Regression with L1-regularization, Lasso, is a popular algorithm for recovering the sparsity pattern (also known as model selection) in linear models from observations contaminated by noise. We examine a scenario where a fraction of the zero co-variates are highly correlated with non-zero co-variates making sparsity recovery difficult. We propose two methods that adaptively increment the regularization parameter to prune the Lasso solution set. We prove that the algorithms achieve consistent model selection with high probability while using fewer samples than traditional Lasso. The algorithm can be extended to a broad set of L1-regularized M-estimators for linear statistical models.

Demonstrating strength and agility on virtual and real humanoids has been an important goal in computer graphics and robotics. However, developing physics- based controllers for various agile motor skills requires a tremendous amount of prior knowledge and manual labor due to complex mechanisms of the motor skills. The focus of the dissertation is to develop a set of computational tools to expedite the design process of physics-based controllers that can execute a variety of agile motor skills on virtual and real humanoids. Instead of designing directly controllers real humanoids, this dissertation takes an approach that develops appropriate theories and models in virtual simulation and systematically transfers the solutions to hardware systems. The algorithms and frameworks in this dissertation span various topics from spe- cific physics-based controllers to general learning frameworks. We first present an online algorithm for controlling falling and landing motions of virtual characters. The proposed algorithm is effective and efficient enough to generate falling motions for a wide range of arbitrary initial conditions in real-time. Next, we present a robust falling strategy for real humanoids that can manage a wide range of perturbations by planning the optimal contact sequences. We then introduce an iterative learning framework to easily design various agile motions, which is inspired by human learn- ing techniques. The proposed framework is followed by novel algorithms to efficiently optimize control parameters for the target tasks, especially when they have many constraints or parameterized goals. Finally, we introduce an iterative approach for exporting simulation-optimized control policies to hardware of robots to reduce the number of hardware experiments, that accompany expensive costs and labors.

The detection of subtypes of complex diseases has important implications for diagnosis and treatment. Numerous prior studies have used data-driven approaches to identify clusters of similar patients, but it is not yet clear how to best specify what constitutes a clinically meaningful phenotype. This study explored disease subtyping on the basis of temporal development patterns. In particular, we attempted to differentiate infants with autism spectrum disorder into more fine-grained classes with distinctive patterns of early skill development. We modeled the progression of autism explicitly using a continuous-time hidden Markov model. Subsequently, we compared subjects on the basis of their trajectories through the model state space. Two approaches to subtyping were utilized, one based on time-series clustering with a custom distance function and one based on tensor factorization. A web application was also developed to facilitate the visual exploration of our results. Results suggested the presence of 3 developmental subgroups in the ASD outcome group. The two subtyping approaches are contrasted and possible future directions for research are discussed.

This research investigates the modeling of randomly distributed surface-breaking microcracks and their effects on higher harmonic generation in Rayleigh surface waves. The modeling is based on micromechanical considerations of rough surface contact. The nonlinear behavior of a single microcrack is described by a hyperelastic effective stress-strain relationship. Finite element simulations of nonlinear wave propagation in a solid with distributed microcracks are performed. The evolution of fundamental and second harmonic amplitudes along the propagation distance is studied and the acoustic nonlinearity parameter is calculated. The results show that the nonlinearity parameter increases with crack density and root mean square roughness of the crack faces. While, for a dilute concentration of microcracks, the increase in acoustic nonlinearity is proportional to the crack density, this is not valid for higher crack densities, as the microcracks start to interact. Finally, it is shown that odd higher harmonic generation in Rayleigh surface waves due to sliding crack faces introduces a friction nonlinearity.

Although several studies have proven the accuracy of using a non-contact, air-coupled receiver in nonlinear ultrasonic (NLU) Rayleigh wave measurements, inconsistent results have been observed when working with narrow specimens. The objectives of this research are first, to develop a 3D numerical finite element (FE) model which predicts nonlinear ultrasonic measurements and second, to apply the validated model on the narrow waveguide to determine causes of the previously observed experimental issues. The commercial FE-solver ABAQUS is used to perform these simulations. Constitutive law and excitation source properties are adjusted to match experiments conducted, considering inherent effects of the non-contact detection, such as frequency dependent pressure wave attenuation and signal averaging. Comparison of “infinite” and narrow width simulations outlines various influences which impair the nonlinear Rayleigh wave measurements. When the wave expansion is restricted, amplitudes of the fundamental and second harmonic components decrease more significantly and the Rayleigh wavefronts show an oscillating interaction with the boundary. Because of the air-coupled receiver’s finite width, it is sensitive to these edge effects which alter the observed signal. Thus, the narrow specimen adversely affects key factors needed for consistent measurement of material nonlinearity with an air-coupled, non-contact receiver.

