This thesis addresses three topics in the area of statistics and probability, with applications in risk management. First, for the testing problems in the high-dimensional (HD) data analysis, we present a novel method to formulate empirical likelihood tests and jackknife empirical likelihood tests by splitting the sample into subgroups. New tests are constructed to test the equality of two HD means, the coefficient in the HD linear models and the HD covariance matrices. Second, we propose jackknife empirical likelihood methods to formulate interval estimations for important quantities in actuarial science and risk management, such as the risk-distortion measures, Spearman's rho and parametric copulas. Lastly, we introduce the theory of completely mixable (CM) distributions. We give properties of the CM distributions, show that a few classes of distributions are CM and use the new technique to find the bounds for the sum of individual risks with given marginal distributions but unspecific dependence structure. The result partially solves a problem that had been a challenge for decades, and directly leads to the bounds on quantities of interest in risk management, such as the variance, the stop-loss premium, the price of the European options and the Value-at-Risk associated with a joint portfolio.

Tracking of human motion and object identification and recognition are important in many applications including motion capture for human-machine interaction systems. This research is part of a global project to enable a service robot to recognize new objects and perform different object-related tasks based on task guidance and demonstration provided by a general user. This research consists of the calibration and testing of two vision systems which are part of a robot-vision system. First, real-time tracking of a human hand is achieved using images acquired from three calibrated synchronized cameras. Hand pose is determined from the positions of physical markers and input to the robot system in real-time. Second, a multi-line laser camera range sensor is designed, calibrated, and mounted on a robot end-effector to provide three-dimensional (3D) geometry information about objects in the robot environment. The laser-camera sensor includes two cameras to provide stereo vision. For the 3D hand tracking, a novel score-based hand tracking scheme is presented employing dynamic multi-threshold marker detection, a stereo camera-pair utilization scheme, marker matching and labeling using epipolar geometry and hand pose axis analysis, to enable real-time hand tracking under occlusion and non-uniform lighting environments. For surface-geometry measurement using the multi-line laser range sensor, two different approaches are analyzed for two-dimensional (2D) to 3D coordinate mapping, using Bezier surface fitting and neural networks, respectively. The neural-network approach was found to be a more viable approach for surface-geometry measurement worth future exploration for its lower magnitude of 3D reconstruction error and consistency over different regions of the object space.

Tracking of human motion and object identification and recognition are important in many applications including motion capture for human-machine interaction systems. This research is part of a global project to enable a service robot to recognize new objects and perform different object-related tasks based on task guidance and demonstration provided by a general user. This research consists of the calibration and testing of two vision systems which are part of a robot-vision system. First, real-time tracking of a human hand is achieved using images acquired from three calibrated synchronized cameras. Hand pose is determined from the positions of physical markers and input to the robot system in real-time. Second, a multi-line laser camera range sensor is designed, calibrated, and mounted on a robot end-effector to provide three-dimensional (3D) geometry information about objects in the robot environment. The laser-camera sensor includes two cameras to provide stereo vision. For the 3D hand tracking, a novel score-based hand tracking scheme is presented employing dynamic multi-threshold marker detection, a stereo camera-pair utilization scheme, marker matching and labeling using epipolar geometry and hand pose axis analysis, to enable real-time hand tracking under occlusion and non-uniform lighting environments. For surface-geometry measurement using the multi-line laser range sensor, two different approaches are analyzed for two-dimensional (2D) to 3D coordinate mapping, using Bezier surface fitting and neural networks, respectively. The neural-network approach was found to be a more viable approach for surface-geometry measurement worth future exploration for its lower magnitude of 3D reconstruction error and consistency over different regions of the object space.

The effects of basin edge slope on the dynamic response of soil deposits are assessed by using one-dimensional and two-dimensional numerical analyses. 24 basin models having trapezoidal cross section are generated to represent different geometries (basin depth, basin edge slope) and soil type. Harmonic base motions with different predominant periods (Tp) are used in the analyses. The results indicate that, for a constant basin edge slope and a constant ratio of fundamental period of site to the predominant period of base motion (Tn/Tp), the response is almost the same for different soil types, basin depths and base motions. In the sloping edge region, one-dimensional response analysis predictions are found to be conservative compared to two-dimensional analysis predictions / however beyond this region they are unconservatively biased by a factor as high as 1.5. The sloping edge region and the horizontal region of the basin are denoted by normalized distance (ND) values varying from 0 to 1 and 1 to 2 respectively. The critical region where maximum amplification observed falls in the range of ND=1.0 to ND=1.5 for basins having slopes greater than 30o. The lower boundary of the critical region is shifted towards as low as ND=0.2 for basins having slopes less than 30o. For a constant value of Tn/Tp, the increase in the amplification is smooth for basins with gentle slopes as compared to basins with steep slopes for the region where ND~1. For a basin and earthquake couple approaching to resonance state (Tn/Tp=1), the amplification for the region where ND is greater than 1 is found to be as high as 100% of that is found for the region where ND~1.

