Numerical Analysis and Computation Commons^™

Spectral Tau-Jacobi Algorithm For Space Fractional Advection-Dispersion Problem, Amany S. Mohamed, Mahmoud M. Mokhtar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we use the shifted Jacobi polynomials to approximate the solution of the space fractional advection-dispersion. The method is based on the Jacobi operational matrices of fractional derivative and integration. A double shifted Jacobi expansion is used as an approximating polynomial. We apply this method to solve linear and nonlinear term FDEs by using initial and boundary conditions.

School Policy Evaluated With Time-Reversible Markov Chain, Trajan Murphy, Iddo Ben-Ari

Honors Scholar Theses

In this work we propose a reversible Markov chain scheme to model for the mobility of students affected by a grade school leveling policy. This model provides unified and mathematically tractable framework in which transition functions are sampled uniformly from the set of {\bf reversible} transition functions. The results from the study appear to confirm the disadvantageous effects of this school policy, on par with the of a previous model on the same policy.

Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, Olusegun M. Otunuga, Anna Mummert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

Biology and Medicine Through Mathematics Conference

No abstract provided.

Immunofluorescence Image Feature Analysis And Clustering Pipeline For Distinguishing Epithelial-Mesenchymal Transition, Shreyas Hirway, Nadiah Hassan, Dr. Christopher Lemmon, Dr. Seth Weinberg

Biology and Medicine Through Mathematics Conference

No abstract provided.

Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Effects Of Finite Precision On The Simulation Of The Double Pendulum, Rebecca Wild

Senior Honors Projects, 2010-2019

We use mathematics to study physical problems because abstracting the information allows us to better analyze what could happen given any range and combination of parameters. The problem is that for complicated systems mathematical analysis becomes extremely cumbersome. The only effective and reasonable way to study the behavior of such systems is to simulate the event on a computer. However, the fact that the set of floating-point numbers is finite and the fact that they are unevenly distributed over the real number line raises a number of concerns when trying to simulate systems with chaotic behavior. In this research we …

Enhancement Of Krylov Subspace Spectral Methods Through The Use Of The Residual, Haley Dozier

Dissertations

Depending on the type of equation, finding the solution of a time-dependent partial differential equation can be quite challenging. Although modern time-stepping methods for solving these equations have become more accurate for a small number of grid points, in a lot of cases the scalability of those methods leaves much to be desired. That is, unless the timestep is chosen to be sufficiently small, the computed solutions might exhibit unreasonable behavior with large input sizes. Therefore, to improve accuracy as the number of grid points increases, the time-steps must be chosen to be even smaller to reach a reasonable solution. …

Comparative Error Analysis Of The Black-Scholes Equation, Chuan Chen

Honors Theses

Finance is a rapidly growing area in our banking world today. With this ever-increasing development come more complex derivative products than simple buy-and-sell trades. Financial derivatives such as futures and options have been developed stemming from the traditional stock, bond, currency, and commodity markets. Consequently, the need for more sophisticated mathematical modeling is also rising. The Black-Scholes equation is a partial differential equation that determines the price of a financial option under the Black-Scholes model. The idea behind the equation is that there is a perfect and risk-free way for one to hedge the options by buying and selling the …

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

Undergraduate Theses and Capstone Projects

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic models. …

Reducing Memory Access Latencies Using Data Compression In Sparse, Iterative Linear Solvers, Neil Lindquist

All College Thesis Program, 2016-2019

Solving large, sparse systems of linear equations plays a significant role in certain scientific computations, such as approximating the solutions of partial differential equations. However, solvers for these types of problems usually spend most of their time fetching data from main memory. In an effort to improve the performance of these solvers, this work explores using data compression to reduce the amount of data that needs to be fetched from main memory. Some compression methods were found that improve the performance of the solver and problem found in the HPCG benchmark, with an increase in floating point operations per second …

Predicting Win Rates In Competitive Overwatchtm, Andrea Sibley

Mathematics Senior Capstone Papers

OverwatchTM is a video game published by Blizzard Entertainment R where two teams comprised of six people each compete against one another to accomplish a specific goal. The goal of each game is dependent on which map is being played. The maps are divided into four categories: Assault, Escort, Control, and Hybrid. A data set comprised of 3000 games of competitive OverwatchTM is used to determine how likely a team is to win their match. The factors used to determine the likelihood of winning are the map type and the skill ranking for each team. The data set is pre-processed …

Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli

Masters Theses & Specialist Projects

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that …

Partially Isometric Matrices: A Brief And Selective Survey, Stephan Ramon Garcia, Matthew Okubo Patterson, William T. Ross

Department of Math & Statistics Faculty Publications

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also discuss the unitary similarity problem and several other results.

Modeling The Distribution Of Lightning Strike Distances Outside A Preexisting Lightning Area, Dawn L. Sanderson

Theses and Dissertations

Air Force Instruction 91-203 (AFI 91-203) directs that a lightning warning be issued when lightning is occurring or imminent within a 5 nautical mile (NM) radius of a predetermined location or activity. The 45 Weather Squadron (WS), located on the central eastern coast of Florida, balances the safety of personnel and space launch vehicles with lost productivity of taking shelter from lightning. The primary objective of this study investigates if this 5 NM safety radius can be reduced while maintaining a desired level of safety. The research uses processed Lightning Detection and Ranging (LDAR) data to map the movement of …

Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose

Rose-Hulman Undergraduate Mathematics Journal

The focus of this research was to develop numerical algorithms to approximate solutions of Poisson's equation in three dimensional rectangular prism domains. Numerical analysis of partial differential equations is vital to understanding and modeling these complex problems. Poisson's equation can be approximated with a finite difference approximation. A system of equations can be formed that gives solutions at internal points of the domain. A computer program was developed to solve this system with inputs such as boundary conditions and a nonhomogenous source function. Approximate solutions are compared with exact solutions to prove their accuracy. The program is tested with an …

Numerical Investigation Of Inclination On The Thermal Performance Of Porous Fin Heatsink Using Pseudospectral Collocation Method, George Oguntala, Gbeminiyi Sobamowo, Raed Abd-Alhameed, James Noras

Karbala International Journal of Modern Science

Numerical investigation of inclination effect on the thermal performance of a porous fin heat sink is presented. The developed thermal model is solved using pseudo-spectral collocation method (PSCM). Parametric studies are carried out using PSCM, and the thermal characterization of heat sink with the inclined porous fin of rectangular geometry is presented. Results show that heat sink of inclined porous fin exhibits higher thermal performance than heat sink of vertical porous fin operating under the same thermal conditions with the same geometrical configurations. Performance of inclined or tilted fin increases with decrease in length-thickness aspect ratio. However, increase in the …

Studies Of Boundary Layer Transition From Laminar To Turbulent, Elizabeth Spaulding

Honors Program: Senior Projects (Public)

In engineering applications, there is a strong desire to reduce energy losses due to turbulent energy production. However, the theoretical understanding of turbulent and transition flow is still lacking due to the absence of an exact mathematical solution for turbulent flow. In the current project, transition and turbulent behavior in wall-bounded flow is studied, with an emphasis on concepts from boundary layer theory. Organized structures, such as streaks, waves, and vortices, which occur in such flows, are analyzed. Especially for near-wall structures, control strategies for suppressing such structures are discussed. Using mathematical equations which govern fluid flow, models for different …

Mhd Boundary Layer Slip Flow Over A Flat Plate With Soret And Dufour Effects, B. Shashidar Reddy, K. Saritha

Applications and Applied Mathematics: An International Journal (AAM)

The present paper studies the effects of Soret and Dufour on MHD boundary layer slip flow over a flat plate. The governing partial differential equations are converted to a set of nonlinear ordinary differential equations by using similarity transformations. Then, these equations are solved numerically by implicit Finite Difference Scheme. The numerical solutions for Velocity, Temperature and Concentration profiles for the related essential physical parameters are visualized through graphs and discussed. Results show that the velocity rises whereas the temperature and concentration reduces with the respective slip parameters. The increase in Soret number or decrease in Dufour number reduces the …

Spectral Discretization Errors In Filtered Subspace Iteration, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. The algorithm is motivated by a quadrature approximation of an operator-valued contour integral of the resolvent. Resolvents on infinite dimensional spaces are discretized in computable finite-dimensional spaces before the algorithm is applied. This study focuses on how such discretizations result in errors in the eigenspace approximations computed by the algorithm. The computed eigenspace is then used to obtain approximations of the eigenvalue cluster. Bounds for the Hausdorff distance between the computed and exact eigenvalue clusters …

Universal Quantum Computation, Junya Kasahara

Theses, Dissertations and Capstones

We study quantum computers and their impact on computability. First, we summarize the history of computer science. Only a few articles have determined the direction of computer science and industry despite the fact that many works have been dedicated to the present success. We choose articles by A. M. Turing and D. Deutsch, because A. M. Turing proposed the basic architecture of modern computers while D. Deutsch proposed an architecture for the next generation of computers called quantum computers. Second, we study the architecture of modern computers using Turing machines. The Turing machine has the basic design of modern computers …

