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Physical Sciences and Mathematics Commons™
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- Wound healing (2)
- Big Rip (1)
- Chaos (1)
- Chronic wounds (1)
- Common factor analysis (1)
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- Cosmology (1)
- Diabetes (1)
- Diabetic foot ulcer (1)
- Eigenvalues (1)
- Factor analysis (1)
- Factors (1)
- Finite volume method (1)
- Latin hypercube sampling (1)
- Mathematical modeling (1)
- Mixed-modeling (1)
- Nonlinear Dynamics (1)
- Numerical algorithm (1)
- Optimal design (1)
- Ordinary differential equations (1)
- Oxygen therapy (1)
- Partial Rank Correlation Coefficient procedure (1)
- Partial differential equation (1)
- Predictability Time (1)
- Principal component analysis (1)
- Sensitivity Analysis (1)
- Statistical analysis (1)
- Uncertainty (1)
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
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 …
An Investigation Of The Accuracy Of Parallel Analysis For Determining The Number Of Factors In A Factor Analysis, Mandy Matsumoto
An Investigation Of The Accuracy Of Parallel Analysis For Determining The Number Of Factors In A Factor Analysis, Mandy Matsumoto
Mahurin Honors College Capstone Experience/Thesis Projects
Exploratory factor analysis is an analytic technique used to determine the number of factors in a set of data (usually items on a questionnaire) for which the factor structure has not been previously analyzed. Parallel analysis (PA) is a technique used to determine the number of factors in a factor analysis. There are a number of factors that affect the results of a PA: the choice of the eigenvalue percentile, the strength of the factor loadings, the number of variables, and the sample size of the study. Although PA is the most accurate method to date to determine which factors …
Numerically Solving A System Of Pdes Modeling Chronic Wounds Treated With Oxygen Therapy, Stefan Stryker
Numerically Solving A System Of Pdes Modeling Chronic Wounds Treated With Oxygen Therapy, Stefan Stryker
Mahurin Honors College Capstone Experience/Thesis Projects
Chronic wounds such as diabetic foot ulcers are the leading cause of non-traumatic amputations in developed countries. For researchers to better understand the physiology of these wounds, a mathematical model describing oxygen levels at the wound site can be used to help predict healing responses. The model utilizes equations that are modified from work by Guffey (2015) that consists of four variables – oxygen, bacteria, neutrophils, and chemoattractant within a system of partial differential equations. Our research focuses on numerically solving these partial differential equations using a finite volume approach. This numerical solver will be important for future research in …
Applications Of Latin Hypercube Sampling Scheme And Partial Rank Correlation Coefficient Analysis To Mathematical Models On Wound Healing, Hannah M. Pennington
Applications Of Latin Hypercube Sampling Scheme And Partial Rank Correlation Coefficient Analysis To Mathematical Models On Wound Healing, Hannah M. Pennington
Mahurin Honors College Capstone Experience/Thesis Projects
Latin hypercube sampling and Partial Rank Correlation Coefficient procedure (LHS/PRCC) can be used in combination to perform a sensitivity analysis that assesses a model over a global parameter space. Through this analysis, the uncertainty of the parameters and therefore the variability of the model output in response to this uncertainty can be observed. Latin hypercube sampling divides the parameter space into equiprobable regions and sample without replacement, producing a global, unbiased selection of parameter values. For montonic, non-linear relationships, the correlation between the outputs and parameters can be understood by performing a Partial Rank Correlation Coefficient procedure. This sensitivity analysis …
Predictability Time Of Chaotic Cosmologies, John Max Wilson
Predictability Time Of Chaotic Cosmologies, John Max Wilson
Mahurin Honors College Capstone Experience/Thesis Projects
We examine the predictability time scales for a cosmological model from the Einstein field equations coupled to the Klein-Gordon equations for a spin zero scalar field with an interaction potential V(φ). The cosmological equations resulting from this coupling are nonlinear in the scale cosmic parameter and scalar field, thus exhibiting characteristics of chaos. The equations can be linearized in the neighborhood of equilibrium points and then diagonalized to yield its Lyapunov exponents. One e-folding time of the system is then found to estimate the predictability time. This time is compared to the Big Rip time theorized by Yurov, Moruno, and …