In this work we present a novel computational framework for analyzing evolution of uncertainty in state trajectories of a hypersonic air vehicle due to uncertainty in initial conditions and other system parameters. The framework is built on the so called generalized Polynomial Chaos expansions. In this framework, stochastic dynamical systems are transformed into equivalent deterministic dynamical systems in higher dimensional space. In the research presented here we study evolution of uncertainty due to initial condition, ballistic coefficient, lift over drag ratio and atmospheric density. We compute the statistics using the continuous linearization (CL) approach. This approach computes the jacobian of the perturbational variables about the nominal trajectory. The covariance is then propagated using the riccati equation and the statistics is compared with the Polynomial Chaos method. The latter gives better accuracy as compared to the CL method. The simulation is carried out assuming uniform distribution on the parameters (initial condition, density, ballistic coefficient and lift over drag ratio). The method is then extended for Gaussian distribution on the parameters and the statistics, mean and variance of the states are matched with the standard Monte Carlo methods. The problem studied here is related to the Mars entry descent landing problem.

For decades, advances in device scaling has proven to be critical in improving the performance and productivity of 2D systems. In this thesis, we explore how advances in technology have pushed functional integration to such a high-level that interconnection and packaging issues represent real barriers to further progress. While three-dimensional (3D) integration offers to be a potential contender to overcome the barriers of increased energy consumption due to interconnects and bandwidth limitations, there are certain challenges that must be overcome before systems can be successfully stacked. Cooling and power delivery are among these key challenges in the integration of high performance 3D ICs. To address these challenges, microchannel heat sinks for inter-stratum cooling and through-silicon vias (TSVs) for signaling and power delivery between stacked ICs were explored. Novel integration schemes to integrate these uidic and electrical interconnects in conventional CMOS processes were also explored. Compact physical modeling was utilized to understand the trade-offs involved in the integration of electrical and microfluidic interconnects in a 3D IC stack. These concepts were demonstrated experimentally by showing different CMOS compatible methods of fabricating microchannels and integration of high aspect ratio (~20:1) and high density (200,000/cm²) electrical TSVs in the fins of the microchannels for signaling and power delivery. A novel mesh process for bottom up plating of high aspect ratio TSVs is also shown in this work. Fluidic reliability measurements are shown to demonstrate the feasibility of this technology. This work also demonstrates the design and fabrication of a 3D testbed which consists of a 2 chip stack with microchannel cooling on each level. Preliminary testing of the stack along with interlayer electro-fluidic I/Os has also been demonstrated.

Three dimensional television (3DTV) is believed to be the future of television broadcasting that will replace current 2D HDTV technology. In the future, 3DTV will bring a more life-like and visually immersive home entertainment experience, in which users will have the freedom to navigate through the scene to choose a different viewpoint. A desired view can be synthesized at the receiver side using depth image-based rendering (DIBR). While this approach has many advantages, one of the key challenges in DIBR is generating high quality synthesized views. This work presents novel methods to measure and enhance the quality of 3D videos generated through DIBR. For quality measurements we describe a novel method to characterize and measure distortions by multiple cameras used to capture stereoscopic images. In addition, we present an objective quality measure for DIBR-based 3D videos by evaluating the elements of visual discomfort in stereoscopic 3D videos. We also introduce a new concept called the ideal depth estimate, and define the tools to estimate that depth. Full-reference and no-reference profiles for calculating the proposed measures are also presented. Moreover, we introduce two innovative approaches to improve the quality of the synthesized views generated by DIBR. The first approach is based on hierarchical blending of the background and foreground information around the disocclusion areas which produces a natural looking, synthesized view with seamless hole-filling. This approach yields virtual images that are free of any geometric distortions, unlike other algorithms that preprocess the depth map. In contrast to the other hole-filling approaches, our approach is not sensitive to depth maps with high percentage of bad pixels from stereo matching. The second approach further enhances the results through a depth-adaptive preprocessing of the colored images. Finally, we propose an enhancement over depth estimation algorithm using the depth monocular cues from luminance and chrominance. The estimated depth will be evaluated using our quality measure, and the hole-filling algorithm will be used to generate synthesized views. This application will demonstrate how our quality measures and enhancement algorithms could help in the development of high quality stereoscopic depth-based synthesized videos.

<p>In this thesis, two applications of dimensional deconstruction are studied. The first application is a model for neutrino oscillations in the presence of a large decon- structed extra dimension. In the second application, Kaluza{Klein dark matter from a latticized universal extra dimension is studied. The goal of these projects have been twofold. First, to see whether it is possible to reproduce the relevant features of the higher-dimensional continuum theory, and second, to examine the effect of the latticization in experiments. In addition, an introduction to the the- ory of dimensional deconstruction as well as to the theory of continuous extra dimensions is given. Furthermore, the various higher-dimensional models, such as Arkani-Hamed{Dvali{Dimopolous (ADD) models and models with universal extra dimensions, that have been intensively studied in recent years, are discussed.</p>

The paper describes how a two-dimensional absolute measuring system can explicitly be realized. The theoretical background, the experimental setup, the evaluation algorithm, and the results of measurement are discussed in detail.

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.