Battail [1989] shows that an appropriate criterion for the design of long block codes is the closeness of the normalized weight distribution to a Gaussian distribution. A subsequent work shows that iterated product of single parity check codes satisfy this criterion [1994]. Motivated by these earlier works, in this thesis, we study the effect of the interleaver on the performance of turbo codes for large block lengths, $N\rightarrow\infty$. A parallel concatenated turbo code that consists of two or more component codes is considered. We demonstrate that for $N\rightarrow\infty$, the normalized weight of the systematic $\widehat{w_1}=\displaystyle\frac{w_1}{\sqrt{N}}$, and the parity check sequences $\widehat{w_2}=\displaystyle\frac{w_2}{\sqrt{N}}$ and $\widehat{w_3}=\displaystyle\frac{w_3}{\sqrt{N}}$ become a set of jointly Gaussian distributions for the typical values of $\widehat{w_i},i=1,2,3$, where the typical values of $\widehat{w_i}$ are defined as $\displaystyle\lim_{N\rightarrow\infty}\frac{\widehat{w_i}}{\sqrt{N}}\neq 0,1$ for $i=1,2,3$. To optimize the turbo code performance in the waterfall region which is dominated by high-weight codewords, it is desirable to reduce $\rho_{ij}$, $i,j=1,2,3$ as much as possible, where $\rho_{ij}$ is the correlation coefficient between $\widehat{w_i}$ and $\widehat{w_j}$. It is shown that: (i)~$\rho_{ij}>0$, $i,j=1,2,3$, (ii)~$\rho_{12},\rho_{13}\rightarrow 0$ as $N\rightarrow\infty$, and (iii)~$\rho_{23}\rightarrow 0$ as $N\rightarrow\infty$ for "almost" any random interleaver. This indicates that for $N\rightarrow\infty$, the optimization of the interleaver has a diminishing effect on the distribution of high-weight error events, and consequently, on the error performance in the waterfall region. We show that for the typical weights, this weight distribution approaches the average spectrum defined by Poltyrev [1994]. We also apply the tangential sphere bound (TSB) on the Gaussian distribution in AWGN channel with BPSK signalling and show that it performs very close to the capacity for code rates of interest. We also study the statistical properties of the low-weight codeword structures. We prove that for large block lengths, the number of low-weight codewords of these structures are some Poisson random variables. These random variables can be used to evaluate the asymptotic probability mass function of the minimum distance of the turbo code among all the possible interleavers. We show that the number of indecomposable low-weight codewords of different types tend to a set of independent Poisson random variables. We find the mean and the variance of the union bound in the error floor region and study the effect of expurgating low-weight codewords on the performance. We show that the weight distribution in the transition region between Poisson and Gaussian follows a negative binomial distribution. We also calculate the interleaver gain for multi-component turbo codes based on these Poisson random variables. We show that the asymptotic error performance for multi-component codes in different weight regions converges to zero either exponentially (in the Gaussian region) or polynomially (in the Poisson and negative binomial regions) with respect to the block length, with the code-rate and energy values close to the channel capacity.

This thesis is concerned with development of a terrain model using Gaussian Processes to support the automation of open-pit mines. Information can be provided from a variety of sources including GPS, laser scans and manual surveys. The information is then fused together into a single representation of the terrain together with a measure of uncertainty of the estimated model. The model is also used to detect and label specific features in the terrain. In the context of mining, theses features are edges known as toes and crests. A combination of clustering and classification using supervised learning detects and labels these regions. Data gathered from production iron ore mines in Western Australia and a farm in Marulan outside Sydney is used to demonstrate and verify the ability of Gaussian Processes to estimate a model of the terrain. The estimated terrain model is then used for detecting features of interest.Results show that the Gaussian Process correctly estimates the terrain and uncertainties, and provide a good representation of the area. Toes and crests are also successfully identified and labelled.

