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 …

Mapping Urban Tree Canopy Using Publicly Available Satellite Data, Rosemary Mcguinness

Theses and Dissertations

This project addresses the need for accessible, cost-effective tools for quantifying spatial and temporal changes in tree canopy cover in urban areas. Urban tree canopy provides a wide range of ecosystem services, including lowering air temperatures, reducing pollution, and mitigating stormwater runoff. Cities around the world have placed the expansion of their urban forests at the center of their sustainability goals. Consistent and timely data on urban tree canopy is essential for urban greening initiatives to succeed. Existing methods of accessing information about urban tree canopy are highly technical, costly, and labor-intensive, while the freely available source of tree canopy …

Optical Response Of 3d Model Topological Nodal-Line Semimetal, Sita Kandel, Godfrey Gumbs, Oleg L. Berman

Publications and Research

Wepresent a semi-analytical expression for both longitudinal and transverse optical conductivities of a model TNLSM employing the Kubo formula with emphasis on the optical spectral weight redistribution, deduced from appropriate Green’s func tions. In this semimetal, the conduction and valence bands cross each other along a one- dimensional curve protected by certain symmetry group in the 3D Brillouin zone. Although the crossing cannot be removed by any perturbations, it can be adjusted by continuous tuning of the Hamiltonian with a parameter α. When α>0, the two bands cross each other near the Γ point in the (kx,ky) plane of …

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 …

Phys 275: Intro To Scientific Computing, David Goldberg

Open Educational Resources

No abstract provided.

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 …

Positive Rate-Dependent Action Potential Prolongation By Modulating Potassium Ion Channels, Candido Cabo

Publications and Research

Pharmacological agents that prolong action potential duration (APD) to a larger extent at slow rates than at the fast excitation rates typical of ventricular tachycardia exhibit reverse rate dependence. Reverse rate dependence has been linked to the lack of efficacy of class III agents at preventing arrhythmias because the doses required to have an anti-arrhythmic effect at fast rates may have pro-arrhythmic effects at slow rates due to an excessive APD prolongation. In this report we show that, in computer models of the ventricular action potential, APD prolongation by accelerating phase 2 repolarization (by increasing I_Ks) and decelerating …

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 …

Analyze And Examine Wildfire Events In California, Aleena Hoodith, Sakim Zaman, Safoan Hossain, Jiehao Huang

Publications and Research

•A wildfire is an unplanned, unwanted, uncontrolled fire in an area of combustible vegetation starting in rural areas and urban areas. •Recent studies have shown that the effect of anthropogenic climate change has fueled the wildfire events, leading to an increase in the annual burned areas and number of events. •California is one of the places having the most deadliest and destructive wildfire seasons. With the global warming effect of 1°C since 1850, the 20 largest wildfires events that have occurred in California, 8 of them were in 2017. (Center For Climate And Energy Solutions) •Climate change is primarily caused …

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. …

Graph-Theoretic Partitioning Of Rnas And Classification Of Pseudoknots-Ii, Louis Petingi

Publications and Research

Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called blocks and determine whether each block contains a pseudoknot or not. As pseudoknots can not be contained into two different blocks, this characterization allow us to efficiently isolate smaller RNA fragments and classify them as pseudoknotted or pseudoknot-free regions, while keeping these sub-structures intact. Moreover we have extended the partitioning algorithm by classifying a pseudoknot as either recursive or non-recursive in order to continue with our research …

Snow-Albedo Feedback In Northern Alaska: How Vegetation Influences Snowmelt, Lucas C. Reckhaus

Theses and Dissertations

This paper investigates how the snow-albedo feedback mechanism of the arctic is changing in response to rising climate temperatures. Specifically, the interplay of vegetation and snowmelt, and how these two variables can be correlated. This has the potential to refine climate modelling of the spring transition season. Research was conducted at the ecoregion scale in northern Alaska from 2000 to 2020. Each ecoregion is defined by distinct topographic and ecological conditions, allowing for meaningful contrast between the patterns of spring albedo transition across surface conditions and vegetation types. The five most northerly ecoregions of Alaska are chosen as they encompass …

Qwasi: The Quantum Walk Simulator, Warren V. Wilson

Theses and Dissertations

As quantum computing continues to evolve, the ability to design and analyze novel quantum algorithms becomes a necessary focus for research. In many instances, the virtues of quantum algorithms only become evident when compared to their classical counterparts, so a study of the former often begins with a consideration of the latter. This is very much the case with quantum walk algorithms, as the success of random walks and their many, varied applications have inspired much interest in quantum correlates. Unfortunately, finding purely algebraic solutions for quantum walks is an elusive endeavor. At best, and when solvable, they require simple …

