Numerical Analysis and Computation Commons^™

A Comparison Of Computational Perfusion Imaging Techniques, Shaharina Shoha

Masters Theses & Specialist Projects

Dynamic contrast agent magnetic resonance perfusion imaging plays a vital role in various medical applications, including tumor grading, distinguishing between tumor types, guiding procedures, and evaluating treatment efficacy. Extracting essential biological parameters, such as cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT), from acquired imaging data is crucial for making critical treatment decisions. However, the accuracy of these parameters can be compromised by the inherent noise and artifacts present in the source images.

This thesis focuses on addressing the challenges associated with parameter estimation in dynamic contrast agent magnetic resonance perfusion imaging. Specifically, we aim …

Analysis Of Boundary Observability Of Strongly Coupled One-Dimensional Wave Equations With Mixed Boundary Conditions, Wilson Dennis Horner

Masters Theses & Specialist Projects

*see note below

In control theory, the time it takes to receive a signal after it is sent is referred to as the observation time. For certain types of materials, the observation time to receive a wave signal differs depending on a variety of factors, such as material density, flexibility, speed of the wave propagation, etc. Suppose we have a strongly coupled system of two wave equations describing the longitudinal vibrations on a piezoelectric beam of length L. These two wave equations have non-identical wave propagation speeds c1 and c2. First, we prove the exact observability inequality with the optimal …

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 …

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

Masters Theses & Specialist Projects

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different …

Analysis And Implementation Of Numerical Methods For Solving Ordinary Differential Equations, Muhammad Sohel Rana

Masters Theses & Specialist Projects

Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number of practical fields such as equations arising in population dynamics and astrophysics. It …

Analysis Of A Partial Differential Equation Model Of Surface Electromigration, Selahittin Cinar

Masters Theses & Specialist Projects

A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal …

Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu

Masters Theses & Specialist Projects

This thesis consists of six chapters. In the first chapter, we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to prove that there exists a solution for up to the first order nabla fractional difference equation with an initial condition. In chapter three, we define a lower and an upper solution for up to the first order nabla fractional difference equation with an initial condition. Under certain …

Generalized Bathtub Hazard Models For Binary-Transformed Climate Data, James Polcer

Masters Theses & Specialist Projects

In this study, we use a hazard-based modeling as an alternative statistical framework to time series methods as applied to climate data. Data collected from the Kentucky Mesonet will be used to study the distributional properties of the duration of high and low-energy wind events relative to an arbitrary threshold. Our objectiveswere to fit bathtub models proposed in literature, propose a generalized bathtub model, apply these models to Kentucky Mesonet data, and make recommendations as to feasibility of wind power generation. Using two different thresholds (1.8 and 10 mph respectively), results show that the Hjorth bathtub model consistently performed better …

An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung

Masters Theses & Specialist Projects

The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(n) time where n is the number of crossings …

Random Walks With Elastic And Reflective Lower Boundaries, Lucas Clay Devore

Masters Theses & Specialist Projects

No abstract provided.

Generalized Probabilistic Bowling Distributions, Jennifer Lynn Hohn

Masters Theses & Specialist Projects

Have you ever wondered if you are better than the average bowler? If so, there are a variety of ways to compute the average score of a bowling game, including methods that account for a bowler’s skill level. In this thesis, we discuss several different ways to generate bowling scores randomly. For each distribution, we give results for the expected value and standard deviation of each frame's score, the expected value of the game’s final score, and the correlation coefficient between the score of the first and second roll of a single frame. Furthermore, we shall generalize the results in …

Fractional Calculus: Definitions And Applications, Joseph M. Kimeu

Masters Theses & Specialist Projects

No abstract provided.