The bin packing problem has been the corner stone of approximation algorithms and has been extensively studied starting from the early seventies. In the classical bin packing problem, we are given a list of real numbers in the range (0, 1], the goal is to place them in a minimum number of bins so that no bin holds numbers summing to more than 1. In this thesis we study approximation algorithms for three generalizations of bin packing: geometric bin packing, vector bin packing and weighted bipartite edge coloring. In two-dimensional (2-D) geometric bin packing, we are given a collection of rectangular items to be packed into a minimum number of unit size square bins. Geometric packing has vast applications in cutting stock, vehicle loading, pallet packing, memory allocation and several other logistics and robotics related problems. We consider the widely studied orthogonal packing case, where the items must be placed in the bin such that their sides are parallel to the sides of the bin. Here two variants are usually studied, (i) where the items cannot be rotated, and (ii) they can be rotated by 90 degrees. We give a polynomial time algorithm with an asymptotic approximation ratio of $\ln(1.5) + 1 \approx 1.405$ for the versions with and without rotations. We have also shown the limitations of rounding based algorithms, ubiquitous in bin packing algorithms. We have shown that any algorithm that rounds at least one side of each large item to some number in a constant size collection values chosen independent of the problem instance, cannot achieve an asymptotic approximation ratio better than 3/2. In d-dimensional vector bin packing (VBP), each item is a d-dimensional vector that needs to be packed into unit vector bins. The problem is of great significance in resource constrained scheduling and also appears in recent virtual machine placement in cloud computing. Even in two dimensions, it has novel applications in layout design, logistics, loading and scheduling problems. We obtain a polynomial time algorithm with an asymptotic approximation ratio of $\ln(1.5) + 1 \approx 1.405$ for 2-D VBP. We also obtain a polynomial time algorithm with almost tight (absolute) approximation ratio of $1+\ln(1.5)$ for 2-D VBP. For $d$ dimensions, we give a polynomial time algorithm with an asymptotic approximation ratio of $\ln(d/2) + 1.5 \approx \ln d+0.81$. We also consider vector bin packing under resource augmentation. We give a polynomial time algorithm that packs vectors into $(1+\epsilon)Opt$ bins when we allow augmentation in (d - 1) dimensions and $Opt$ is the minimum number of bins needed to pack the vectors into (1,1) bins. In weighted bipartite edge coloring problem, we are given an edge-weighted bipartite graph $G=(V,E)$ with weights $w: E \rightarrow [0,1]$. The task is to find a proper weighted coloring of the edges with as few colors as possible. An edge coloring of the weighted graph is called a proper weighted coloring if the sum of the weights of the edges incident to a vertex of any color is at most one. This problem is motivated by rearrangeability of 3-stage Clos networks which is very useful in various applications in interconnected networks and routing. We show a polynomial time approximation algorithm that returns a proper weighted coloring with at most $\lceil 2.2223m \rceil$ colors where $m$ is the minimum number of unit sized bins needed to pack the weight of all edges incident at any vertex. We also show that if all edge weights are $>1/4$ then $\lceil 2.2m \rceil$ colors are sufficient.

Internal waves are ubiquitous features in coastal marine environments and have been observed to mediate vertical distributions of zooplankton in situ. Internal waves create fine-scale hydrodynamic cues that copepods and other zooplankton are known to sense, such as fluid density gradients and velocity gradients (quantified as shear deformation rate). The role of copepod behavior in response to cues associated with internal waves is largely unknown. The objective is to provide insight to the bio-physical interaction and the role of biological versus physical forcing in mediating organism distributions. We constructed a laboratory-scale internal wave apparatus to facilitate fine-scale observations of copepod behavior in flows that replicate in situ conditions of internal waves in a two-layer stratification. Three cases were chosen with density jump of 0.75, 1.0, and 1.5 sigma-t units. Analytical analysis of the two-layer system provided guidance to the target forcing frequency needed to generate a standing internal wave with a single dominate frequency of oscillation. Flow visualization and signal processing of the interface location were used to quantify the wave characteristics. The results show a close match to the target wave parameters. Marine copepod (mixed population of Acartia tonsa, Temora longicornis, and Eurytemora affinis) behavior assays were conducted for three different physical arrangements: (1) no density stratification, (2) stagnant two-layer density stratification, and (3) two-layer density stratification with internal wave motion. Digitized trajectories of copepod swimming behavior indicate that in the control (case 1) the animals showed no preferential motion in terms of direction. In the stagnant density jump treatment (case 2) copepods preferentially moved horizontally, parallel to the density interface. In the internal wave treatment (case 3) copepods demonstrated orbital trajectories near the density interface. Further analysis showed that the copepods swim closer to the interface in the presence of internal waves.

