Doctor of Philosophy / Department of Statistics / Wei-Wen Hsu / The classification methods based on a linear combination of multiple biomarkers have been widely used to improve the accuracy in disease screening and diagnosis. However, it is seldom to include covariates such as gender and age at diagnosis into these classification procedures. It is known that biomarkers or patient outcomes are often associated with some covariates in practice, therefore the inclusion of covariates may further improve the power of prediction as well as the classification accuracy. In this study, we focus on the classification methods for multiple biomarkers adjusting for covariates. First, we proposed a covariate-adjusted classification model for multiple cross-sectional biomarkers. Technically, it is a two-stage method with a parametric or non-parametric approach to combine biomarkers first, and then incorporating covariates with the use of the maximum rank correlation estimators. Specifically, these parameter coefficients associated with covariates can be estimated by maximizing the area under the receiver operating characteristic (ROC) curve. The asymptotic properties of these estimators in the model are also discussed. An intensive simulation study is conducted to evaluate the performance of this proposed method in finite sample sizes. The data of colorectal cancer and pancreatic cancer are used to illustrate the proposed methodology for multiple cross-sectional biomarkers. We further extend our classification method to longitudinal biomarkers. With the use of a natural cubic spline basis, each subject's longitudinal biomarker profile can be characterized by spline coefficients with a significant reduction in the dimension of data. Specifically, the maximum reduction can be achieved by controlling the number of knots or degrees of freedom in the spline approach, and its coefficients can be obtained by the ordinary least squares method. We consider each spline coefficient as ``biomarker'' in our previous method, then the optimal linear combination of those spline coefficients can be acquired using Stepwise method without any distributional assumption. Afterward, covariates are included by maximizing the corresponding AUC as the second stage. The proposed method is applied to the longitudinal data of Alzheimer's disease and the primary biliary cirrhosis data for illustration. We conduct a simulation study to assess the finite-sample performance of the proposed method for longitudinal biomarkers.

The purposes of this dissertation were to examine the phase characteristics of the countermovement jump force-time curve between athletes based on jumping ability, examine the influence of maximal muscular strength on the countermovement jump force-time curve phase characteristics of athletes, and to examine the behavior of the countermovement jump force-time curve phase characteristics over the course of a training process in athletes of varying strength levels. The following are the major findings of these dissertations. The analysis of athletes by jumping ability suggested that proficient jumpers are associated with greater relative phase magnitude and phase impulse throughout the phases contained in the positive impulse of the countermovement jump force-time curve. Additionally, phase duration was not found to differ between athletes based on jumping ability or between male and female athletes. The analysis of athletes based on maximal muscular strength suggested that only unweighted phase duration differs between strong and less-strong athletes. Interestingly, in both investigations based on jumping ability and maximal strength indicated the relative shape of the stretching phase representing the rise in positive force was related to an athlete’s jumping ability (jump height). The results of the longitudinal analysis of countermovement jump force-time phase characteristics identified that these variables can be frequently assessed throughout a training process to provide information of regarding an athlete performance state. Furthermore, based on the contrasting behaviors of many of the countermovement jump force-time curve phase characteristics over time, an athlete’s level of muscular strength may influence how these characteristics are expressed in the context of a training process.

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Since the beginning of humankind, architecture has been a sacred source for all civilizations, and that has provided a gateway for man to reach the heavens above. In terms of concept and value, Persian art and architecture is considered as a rich source to be acknowledged. Within Persian architecture, the emphasis was placed strongly on beauty and sacred geometry; Persians calculated the proportions of heaven reflected upon them in the dimensions of buildings on the earth. Iranian culture has utilized the written word as an art form; this goes beyond normal means of communication. Iranian calligraphers produced eloquent styles and patterns through their divine talent, and this was displayed in the architecture. Parviz Tanavoli, as the greatest contemporary artist of Iran, has a strong tendency to be attracted to words and letters which has a long history in Iranian culture. Experimenting through aspects of cultural interaction in fine and applied arts has led to the understanding that when aesthetic elements of cultures are used to create a new design, it leads to both a new aesthetic creation and a fresh understanding of the cultures involved. This collection was designed and manufactured by concentrating on organic and curved forms and utilizing them in the design practice, while having a touch on cultural elements such as patterns and alphabets. The curved abstract shapes create a conceptual harmony, depicted in Persian patterns via functional three dimensional pieces.

