory of differential equations, an important role is played by special classes of solutions, like periodic solutions or solutions to some boundary value problems. When a system of ordinary differential equations has equilibria, i.e. constant solutions, whose stability properties are known, it is significant to search for connections between them by trajectories of solutions of the given system. These are called homoclinic or heteroclinic, according to whether they describe a loop based at one single equilibrium or they "start" and "end" at two distinct equilibria. This thesis is devoted to the study of heteroclinic solutions for a specific class of ordinary differential equations related to the Extended Fisher-Kolmogorov equation and the Swift-Hohenberg equation. These are semilinear fourth order bi-stable evolution equations which appear as mathematical models for problems arising in Mechanics, Chemistry and Biology. For such equations, the set of bounded stationary solutions is of great interest. These solve an autonomous fourth order equation. In this thesis, we focus on such equations having a variational structure. In that case, the solutions are critical points of an associated action functional defined in convenient functional spaces. We then look for heteroclinic solutions as minimizers of the action functional. Our main contributions concern existence and multiplicity results of such global and local minimizers in the case where the functional is defined from sign changing Lagrangians. The underlying idea is to impose conditions which imply a lower bound on the action over all admissible functions. We then combine classical arguments of the Calculus of Variations with careful estimates on minimizing sequences to prove the existence of a minimum.

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior. Cholera remains a public health threat in many parts of the world and improved intervention strategies are needed. We investigate a key intervention strategy, vaccination, with optimal control applied to a cholera model. This system of differential equations has human compartments with susceptibles with different levels of immunity, symptomatic and asymptomatic infecteds, and two cholera vibrio compartments, hyperinfectious and non-hyperinfectious. The spread of the infection in the model is shown to be most sensitive to certain parameters, and the effect of varying these parameters on the optimal vaccination strategy is shown in numerical simulations. Our simulations also show the importance of the infection rate under various parameter cases.

Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this dissertation, species augmentation is analyzed in an optimal control setting to determine the optimal augmentation strategies given various constraints and settings. In each setting, we consider the effects on both the target/endangered population and a reserve population from which the individuals translocated in the augmentation are harvested. Four different optimal control formulations are explored. The first two optimal control formulations model the underlying population dynamics with a system of ordinary differential equations. Each of these two formulations utilizes a different function to model the cost of augmentation. For each optimal control formulation we find a characterization for the optimal control and show numerical results for scenarios of different illustrative parameter sets. The second two optimal control formulations model the underlying population dynamics with systems of discrete difference equations. The difference between these two optimal control formulations is the order in which events occur within each time step in the population models. In the first formulation the population is augmented before the natural growing season in each time step (augment then grow model), whereas in the second formulation the population is augmented after the natural growing season in each time step (grow then augment model). These two discrete time models, which differ only in their order of events, lead to structurally different models. The formulation with the augment then grow model cannot utilize discrete time optimal control theory and a brute force method of finding the optimal augmentation strategy is used. The formulation with the grow then augment model does utilize optimal control theory and we find the characterization of the optimal control. For both formulations, we explore several scenarios of different illustrative parameter sets. In each of the four optimal control formulations, the numerical results provide considerably more detail about the exact dynamics of optimal augmentation than can be readily intuited. The work presented here are the first steps toward building a general theory of population augmentation, which accounts for the complexities inherent in many conservation biology applications.