Numerical Analysis and Scientific Computing Commons^™

Novel Monte Carlo Methods For Large-Scale Linear Algebra Operations, Hao Ji

Computer Science Theses & Dissertations

Linear algebra operations play an important role in scientific computing and data analysis. With increasing data volume and complexity in the "Big Data" era, linear algebra operations are important tools to process massive datasets. On one hand, the advent of modern high-performance computing architectures with increasing computing power has greatly enhanced our capability to deal with a large volume of data. One the other hand, many classical, deterministic numerical linear algebra algorithms have difficulty to scale to handle large data sets.

Monte Carlo methods, which are based on statistical sampling, exhibit many attractive properties in dealing with large volume of …

Machine Learning Methods For Brain Image Analysis, Ahmed Fakhry

Computer Science Theses & Dissertations

Understanding how the brain functions and quantifying compound interactions between complex synaptic networks inside the brain remain some of the most challenging problems in neuroscience. Lack or abundance of data, shortage of manpower along with heterogeneity of data following from various species all served as an added complexity to the already perplexing problem. The ability to process vast amount of brain data need to be performed automatically, yet with an accuracy close to manual human-level performance. These automated methods essentially need to generalize well to be able to accommodate data from different species. Also, novel approaches and techniques are becoming …

Computational Analysis Of Gene Expression And Connectivity Patterns In The Convoluted Structures Of Mouse Cerebellum, Tao Zeng

Computer Science Theses & Dissertations

One significant difference between evolved mammalian brains and other species is that mammalian brains exhibit increasingly convoluted structures in the cerebral cortex. Groove and ridge shaped structures named gyri and sulci expand surface area of cerebral cortex, making more functions possible. Prior studies using neuroimaging techniques such as dMRI and DTI have revealed that neural fibers are heavily connected to gyri comparing to those connected to sulci, such macro-scale experiments indicates that gyri are involved in large scale information processing while sulci process information locally. However, molecular and cellar level evidences, namely, gene expression pattern and its resulting neuronal connectivity …

Generating Combinatorial Objects- A New Perspective, Alexander Chizoma Nwala

Computer Science Theses & Dissertations

Combinatorics is the science of "possibilities." This definition, while not formal is a fair statement because all too often, in order to gain insight into the solution of many counting problems, we explore the possibilities. In some cases we seek to know how many options, while in other cases we seek to enumerate or list the options. Irrespective of the scenario, combinatorics plays a vital role today. In many instances such as exploring the options for choosing a new password for a combination lock, we employ combinatorics. In considering the possible license plate permutations for a state, or to see …

A Probabilistic Analysis Of Misparking In Reservation Based Parking Garages, Vikas G. Ashok

Computer Science Theses & Dissertations

Parking in major cities is an expensive and annoying affair, the reason ascribed to the limited availability of parking space. Modern parking garages provide parking reservation facility, thereby ensuring availability to prospective customers. Misparking in such reservation based parking garages creates confusion and aggravates driver frustration. The general conception about misparking is that it tends to completely cripple the normal functioning of the system leading to chaos and confusion. A single mispark tends to have a ripple effect and therefore spawns a chain of misparks. The chain terminates when the last mispark occurs at the parking slot reserved by the …

Parallel Newton-Krylov-Schwarz Solvers For The Full Potential Flow Equation, Jie Zhang

Computer Science Theses & Dissertations

Newton-Krylov-Schwarz methods are increasingly applied in Computational Fluid Dynamics (CFD). We develop a parallel analysis code based on this method for the full potential flow model. The full potential model consists of a single nonlinear second-order partial differential equation of mixed type (elliptic/hyperbolic), which we solve as a steady boundary-value problem.

We use a nine-point finite-difference stencil to discretize the equation. A Newtonlike linearization and correction method is used to solve the resulting set of nonlinear algebraic equations. To solve the inner linear equations, we employ a Krylov space method. Preconditioners are used to improve the convergence rate. In order …

Real Time Texture Analysis From The Parallel Computation Of Fractal Dimension, Halford I. Hayes Jr.

Computer Science Theses & Dissertations

The discrimination of texture features in an image has many important applications: from detection of man-made objects from a surrounding natural background to identification of cancerous from healthy tissue in X-ray imagery. The fractal structure in an image has been used with success to identify these features but requires unacceptable processing time if executed sequentially.

The paradigm of data parallelism is presented as the best method for applying massively parallel processing to the computation of fractal dimension of an image. With this methodology, and sufficient numbers of processors, this computation can reach real time speeds necessary for many applications. A …

Multiple Learner Systems Using Resampling Methods, Binyun Xie

Computer Science Theses & Dissertations

The N-Learners Problem deals with combining a number of learners such that the resultant system is "better", under some criterion, than the best of the individual learners. We consider a system of probably approximately correct concept learners. Depending on the available information, there are several methods to make the composite system better than the best of the individual learners. If a sample and an oracle that generates data points (but, not their classification) is available, then we show that we can achieve arbitrary levels of the normalized confidence of the composite system if (a) a robust learning algorithm is available, …

Single Object Detection Using Multiple Sensors With Unknown Noise Distributions, Shaofen Chen

Computer Science Theses & Dissertations

We consider the design of an object classification system that identifies single objects using a system of sensors; each sensor outputs a random vector, according to an unknown (noise) probability distribution, in response to a sensed object. We consider a special class of systems, called the linearly separable systems, where the error-free sensor outputs corresponding to distinct objects can be mapped into disjoint intervals on real line. Given a set of sensor outputs corresponding to known objects, we show that a detection rule α_emp that approaches the correct rule with a high probability can be computed. We show …