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Articles 1 - 10 of 10
Full-Text Articles in Other Applied Mathematics
A Comparison Of Computational Perfusion Imaging Techniques, Shaharina Shoha
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 …
Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher
Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher
Mahurin Honors College Capstone Experience/Thesis Projects
A mathematical model for the healing response of diabetic foot ulcers was developed using averaged data (Krishna et al., 2015). The model contains four major factors in the healing of wounds using four separate differential equations with 12 parameters. The four differential equations describe the interactions between matrix metalloproteinases (MMP-1), tissue inhibitors of matrix metalloproteinases (TIMP-1), the extracellular matrix (ECM) of the skin, and the fibroblasts, which produce these proteins. Recently, our research group obtained the individual patient data that comprised the averaged data. The research group has since taken several approaches to analyze the model with the individual …
Score Test And Likelihood Ratio Test For Zero-Inflated Binomial Distribution And Geometric Distribution, Xiaogang Dai
Score Test And Likelihood Ratio Test For Zero-Inflated Binomial Distribution And Geometric Distribution, Xiaogang Dai
Masters Theses & Specialist Projects
The main purpose of this thesis is to compare the performance of the score test and the likelihood ratio test by computing type I errors and type II errors when the tests are applied to the geometric distribution and inflated binomial distribution. We first derive test statistics of the score test and the likelihood ratio test for both distributions. We then use the software package R to perform a simulation to study the behavior of the two tests. We derive the R codes to calculate the two types of error for each distribution. We create lots of samples to approximate …
Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik
Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik
Masters Theses & Specialist Projects
This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental …
Leslie Matrices For Logistic Population Modeling, Bruce Kessler
Leslie Matrices For Logistic Population Modeling, Bruce Kessler
Mathematics Faculty Publications
Leslie matrices are taught as a method of modeling populations in a discrete-time fashion with more detail in the tracking of age groups within the population. Leslie matrices have limited use in the actual modeling of populations, since when the age groups are summed, it is basically equivalent to discrete-time modeling assuming exponential population growth. The logistic model of population growth is more realistic, since it takes into account a carrying capacity for the environment of the population. This talk will describe an adjustment to the Leslie matrix approach for population modeling that is both takes into account the carrying …
Leslie Matrices For Logistic Population Modeling, Bruce Kessler
Leslie Matrices For Logistic Population Modeling, Bruce Kessler
Bruce Kessler
Leslie matrices are taught as a method of modeling populations in a discrete-time fashion with more detail in the tracking of age groups within the population. Leslie matrices have limited use in the actual modeling of populations, since when the age groups are summed, it is basically equivalent to discrete-time modeling assuming exponential population growth. The logistic model of population growth is more realistic, since it takes into account a carrying capacity for the environment of the population. This talk will describe an adjustment to the Leslie matrix approach for population modeling that is both takes into account the carrying …
Peaklet Analysis: Software For Spectrum Analysis, Bruce Kessler
Peaklet Analysis: Software For Spectrum Analysis, Bruce Kessler
Mathematics Faculty Publications
This is the presentation I was invited to give at the Kentucky Innovation and Entrepreneurship Conference, regarding the software that I have developed and worked at commercializing with the help of Kentucky Science and Technology Corporation.
Peaklet Analysis: Software For Spectrum Analysis, Bruce Kessler
Peaklet Analysis: Software For Spectrum Analysis, Bruce Kessler
Bruce Kessler
This is the presentation I was invited to give at the Kentucky Innovation and Entrepreneurship Conference, regarding the software that I have developed and worked at commercializing with the help of Kentucky Science and Technology Corporation.
A Normal Truncated Skewed-Laplace Model In Stochastic Frontier Analysis, Junyi Wang
A Normal Truncated Skewed-Laplace Model In Stochastic Frontier Analysis, Junyi Wang
Masters Theses & Specialist Projects
Stochastic frontier analysis is an exciting method of economic production modeling that is relevant to hospitals, stock markets, manufacturing factories, and services. In this paper, we create a new model using the normal distribution and truncated skew-Laplace distribution, namely the normal-truncated skew-Laplace model. This is a generalized model of the normal-exponential case. Furthermore, we compute the true technical efficiency and estimated technical efficiency of the normal-truncated skewed-Laplace model. Also, we compare the technical efficiencies of normal-truncated skewed-Laplace model and normal-exponential model.
Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul
Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul
Masters Theses & Specialist Projects
Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …