Physical Sciences and Mathematics Commons^™

Nonsmooth Epidemic Models With Evolutionary Game Theory, Cameron Morin

Electronic Theses and Dissertations

This thesis explores the utilization of game theory and nonsmooth functions to enhance the accuracy of epidemiological simulations. Traditional sensitivity analysis encounters difficulties when dealing with nondifferentiable points in nonsmooth functions. However, by incorporating recent advancements in nonsmooth analysis, sensitivity analysis techniques have been adapted to accommodate these complex functions. In pursuit of more accurate simulations, evolutionary game theory, primarily the replicator equation, is introduced, modeling individuals’ decision making processes when observing others’ choices. The SEIR model is explored in depth, and additional complexities are incorporated, leading to the creation of an expanded SEIR model, the Be-SEIMR model.

Hybrid Power Spectral And Wavelet Image Roughness Analysis, Basel White

Electronic Theses and Dissertations

The Two-Dimensional Wavelet Transform Modulus Maxima (2D WTMM) sliding window methodology has proven to be a robust approach, in particular for the extraction of the Hurst (H) roughness exponent from grayscale mammograms. The power spectrum is a computational analysis based on the Fourier transform that can be used to estimate the roughness of a scale-invariant image or region via the calculation of H. We aim to examine how the calculation of H in fractional Brownian motion (fBm) images and mammograms can be improved. fBm images are generated for H ∈ [0.00,1.00] for testing through the previous 2D …

Everyone's A Waiter: A Data-Driven Queuing Simulation Model Of Mike's Clam Shack, Natalie Robinson

Honors College

This thesis seeks to understand the mathematical foundation of several prominent concepts in queuing theory and apply them to gain a better understanding of nightly business levels and dining room queue behavior during the summer tourist season at Mike’s Clam Shack, which is a restaurant located in Wells, Maine. To do so, a variety of queue and server section data has been collected from Mike’s and analyzed to determine probability distributions for interarrival and service times. In addition, a queuing simulation model has been constructed in the R Programming Language, which uses this data to generate dining room and queue …

From Points To Potlucks: An Exploration Of Fixed Point Theorems With Applications To Game Theory Models Of Successful Integration Practices, Llewellyn Searing

Honors College

Potlucks have many names: shared community dinners, faith suppers, “bring-a-dish” dinners, etc. They represent the desire to share food with other people and make new friends, sometimes learning about other cultures in the process. Not only does one have to decide what dish to bring, but one must also decide how large of a dish, if there will be a theme, and what course it will fit. For instance, if everyone brings side dishes, there will not be enough food for everyone, and if someone brings food that most of the group cannot eat, then feelings will be hurt on …

Development And Evaluation Of Modeling Approaches For Extrusion-Based Additive Manufacturing Of Thermoplastics, Christopher C. Bock

Electronic Theses and Dissertations

This work focuses on evaluating different modeling approaches and model parameters for thermoplastic AM, with the goal of informing more efficient and effective modeling approaches. First, different modeling approaches were tested and compared to experiments. From this it was found that all three of the modeling approaches provide comparable results and provide similar results to experiments. Then one of the modeling approaches was tested on large scale geometries, and it was found that the model results matched experiments closely. Then the effect of different material properties was evaluated, this was done by performing a fractional factorial design of experiments where …

Computationally Modeling Dynamic Biological Systems, Katherine Jarvis

Electronic Theses and Dissertations

Modeling biological systems furthers our understanding of dynamic relationships and helps us make predictions of the unknown properties of the system. The simple interplay between individual species in a dynamic environment over time can be modeled by equation-based modeling or agent- based modeling (ABM). Equation based modeling describes the change in species quantity using ordinary differential equations (ODE) and is dependent on the quantity of other species in the system as well as a predetermined rates of change. Unfortunately, this method of modeling does not model each individual agent in each species over time so individual dynamics are assumed to …

Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley

Electronic Theses and Dissertations

Systems of ordinary differential equations (ODEs) may be used to model a wide variety of real-world phenomena in biology and engineering. Classical sensitivity theory is well-established and concerns itself with quantifying the responsiveness of such models to changes in parameter values. By performing a sensitivity analysis, a variety of insights can be gained into a model (and hence, the real-world system that it represents); in particular, the information gained can uncover a system's most important aspects, for use in design, control or optimization of the system. However, while the results of such analysis are desirable, the approach that classical theory …

Toward Improving Understanding Of The Structure And Biophysics Of Glycosaminoglycans, Elizabeth K. Whitmore

Electronic Theses and Dissertations

Glycosaminoglycans (GAGs) are the linear carbohydrate components of proteoglycans (PGs) that mediate PG bioactivities, including signal transduction, tissue morphogenesis, and matrix assembly. To understand GAG function, it is important to understand GAG structure and biophysics at atomic resolution. This is a challenge for existing experimental and computational methods because GAGs are heterogeneous, conformationally complex, and polydisperse, containing up to 200 monosaccharides. Molecular dynamics (MD) simulations come close to overcoming this challenge but are only feasible for short GAG polymers. To address this problem, we developed an algorithm that applies conformations from unbiased all-atom explicit-solvent MD simulations of short GAG polymers …

A Method To Reclaim Multifractal Statistics From Saturated Images, Jeremy Juybari