Decision Tree For Predicting The Party Of Legislators, Afsana Mimi

Publications and Research

The motivation of the project is to identify the legislators who voted frequently against their party in terms of their roll call votes using Office of Clerk U.S. House of Representatives Data Sets collected in 2018 and 2019. We construct a model to predict the parties of legislators based on their votes. The method we used is Decision Tree from Data Mining. Python was used to collect raw data from internet, SAS was used to clean data, and all other calculations and graphical presentations are performed using the R software.

Arecibo Message, Joshua P. Tan

Open Educational Resources

This two week assignment asks students to interpret and analyze the 1974 Arecibo Message sent by Drake and Sagan. Week 1 introduces the concepts behind the construction of the message and engages with a critical analysis of the architecture and the contents of the message. Week 2 asks students to develop software in a Jupyter Notebook (available for free from the Anaconda Python Distribution) to interpret messages that were similar to those produced by Drake and Sagan.

Cs04all: Machine Learning Module, Hunter R. Johnson

Open Educational Resources

These are materials that may be used in a CS0 course as a light introduction to machine learning.

The materials are mostly Jupyter notebooks which contain a combination of labwork and lecture notes. There are notebooks on Classification, An Introduction to Numpy, and An Introduction to Pandas.

There are also two assessments that could be assigned to students. One is an essay assignment in which students are asked to read and respond to an article on machine bias. The other is a lab-like exercise in which students use pandas and numpy to extract useful information about subway ridership in NYC. …

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 …

An Algorithm For Calculating Top-Dimensional Bounding Chains, J. Frederico Carvalho​, Mikael Vejdemo-Johansson, Danica Kragic, Florian T. Pokorny

Publications and Research

We describe the Coefficient-Flow algorithm for calculating the bounding chain of an (n-1)-boundary on an n-manifold-like simplicial complex S. We prove its correctness and show that it has a computational time complexity of O(|S(n−1)|) (where S(n−1) is the set of (n-1)-faces of S). We estimate the big-O coefficient which depends on the dimension of S and the implementation. We present an implementation, experimentally evaluate the complexity of our algorithm, and compare its performance with that of solving the underlying linear system.

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 …

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Publications and Research

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

Study Of Self-Similarity In Brain Data, Jennifer Holst

Student Theses

In the area of computer science, past research has found that the concept of self-similarity is present in local and Internet-based network traffic. This study considers the possibility that data traveling through the neuronal network in the human brain is also self-similar. By analyzing publicly available raw EEG data and estimating its Hurst parameter, we find indications that brain data traffic may in fact be self-similar.

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 …

Comparing Tensorflow Deep Learning Performance Using Cpus, Gpus, Local Pcs And Cloud, John Lawrence, Jonas Malmsten, Andrey Rybka, Daniel A. Sabol, Ken Triplin

Publications and Research

Deep learning is a very computational intensive task. Traditionally GPUs have been used to speed-up computations by several orders of magnitude. TensorFlow is a deep learning framework designed to improve performance further by running on multiple nodes in a distributed system. While TensorFlow has only been available for a little over a year, it has quickly become the most popular open source machine learning project on GitHub. The open source version of TensorFlow was originally only capable of running on a single node while Google’s proprietary version only was capable of leveraging distributed systems. This has now changed. In this …

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 …

Creating Art Patterns With Math And Code, Boyan Kostadinov

Publications and Research

The goal of this talk is to showcase some visualization projects that we developed for a 3-day Code in R summer program, designed to inspire the creative side of our STEM students by engaging them with computational projects that we developed with the purpose of mixing calculus level math and code to create complex geometric patterns. One of the goals of this program was to attract more minority and female students into applied math and computer science majors.

The projects are designed to be implemented using the high-level, open-source and free computational environment R, a popular software in industry for …

Exploring Data Mining Techniques For Tree Species Classification Using Co-Registered Lidar And Hyperspectral Data, Julia K. Marrs

Theses and Dissertations

NASA Goddard’s LiDAR, Hyperspectral, and Thermal imager provides co-registered remote sensing data on experimental forests. Data mining methods were used to achieve a final tree species classification accuracy of 68% using a combined LiDAR and hyperspectral dataset, and show promise for addressing deforestation and carbon sequestration on a species-specific level.