Doctor of Philosophy (Ph.D.), Bowling Green State University, 2018, Statistics

Recently the asymmetric Laplace distribution and its extensions have gained attention in the statistical literature. This may be due to its relatively simple form and its ability to model skewness and outliers. For these reasons, the asymmetric Laplace distribution is a reasonable candidate model for certain data that arise in finance, biology, engineering, and other disciplines. For a practitioner that wishes to use this distribution, it is very important to check the validity of the model before making inferences that depend on the model. These types of questions are traditionally addressed by goodness-of-fit tests in the statistical literature. In this dissertation, a new goodness-of-fit test is proposed based on energy statistics, a widely applicable class of statistics for which one application is goodness-of-fit testing. The energy goodness-of-fit test has a number of desirable properties. It is consistent against general alternatives. If the null hypothesis is true, the distribution of the test statistic converges in distribution to an infinite, weighted sum of Chi-square random variables. In addition, we find through simulation that the energy test is among the most powerful tests for the asymmetric Laplace distribution in the scenarios considered. In studying this statistic, we found that the current methods for parameter estimation of this distribution were lacking, and proposed a new method to calculate the maximum likelihood estimates of the multivariate asymmetric Laplace distribution through the expectation-maximization (E-M) algorithm. Our proposed E-M algorithm has a fast computational formula and often yields parameter estimates with a smaller mean squared error than other estimators.

Committee: Maria Rizzo Ph.D. (Advisor); Craig Zirbel Ph.D. (Committee Member); Wei Ning Ph.D. (Committee Member); Joseph Chao Ph.D. (Other) Subjects: Statistics

Master of Science, The Ohio State University, 2009, Computer Science and Engineering

One of the key topics in computer graphics and geometric optimization is surface representation and processing. Many recent advances in these areas are based on the Laplace-Beltrami operator on a surface. Discrete approximations of the operator such as the cotangent scheme are popular in applications like shape approximation and compact representation, mesh editing, surface smoothing, shape interpolation, watermarking etc. Belkin et al proposed a new algorithm for approximating the Laplace operator on a surface mesh with point-wise convergence, which, is not guaranteed in the cotangent schemes. In this thesis, we present an experimental study on how the performance of this method and its variants compare to that of the cotangent scheme under various scenarios like noise, boundary and sampling conditions. We use the diffusion distance metric to study the stability and the ground truth to measure the accuracy of these methods.

Committee: Yusu Wang PhD (Advisor); Tamal Dey PhD (Committee Member) Subjects: Computer Science

Master of Arts (MA), Bowling Green State University, 1954, Mathematics

Committee: David M. Krabill (Advisor) Subjects: Mathematics

Master of Arts (MA), Bowling Green State University, 1954, Mathematics

Committee: David M. Krabill (Advisor) Subjects: Mathematics

Doctor of Philosophy (PhD), Ohio University, 2022, Mathematics (Arts and Sciences)

This study is devoted to the construction of reflection formulae for solutions to elliptic differential equations subject to various boundary conditions on a real analytic arc about that arc. Most of the results known in the literature deal with the Dirichlet condition. One of the main results of this work is a derivation of the reflection law for a harmonic function w(x,y), defined in a neighborhood of a real-analytic curve in the plane subject to a non-homogeneous Robin condition, aw+b_nw=phi_w on that curve. Here a and b are constants, and phi_w is the restriction of a holomorphic function onto the curve. For the case of the homogeneous condition, when phi_w=0, while a and b are real-analytic functions, a reflection formula was derived in Belinskiy and Savina, using the reflected fundamental solution method. Here, we construct a Robin-to-Neumann mapping and use it for obtaining the reflection operator. Since the two formulae look different, we show their equivalence when a and b are constants and phi_w=0. As examples, we show reflection formulae for non-homogeneous Neumann and Robin conditions on the most important for applications boundaries, such as circles and lines. Construction of Neumann-to-Dirichlet and Neumann-to-Robin operators in the form that allows to obtain reflection formulae to solutions of elliptic equations subject to Neumann and Robin conditions given on a real analytic arc is also an important result by itself. In chapter 3, we discuss the simplest version of our approach, specifically what we are talking about is harmonic functions in a neighborhood of the unit circle. The results of this chapter are published in Analysis and Mathematical Physics (2019). In chapter 4, we discuss reflections for harmonic functions near a real-analytic arc. The results of this chapter are published in Applicable Analysis (2022). Chapter 5 is devoted to the reflections of solutions to the Helmholtz equation, where we expand our approach earlier developed fo (open full item for complete abstract)