Battail [1989] shows that an appropriate criterion for the design of long block codes is the closeness of the normalized weight distribution to a Gaussian distribution. A subsequent work shows that iterated product of single parity check codes satisfy this criterion [1994]. Motivated by these earlier works, in this thesis, we study the effect of the interleaver on the performance of turbo codes for large block lengths, $N\rightarrow\infty$. A parallel concatenated turbo code that consists of two or more component codes is considered. We demonstrate that for $N\rightarrow\infty$, the normalized weight of the systematic $\widehat{w_1}=\displaystyle\frac{w_1}{\sqrt{N}}$, and the parity check sequences $\widehat{w_2}=\displaystyle\frac{w_2}{\sqrt{N}}$ and $\widehat{w_3}=\displaystyle\frac{w_3}{\sqrt{N}}$ become a set of jointly Gaussian distributions for the typical values of $\widehat{w_i},i=1,2,3$, where the typical values of $\widehat{w_i}$ are defined as $\displaystyle\lim_{N\rightarrow\infty}\frac{\widehat{w_i}}{\sqrt{N}}\neq 0,1$ for $i=1,2,3$. To optimize the turbo code performance in the waterfall region which is dominated by high-weight codewords, it is desirable to reduce $\rho_{ij}$, $i,j=1,2,3$ as much as possible, where $\rho_{ij}$ is the correlation coefficient between $\widehat{w_i}$ and $\widehat{w_j}$. It is shown that: (i)~$\rho_{ij}>0$, $i,j=1,2,3$, (ii)~$\rho_{12},\rho_{13}\rightarrow 0$ as $N\rightarrow\infty$, and (iii)~$\rho_{23}\rightarrow 0$ as $N\rightarrow\infty$ for "almost" any random interleaver. This indicates that for $N\rightarrow\infty$, the optimization of the interleaver has a diminishing effect on the distribution of high-weight error events, and consequently, on the error performance in the waterfall region. We show that for the typical weights, this weight distribution approaches the average spectrum defined by Poltyrev [1994]. We also apply the tangential sphere bound (TSB) on the Gaussian distribution in AWGN channel with BPSK signalling and show that it performs very close to the capacity for code rates of interest. We also study the statistical properties of the low-weight codeword structures. We prove that for large block lengths, the number of low-weight codewords of these structures are some Poisson random variables. These random variables can be used to evaluate the asymptotic probability mass function of the minimum distance of the turbo code among all the possible interleavers. We show that the number of indecomposable low-weight codewords of different types tend to a set of independent Poisson random variables. We find the mean and the variance of the union bound in the error floor region and study the effect of expurgating low-weight codewords on the performance. We show that the weight distribution in the transition region between Poisson and Gaussian follows a negative binomial distribution. We also calculate the interleaver gain for multi-component turbo codes based on these Poisson random variables. We show that the asymptotic error performance for multi-component codes in different weight regions converges to zero either exponentially (in the Gaussian region) or polynomially (in the Poisson and negative binomial regions) with respect to the block length, with the code-rate and energy values close to the channel capacity.

Measurement of visual quality is crucial for various image and video processing applications. <br /><br /> The goal of objective image quality assessment is to introduce a computational quality metric that can predict image or video quality. Many methods have been proposed in the past decades. Traditionally, measurements convert the spatial data into some other feature domains, such as the Fourier domain, and detect the similarity, such as mean square distance or Minkowsky distance, between the test data and the reference or perfect data, however only limited success has been achieved. None of the complicated metrics show any great advantage over other existing metrics. <br /><br /> The common idea shared among many proposed objective quality metrics is that human visual error sensitivities vary in different spatial and temporal frequency and directional channels. In this thesis, image quality assessment is approached by proposing a novel framework to compute the lost information in each channel not the similarities as used in previous methods. Based on natural scene statistics and several image models, an information theoretic framework is designed to compute the perceptual information contained in images and evaluate image quality in the form of entropy. <br /><br /> The thesis is organized as follows. Chapter I give a general introduction about previous work in this research area and a brief description of the human visual system. In Chapter II statistical models for natural scenes are reviewed. Chapter III proposes the core ideas about the computation of the perceptual information contained in the images. In Chapter IV, information theoretic criteria for image quality assessment are defined. Chapter V presents the simulation results in detail. In the last chapter, future direction and improvements of this research are discussed.

<p>The dissertation focuses on solving some important theoretical and methodological problems associated with Bayesian modeling of infinite dimensional `objects', popularly called nonparametric Bayes. The term `infinite dimensional object' can refer to a density, a conditional density, a regression surface or even a manifold. Although Bayesian density estimation as well as function estimation are well-justified in the existing literature, there has been little or no theory justifying the estimation of more complex objects (e.g. conditional density, manifold, etc.). Part of this dissertation focuses on exploring the structure of the spaces on which the priors for conditional densities and manifolds are supported while studying how the posterior concentrates as increasing amounts of data are collected.</p><p>With the advent of new acquisition devices, there has been a need to model complex objects associated with complex data-types e.g. millions of genes affecting a bio-marker, 2D pixelated images, a cloud of points in the 3D space, etc. A significant portion of this dissertation has been devoted to developing adaptive nonparametric Bayes approaches for learning low-dimensional structures underlying higher-dimensional objects e.g. a high-dimensional regression function supported on a lower dimensional space, closed curves representing the boundaries of shapes in 2D images and closed surfaces located on or near the point cloud data. Characterizing the distribution of these objects has a tremendous impact in several application areas ranging from tumor tracking for targeted radiation therapy, to classifying cells in the brain, to model based methods for 3D animation and so on. </p><p> </p><p> The first three chapters are devoted to Bayesian nonparametric theory and modeling in unconstrained Euclidean spaces e.g. mean regression and density regression, the next two focus on Bayesian modeling of manifolds e.g. closed curves and surfaces, and the final one on nonparametric Bayes spatial point pattern data modeling when the sampling locations are informative of the outcomes.</p> / Dissertation

