Testing uniformity in the univariate case has been studied by many researchers. Many papers have been published on this issue, whereas the multi-dimensional uniformity test seems to have received less attention in the literature. A new test statistic for the multi-dimensional uniformity is proposed in this thesis. The proposed test statistic can be used to test whether an underlying multivariate probability distribution differs from a multi-dimensional uniform distribution. Some important properties of the proposed test statistic are discussed. As a special case, the bivariate test statistic is discussed in detail and the critical values of test statistic are obtained. By performing Monte Carlo simulation, the power of the new test is compared with the Distance to Boundary test, which was a recently proposed statistical test for multi-dimensional uniformity by Berrendero, Cuevas and Vazquez-Grande (2006). It has been shown that the test proposed in this thesis is more powerful than the Distance to Boundary test in some cases.

Indiana University-Purdue University Indianapolis (IUPUI) / Too few studies relating to motivation and wellness have targeted the NCAA Division II student-athlete (SA) population. PURPOSES: To examine differences in SAs’ sport motivation (SM) types over three time points as well as multi-dimensional wellness (MDW) levels in SAs during one time point. METHODS: Overall, 530 Division II SAs (nmales = 355, nfemales = 175) with an overall age range of 18 to 23 (M = 19.40, SD = 1.33) from 21 teams voluntarily completed the 18-item Self-Determination Theory-based SM Scale II used to measure six motivation types, the 45-item MDW Inventory used to measure nine wellness dimensions, and a demographics questionnaire. Repeated measures Analyses of Variance (ANOVA) and 2x2x3 Mixed ANOVAs were used to analyze SM types while a multivariate ANOVA was used to analyze MDW with an alpha level of 0.05 set for statistical significance. RESULTS: Analyses demonstrated statistically significant differences in SM types over time (p = .05), interactions and differences in SM types between interactive/coactive and male/female SAs (p = .05), and interactions and differences in MDW levels between male/female SAs and SAs who completed/did not complete a college wellness course (p = .05). CONCLUSIONS: Findings suggested that autonomous-based SM types decreased over time whereas amotivation increased over time indicating possible athlete burnout. Interactive and female SAs showed similarities also representative of athlete burnout. SAs who completed the MDW course demonstrated higher physical wellness exercise scores than SAs who did not. Female SAs had higher means in five wellness dimensions when compared to male SAs. SAs who completed the course showed higher means for seven wellness dimensions versus SAs who did not. Further research should ensue to better understand motivation and wellness on a national scale examining Division I, II and III and NAIA athletes in order to provide more generalizable results.

Water distribution system (WDS) is very critical to human health and societal welfare. Maintaining the quality of the water so that potable water gets distributed to consumers has always been a challenge in the water industry. Deterioration of water quality can happen either accidentally or deliberately and the widespread geography of the water system makes it even more vulnerable to contamination. In this respect, researchers and utilities have some response action to flush out the contaminants when they are detected. But not all networks have reliable sensors to detect the contamination and lack of guidelines for sensor deployment has made the situation even more serious. Given this context, framework for decision-making in the case of WDN against contamination is a much-needed approach. Understanding the capability of the water system to handle the contamination event could provide ample insight on how to better protect the system and how to handle if the contamination does enter the system. In this regard, this study explores the concept of resilience to define the system performance when a disruption occurs, which in this case is the intrusion of contaminants. Resilience of a system can be viewed from different perspectives, each highlighting different aspect of the system. With this insight, the objective of this research is to characterize the resilience of the water system against contamination for multiple aspects of performance or functionalities and use that concept to further elucidate the decision-making process. Hydraulic and quality simulation to emulate the contamination intrusion in WDN is performed by using EPANET-MATLAB Toolkit which has the needed package for both EPANET and EPANET-MSX. EPANET-MSX is widely used for simulating multiple intrusions in the system. The result from the MATLAB simulation gives the quality at each node which is then used to draw the performance time-series curve. Resilience is then computed for each of the performance metrics using the area under the curve method. This study makes a comparison study for multi-dimensional resilience and describes in detail the need of considering the attributes of resilience which are resistance, loss rate, recovery rate, failure duration, and recovery ability. To perceive the concept of resilience with respect to the failure scenarios, a sensitivity analysis was performed for four failure contexts namely, intrusion time, intrusion duration, intruded contaminated mass, and the number of intrusion nodes. Furthermore, a system measure is defined to aggregate different individual resilience to overcome the challenge of multi-objective decision-making. Application of both integrated and multi-dimensional resilience was conducted for optimal sensor placement in the network to maximize the resilience of the whole system. The goal of this thesis is to introduce the multi-dimensional resilience concept as a tool for decision-making based on multiple aspects of system performance by characterizing the WDS resilience and water quality sensor optimization based on different aspects of system functionality under contaminant intrusion events.