Committee: Tatiana Savin (Advisor); Qiliang Wu (Committee Member); Alexander Neiman (Committee Member); Archil Gulisashvili (Committee Member) Subjects: Applied Mathematics; Mathematics

Doctor of Philosophy, The Ohio State University, 2020, Mechanical Engineering

Bioinspiration is an emerging field of study. It translates to the creation of products, devices, and processes by using materials and processes found in living nature. Economic impact of bioinspired materials and surfaces is significant, on the order of several hundred billion dollars per year worldwide. Along the same line, this PhD dissertation attempts on solving two problems using bioinspired solutions: 1) the water crisis and 2) gas bubbles movement. Fresh water sustains human life and is vital for human health. Water scarcity affects more than 40% of the global population and is projected to rise. Furthermore, various factors, including population growth and unsafe industrial practices, have put strain on “clean” water supply in many parts of the world, including the Americas. It is certain than the current supply of fresh water needs to be supplemented to meet future needs. Living nature provides many lessons for water source. It has evolved species, which can survive in the most arid regions of the world by water collection from fog and condensation in the night. Before the collected water evaporates, species have mechanisms to transport water for storage or consumption. In this dissertation, first, an overview of these mechanisms is presented. Then, based on these mechanisms, the work done on bioinspired water harvesters is presented. Based on the results, design and projections of water harvesting towers is also presented. Gas bubbles are of interest in natural and technological applications. These applications include biomedicine, food production, drag reduction, water treatment, oil removal and surface cleaning. On the contrary, gas bubbles may also have a deleterious effect. For example, the gas bubbles produced in oil could potentially cause corrosion of pipelines resulting in reduced equipment life and wasted resources. Therefore, the study of gas bubbles movement in terms of their formation, interaction with underlying surfaces, and their movemen (open full item for complete abstract)

Committee: Bharat Bhushan (Advisor); Carlos Castro (Committee Member); Manoj Srinivasan (Committee Member) Subjects: Mechanical Engineering

PHD, Kent State University, 2019, College of Arts and Sciences / Department of Mathematical Sciences

The Laplace transforms of the stopping times related to the SPRT process for testing the mean of geometric and exponential distributions are presented. This leads us to find the exact distribution of the stopping times. The closed forms of the 1st and 2nd moments of this stopping time are also provided. We also extend these results to SPRT process associated to multi-dimensional geometric and exponential distributions in some certain case. We also provide a closed form expression for the ARL (average run length) of a multi-dimensional CUSUM stopping rule in the multinomial model. Some open questions are presented as well.

Committee: Mohammad Khan (Advisor) Subjects: Mathematics; Statistics

Master of Mathematical Sciences, The Ohio State University, 2018, Mathematical Sciences

The goal of this Masters Thesis is to explore methods used to solve for the wave function of a particle in an external, oscillating field. There is a particular focus on such methods applied to situations with linear potentials. Finally, a model is presented which explores the current leakage across a charged capacitor exposed to an external oscillating electric field.