It has been twelve years since the last time the yield curve was inverted. Since 2017, the yield curve has been continuing to flatten and has almost entered an inverted state. The last five recessions have been preceded by the inversion of the yield curve. I examine momentum trading strategy’s ability to outperform during an inverted yield curve state. The yield curve can enter the momentum portfolio strategy through the portfolio’s formation and holding period. I document the increased performance of the momentum strategy’s total portfolio return in an inverted state. These results have implications on the timing a momentum trading strategy might be implemented.

Ratings curves are conventional means to continuously provide estimates of discharges in rivers. Among the most-often adopted assumptions in building these curves are the steady and uniform flow conditions for the open-channel flow that in turn provide a one-to-one relationships between the variables involved in discharge estimation. The steady flow assumption is not applicable during propagation of storm-generated waves hence the question on the validity of the steady rating curves during unsteady flow is of both scientific and practical interest. Scarce experimental evidence and analytical inferences substantiate that during unsteady flows the relationship between some of the variables is not unique leading to looped rating curves (also labeled hysteresis). Neglecting the unsteadiness of the flow when this is large can significantly affect the accuracy of the flow estimation. Currently, the literature does not offer criteria for a comprehensive evaluation of the methods for estimation of the departure of the looped rating curves from the steady ones nor for identifying the most appropriate means to dynamically capturing hysteresis for different possible river flow conditions. Therefore, the overarching goal of this study was to explore the uncertainty of the conventional approaches for constructing stage-discharge rating curves (hQRCs) and to evaluate methodologies for accurate and continuous discharge monitoring in unsteady open channel flows using analytical inference, index velocity rating curves (VQRCs), and continuous slope area method (CSA) with considerations on discharge measurement uncertainty. The study will demonstrate conceptual and experimental evidences to illustrate some of the unsteady flow impacts on rating curves and suggest the development of a uniform end-to-end methodology to enhance the accuracy of the current protocols for continuous stream flow estimation for both steady and unsteady river conditions. Moreover, hysteresis diagnostic method will be presented to provide the way to conveniently evaluate when and where the hysteresis becomes significant as a function of the site and storm event characteristics. The measurement techniques and analysis methodologies proposed herein will allow to dynamically tracking both the flood wave propagation and the associated uncertainty in the conventional RCs.

The theory of the Environmental Kuznets Curve (EKC) proposes to answer important questions regarding the connections between economic growth (development) and the environment. The theory postulates the environment need not always suffer as the economy develops, and it has generated strong support and opposition. Rather than attempting to defend or debunk EKC theory, this research challenges a practice engaged in by proponents and opponents alike. Simplifying assumptions are a necessary part of economic analysis, but this research shows that any assumptions may not be universally applicable. Utilizing, in turn, a simple one good model and then a more complicated two good model, it is discovered that the competing assumptions utilized by proponents and opponents of the EKC theory may both be valid, depending upon the conditions present in the system being analyzed.

In this thesis, we will relax two major assumptions in economic growth theory. First of all, we will study growth models with eterogeneous capital goods, the so called vintage capital models: technological advances are not incorporated in all generations of capital goods and there is an optimal age distribution of the capital stocks. We will devote the three first chapters of this thesis to this class of models. Several lessons on technology diffusion will be extracted, notably in connection with the nowadays hot debate on energy saving, technology progress, growth and environmental policy. Secondly, we will introduce explicitly the geographical dimension to the neoclassical growth models, which allow us to build a new class of models. We call them geographic growth models. In this framework, we will identify the consequences of capital mobility across space. In particular, we will examine the optimal stationary distribution of capital across space. Under this framework, we could (i) study the continuous space structure, and (ii) allow capital accumulation.

Here we search for the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computer-aided design, curves have been sought which maximize "smoothness". The curve discussed here is the one arising in this way from a commonly used measure of smoothness. The human visual system may use such a curve when it constructs a subjective contour.

Freehand sketching is both a natural and crucial part of design, yet is unsupported by current design automation software. We are working to combine the flexibility and ease of use of paper and pencil with the processing power of a computer to produce a design environment that feels as natural as paper, yet is considerably smarter. One of the most basic steps in accomplishing this is converting the original digitized pen strokes in the sketch into the intended geometric objects using feature point detection and approximation. We demonstrate how multiple sources of information can be combined for feature detection in strokes and apply this technique using two approaches to signal processing, one using simple average based thresholding and a second using scale space.