Estimation Of Multivariate Asset Models With Jumps, Angela Loregian, Laura Ballotta, Gianluca Gianluca Fusai, Marcos Fabricio Perez

Business Faculty Publications

We propose a consistent and computationally efficient two-step methodology for the estimation of multidimensional non-Gaussian asset models built using Levy processes. The proposed framework allows for dependence between assets and different tail behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets as it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail …

Stair Climbing Hand Truck, James Mcpherson

All Undergraduate Projects

Abstract

Getting a heavy object up a flight of stairs usually requires a team of two or more people. Even with a team of people, the task is often still difficult, dangerous, and possibly insurmountable by one person. This problem is especially prevalent in for those who are moving into apartment complexes. Most apartment complexes have many buildings with two or more floors of living quarters, and elevators are often missing. This project sought to offer a solution to this problem. The solution in question; a motorized hand-truck with 2, trigonal planar pinwheels in place of the stock wheels. The …

Numerical Simulations For Optimal Control Of A Cancer Cell Model With Delay, Jessica S. Lugo

Murray State Theses and Dissertations

Mathematical models are often created to analyze the complicated behavior of many physical systems. One such system is that of the interaction between cancer cells, the immune system, and various treatments such as chemotherapy, radiation, and immunotherapy. Using models that depict these relationships gives researchers insight on the dynamics of this complicated system and possibly ideas for improved treatment schedules.

The model presented here gives the relationship of cancer cells in development phases with immune cells and cycle-specific chemotherapy treatment. This model includes a constant delay term in the mitotic phase. Optimal control theory is used to minimize the cost …

Pawnee Dam Inflow Design Flood (Idf) Update And Stage-Frequency Curve Development Using Rmcrfa, Jennifer P. Christensen, Joshua J. Melliger

United States Geological Survey: Water Reports and Publications

Pawnee Dam is one of the ten Salt Creek Dams designed and built in the 1960s to mitigate flooding in Lincoln, Nebraska. This short paper illustrates the update of the Pawnee Dam inflow design flood (IDF) through calibration to recent high flow events and the development of its stage-frequency or hydrologic loading curve with the U.S. Army Corps of Engineers’ Risk Management Center Reservoir Frequency Analysis (RMC-RFA) model. The IDF update follows Engineering Regulation 1110-8-2, Inflow Design Flood for Dams and Reservoirs, including unit hydrograph peaking and two antecedent pool elevations. Background information on the original design of the dam …

Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …

A Statistical Investigation Of Stock Market Activity And Instances Of Financial Crime, Elizabeth G. Biggs

Theses and Dissertations

This project aims to identify a possible statistical relationship between the stock market and incidences of financial crime in Illinois, Texas, and Utah through big data analysis techniques using data from the FBI’s Federal Bureau of Investigation’s National Incident-Based Reporting System (NIBRS) database. By analyzing the occurrences of financial crime by location, year, and type in relation to the S&P 500’s percent change in close price on the first day of the calendar year, it will be possible to determine if a statistical relationship exists between the two. In addition, regression analysis was performed in order to predict financial crime …

On The Role Of Ill-Conditioning: Biharmonic Eigenvalue Problem And Multigrid Algorithms, Kasey Bray

Theses and Dissertations--Mathematics

Very fine discretizations of differential operators often lead to large, sparse matrices A, where the condition number of A is large. Such ill-conditioning has well known effects on both solving linear systems and eigenvalue computations, and, in general, computing solutions with relative accuracy independent of the condition number is highly desirable. This dissertation is divided into two parts.

In the first part, we discuss a method of preconditioning, developed by Ye, which allows solutions of Ax=b to be computed accurately. This, in turn, allows for accurate eigenvalue computations. We then use this method to develop discretizations that yield accurate computations …

Randomized Algorithms For Preconditioner Selection With Applications To Kernel Regression, Conner Dipaolo

HMC Senior Theses

The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M^-1A ||_F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which …

Rule Extraction And Insertion To Improve The Performance Of A Dynamic Cell Structure Neural Network, Osama Amhamed Elsarrar

Graduate Theses, Dissertations, and Problem Reports (ETD)

Artificial Neural Networks are extremely useful machine learning tools. They are used for many purposes, such as prediction, classification, pattern recognition, etc. Although neural networks have been used for decades, they are still often not completely understood or trusted, especially in safety and mission critical situations. Typically, neural networks are trained on data sets that are representative of what needs to be learned. Sometimes training sets are constructed in order to train the neural network in a certain way, in order to embed appropriate knowledge. The purpose of this research is to determine if there is another method that can …