Committee: Rodica Costin (Advisor); Krystal Taylor (Committee Member) Subjects: Mathematics; Physics

Doctor of Philosophy, The Ohio State University, 2002, Graduate School

Committee: Not Provided (Other) Subjects: Mathematics

Doctor of Philosophy (PhD), Ohio University, 2016, Electrical Engineering & Computer Science (Engineering and Technology)

The technological advantages of III-nitride semiconductors (III-Ns) have been demonstrated among others in the area of light emitting applications. Due to fundamental reasons limiting growth of InGaN with high Indium content, rare earth (RE) doped III-Ns provide an alternative way to achieve monolithic red, green, blue (RGB) emitters on the same III-Ns host material. However, the excitation efficiency of RE3+ ions in III-Ns is still insufficient due to the complexity of energy transfer processes involved. In this work, we consider the current understanding of the excitation mechanisms of RE3+ ions doped III-Ns, specifically Yb3+ and Eu3+ ions, and theories toward the excitation mechanism involving RE induced defects. In particular, we demonstrate and emphasize that the RE induced structural isovalent (RESI) trap model can be applied to explain the excitation mechanism of III-Ns:RE3+. Specifically, we have investigated the Yb3+ ion doped into III-Ns hosts having different morphologies. The observed emission peaks of Yb3+ ion were analyzed and fitted with theoretical calculations. The study of Yb3+ ion doped InxGa1-xN nano-rod films with varied indium (In) concentration shown the improvement of luminescence quality from the nanorod due to the presence of Yb dopant. Then we report the optical spectroscopy and DLTS study toward an Eu and Si co-doped GaN and its control counterpart. The Laplace-DLTS and optical-DLTS system developed in this work improved spectrum resolution compared to the conventional DLTS. The high resolution L-DLTS revealed at least four closely spaced defect levels associated with the Trap B, identified with regular DLTS, with activation energy 0.259±0.032 eV (Trap B1), 0.253±0.020 eV (Trap B2), 0.257±0.017 eV (Trap B3), and 0.268±0.025 eV (Trap B4) below the conduction band edge, respectively. Most importantly, a shallow hole trap was observed at energy 30±20 meV above the valence band edge of the GaN:Si,Eu3+ which can be attributed to the RESI hole (open full item for complete abstract)

Committee: Wojciech Jadwisienczak (Advisor); Savas Kaya (Committee Member); Martin Kordesch (Committee Member); Eric Stinaff (Committee Member); Kodi Avinash (Committee Member); Harsha Chenji (Committee Member) Subjects: Electrical Engineering; Materials Science; Nanotechnology; Optics

Doctor of Philosophy, University of Akron, 2015, Chemistry

Multiple systems were studied to advance the understanding of the chemical composition of the materials. These materials contained various structures or structures within different physical phases. Solid-state NMR techniques were used to probe effects of different chemical processes and environmental conditions on the chemical structures and phase composition of these materials. Much of the high thermal and chemical resistance of poly(vinylidene-co-hexafluoropropylene) is gained from cross-linking. The insolubility of the cross-linked fluoroelastomer has prevented the characterization of the structure at the cross-link site by NMR. Samples from each of the four stages of the cross-linking of poly(vinylidene-co-hexafluoropropylene) were analyzed with solid-state NMR to determine the chemical structure at the cross-linking site and the effects of cross-linking on the mobility of the elastomer chains. Spectral overlap from chemical shift dispersion hindered the use of simple 1D techniques to assign structural components to peaks in the NMR spectra. Relaxation studies that measured T1, T2, and T1ρ relaxation times were used to assign new peaks in the NMR spectra to the fluoride salts that are produced during cross-linking. The NMR relaxation data also indicated no reduction in the mobility of the fluoroelastomer from cross-linking. The chemical structure of the cross-link site was partially characterized by 2D-NMR. However, the amorphous nature of the polymer inhibited a full characterization of this location with 2D-NMR techniques. The structures that were identified at the cross-link site supported proposed structures. Solutions of NaCl and dextrose used in the preservation of premixed drugs were analyzed to distinguish the solid and liquid phases over a temperature range of -60 to 20 °C. The large chemical shift dispersion in the NMR spectra made analysis of the frequency domain data difficult. The time domain data of the single pulse NMR experiments were analyzed (open full item for complete abstract)

Committee: Peter Rinaldi Dr. (Advisor); Chrys Wesdemiotis Dr. (Committee Member); David Modarelli Dr. (Committee Member); Leah Shriver Dr. (Committee Member); Elizabeth McCord Dr. (Committee Member); Toshikazu Miyoshi Dr. (Committee Member) Subjects: Analytical Chemistry; Chemistry

