Matching Items (11)
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
The purpose of this thesis is to examine the events surrounding the creation of the oboe and its rapid spread throughout Europe during the mid to late seventeenth century. The first section describes similar instruments that existed for thousands of years before the invention of the oboe. The following sections examine reasons and methods for the oboe's invention, as well as possible causes of its migration from its starting place in France to other European countries, as well as many other places around the world. I conclude that the oboe was invented to suit the needs of composers in the court of Louis XIV, and that it was brought to other countries by French performers who left France for many reasons, including to escape from the authority of composer Jean-Baptiste Lully and in some cases to promote French culture in other countries.
ContributorsCook, Mary Katherine (Author) / Schuring, Martin (Thesis director) / Micklich, Albie (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Music (Contributor)
Created2015-05
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
Science fiction has a unique ability to express, analyze, and critique concepts in a subtle way that emphasizes a point but is still entertaining to the audience. Because of science fiction's ability to do this it has long been a powerful way to ask questions that would normally not be addressed. As such, this paper provides an overview of the effects of biomedical technology in science fiction films. The discussions in this paper will analyze the different portrayals of the technology in the viewed cinematic pieces and the effects they have on the characters in the film. The discussion will begin with the films that have technology based in Genetic Engineering. This will then be followed by a discussion of the biomedical technology based in the fields of Endocrinology; Reanimation; Preservation; Prosthetics; Physical Metamorphosis; Super-Drugs and Super-Viruses; and Diagnostic, Surgical, and Monitoring Equipment. At the end of this paper movie summaries are provided to assist in clarifying plot details.
ContributorsGrzybowski, Amanda Ann (Author) / Foy, Joseph (Thesis director) / Facinelli, Diane (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05
Description
Abstract Modern imaging techniques for sciatic nerves often use imaging techniques that can clearly find myelinated axons (Group A and Group B and analyze their properties, but have trouble with the more numerous Remak Fibers (Group C). In this paper, Group A and B fibers are analyzed while also analyzing Remak fibers using osmium tetroxide staining and imaging with the help of transmission electron microscopy. Using this method, nerves had various electrical stimuli attached to them and were analyzed as such. They were analyzed with a cuff electrode attached, a stimulator attached, and both, with images taken at the center of the nerve and the ends of them. The number and area taken by the Remak fibers were analyzed, along with the g-ratios of the Group A and B fibers. These were analyzed to help deduce the overall health of the fibers along with vacuolization, and mitochondria available. While some important information was gained from this evaluation, further testing has to be done to improve the myelin detection system, along with analyzing the proper and necessary Remak fibers and the role they play. The research tries to thoroughly look at the necessary material and find a way to use it as a guide to further experimentation with electrical stimuli, and notes the differences found within and without various groups, various points of observation, and various stimuli as a whole. Nevertheless, this research allows a strong look into the benefits of transmission electron microscopy and the ability to assess electrical stimulation from these points.
ContributorsNambiar, Karthik (Author) / Muthuswamy, Jitendran (Thesis director) / Towe, Bruce (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The role of retention and forgetting of context dependent sensorimotor memory of dexterous manipulation was explored. Human subjects manipulated a U-shaped object by switching the handle to be grasped (context) three times, and then came back two weeks later to lift the same object in the opposite context relative to that experience on the last block. On each context switch, an interference of the previous block of trials was found resulting in manipulation errors (object tilt). However, no significant re-learning was found two weeks later for the first block of trials (p = 0.826), indicating that the previously observed interference among contexts lasted a very short time. Interestingly, upon switching to the other context, sensorimotor memories again interfered with visually-based planning. This means that the memory of lifting in the first context somehow blocked the memory of lifting in the second context. In addition, the performance in the first trial two weeks later and the previous trial of the same context were not significantly different (p = 0.159). This means that subjects are able to retain long-term sensorimotor memories. Lastly, the last four trials in which subjects switched contexts were not significantly different from each other (p = 0.334). This means that the interference from sensorimotor memories of lifting in opposite contexts was weaker, thus eventually leading to the attainment of steady performance.
