Physical Sciences and Mathematics Commons^™

A Qualitative Representation Of Spatial Scenes In R2 With Regions And Lines, Joshua Lewis

Electronic Theses and Dissertations

Regions and lines are common geographic abstractions for geographic objects. Collections of regions, lines, and other representations of spatial objects form a spatial scene, along with their relations. For instance, the states of Maine and New Hampshire can be represented by a pair of regions and related based on their topological properties. These two states are adjacent (i.e., they meet along their shared boundary), whereas Maine and Florida are not adjacent (i.e., they are disjoint).

A detailed model for qualitatively describing spatial scenes should capture the essential properties of a configuration such that a description of the represented objects …

Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi

Electronic Theses and Dissertations

Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this thesis, we will first take a look at Clarke’s generalized derivative for locally Lipschitz continuous functions between Euclidean spaces, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative in this setting possesses a strong theoretical and numerical toolkit, which is analogous to that of the classical derivative. It includes nonsmooth versions …

Three-Dimensional Analytical Model Of Tidal Flow In The Damariscotta River Estuary, Me, Stephanie L. Ayres

Electronic Theses and Dissertations

Estuaries are coastal bodies of water subjected to strong tidal influence and characterized by their morphology, tidal dynamics, topography, and stratification. Tidal flow is critically important to the water circulation, nutrient influx, and sediment transport in or out of an estuary. However, tidal asymmetry enhanced by estuary shape and nonlinear processes can lead to complications in estuarine flow. Analytical models are used to systematically study tidal flow within an estuary. Previous studies have derived analytical models of varying complexity and applied them to investigate tidal and residual flow. This thesis derives a three-dimensional analytical model with a perturbation expansion of …

Investigation Of Student Understanding Of Implicit Differentiation, Connor Chu

Electronic Theses and Dissertations

Challenges that students face in first semester calculus have been found to be a factor in high attrition rates of students from science, technology, engineering, and mathematics (STEM) majors. With an increase in the demand for STEM graduates, an attempt must be made to remedy this issue. Research has shown that students have difficulties with many topics in the realm of calculus. Of these, students have been found to struggle with the concept of derivative and ideas related to it. However, some derivative topics have not been examined as thoroughly as others. Implicit differentiation, a technique that allows us to …

Understanding Volume Transport In The Jordan River: An Application Of The Navier-Stokes Equations, Gwyneth E. Roberts

Honors College

This study aims to characterize the circulation patterns in short and narrow estuarine systems on various temporal scales to identify the controls of material transport. In order to achieve this goal, a combination of in situ collected data and analytical modeling was used. The model is based on the horizontal Reynolds Averaged Navier-Stokes equations in the shallow water limit with scaling parameters defined from the characteristics of the estuary. The in situ measurements were used to inform a case study, seeking to understand water level variations and tidal current velocity patterns in the Jordan River and to improve understanding of …

Predictive Diagnostic Analysis Of Mammographic Breast Tissue Microenvironment, Dexter G. Canning

Honors College

Improving computer-aided early detection techniques for breast cancer is paramount because current technology has high false positive rates. Existing methods have led to a substantial number of false diagnostics, which lead to stress, unnecessary biopsies, and an added financial burden to the health care system. In order to augment early detection methodology, one must understand the breast microenvironment. The CompuMAINE Lab has researched computational metrics on mammograms based on an image analysis technique called the Wavelet Transform Modulus Maxima (WTMM) method to identify the fractal and roughness signature from mammograms. The WTMM method was used to color code the mammograms …

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 …

Fitting The Sir Epidemiological Model To Influenza Data, Madeline Dorr

Honors College

This project sought to provide thorough instructions to fitting the SIR epidemiological model to influenza data and defend its use in this context. Directions for coding the SIR model in the R programming language are detailed. This includes estimating parameter values, such as infection and recovery rate, and how to double check these values. This project also included analysis of problems that can arise when fitting this model. This includes accounting for vaccination rate and issues with the nature of this type of data. Either these problems were explored, and solutions were provided, or suggestions were provided for future research.