Reaching is a fundamental movement and has been studied widely in the motor control area. To my knowledge no one has directly compared the planning and kinematic characteristics of these two movements. These different definitions of reaching movements may also explain why researchers have reported different results when examining reaching movements of individuals with Autism Spectrum Disorder (ASD). The present study designed three movement types to examine how people with and without ASD plan and execute three different types of reaching movements. The results revealed that typically developing (TD) participants moved faster compared to ASD participants in three dimensional movements, but not in one dimensional and two dimensional movements. Based on the above results it is proposed that the observed difference in movement control resulted from a preference for different sensory feedback for on-line control of limb movements. / October 2015

Finding a local minimizer in unconstrained nonlinear optimization and a fixed point of a gradient system of ordinary differential equations (ODEs) are two closely related problems. Quasi-Newton algorithms are widely used in unconstrained nonlinear optimization while Runge-Kutta methods are widely used for the numerical integration of ODEs. In this thesis, hybrid algorithms combining low-order implicit Runge-Kutta methods for gradient systems and quasi-Newton type updates of the Jacobian matrix such as the BFGS update are considered. These hybrid algorithms numerically approximate the gradient flow, but the exact Jacobian matrix is not used to solve the nonlinear system at each step. Instead, a quasi-Newton matrix is used to approximate the Jacobian matrix and matrix-vector multiplications are performed in a limited memory setting to reduce storage, computations, and the need to calculate Jacobian information. For hybrid algorithms based on Runge-Kutta methods of order at least two, a curve search is implemented instead of the standard line search used in quasi-Newton algorithms. Stepsize control techniques are also performed to control the stepsize associated with the underlying Runge-Kutta method. These hybrid algorithms are tested on a variety of test problems and their performance is compared with that of the limited memory BFGS algorithm.

Trust region subproblems arise within a class of unconstrained methods called trust region methods. The subproblems consist of minimizing a quadratic function subject to a norm constraint. This thesis is a survey of different methods developed to find an approximate solution to the subproblem. We study the well-known method of More and Sorensen and two recent methods for large sparse subproblems: the so-called Lanczos method of Gould et al. and the Rendland Wolkowicz algorithm. The common ground to explore these methods will be semidefinite programming. This approach has been used by Rendl and Wolkowicz to explain their method and the More and Sorensen algorithm; we extend this work to the Lanczos method. The last chapter of this thesis is dedicated to some improvements done to the Rendl and Wolkowicz algorithm and to comparisons between the Lanczos method and the Rendl and Wolkowicz algorithm. In particular, we show some weakness of the Lanczos method and show that the Rendl and Wolkowicz algorithm is more robust.

Trust region subproblems arise within a class of unconstrained methods called trust region methods. The subproblems consist of minimizing a quadratic function subject to a norm constraint. This thesis is a survey of different methods developed to find an approximate solution to the subproblem. We study the well-known method of More and Sorensen and two recent methods for large sparse subproblems: the so-called Lanczos method of Gould et al. and the Rendland Wolkowicz algorithm. The common ground to explore these methods will be semidefinite programming. This approach has been used by Rendl and Wolkowicz to explain their method and the More and Sorensen algorithm; we extend this work to the Lanczos method. The last chapter of this thesis is dedicated to some improvements done to the Rendl and Wolkowicz algorithm and to comparisons between the Lanczos method and the Rendl and Wolkowicz algorithm. In particular, we show some weakness of the Lanczos method and show that the Rendl and Wolkowicz algorithm is more robust.

Most classical unconstrained optimization methods require derivative information. Different methods have been proposed for problems where derivative information cannot be used. One class of these methods is heuristics including Evolutionary Algorithms (EAs). In this study, we propose EAs for unconstrained optimization under both deterministic and stochastic environments. We design a crossover operator that tries to lead the algorithm towards the global optimum even when the starting solutions are far from the optimal solution. We also adapt this algorithm to a stochastic environment where there exist only estimates for the function values. We design new parent selection schemes based on statistical grouping methods and a replacement scheme considering existing statistical information. We test the performance of our algorithms using functions from the literature and newly introduced functions and obtain promising results.

