People at risk for blood clots are often treated with anticoagulants, warfarin is such an anticoagulant. The dose's effect is measured by comparing the time for blood to clot to a control time called an INR value. Previous anticoagulant studies have addressed agreement between fingerstick (POC) devices and the standard laboratory, however these studies rely on mathematical formulas as criteria for clinical evaluations, i.e. clinical evaluation vs. precision and bias. Fourteen such criteria were found in the literature. There exists little consistency among these criteria for assessing clinical agreement, furthermore whether these methods of assessing agreement are reasonable estimates of clinical decision-making is unknown and has yet to be validated. One previous study compared actual clinical agreement by having two physicians indicate a dosing decision based on patient history and INR values. This analysis attempts to justify previously used mathematical criteria for clinical agreement. Generalized additive models with smoothing spline estimates were calculated for each of the 14 criteria and compared to the smoothing spline estimate for the method using actual physician decisions (considered the "gold standard"). The area between the criteria method spline and the gold standard method spline served as the comparison, using bootstrapping for statistical inference. Although some of the criteria methods performed better than others, none of them matched the gold standard. This stresses the need for clinical assessment of devices.

The purpose of this thesis is to provide an in-depth understanding of tooth engagement in splined couplings based on variations in clearances between mating teeth. It is standard practice to assume that 25-50% of the total spline teeth in a coupling are engaged due to variations from manufacture. Based on the assumed number of teeth engaged, the load capability of a splined coupling is determined. However, due to the variations in tooth geometry from manufacuture, the number of teeth actually engaged is dependent on the applied load and the tooth errors. The variations result in sequential tooth engagement with increasing load. To date, little work has been done to model tooth engagement and the stresses resulting from unequal load sharing among engaged teeth. A Statistical Tooth Engagement Model (STEM) has been developed which allows designers to estimate tooth engagement and resulting stress based on a statistical representation of the tooth errors. STEM is validated with finite element models as well as some preliminary experimental tests. Parametric studies are performed to determine the effect and sensitivities of variations in tooth parameters and tooth errors.

State estimation is an essential part of any robotic autonomy solution. Continuous-time trajectory estimation is an attractive method because continuous trajectories can be queried at any time, allowing for fusion of multiple asynchronous, high-frequency measurement sources. This dissertation investigates various continuous-time estimation algorithms and their application to a handful of mobile robot autonomy and sensor calibration problems. In particular, we begin by analyzing and comparing two prominent continuous-time trajectory representations from the literature: Gaussian processes and splines, both on vector spaces and Lie groups. Our comparisons show that the two methods give comparable results so long as the same measurements and motion model are used. We then apply spline-based estimation to the problem of calibrating the extrinsic parameters between a camera and a GNSS receiver by fusing measurements from these two sensors and an IMU in continuous-time. Next, we introduce a novel estimation technique that uses the differential flatness property of dynamic systems to model the continuous-time trajectory of a robot on its flat output space, and show that estimating in the flat output space can provide superior accuracy and computation time than estimating on the configuration manifold. We use this new flatness-based estimation technique to perform pose estimation for velocity-constrained vehicles using only GNSS and IMU and show that modeling on the flat output space renders the global heading of the system observable, even when the motion of the system is insufficient to observe attitude from the measurements alone. We then show how flatness-based estimation can be used to calibrate the transformation between the dynamics coordinate frame and the coordinate frame of a sensor, along with other sensor-to-dynamics parameters, and use this calibration to improve the performance of flatness-based estimation when six-degree-of-freedom measurements are involved. Our final contribution involves nonlinear control of a quadrotor aerial vehicle. We use Lie theoretic concepts to develop a geometric attitude controller that utilizes logarithmic rotation error and prove that this controller is globally-asymptotically stable. We then demonstrate the ability of this controller to track highly-aggressive quadrotor trajectories.

In this dissertation, I provide a robust, efficient inverse mapping algorithm for use in immersed simulation methods, specifically in the Flex Representation Method. I also explore a structural theory that unifies the theories of solids, shells, beams, and rigid bodies. As part of this, I preform a preliminary exploration of applying the Flex Representation Method to shells. Finally, I explore why higher order elements suffer from small critical time steps in explicit dynamics. I then propose a simple method of remedying this issue by exploiting the properties of U-splines.

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The generalized linear model (GLM) is a popular model in many research areas. In the GLM, each outcome of the dependent variable is assumed to be generated from a particular distribution function in the exponential family. The mean of the distribution depends on the independent variables. The link function provides the relationship between the linear predictor and the mean of the distribution function. In this dissertation, two semiparametric extensions of the GLM will be developed. In the first part of this dissertation, we have proposed a new model, called a semiparametric generalized linear model with a log-concave random component (SGLM-L). In this model, the estimate of the distribution of the random component has a nonparametric form while the estimate of the systematic part has a parametric form. In the second part of this dissertation, we have proposed a model, called a generalized semiparametric single-index mixed model (GSSIMM). A nonparametric component with a single index is incorporated into the mean function in the generalized linear mixed model (GLMM) assuming that the random component is following a parametric distribution. In the first part of this dissertation, since most of the literature on the GLM deals with the parametric random component, we relax the parametric distribution assumption for the random component of the GLM and impose a log-concave constraint on the distribution. An iterative numerical algorithm for computing the estimators in the SGLM-L is developed. We construct a log-likelihood ratio test for inference. In the second part of this dissertation, we use a single index model to generalize the GLMM to have a linear combination of covariates enter the model via a nonparametric mean function, because the linear model in the GLMM is not complex enough to capture the underlying relationship between the response and its associated covariates. The marginal likelihood is approximated using the Laplace method. A penalized quasi-likelihood approach is proposed to estimate the nonparametric function and parameters including single-index coe±cients in the GSSIMM. We estimate variance components using marginal quasi-likelihood. Asymptotic properties of the estimators are developed using a similar idea by Yu (2008). A simulation example is carried out to compare the performance of the GSSIMM with that of the GLMM. We demonstrate the advantage of my approach using a study of the association between daily air pollutants and daily mortality adjusted for temperature and wind speed in various counties of North Carolina. / Ph. D.

The proportional hazard model plays a fundamental role in the analysis of time-to-event data. In this thesis, we conduct a simulation study to evaluate the performance of M-splines to estimate the baseline cumulative hazard function for the proportional hazard model. We assess the effect of sample size and number of knots in the estimation process. Finally, we apply this method to a sample of students from a university where the event of interest is the payment on time of the last tuition fee.