PhD, University of Cincinnati, 2015, Engineering and Applied Science: Electrical Engineering

Microfluidics is a broad research field that encompasses applications for the medical, chemical, industrial and environment industries by leveraging the ability to control and manipulate micro-scale volumes of fluids. Most applications involve some sort of sensing capability for the presence of specific biological, chemical, or mineral compounds which has been termed Lab-on-a-chip(LOC). This refers to the miniaturization of standard laboratory analysis systems on to a single device to allow for faster yield times, reduced reagent and sample use and overall reduced costs. There are currently two primary fluid handling methods used involving fixed-channel, continuous flow or discrete droplet manipulation. Fixed-channel microfluidic devices have been proven to be reliable for several LOC applications, however, there is no ability to reconfigure or repurpose a device without a complete redesign and fabrication. The second handling method, known as digital microfluidics, uses electrical stimuli to move and manipulate individual droplets over an array of electrodes. By using this method, reconfigurability can be realized simply by changing a sequence of droplet(s) movements and therefore, a single platform can be used for a multitude of LOC applications without a complete device redesign. To further the overall capabilities of a digital microfluidic platform, the ability to control and hold some fluidic shape without an applied voltage adds not only bistability to the system, but can be advantageous for reduced energy consumption, extra functionalities and improved fluidic control. This also allows for simple displays applications to be realized. Presented in this dissertation is a cross-platform digital microfluidic device developed for both LOC and simple displays applications which utilizes an electrowetting grid array and Laplace barriers for bistability. Materials improvements, electrical control methods and the ability to perform all necessary tasks for both typ (open full item for complete abstract)

Committee: Jason Heikenfeld Ph.D. (Committee Chair); Philip Rack Ph.D. (Committee Member); Fred Beyette Ph.D. (Committee Member); Marc Cahay Ph.D. (Committee Member); Ian Papautsky Ph.D. (Committee Member) Subjects: Electrical Engineering

PhD, University of Cincinnati, 2014, Engineering and Applied Science: Electrical Engineering

Present day electronics are now taking on small form factors, unexpected uses, adaptability, and other features that only a decade ago were unimaginable even for most engineers. These electronic devices, such as tablets, smart phones, wearable sensors, and others, have further had a profound impact on how society interacts, works, maintains health, etc. To optimize electronics a growing trend has been to both minimize the physical space taken up by the individual electronic components as well as to maximize the number of functionalities in a single electronic device, forming a compact and efficient package. To accomplish this challenge in one step, many groups have used a design that has reconfigurable electromagnetic properties, maximizing the functionality density of the device. This would allow the replacement of multiple individual components into an integrated system that would achieve a similar result as the separate individual devices while taking up less space. For example, could a device have a reconfigurable antenna, allowing it optimal communication in various settings and across multiple communication bands, thus increasing functionality, range, and even reducing total device size. Thus far a majority of such reconfigurable devices involve connecting/disconnecting various physically static layouts to achieve a summation of individual components that give rise to multiple effects. However, this is not an ideal situation due to the fact that the individual components whether connected or not are taking up real-estate as well as electrical interference with adjacent connected components. This dissertation focuses on the reconfigurability of the metallic component of the electronic device, specifically microwave devices. This component used throughout this dissertation is that of an eutectic liquid metal alloy. The liquid metal allows the utilization of both the inherent compact form (spherical shape) of a liquid in the lowest energy state and t (open full item for complete abstract)

Committee: Jason Heikenfeld Ph.D. (Committee Chair); Michael D. Dickey Ph.D. (Committee Member); Christopher Tabor Ph.D. (Committee Member); Chong Ahn Ph.D. (Committee Member); Andrew Steckl Ph.D. (Committee Member) Subjects: Electromagnetism