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Residual-distribution methods offer several potential benefits over classical methods, such as a means of applying upwinding in a multi-dimensional manner and a multi-dimensional positivity property. While it is apparent that residual-distribution methods also offer higher accuracy than finite-volume methods on similar meshes, few studies have directly compared the performance of the two approaches in a systematic and quantitative manner. In this study, comparisons between residual distribution and finite volume are made for steady-state smooth and discontinuous flows of gas dynamics, governed by hyperbolic conservation laws, to illustrate the strengths and deficiencies of the residual-distribution method. Deficiencies which reduce the accuracy are analyzed and a new nonlinear scheme is proposed that closely reproduces or surpasses the accuracy of the best linear residual-distribution scheme. The accuracy is further improved by extending the scheme to fourth order using established finite-element techniques. Finally, the compact stencil, arithmetic workload, and data parallelism of the fourth-order residual-distribution scheme are exploited to accelerate parallel computations on an architecture consisting of both CPU cores and a graphics processing unit. Numerical experiments are used to assess the gains to efficiency and possible monetary savings that may be provided by accelerated architectures.

Residual-distribution methods offer several potential benefits over classical methods, such as a means of applying upwinding in a multi-dimensional manner and a multi-dimensional positivity property. While it is apparent that residual-distribution methods also offer higher accuracy than finite-volume methods on similar meshes, few studies have directly compared the performance of the two approaches in a systematic and quantitative manner. In this study, comparisons between residual distribution and finite volume are made for steady-state smooth and discontinuous flows of gas dynamics, governed by hyperbolic conservation laws, to illustrate the strengths and deficiencies of the residual-distribution method. Deficiencies which reduce the accuracy are analyzed and a new nonlinear scheme is proposed that closely reproduces or surpasses the accuracy of the best linear residual-distribution scheme. The accuracy is further improved by extending the scheme to fourth order using established finite-element techniques. Finally, the compact stencil, arithmetic workload, and data parallelism of the fourth-order residual-distribution scheme are exploited to accelerate parallel computations on an architecture consisting of both CPU cores and a graphics processing unit. Numerical experiments are used to assess the gains to efficiency and possible monetary savings that may be provided by accelerated architectures.

Medical studies increasingly use multi-modality imaging, producing multidimensional data that bring additional information that are also challenging to process and interpret. As an example, for predicting salvageable tissue, ischemic studies in which combinations of different multiple MRI imaging modalities (DWI, PWI) are used produced more conclusive results than studies made using a single modality. However, the multi-modality approach necessitates the use of more advanced algorithms to perform otherwise regular image processing tasks such as filtering, segmentation and clustering. A robust method for addressing the problems associated with processing data obtained from multi-modality imaging is Mean Shift which is based on feature space analysis and on non-parametric kernel density estimation and can be used for multi-dimensional filtering, segmentation and clustering. In this thesis, we sought to optimize the mean shift process by analyzing the factors that influence it and optimizing its parameters. We examine the effect of noise in processing the feature space and how Mean Shift can be tuned for optimal de-noising and also to reduce blurring. The large success of Mean Shift is mainly due to the intuitive tuning of bandwidth parameters which describe the scale at which features are analyzed. Based on univariate Plug-In (PI) bandwidth selectors of kernel density estimation, we propose the bandwidth matrix estimation method based on multi-variate PI for Mean Shift filtering. We study the interest of using diagonal and full bandwidth matrix with experiment on synthesized and natural images. We propose a new and automatic volume-based segmentation framework which combines Mean Shift filtering and Region Growing segmentation as well as Probability Map optimization. The framework is developed using synthesized MRI images as test data and yielded a perfect segmentation with DICE similarity measurement values reaching the highest value of 1. Testing is then extended to real MRI data obtained from animals and patients with the aim of predicting the evolution of the ischemic penumbra several days following the onset of ischemia using only information obtained from the very first scan. The results obtained are an average DICE of 0.8 for the animal MRI image scans and 0.53 for the patients MRI image scans; the reference images for both cases are manually segmented by a team of expert medical staff. In addition, the most relevant combination of parameters for the MRI modalities is determined.