ContributorsGaw, Nathan Benjamin (Author) / Santello, Marco (Thesis director) / Helms Tillery, Stephen (Committee member) / Buneo, Christopher (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2013-05
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
Rupture of intracranial aneurysms causes a subarachnoid hemorrhage, which is often lethal health event. A minimally invasive method of solving this problem may involve a material, which can be administered as a liquid and then becomes a strong solid within minutes preventing flow of blood in the aneurysm. Here we report on the development of temperature responsive copolymers, which are deliverable through a microcatheter at body temperature and then rapidly cure to form a highly elastic hydrogel. To our knowledge, this is the first physical-and chemical-crosslinked hydrogel capable of rapid crosslinking at temperatures above the gel transition temperature. The polymer system, poly(N-isopropylacrylamide-co-cysteamine-co-Jeffamine® M-1000 acrylamide) and poly(ethylene glycol) diacrylate, was evaluated in wide-neck aneurysm flow models to evaluate the stability of the hydrogels. Investigation of this polymer system indicates that the Jeffamine® M-1000 causes the gels to retain water, resulting in gels that are initially weak and viscous, but become stronger and more elastic after chemical crosslinking.
ContributorsLee, Elizabeth Jean (Author) / Vernon, Brent (Thesis director) / Brennecka, Celeste (Committee member) / Overstreet, Derek (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
Description
The development of computational systems known as brain-computer interfaces (BCIs) offers the possibility of allowing individuals disabled by neurological disorders such as Amyotrophic Lateral Sclerosis (ALS) and ischemic stroke the ability to perform relatively complex tasks such as communicating with others and walking. BCIs are closed-loop systems that record physiological signals from the brain and translate those signals into commands that control an external device such as a wheelchair or a robotic exoskeleton. Despite the potential for BCIs to vastly improve the lives of almost one billion people, one question arises: Just because we can use brain-computer interfaces, should we? The human brain is an embodiment of the mind, which is largely seen to determine a person's identity, so a number of ethical and philosophical concerns emerge over current and future uses of BCIs. These concerns include privacy, informed consent, autonomy, identity, enhancement, and justice. In this thesis, I focus on three of these issues: privacy, informed consent, and autonomy. The ultimate purpose of brain-computer interfaces is to provide patients with a greater degree of autonomy; thus, many of the ethical issues associated with BCIs are intertwined with autonomy. Currently, brain-computer interfaces exist mainly in the domain of medicine and medical research, but recently companies have started commercializing BCIs and providing them at affordable prices. These consumer-grade BCIs are primarily for non-medical purposes, and so they are beyond the scope of medicine. As BCIs become more widespread in the near future, it is crucial for interdisciplinary teams of ethicists, philosophers, engineers, and physicians to collaborate to address these ethical concerns now before BCIs become more commonplace.
ContributorsChu, Kevin Michael (Author) / Ankeny, Casey (Thesis director) / Robert, Jason (Committee member) / Frow, Emma (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor) / School for the Future of Innovation in Society (Contributor) / Lincoln Center for Applied Ethics (Contributor)
Created2016-05
Description
This Creative Project was carried out in coordination with the capstone project, Around the Corner Imaging with Terahertz Waves. This capstone project deals with a system designed to implement Around the Corner, or Non Line-of-Sight (NLoS) Imaging. This document discusses the creation of a GUI using MATLAB to control the Terahertz Imaging system. The GUI was developed in response to a need for synchronization, ease of operation, easy parameter modification, and data management. Along the way, many design decisions were made ranging from choosing a software platform to determining how variables should be passed. These decisions and considerations are discussed in this document. The resulting GUI has measured up to the design criteria and will be able to be used by anyone wishing to use the Terahertz Imaging System for further research in the field of Around the Corner or NLoS Imaging.
ContributorsWood, Jacob Cannon (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05