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- Creators: Kostelich, Eric
- Creators: Platte, Rodrigo
- Creators: Ahn, Gail-Joon
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
Food safety is vital to the well-being of society; therefore, it is important to inspect food products to ensure minimal health risks are present. A crucial phase of food inspection is the identification of foreign particles found in the sample, such as insect body parts. The presence of certain species of insects, especially storage beetles, is a reliable indicator of possible contamination during storage and food processing. However, the current approach to identifying species is visual examination by human analysts; this method is rather subjective and time-consuming. Furthermore, confident identification requires extensive experience and training. To aid this inspection process, we have developed in collaboration with FDA analysts some image analysis-based machine intelligence to achieve species identification with up to 90% accuracy. The current project is a continuation of this development effort. Here we present an image analysis environment that allows practical deployment of the machine intelligence on computers with limited processing power and memory. Using this environment, users can prepare input sets by selecting images for analysis, and inspect these images through the integrated pan, zoom, and color analysis capabilities. After species analysis, the results panel allows the user to compare the analyzed images with referenced images of the proposed species. Further additions to this environment should include a log of previously analyzed images, and eventually extend to interaction with a central cloud repository of images through a web-based interface. Additional issues to address include standardization of image layout, extension of the feature-extraction algorithm, and utilizing image classification to build a central search engine for widespread usage.
ContributorsMartin, Daniel Luis (Author) / Ahn, Gail-Joon (Thesis director) / Doupé, Adam (Committee member) / Xu, Joshua (Committee member) / Computer Science and Engineering Program (Contributor) / Department of Finance (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05