Solving real world problems with mixed integer programming (MIP) involves efforts in modeling and efficient algorithms. To solve a minimization MIP problem, a lower bound is needed in a branch-and-bound algorithm to evaluate the quality of a feasible solution and to improve the efficiency of the algorithm. This thesis develops a new MIP model and studies algorithms for obtaining lower bounds for MIP. The first part of the thesis is dedicated to a new production planning model with pricing decisions. To increase profit, a company can use pricing to influence its demand to increase revenue, decrease cost, or both. We present a model that uses pricing discounts to increase production and delivery flexibility, which helps to decrease costs. Although the revenue can be hurt by introducing pricing discounts, the total profit can be increased by properly choosing the discounts and production and delivery decisions. We further explore the idea with variations of the model and present the advantages of using flexibility to increase profit. The second part of the thesis focuses on solving integer programming(IP) problems by improving lower bounds. Specifically, we consider obtaining lower bounds for the multi- dimensional knapsack problem (MKP). Because MKP lacks special structures, it allows us to consider general methods for obtaining lower bounds for IP, which includes various relaxation algorithms. A problem relaxation is achieved by either enlarging the feasible region, or decreasing the value of the objective function on the feasible region. In addition, dual algorithms can also be used to obtain lower bounds, which work directly on solving the dual problems. We first present some characteristics of the value function of MKP and extend some properties from the knapsack problem to MKP. The properties of MKP allow some large scale problems to be reduced to smaller ones. In addition, the quality of corner relaxation bounds of MKP is considered. We explore conditions under which the corner relaxation is tight for MKP, such that relaxing some of the constraints does not affect the quality of the lower bounds. To evaluate the overall tightness of the corner relaxation, we also show the worst-case gap of the corner relaxation for MKP. To identify parameters that contribute the most to the hardness of MKP and further evaluate the quality of lower bounds obtained from various algorithms, we analyze the characteristics that impact the hardness of MKP with a series of computational tests and establish a testbed of instances for computational experiments in the thesis. Next, we examine the lower bounds obtained from various relaxation algorithms com- putationally. We study methods of choosing constraints for relaxations that produce high- quality lower bounds. We use information obtained from linear relaxations to choose con- straints to relax. However, for many hard instances, choosing the right constraints can be challenging, due to the inaccuracy of the LP information. We thus develop a dual heuristic algorithm that explores various constraints to be used in relaxations in the Branch-and- Bound algorithm. The algorithm uses lower bounds obtained from surrogate relaxations to improve the LP bounds, where the relaxed constraints may vary for different nodes. We also examine adaptively controlling the parameters of the algorithm to improve the performance. Finally, the thesis presents two problem-specific algorithms to obtain lower bounds for MKP: A subadditive lifting method is developed to construct subadditive dual solutions, which always provide valid lower bounds. In addition, since MKP can be reformulated as a shortest path problem, we present a shortest path algorithm that uses estimated distances by solving relaxations problems. The recursive structure of the graph is used to accelerate the algorithm. Computational results of the shortest path algorithm are given on the testbed instances.

As mobility and computing becomes ever more pervasive in society and business, the non-optimal use of radio resources has created many new challenges for telecommunication operators. Usage patterns of modern wireless handheld devices, such as smartphones and surfboards, have indicated that the signaling traffic generated is many times larger than at a traditional laptop. Furthermore, in spite of approaching theoretical limits by, e.g., the spectral efficiency improvements brought by 4G, this is still not sufficient for many practical applications demanded by end users. Essentially, users located at the edge of a cell cannot achieve the high data throughputs promised by 4G specifications. Worst yet, the Quality of Service bottlenecks in 4G networks are expected to become a major issue over the next years given the rapid growth of mobile devices. The main problems are because of rigid mobile systems architectures with limited possibilities to reconfigure terminals and base stations depending on spectrum availability. Consequently, new solutions must be developed that coexist with legacy infrastructures and more importantly improve upon them to enable flexibility in the modes of operation. To control the intelligence required for such modes of operation, cognitive radio technology is a key concept suggested to be part of the so-called beyond 4th generation mobile networks. The basic idea is to allow unlicensed users access to licensed spectrum, under the condition that the interference perceived by the licensed users is minimal. This can be achieved with the help of devices capable of accurately sensing the spectrum occupancy, learning about temporarily unused frequency bands and able to reconfigure their transmission parameters in such a way that the spectral opportunities can be effectively exploited. Accordingly, this indicates the need for a more flexible and dynamic allocation of the spectrum resources, which requires a new approach to cognitive radio network management. Subsequently, a novel architecture designed at the application layer is suggested to manage communication in cognitive radio networks. The goal is to improve the performance in a cognitive radio network by sensing, learning, optimization and adaptation.

Multi-resolution visualization (MRV) systems are widely used for handling large amounts of information. These systems look different but they share many common features. The visualization research community lacks a general framework that summarizes the common features among the wide variety of MRV systems in order to help in MRV system design, analysis, and enhancement. This dissertation proposes such a general framework. This framework is based on the definition that a MRV system is a visualization system that visually represents perceptions in different levels of detail and allows users to interactively navigate among the representations. The visual representations of a perception are called a view. The framework is composed of two essential components: view simulation and interactive visualization. View simulation means that an MRV system simulates views of non-existing perceptions through simplification on the data structure or the graphics generation process. This is needed when the perceptions provided to the MRV system are not at the user's desired level of detail. The framework identifies classes of view simulation approaches and describes them in terms of simplification operators and operands (spaces). The simplification operators are further divided into four categories, namely sampling operators, aggregation operators, approximation operators, and generalization operators. Techniques in these categories are listed and illustrated via examples. The simplification operands (spaces) are also further divided into categories, namely data space and visualization space. How different simplification operators are applied to these spaces is also illustrated using examples. Interactive visualization means that an MRV system visually presents the views to users and allows users to interactively navigate among different views or within one view. Three types of MRV interface, namely the zoomable interface, the overview + context interface, and the focus + detail interface, are presented with examples. Common interaction tools used in MRV systems, such as zooming and panning, selection, distortion, overlap reduction, previewing, and dynamic simplification are also presented. A large amount of existing MRV systems are used as examples in this dissertation, including several MRV systems developed by the author based on the general framework. In addition, a case study that analyzes and suggests possible improvements for an existing MRV system is described. These examples and the case study reveal that the framework covers the common features of a wide variety of existing MRV systems, and helps users analyze and improve existing MRV systems as well as design new MRV systems.