Master of Science (M.S.), University of Dayton, 2014, Electrical Engineering

An analytic examination of 3-D holography under a recording geometry was carried out earlier in which 2-D spatial Laplace transforms were introduced in order to develop transfer functions for the scattered outputs under readout [1]. Thereby, the resulting reconstructed output was obtained in the 2-D Laplace domain whence the spatial information would be found only by performing a 2-D Laplace inversion. Laplace inversion in 2-D was attempted by testing a prototype function for which the analytic result was known using two known inversion algorithms via the Brancik and the Abate [2]. The results indicated notable differences in the 3-D plots between the algorithms and the analytic result, and hence were somewhat inconclusive. In this research, we take a close look at the Brancik algorithm in order to understand better the implications of the choices of key parameters such as the real and imaginary parts of the Bromwich contour and the grids sizes of the summation operations [3]. To assess the inversion findings, three prototype test cases are considered for which the analytic solutions are known. For specific choices of the algorithm parameters, optimal values are determined that would minimize errors in general. It is found that even though errors accumulate near the edges of the grid, overall reasonably accurate inversions are possible to obtain with optimal parameter choices that are verifiable via cross-sectional views. For a holographic problem, a 90-deg geometry recording model is established to derive two important coupled equations [4]. The optimum parameters are used to find the output field profiles under readout for a uniform plane wave, a point source wave and a Gaussian profile input. To understand the results better, a convolutional approach and a holistic approach are compared. Further work may include recording and reconstructing a dynamic object wave whose wave representations are more complicated. Also, the observed “right shift” phenomeno (open full item for complete abstract)

Committee: Monish Chatterjee (Advisor) Subjects: Optics

Doctor of Philosophy (PhD), Wright State University, 2013, Environmental Sciences PhD

Time series that exhibit multiple scaling properties in the frequency domain are common in natural systems (e.g., temperature through geologic time). NOAA verified hourly water level data ranging from 20 to 30 years in duration for nine stations in the North American Great Lakes is converted to the frequency domain using a complex discrete fast Fourier transform (FFT) and then expressed as a power spectrum in terms of frequency versus power. To quantify power law scaling behavior, a scaling exponent (β) is determined by fitting a power function to a log-log plot of frequency (f ) or period (T) versus power in the frequency domain. For water level fluctuations in the Great Lakes, the frequency domain exhibits four distinct regions of power law scaling. The mathematical relationship of the scaling exponent (β) to 1/f time series behavior is examined employing Bode analysis. Variations in scaling behavior of water level data, indicated by the patterns of change in amplitude and phase across frequencies, can be expressed through transfer functions. The transfer functions are created using Laplace transforms. Each Laplace term (s) has a fractional exponent based on the scaling exponent (β) derived from the Bode magnitude plot. Convolution of the transfer function in the time domain is equivalent to multiplication in the frequency domain (Laplace space). Combining the transfer functions for all frequencies yields a Frequency Response Model and provides a basis to determine how the system that created the time series will respond to any given input over all frequencies. For water level fluctuations in the Great Lakes, the scaling behavior pattern is well approximated by a combination of four linear differential equations or transfer functions, one primary equation for each distinct scaling region. The collective interactions of all equations over all frequencies create the Great Lakes Frequency Response Model and represent the underlying physical dynamics of the Great La (open full item for complete abstract)

Committee: Sarah Tebbens Ph.D. (Advisor); Christopher Barton Ph.D. (Committee Member); John Flach Ph.D. (Committee Member); Paul Seybold Ph.D. (Committee Member); Brian Tsou Ph.D. (Committee Member) Subjects: Applied Mathematics; Environmental Science; Geophysical; Geophysics; Hydrologic Sciences; Mathematics; Systems Design; Systems Science; Water Resource Management

Doctor of Philosophy (PhD), Ohio University, 2013, Physics and Astronomy (Arts and Sciences)

