Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com

The goal of neuromorphic engineering is to create electronic systems that model the behavior of biological neural systems. Neuromorphic systems can leverage a combination of analog and digital circuit design techniques to enable computational modeling, with orders of magnitude of reduction in size, weight, and power consumption compared to the traditional modeling approach based upon numerical integration. These benefits of neuromorphic modeling have the potential to facilitate neural modeling in resource-constrained research environments. Moreover, they will make it practical to use neural computation in the design of intelligent machines, including portable, battery-powered, and energy harvesting applications. Floating-gate transistor technology is a powerful tool for neuromorphic engineering because it allows dense implementation of synapses with nonvolatile storage of synaptic weights, cancellation of process mismatch, and reconfigurable system design. A novel neuromorphic hardware system, featuring compact and efficient channel-based model neurons and floating-gate transistor synapses, was developed. This system was used to model a variety of network topologies with up to 100 neurons. The networks were shown to possess computational capabilities such as spatio-temporal pattern generation and recognition, winner-take-all competition, bistable activity implementing a "volatile memory", and wavefront-based robotic path planning. Some canonical features of synaptic plasticity, such as potentiation of high frequency inputs and potentiation of correlated inputs in the presence of uncorrelated noise, were demonstrated. Preliminary results regarding formation of receptive fields were obtained. Several advances in enabling technologies, including methods for floating-gate transistor array programming, and the creation of a reconfigurable system for studying adaptation in floating-gate transistor circuits, were made.

In this study, an appearance reconstruction method based on extraction of material re&amp / #64258 / ectance properties of a three-dimensional (3D) object from its twodimensional (2D) images is explained. One of the main advantages of this system is that the reconstructed object can be rendered in real-time with photorealistic quality in varying illumination conditions. Bidirectional Re&amp / #64258 / ectance Distribution Functions (BRDFs) are used in representing the re&amp / #64258 / ectance of the object. The re&amp / #64258 / ectance of the object is decomposed into di&amp / #64256 / use and specular components and each component is estimated seperately. While estimating the di&amp / #64256 / use components, illumination-invariant images of the object are computed from the input images, and a global texture of the object is extracted from these images by using surface particles. The specular re&amp / #64258 / ectance data are collected from the residual images obtained by taking di&amp / #64256 / erence between the input images and corresponding illumination-invariant images, and a Lafortune BRDF model is &amp / #64257 / tted to these data. At the rendering phase, the di&amp / #64256 / use and specular components are blended into each other to achieve a photorealistic appearance of the reconstructed object.

As the size of image databases increases in time, the need for content based image indexing and retrieval become important. Image classification is a key to content based image indexing. In this thesis supervised learning with feed forward back propagation artificial neural networks is used for image classification. Low level features derived from the images are used to classify the images to interpret the high level features that yield semantics. Features are derived using detail histogram correlations obtained by Wavelet Transform, directional edge information obtained by Fourier Transform and color histogram correlations. An image database consisting of 357 color images of various sizes is used for training and testing the structure. The database is indexed into seven classes that represent scenery contents which are not mutually exclusive. The ground truth data is formed in a supervised fashion to be used in training the neural network and testing the performance. The performance of the structure is tested using leave one out method and comparing the simulation outputs with the ground truth data. Success, mean square error and the class recall rates are used as the performance measures. The performances of the derived features are compared with the color and texture descriptors of MPEG-7 using the structure designed. The results show that the performance of the method is comparable and better. This method of classification for content based image indexing is a reliable and valid method for content based image indexing and retrieval, especially in scenery image indexing.

Virtual three-dimensional auditory displays (V3DADs) use digital signal processing to deliver sounds (typically through headphones) that seem to originate from specific external spatial locations. This set of studies investigates the delivery of V3DADs through bone-conduction transducers (BCTs) in addition to conventional headphones. Although previous research has shown that spatial separation can be induced through BCTs, some additional signal adjustments are required for optimization of V3DADs, due to the difference in hearing pathways. The present studies tested a bone-conduction adjustment function (BAF) derived from equal-loudness judgments on pure tones whose frequencies were spaced one critical band apart. Localization performance was assessed through conventional air-conduction headphones, BCTs with only transducer correction, and BCTs with a BAF. The results showed that in the elevation plane, the BAF was effective in restoring the spectral cues altered by the bone-conduction pathway. No evidence for increased percept variability or decreased lateralization in the bone-conduction conditions was found. These findings indicate that a V3DAD can be implemented on a BCT and that a BAF will improve performance, but that there is an apparent performance cost that cannot be addressed with BAFs measured using the methodology in the present studies.

