Numerical Analysis and Scientific Computing Commons^™

New Fast Polynomial Root-Finders, Soo Go

Dissertations, Theses, and Capstone Projects

Univariate polynomial root-finding has been studied for four millennia and very intensively in the last decades. Our {\em black box root-finder} involves no coefficients and works for a black box polynomial, defined by an oracle (that is, black box subroutine) for its evaluation. Such root-finders have various benefits, e.g., are particularly efficient where a polynomial can be evaluated fast, say, is a sum of a small number of shifted monomials (x-c)^a.

Our root-finder approximates all d complex zeros of a dth degree polynomial p(x) (aka roots of equation p(x)=0) by using Las Vegas expected number of bit-operations within a factor …

Pulsey: Stellar Pulsation Models In Python, Andrew Ayala

Dissertations, Theses, and Capstone Projects

The era of the Kepler/K2 and TESS space-telescope missions has inundated the astrophysics community with photometric data for millions of stars with continuous observation and very high cadence. This data confirms that nearly every observed stellar source exhibits an oscillating luminosity, with stellar pulsation being the driving mechanism behind a large fraction of the cause. The result has been an explosion in the field of asteroseismology, where the recorded luminosity variations, or "light curves", of pulsating stars to probe their interior structures. By modeling observed light curves, we can constrain values of the physical stellar parameters producing them. The brightness …

Accelerating Parameter Identifiability Of Differential Models With Applications To Parameter Estimation, Ilia Ilmer

Dissertations, Theses, and Capstone Projects

The task of mathematical modeling involves working with real world phenomena described via parametric ordinary differential equations (ODE). Typically, an ODE model consists of states, parameters, inputs, and outputs. The states represent quantities whose dynamics the model describes, the parameters are quantities that are specific to the phenomenon being studied. Finally, inputs and outputs represent functions that are being added and measured from experiments, respectively. One of the questions that arises in studies of such models, is whether for given input-output setup one can efficiently and correctly estimate the values of parameters or initial conditions. This property of parameters or …

The Interaction Of Different Primary Producers And Physical And Chemical Dynamics Of An Urban Shallow Lake, Majid Sahin

Dissertations, Theses, and Capstone Projects

An artificial urban shallow lake, Prospect Park Lake (PPL), is situated on a terminal moraine in Brooklyn New York, and supplied with municipal water treated with ortho-phosphates. The constant input of the phosphate nutrient is the primary source of eutrophication in the lake. The numerous pools along the water course houses various aquatic phototrophs, which influence the water quality and the state of the system, driving conditions into favoring the survival of their species. In the first half of the dissertation, the focus of the project is on analyzing how the different primary producers in different regions of PPL affect …

Coded Distributed Function Computation, Pedro J. Soto

Dissertations, Theses, and Capstone Projects

A ubiquitous problem in computer science research is the optimization of computation on large data sets. Such computations are usually too large to be performed on one machine and therefore the task needs to be distributed amongst a network of machines. However, a common problem within distributed computing is the mitigation of delays caused by faulty machines. This can be performed by the use of coding theory to optimize the amount of redundancy needed to handle such faults. This problem differs from classical coding theory since it is concerned with the dynamic coded computation on data rather than just statically …

Molecular Dynamics Simulations Of Self-Assemblies In Nature And Nanotechnology, Phu Khanh Tang

Dissertations, Theses, and Capstone Projects

Nature usually divides complex systems into smaller building blocks specializing in a few tasks since one entity cannot achieve everything. Therefore, self-assembly is a robust tool exploited by Nature to build hierarchical systems that accomplish unique functions. The cell membrane distinguishes itself as an example of Nature’s self-assembly, defining and protecting the cell. By mimicking Nature’s designs using synthetically designed self-assemblies, researchers with advanced nanotechnological comprehension can manipulate these synthetic self-assemblies to improve many aspects of modern medicine and materials science. Understanding the competing underlying molecular interactions in self-assembly is always of interest to the academic scientific community and industry. …

Enhancing 3d Visual Odometry With Single-Camera Stereo Omnidirectional Systems, Carlos A. Jaramillo

Dissertations, Theses, and Capstone Projects

We explore low-cost solutions for efficiently improving the 3D pose estimation problem of a single camera moving in an unfamiliar environment. The visual odometry (VO) task -- as it is called when using computer vision to estimate egomotion -- is of particular interest to mobile robots as well as humans with visual impairments. The payload capacity of small robots like micro-aerial vehicles (drones) requires the use of portable perception equipment, which is constrained by size, weight, energy consumption, and processing power. Using a single camera as the passive sensor for the VO task satisfies these requirements, and it motivates the …

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …

Machine Learning Algorithms For Automated Satellite Snow And Sea Ice Detection, George Bonev

Dissertations, Theses, and Capstone Projects

The continuous mapping of snow and ice cover, particularly in the arctic and poles, are critical to understanding the earth and atmospheric science. Much of the world's sea ice and snow covers the most inhospitable places, making measurements from satellite-based remote sensors essential. Despite the wealth of data from these instruments many challenges remain. For instance, remote sensing instruments reside on-board different satellites and observe the earth at different portions of the electromagnetic spectrum with different spatial footprints. Integrating and fusing this information to make estimates of the surface is a subject of active research.

In response to these challenges, …

Machine Learning Approach To Retrieving Physical Variables From Remotely Sensed Data, Fazlul Shahriar

Dissertations, Theses, and Capstone Projects

Scientists from all over the world make use of remotely sensed data from hundreds of satellites to better understand the Earth. However, physical measurements from an instrument is sometimes missing either because the instrument hasn't been launched yet or the design of the instrument omitted a particular spectral band. Measurements received from the instrument may also be corrupt due to malfunction in the detectors on the instrument. Fortunately, there are machine learning techniques to estimate the missing or corrupt data. Using these techniques we can make use of the available data to its full potential.

We present work on four …

Computerized Classification Of Surface Spikes In Three-Dimensional Electron Microscopic Reconstructions Of Viruses, Younes Benkarroum

Dissertations, Theses, and Capstone Projects

The purpose of this research is to develop computer techniques for improved three-dimensional (3D) reconstruction of viruses from electron microscopic images of them and for the subsequent improved classification of the surface spikes in the resulting reconstruction. The broader impact of such work is the following.

Influenza is an infectious disease caused by rapidly-changing viruses that appear seasonally in the human population. New strains of influenza viruses appear every year, with the potential to cause a serious global pandemic. Two kinds of spikes – hemagglutinin (HA) and neuraminidase (NA) – decorate the surface of the virus particles and these proteins …