Electronic Theses and Dissertations

The CompuMAINE lab has developed a patented computational cancer detection method utilizing the 2D Wavelet Transform Modulus Maxima (WTMM) method to help predict disrupted, tumor-associated breast tissue from mammography. The lab has a database of mammograms in which some of the image subregions contain artefacts which are excluded from the analysis, image saturation is one such artefact. To maximize statistical power in our clinical analyses, our goal is therefore to minimize the rejection of image subregions containing artefacts. The goal of this particular project is to explore the effects of image saturation on the resulting multifractal statistics from the 2D …

An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber

Electronic Theses and Dissertations

Epidemiological models are an essential tool in understanding how infection spreads throughout a population. Exploring the effects of varying parameters provides insight into the driving forces of an outbreak. In this thesis, an SIS (susceptible-infectious-susceptible) model is built partnering simulation methods, differential equations, and transition matrices with the intent to describe how simultaneous recoveries influence the spread of a disease in a well-mixed population. Individuals in the model transition between only two states; an individual is either susceptible — able to be infected, or infectious — able to infect others. Events in this model (infections and recoveries) occur by way …

Paper Structure Formation Simulation, Tyler R. Seekins

Electronic Theses and Dissertations

On the surface, paper appears simple, but closer inspection yields a rich collection of chaotic dynamics and random variables. Predictive simulation of paper product properties is desirable for screening candidate experiments and optimizing recipes but existing models are inadequate for practical use. We present a novel structure simulation and generation system designed to narrow the gap between mathematical model and practical prediction. Realistic inputs to the system are preserved as randomly distributed variables. Rapid fiber placement (~1 second/fiber) is achieved with probabilistic approximation of chaotic fluid dynamics and minimization of potential energy to determine flexible fiber conformations. Resulting digital packed …

Determining The Influence Of Lateral Margin Mechanical Properties On Glacial Flow, Kate Hruby

Electronic Theses and Dissertations

The lateral margins of glaciers and ice streams play a significant role in glacial flow. Depending on their properties, like temperature and ice crystal orientation, they can cause a resistance to flow or enhance it. In combination with our current changing climate, flow patterns can dictate the mass balance of an ice body. It is therefore more important than ever to understand the impact that variations at the margins can have on flow. However, the lateral margins of glaciers and ice streams are an often-neglected part of ice dynamics; they are harder to sample than the center of a glacier’s …

The Hilbert-Huang Transform: A Theoretical Framework And Applications To Leak Identification In Pressurized Space Modules, Kenneth R. Bundy

Electronic Theses and Dissertations

Any manned space mission must provide breathable air to its crew. For this reason, air leaks in spacecraft pose a danger to the mission and any astronauts on board. The purpose of this work is twofold: the first is to address the issue of air pressure loss from leaks in spacecraft. Air leaks present a danger to spacecraft crew, and so a method of finding air leaks when they occur is needed. Most leak detection systems localize the leak in some way. Instead, we address the identification of air leaks in a pressurized space module, we aim to determine the …

Jensen (Robert E.) Records, 1967-1971, Special Collections, Raymond H. Fogler Library, University Of Maine

Finding Aids

Robert E. Jensen was born in Iowa in 1938. A summa cum laude graduate of the University of Denver in 1961 with an M.B.A. in accounting, he received a Ph.D. from Stanford University in 1966. He was a Certified Public Accountant and taught at the University of Denver, Stanford University, and Michigan State University. He came to the University of Maine at Orono in 1968 as the Nicolas M. Salgo Professor in the College of Business Administration.

In 1971-1972 Jensen was selected as a Fellow at the Center for Advanced Study in the Behavioral Sciences at Stanford University where he …

Microstructural Analysis Of Thermoelastic Response, Nonlinear Creep, And Pervasive Cracking In Heterogeneous Materials, Alden C. Cook

Electronic Theses and Dissertations

This dissertation is concerned with the development of robust numerical solution procedures for the generalized micromechanical analysis of linear and nonlinear constitutive behavior in heterogeneous materials. Although the methods developed are applicable in many engineering, geological, and materials science fields, three main areas are explored in this work. First, a numerical methodology is presented for the thermomechanical analysis of heterogeneous materials with a special focus on real polycrystalline microstructures obtained using electron backscatter diffraction techniques. Asymptotic expansion homogenization and finite element analysis are employed for micromechanical analysis of polycrystalline materials. Effective thermoelastic properties of polycrystalline materials are determined and compared …

Topographic Signatures Of Geodynamics, Samuel G. Roy

Electronic Theses and Dissertations

The surface of the Earth retains an imperfect memory of the diverse geodynamic, climatic, and surface transport processes that cooperatively drive the evolution of Earth. In this thesis I explore the potential of using topographic analysis and landscape evolution models to unlock past and/or present evidence for geodynamic activity. I explore the potential isolated effects of geodynamics on landscape evolution, particularly focusing on two byproducts of tectonic strain: rock displacement and damage. Field evidence supports a strong correlation between rock damage and erodibility, and a numerical sensitivity analysis supports the hypothesis that an order of magnitude weakening in rock, well …

Estimation Of Standardized Mortality Ratio In Geographic Epidemiology, Anna Kettermann

Electronic Theses and Dissertations

The analysis of geographic variation of disease and its representation on a map form an important topic of research in epidemiology and in public health in general. Identification of spatial heterogeneity of relative risk using morbidity and mortality data is required. The usual technique of disease atlas generation consists of data collection (observed number of disease cases). These data are collected during a continuous period of time (5 to 10 years). The second aspect of atlas creation relates to the analysis of these data. A traditional measure of the spatial variation is usually taken as a ratio of the number …