A scaled gradient descent method for competition of applications of conjugate gradient with priori estimations of the minimum value / This research proposes a novel method of improving the Gradient Descent method in an effort to be competitive with applications of the conjugate gradient method while reducing computation per iteration. Iterative methods for unconstrained optimization have found widespread application in digital signal processing applications for large inverse problems, such as the use of conjugate gradient for parallel image reconstruction in MR Imaging. In these problems, very good estimates of the minimum value at the objective function can be obtained by estimating the noise variance in the signal, or using additional measurements. The method proposed uses an estimation of the minimum to develop a scaling for Gradient Descent at each iteration, thus avoiding the necessity of a computationally extensive line search. A sufficient condition for convergence and proof are provided for the method, as well as an analysis of convergence rates for varying conditioned problems. The method is compared against the gradient descent and conjugate gradient methods. A method with a computationally inexpensive scaling factor is achieved that converges linearly for well-conditioned problems. The method is tested with tricky non-linear problems against gradient descent, but proves unsuccessful without augmenting with a line search. However with line search augmentation the method still outperforms gradient descent in iterations. The method is also benchmarked against conjugate gradient for linear problems, where it achieves similar convergence for well-conditioned problems even without augmenting with a line search. / Thesis / Master of Science (MSc) / This research proposes a novel method of improving the Gradient Descent method in an effort to be competitive with applications of the conjugate gradient method while reducing computation per iteration. Iterative methods for unconstrained optimization have found widespread application in digital signal processing applications for large inverse problems, such as the use of conjugate gradient for parallel image reconstruction in MR Imaging. In these problems, very good estimates of the minimum value at the objective function can be obtained by estimating the noise variance in the signal, or using additional measurements. The method proposed uses an estimation of the minimum to develop a scaling for Gradient Descent at each iteration, thus avoiding the necessity of a computationally extensive line search. A sufficient condition for convergence and proof are provided for the method, as well as an analysis of convergence rates for varying conditioned problems. The method is compared against the gradient descent and conjugate gradient methods. A method with a computationally inexpensive scaling factor is achieved that converges linearly for well-conditioned problems. The method is tested with tricky non-linear problems against gradient descent, but proves unsuccessful without augmenting with a line search. However with line search augmentation the method still outperforms gradient descent in iterations. The method is also benchmarked against conjugate gradient for linear problems, where it achieves similar convergence for well-conditioned problems even without augmenting with a line search.

The purpose of this Clinic project is to help Expedia, Inc. expand the search capabilities it offers to its users. In particular, the goal is to help the company respond to unconstrained search queries by generating a method to associate hotels and regions around the world with the higher-level attributes that describe them, such as “family- friendly” or “culturally-rich.” Our team utilized machine-learning algorithms to extract metadata from textual data about hotels and cities. We focused on two machine-learning models: decision trees and Latent Dirichlet Allocation (LDA). The first appeared to be a promising approach, but would require more resources to replicate on the scale Expedia needs. On the other hand, we were able to generate useful results using LDA. We created a website to visualize these results.

In this study analysis and design procedures of partially compliant mechanisms using two degree of freedom mechanism model are developed. The flexible segments are modeled as revolute joints with torsional springs. While one freedom is controlled by the input to the mechanism, the motion of the parts are governed both by the kinematics and the force balance. The procedure developed for the analysis of such mechanisms is shown on two different mechanisms: a five link mechanism with crank input and slider output (five-bar mechanism) / a five link mechanism with crank input and rocker output. Design charts are prepared according to output-link oscillation and dimensionless design parameters

Quality of Service (QoS) in real-time media applications can be defined as the ability to guarantee the delivery of packets from source to destination over best-effort networks within some constraints. These constraints defined as the QoS metrics are end-to-end packet delay, delay jitter, throughtput, and packet losses. Transporting real-time media applications over best-effort networks, e.g. the Internet, is an area of current research. Both the Transmission Control Protocol (TCP) and the User Datagram Protocol (UDP) have failed to provide the desired QoS. This research aims at developing application-level end-to-end QoS controls to improve the user-perceived quality of real-time media applications over best-effort networks, such as, the public Internet. In this research an end-to-end packet based approach is developed. The end-to- end packet based approach consists of source buffer, network simulator ns-2, destina- tion buffer, and controller. Unconstrained model predictive control (MPC) methods are implemented by the controller at the application layer. The end-to-end packet based approach uses end-to-end network measurements and predictions as feedback signals. Effectiveness of the developed control methods are examined using Matlab and ns-2. The results demonstrate that sender-based control schemes utilizing UDP at transport layer are effective in providing QoS for real-time media applications transported over best-effort networks. Significant improvements in providing QoS are visible by the reduction of packet losses and the elimination of disruptions during the playback of real-time media. This is accompanied by either a decrease or increase in the playback start-time.

Despite decades of effort in academia and industry, it is not yet possible to build machines that can replicate many seemingly-basic human perceptual abilities. This work focuses on the problem of face identification that most of us effortlessly solve daily. Substantial progress has been made towards the goal of automatically identifying faces under tightly controlled conditions; however, in the domain of unconstrained face images, many challenges remain. We observe that the recent combination of widespread digital photography, inexpensive digital storage and bandwidth, and online social networks has led to the sudden creation of repositories of billions of shared photographs and opened up an important new domain for unconstrained face identification research. Drawing upon the newly-popular phenomenon of “tagging,” we construct some of the first face identification datasets that are intended to model the digital social spheres of online social network members, and we examine various qualitative and quantitative properties of these image sets. The identification datasets we present here include up to 100 individuals, making them comparable to the average size of members’ networks of “friends” on a popular online social network, and each individual is represented by up to 100 face samples that feature significant real-world variation in appearance, expression, and pose. We demonstrate that biologically-inspired visual representations can achieve state-of-the-art face identification performance on our novel frontal and multi-pose face datasets. We also show that the addition of a tree-structured classifier and training set augmentation can enhance accuracy in the multi-pose setting. Finally, we illustrate that the machine-readable “social context” in which shared photos are often embedded can be applied to further boost face identification accuracy. Taken together, our results suggest that accurate automated face identification in vast online shared photo collections is now feasible. / Engineering and Applied Sciences