Neurons communicate with each other through dendrites and axons. Typically, dendrites are responsible for receiving signals from other neurons, while axons are the pathways to send out signals. Signal propagation through axons is closely correlated with their morphology. It is well known that the rate of signal propagation is proportional to the caliber of axons[2]. The intrinsic determinant of axonal caliber is the abundance of cytoskeletal protein, neurofilament (NF)[6]. NFs are not static but undergo "slow axonal transport", which is characterized by rapidly intermittent, asynchronous and bidirectional motion[21-23]. Many neurodegenerative diseases are related to the malfunction of neurofilament transport, either by accumulation of neurofilaments leading to swelling of the axon or by deficiency in neurofilaments resulting in axonal atrophy[9-12]. The mechanism of neurofilament transport can be explained by the "stop-and-go"; hypothesis[21, 24, 28], according to which neurofilaments spend long periods of time pausing interrupted by bouts of rapid movements. By the "stop-and-go" hypothesis, a compact and powerful mathematical model was proposed in [27], which connects the group behavior of neurofilaments as a wave to the individual neurofilament kinetics, which are observed directly from time-lapse imaging. Our main hypothesis is that axonal morphology is determined by the kinetics of NFs. According to this hypothesis, an increase in axonal caliber must go along with a decrease in speed of NFs and accordingly a modified kinetics. Two main examples, the distally increasing accumulation of NFs in the mouse optic nerve and the constrictions of myelinated axons at the nodes of Ranvier, demonstrate this hypothesis and support it with detailed experimental data. In the mouse optic nerve, sufficient data about the abundance of NFs proximal to distal as well as kinetic data are available to extract differential kinetics using our computational model. The most rema (open full item for complete abstract)

Committee: Peter Jung (Advisor); David F. J. Tees (Committee Member); Markus Böttcher (Committee Member); Ralph DiCaprio (Committee Member) Subjects: Biophysics; Physics

PhD, University of Cincinnati, 2012, Engineering and Applied Science: Electrical Engineering

The field of microfluidics involves the ability to manipulate small volumes of fluid (typically 10's of nanoliters) through small channels (diameters of 10's to 100's of microns). The main application of microfluidics to date has been in Lab on a Chip (LOC). The term Lab on a Chip implies that all of the analyses performed in a standard laboratory are consolidated onto a single chip device. This allows for: the use of less sample volume and reagents, improved separations, lower costs, shorter analysis times, and smaller footprints of analyzers. Recently there has also been a growing interest in the ability to manipulate small volumes of fluids (particularly colored ones) in the displays industry. Here, the ability to precisely control the fluids can be leveraged into making a highly reflective display. In both LOC and display applications it is imperative to be able to move the fluids reliably within the device. To date the dominant approach in microfluidics is to create a solid channel and flow the fluid through it using an external application of pressure. While this approach has proven to be very reliable it is not easily reconfigurable. If any change in the fluid path is desired a new channel configuration must be fabricated. The most robust approach to microfluidics leading to the widest range of applications would be one where fluid shape and/or position could be manipulated reversibly such that the same chip area could be utilized for a variety of fluidic functions. Various electrical approaches have been demonstrated to have the capability of manipulating fluid shape. This behavior of electrically manipulating a bulk fluid is commonly referred to as electrofluidics. To date, none of the electrofluidic approaches have shown the ability to maintain fluid shape after the electrical stimulus has been removed. This is a major issue as constant application of electrical stimulus causes high power consumption, increases the complexity of the drive electrodes an (open full item for complete abstract)

Committee: Jason Heikenfeld PhD (Committee Chair); Rajesh Naik PHD (Committee Member); Punit Boolchand PhD (Committee Member); Ian Papautsky PhD (Committee Member); Andrew Steckl PhD (Committee Member) Subjects: Electrical Engineering

MS, University of Cincinnati, 2007, Engineering : Electrical Engineering

In orthopaedics, current methods of drug delivery are technologically primitive in that they limit the control over dosing parameters including amplitude, frequency, and chronology of delivery. The research in this thesis works toward a sonofluidic delivery system that would allow control over these parameters. A drug-containing textile would be placed in-vivo at the delivery site, remaining non-permeated until the application of ultrasound. With ultrasound, the ambient fluid would permeate the textile, mix with the enclosed product, and release the product via diffusion. Chronologically separate delivery may be achieved by adjusting parameters of the textile and applied ultrasonic signal. This would allow delivery of product in controlled quantities, thus maximizing product absorption. This thesis discusses the design, fabrication, and testing of six generations of sonofluidic devices, along with future research directions, where recommendations are made for the design of a device conforming more to the standards of a commercial prototype.