This thesis consists of a summary and five papers, dealing with self-normalized sums of independent, identically distributed random variables, and three-decision procedures for directional conclusions. In Paper I, we investigate a general set-up for Student's t-statistic. Finiteness of absolute moments is related to the corresponding degree of freedom, and relevant properties of the underlying distribution, assuming independent, identically distributed random variables. In Paper II, we investigate a certain kind of self-normalized sums. We show that the corresponding quadratic moments are greater than or equal to one, with equality if and only if the underlying distribution is symmetrically distributed around the origin. In Paper III, we study linear combinations of independent Rademacher random variables. A family of universal bounds on the corresponding tail probabilities is derived through the technique known as exponential tilting. Connections to self-normalized sums of symmetrically distributed random variables are given. In Paper IV, we consider a general formulation of three-decision procedures for directional conclusions. We introduce three kinds of optimality characterizations, and formulate corresponding sufficiency conditions. These conditions are applied to exponential families of distributions. In Paper V, we investigate the Benjamini-Hochberg procedure as a means of confirming a selection of statistical decisions on the basis of a corresponding set of generalized p-values. Assuming independence, we show that control is imposed on the expected average loss among confirmed decisions. Connections to directional conclusions are given.

This thesis investigates topology optimization techniques for periodic continuum structures at the macroscopic level. Periodic structures are increasingly used in the design of structural systems and sub-systems of buildings, vehicles, aircrafts, etc. The duplication of identical or similar modules significantly reduces the manufacturing cost and greatly simplifies the assembly process. Optimization of periodic structures in the micro level has been extensively researched in the context of material design, while research on topology optimization for macrostructures is very limited and has great potential both economically and intellectually. In the present thesis, numerical algorithms based on the bi-directional evolutionary structural optimization method (BESO) are developed for topology optimization for various objectives and constraints. Soft-kill (replacing void elements with soft elements) formulations of topology optimization problems for solid-void solutions are developed through appropriate material interpolation schemes. Incorporating the optimality criteria and algorithms for mesh-independence and solution-convergence, the present BESO becomes a reliable gradient based technique for topology optimization. Additionally, a new combination of genetic algorithms (GAs) with BESO is developed in order to stochastically search for the global optima. These enhanced BESO algorithms are applied to various optimization problems with the periodicity requirement as an extra constraint aiming at producing periodicity in the layout. For structures under static loading, the present thesis addresses minimization of the mean compliance and explores the applications of conventional stiffness optimization for periodic structures. Furthermore, this thesis develops a volume minimization formulation where the maximum deflection is constrained. For the design of structures subject to dynamic loading, this thesis develops two different approaches (hard-kill and soft-kill) to resolving the problem of localized or artificial modes. In the hard-kill (completely removing void elements) approach, extra control measures are taken in order to eliminate the localized modes in an explicit manner. In the soft-kill approach, a modified power low material model is presented to prevent the occurrence of artificial and localized modes. Periodic stress and strain fields cannot be assumed in structures under arbitrary loadings and boundaries at the macroscopic level. Therefore being different from material design, no natural base cell can be directly extracted from macrostructures. In this thesis, the concept of an imaginary representative unit cell (RUC) is presented. For situations when the structure cannot be discretized into equally-sized elements, the concept of sensitivity density is developed in order for mesh-independent robust solutions to be produced. The RUC and sensitivity density based approach is incorporated into various topology optimization problems to obtain absolute or scaled periodicities in structure layouts. The influence of this extra constraint on the final optima is investigated based on a large number of numerical experiments. The findings shown in this thesis have established appropriate techniques for designing and optimizing periodic structures. The work has provided a solid foundation for creating a practical design tool in the form of a user-friendly computer program suitable for the conceptual design of a wide range of structures.