<p>The immune system is constantly faced with the daunting task of protecting the host from a large number of ever-evolving pathogens. In vertebrates, the immune response results from the interplay of two cellular systems: the innate immunity and the adaptive immunity. In the past decades, dendritic cells have emerged as major players in the modulation of the immune response, being one of the primary links between these two branches of the immune system.</p><p>Dendritic cells are pathogen-sensing cells that alert the rest of the immune system of the presence of infection. The signals sent by dendritic cells result in the recruitment of the appropriate cell types and molecules required for effectively clearing the infection. A question of utmost importance in our understanding of the immune response and our ability to manipulate it in the development of vaccines and therapies is: "How do dendritic cells translate the various cues they perceive from the environment into different signals that specifically activate the appropriate parts of the immune system that result in an immune response streamlined to clear the given pathogen?"</p><p>Here we have developed computational and statistical methods aimed to address specific aspects of this question. In particular, understanding how dendritic cells ultimately modulate the immune response requires an understanding of the subtleties of their maturation process in response to different environmental signals. Hence, the first part of this dissertation focuses on elucidating the changes in the transcriptional</p><p>program of dendritic cells in response to the detection of two common pathogen- associated molecules, LPS and CpG. We have developed a method based on Langevin and Dirichlet processes to model and cluster gene expression temporal data, and have used it to identify, on a large scale, genes that present unique and common transcriptional behaviors in response to these two stimuli. Additionally, we have also investigated a different, but related, aspect of dendritic cell modulation of the adaptive immune response. In the second part of this dissertation, we present a method to predict peptides that will bind to MHC molecules, a requirement for the activation of pathogen-specific T cells. Together, these studies contribute to the elucidation of important aspects of dendritic cell biology.</p> / Dissertation

<p>Our interest is the risk assessment of rare natural hazards, such as</p><p>large volcanic pyroclastic flows. Since catastrophic consequences of</p><p>volcanic flows are rare events, our analysis benefits from the use of</p><p>a computer model to provide information about these events under</p><p>natural conditions that may not have been observed in reality.</p><p>A common problem in the analysis of computer experiments, however, is the high computational cost associated with each simulation of a complex physical process. We tackle this problem by using a statistical approximation (emulator) to predict the output of this computer model at untried values of inputs. Gaussian process response surface is a technique commonly used in these applications, because it is fast and easy to use in the analysis.</p><p>We explore several aspects of the implementation of Gaussian process emulators in a Bayesian context. First, we propose an improvement for the implementation of the plug-in approach to Gaussian processes. Next, we also evaluate the performance of a spatial model for large data sets in the context of computer experiments.</p><p>Computer model data can also be combined to field observations in order to calibrate the emulator and obtain statistical approximations to the computer model that are closer to reality. We present an application where we learn the joint distribution of inputs from field data and then bind this auxiliary information to the emulator in a calibration process.</p><p>One of the outputs of our computer model is a surface of maximum volcanic flow height over some geographical area. We show how the topography of the volcano area plays an important role in determining the shape of this surface, and we propose methods</p><p>to incorporate geophysical information in the multivariate analysis of computer model output.</p> / Dissertation