Committee: Dr. Jason Heikenfeld (Advisor) Subjects:

PhD, University of Cincinnati, 2007, Engineering : Mechanical Engineering

As a numerical method used in the simulations of many potential and acoustic problems, the boundary element method (BEM) has suffered from high solution cost for quite some time, although it has the advantage in the modeling or meshing stage. One way to improve the solution efficiency of the BEM is to use the fast multipole method (FMM). The reduction of the computing cost with the FMM is achieved by using multilevel clustering of the boundary elements, the use of multipole expansions of the fundamental solutions and adaptive fast multipole algorithms. In combination with iterative solvers, the fast multipole boundary element method (FMBEM) is capable of solving many large-scale 3-D problems on desktop PCs. In this dissertation, 3-D adaptive fast multipole boundary element methods for solving large-scale potential (e.g., thermal and electrostatic) and acoustic wave problems are developed. For large-scale potential problems, an adaptive fast multipole algorithm is developed in the FMBEM implementation. The conventional boundary integral equation (CBIE), hyper-singular boundary integral equation (HBIE) and their combination, dual boundary integral equation (CHBIE), are adopted and can be selectively chosen to solve different models. Both the conventional and the new fast multipole method with diagonal translations are implemented and their performances are compared. Implementation issues related to reusing the pre-conditioner and storing the coefficients to further improve the efficiency are addressed. Numerical examples, ranging from simple block models to heat sink and large-scale models of micro-electro-mechanical-systems are tested and presented. For large-scale acoustic problems, a modified version of adaptive fast multipole algorithm is developed for full-space problems first. The Burton-Miller formulation using a linear combination of the CBIE and HBIE is used to overcome the non-uniqueness difficulties in the BIEs for exterior problems. Several large-scale rad (open full item for complete abstract)

Committee: Dr. Yijun Liu (Advisor) Subjects: Engineering, Mechanical

Doctor of Philosophy, The Ohio State University, 2012, Statistics

This dissertation is comprised of an introductory chapter and three stand-alone chapters. The three main chapters are tied together by a common theme: empirical hierarchical spatial-statistical modeling of non-Gaussian datasets. Such non-Gaussian datasets arise in a variety of disciplines, for example, in health studies, econometrics, ecological studies, and remote sensing of the Earth by satellites, and they are often very-large-to-massive. When analyzing ``big data,'' traditional spatial statistical methods are computationally intensive and sometimes not feasible, even in supercomputing environments. In addition, these datasets are often observed over extensive spatial domains, which make the assumption of spatial stationarity unrealistic. In this dissertation, we address these issues by using dimension-reduction techniques based on the Spatial Random Effects (SRE) model. We consider a hierarchical spatial statistical model consisting of a conditional exponential-family model for the observed data (which we call the data model), and an underlying (hidden) geostatistical process for some transformation of the (conditional) mean of the data model. Within the hierarchical model, dimension reduction is achieved by modeling the geostatistical process as a linear combination of a fixed number of basis functions, which results in substantial computational speed-ups. These models do not rely on specifying a spatial weights matrix, and no assumptions of homogeneity, stationarity, or isotropy are made. Another focus of the research presented in this dissertation is to properly account for spatial heterogeneity that often exists in these datasets. For example, with county-level health data, the population at risk is different for different counties and is typically a source of heterogeneity. This type of heterogeneity, whenever it exists, needs to be incorporated into the hierarchical model. We address this through the use of an offset term and by properly weighting the SRE (open full item for complete abstract)

Committee: Noel Cressie PhD (Advisor); Radu Herbei PhD (Committee Member); Desheng Liu PhD (Committee Member) Subjects: Statistics