The Explicit Finite Element Method is a powerful tool in nonlinear dynamic finite element analysis. Recent major developments in computational devices, in particular, General Purpose Graphical Processing Units (GPGPU's) now make it possible to increase the performance of the explicit FEM. This dissertation investigates existing explicit finite element method algorithms which are then redesigned for GPU's and implemented. The performance of these algorithms is assessed and a new asynchronous variational integrator spatial decomposition (AVISD) algorithm is developed which is flexible and encompasses all other methods and can be tuned based for a user-defined problem and the performance of the user's computer. The mesh-aware performance of the proposed explicit finite element algorithm is studied and verified by implementation. The current research also introduces the use of a Particle Swarm Optimization method to tune the performance of the proposed algorithm automatically given a finite element mesh and the performance characteristics of a user's computer. For this purpose, a time performance model is developed which depends on the finite element mesh and the machine performance. This time performance model is then used as an objective function to minimize the run-time cost. Also, based on the performance model provided in this research and predictions about the changes in GPU's in the near future, the performance of the AVISD method is predicted for future machines. Finally, suggestions and insights based on these results are proposed to help facilitate future explicit FEM development.

The results from this study show how different precursors affect halonitromethane (HNM) formation as well as how different free chlorine doses can affect HNM speciation. This study shows that the low pressure ultraviolet (LPUV) and free chlorine concurrent exposure can enhance HNM formation. In addition, most previous studies in the literature showed trichloronitromethane (TCNM) forming in greater quantities followed by monochloronitromethane (MCNM) and dichloronitromethane (DCNM). However, the results of this study show that, in deionized (DI) water matrices, MCNM forms in greater quantities at chlorine to nitrogen (Cl:N) ratios less than 3, while TCNM forms in greater quantities at Cl:N ratios greater than 3. Even so, the increase in TCNM formation did not increase linearly as the Cl:N ratio increased; there was a decreased rate of return when Cl:N ratios were greater than 3. The type of nitrogenous precursors can affect the amount of HNMs formed, with glycine forming a higher amount of total HNMs compared to methylamine (MA) and dimethylamine (DMA). The source of water can also affect which HNM species is formed in greater concentrations. The limited number of real water samples showed that the river waters have higher than normal total organic carbon (TOC) and dissolved organic nitrogen (DON), which are associated with greater nitrogenous precursors and higher HNM formation. Each water source can have different nitrogenous precursors; river waters may have more algal organic matter while wastewater would have higher organic matter and synthetic chemicals. In addition, source waters can have different constituents, such as varying dissolved oxygen (DO) levels and inorganic ions, which might inhibit HNM formation or affect specification.

The High Occupancy Vehicle (HOV) lanes on Atlanta, Georgia’s radial I-85 had long been providing sub-optimal throughput in the peak traffic hours, as the two-person occupancy requirement allowed the lanes to become heavily congested. The Georgia Department of Transportation converted 15.5 miles of HOV 2+ lanes to High Occupancy Toll (HOT) lanes, one in each direction on I-85. The lanes use dynamic value pricing to set toll levels based on the volume and average speed of traffic in the lanes. The goal of this research was to investigate the responses to toll lane pricing and the factors that appear to inform lane choice decisions, as well as examining values of travel time savings and toll price elasticity for users of the Express Lanes. This study of the metropolitan Atlanta I-85 Express Lanes operates at the microscopic level to examine the impact of demographic characteristics, congestion levels, and pricing on users’ decisions to use or not use the I-85 Express Lanes. The dissertation examined the value of travel time savings distributions across income segments. The differences in these distributions among lower, medium, and higher income households were marginal at best. The results did not indicate that higher income households had the highest value of travel time savings results, as may have been expected. The modeling work performed here provided a number of insights into toll lane use. The determinants of lane choice decision-making in the morning peak had notable differences from the determinants of the afternoon peak. The initial analysis involved models which were estimated across three different income segments to examine differences in decision making between low, medium, and higher income households. The results indicated that the parameters were largely consistent across the three segments. Further segmenting the households showed that lane choice determinants varied more within the ‘Higher’ income segment than across the original three-segment structure. In particular, the five-segment models illustrated lower elasticities with regard to corridor segment counts and toll levels for the highest-income households in the sample, as well as higher household income level elasticities for afternoon trips by that same cohort. The research was among the first in the available literature to use revealed preference lane use data for both the toll lane users and the unpriced general purpose lane users. The use of household level marketing data, rather than census or survey data, was another unique characteristic of this research. The analysis of value of travel time savings with a demographic component that looks at household income has not yet been seen in the literature; similarly, the findings regarding differing behavior among very high income households appear to be unseen in the existing literature. The results from this analysis, such as willingness-to-pay values for different population segments, will be useful inputs to the decisions surrounding future HOT implementations in the Atlanta region. The use of new data sources, the evaluation of those types of data sources, and the application of methods that have previously been unused in this field make up the primary contributions of this dissertation.