<p>This dissertation is devoted to modeling complex data from the</p><p>Bayesian perspective via constructing priors with latent structures.</p><p>There are three major contexts in which this is done -- strategies for</p><p>the analysis of dynamic longitudinal data, estimating</p><p>shape-constrained functions, and identifying subgroups. The</p><p>methodology is illustrated in three different</p><p>interdisciplinary contexts: (1) adaptive measurement testing in</p><p>education; (2) emulation of computer models for vehicle crashworthiness; and (3) subgroup analyses based on biomarkers.</p><p>Chapter 1 presents an overview of the utilized latent structured</p><p>priors and an overview of the remainder of the thesis. Chapter 2 is</p><p>motivated by the problem of analyzing dichotomous longitudinal data</p><p>observed at variable and irregular time points for adaptive</p><p>measurement testing in education. One of its main contributions lies</p><p>in developing a new class of Dynamic Item Response (DIR) models via</p><p>specifying a novel dynamic structure on the prior of the latent</p><p>trait. The Bayesian inference for DIR models is undertaken, which</p><p>permits borrowing strength from different individuals, allows the</p><p>retrospective analysis of an individual's changing ability, and</p><p>allows for online prediction of one's ability changes. Proof of</p><p>posterior propriety is presented, ensuring that the objective</p><p>Bayesian analysis is rigorous.</p><p>Chapter 3 deals with nonparametric function estimation under</p><p>shape constraints, such as monotonicity, convexity or concavity. A</p><p>motivating illustration is to generate an emulator to approximate a computer</p><p>model for vehicle crashworthiness. Although Gaussian processes are</p><p>very flexible and widely used in function estimation, they are not</p><p>naturally amenable to incorporation of such constraints. Gaussian</p><p>processes with the squared exponential correlation function have the</p><p>interesting property that their derivative processes are also</p><p>Gaussian processes and are jointly Gaussian processes with the</p><p>original Gaussian process. This allows one to impose shape constraints</p><p>through the derivative process. Two alternative ways of incorporating derivative</p><p>information into Gaussian processes priors are proposed, with one</p><p>focusing on scenarios (important in emulation of computer</p><p>models) in which the function may have flat regions.</p><p>Chapter 4 introduces a Bayesian method to control for multiplicity</p><p>in subgroup analyses through tree-based models that limit the</p><p>subgroups under consideration to those that are a priori plausible.</p><p>Once the prior modeling of the tree is accomplished, each tree will</p><p>yield a statistical model; Bayesian model selection analyses then</p><p>complete the statistical computation for any quantity of interest,</p><p>resulting in multiplicity-controlled inferences. This research is</p><p>motivated by a problem of biomarker and subgroup identification to</p><p>develop tailored therapeutics. Chapter 5 presents conclusions and</p><p>some directions for future research.</p> / Dissertation

In this thesis, we extend applications of Low-Density Parity-Check (LDPC) codes to a combination of constituent sub-channels, which is a mixture of Gaussian channels with erasures. This model, for example, represents a common channel in magnetic recordings where thermal asperities in the system are detected and represented at the decoder as erasures. Although this channel is practically useful, we cannot find any previous work that evaluates performance of LDPC codes over this channel. We are also interested in practical issues such as designing robust LDPC codes for the mixture channel and predicting performance variations due to erasure patterns (random and burst), and finite block lengths. On time varying channels, a common error control strategy is to adapt the coding rate according to available channel state information (CSI). An effective way to realize this coding strategy is to use a single code and puncture it in a rate-compatible fashion, a so-called rate-compatible punctured code (RCPC). We are interested in the existence of good puncturing patterns for rate-changes that minimize performance loss. We show the existence of good puncturing patterns with analysis and verify the results with simulations. Universality of a channel code across a broad range of coding rates is a theoretically interesting topic. We are interested in the possibility of using the puncturing technique proposed in this thesis for designing universal LDPC codes. We also consider how to design high rate LDPC codes by puncturing low rate LDPC codes. The new design method can take advantage of longer effect block lengths, sparser parity-check matrices, and larger minimum distances of low rate LDPC codes.

In the first half of this thesis, we extend the results of Halfin and Whitt to generally distributed service times. This is accomplished by first writing the system equations for the G/GI/N queue in a manner similar to the system equations for G/GI/Infinity queue. We next identify a key relationship between these two queues. This relationship allows us to leverage several existing results for the G/GI/Infinity queue in order to prove our main result. Our main result in the first part of this thesis is to show that the diffusion scaled queue length process for the G/GI/N queue in the Halfin-Whitt regime converges to a limiting stochastic process which is driven by a Gaussian process and satisfies a stochastic convolution equation. We also show that a similar result holds true for the fluid scaled queue length process under general initial conditions. Customer abandonment is also a common feature of many call centers. Some researchers have even gone so far as to suggest that the level of customer abandonment is the single most important metric with regards to a call center's performance. In the second half of this thesis, we improve upon a result of Ward and Glynn's concerning the GI/GI/1+GI queue in heavy traffic. Whereas Ward and Glynn obtain a diffusion limit result for the GI/GI/1+GI queue in heavy traffic which incorporates only the density the abandonment distribution at the origin, our result incorporate the entire abandonment distribution. This is accomplished by a scaling the hazard rate function of the abandonment distribution as the system moves into heavy traffic. Our main results are to obtain diffusion limits for the properly scaled workload and queue length processes in the GI/GI/1+GI queue. The limiting diffusions we obtain are reflected at the origin with a negative drift which is dependent upon the hazard rate of the abandonment distribution. Because these diffusions have an analytically tractable steady-state distribution, they can be used to provide a closed-form approximation for the steady-state distribution of the queue length and workload processes in a GI/GI/1+GI queue. We demonstrate the accuracy of these approximations through simulation.