Les régions de montagne sont parfois le siège de phénomènes dévastateurs brutaux, tels que les éboulements, les glissements de terrains, ou encore les avalanches. Fondamentalement, ces phénomènes sont issus de la rupture d’un volume de matériau qui va alors s’écouler sous l’effet de son poids propre. Prévoir ces phénomènes impose donc de mieux décrire la phase initiale de rupture. Ce travail de thèse s’inscrit dans cette volonté, en considérant le cas très général de la rupture dans un milieu granulaire. Pour cela, des simulations numériques utilisant une méthode aux éléments discrets ont été mises en œuvre, afin de vérifier la pertinence des critères usuels de rupture et d’instabilité. Dans un second temps, des analyses plus fines basées sur le travail du second ordre calculé à partir des variables microscopiques ont été menées afin de cerner comment évolue la microstructure de l’assemblage granulaire juste avant et pendant la rupture. Finalement, l’influence du chemin de chargement et des paramètres de contrôle sur la nature (effective ou non effective) et le mode (diffus ou localisé) de rupture a été examinée à travers une série d’essais biaxiaux sur deux échantillons numériques bidimensionnels (dense et moyennement dense). / Landslides and avalanches are the most common brutal and devastating natural hazards in mountain regions. Basically, these phenomena are derived from the failure of a material volume which will then flow under the effect of its own weight. Therefore, predicting these phenomena requires a better description of the initial phase of failure. This work comes within this willingness, considering the very general case of failure in granular media. For this purpose, numerical simulations using a discrete element method were carried out in order to investigate the relevance of the common failure and instability criteria. In a second step, more detailed analyses based on the second order work computed from the microscopic variables were conducted in order to describe the evolution of the microstructure of a granular assembly just before and during the failure. Finally, the influence of the loading path and the control parameters on the nature (effective or non-effective) and the mode (diffuse or localized) of failure was discussed through a series of biaxial tests performed on two-dimensional numerical samples depicting respectively a dense and a medium dense dry sand.

Nous nous intéressons dans cette thèse au développement et à la mise en oeuvre de schémas numériques Volumes Finis d’ordre élevé pour des maillages non-structurés. Il s’agit de mettre en place les ingrédients numériques pour réaliser des simulations aux grandes échelles avec le code numérique elsA. Les schémas numériques proposés sont basés sur une approche directionnelle, afin de limiter le coût CPU et de réduire la molécule de points. La partie convective du schéma numérique doit être d’ordre élevé. L’ordre élevé est obtenu en utilisant différents gradients sur un stencil prédéféni utilisant 4 cellules. Deux gradients sont utilisés pour la partie convective : le gradient GreenGauss et le gradient “UIG”. Pour la partie diffusive, le gradient “UIG” est utilisé. Ce gradient a été développé durant la thèse et permet d’avoir un gradient moyen d’ordre 2 sur chaque interface. Ce gradient a été étudié et validé sur différents cas-tests. Les schémas numériques d’ordre élevé ont été analysés théoriquement avec des analyses d’ordre et de stabilité. Il a été montré que ces schémas peuvent atteindre l’ordre 5 sur des hexaèdres et l’ordre 3 sur des triangles équilatéraux. Suite à cette analyse, les différents schémas ont été d’abord testés en 1D sur un cas classique d’advection, puis ont été validés sur le cas de convection du vortex isentropique. / This study will present the development and results of high-order Finite Volume schemes for unstructured grids. The goal is to prepare numerical tools to perform Large Eddy Simulations with the indutrial solver elsA. These numerical schemes are based on a directional approach in order to limitate the CPU cost and reduce the stencil. The convective part of the scheme needs to be high order and this is obtained by the use of gradients on a four-cell stencil. Two gradients are used for the convective part, the Green-Gauss gradient and the “UIG” gradient. For the diffusive part, the “UIG” gradient is used. It was developped during this study and allows to recover a secondorder accurate scheme. This gradient was validated theorically and numerically on some test cases. High order numerical schemes were studied theorically with order and frequency analysis. It was shown that these schemes are fifth-order accurate on regular hexaedral elements and third-order accurate on equilateral triangles. Following this analysis, these schemes were tested in 1D on an advection test case and were then validated on the convection of an isentropic vortex.