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Description
Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.
ContributorsAnderies, Barrett James (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Stepien, Tracy (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Aberrant glycosylation has been shown to be linked to specific cancers, and using this idea, it was proposed that the levels of glycans in the blood could predict stage I adenocarcinoma. To track this glycosylation, glycan were broken down into glycan nodes via methylation analysis. This analysis utilized information from N-, O-, and lipid linked glycans detected from gas chromatography-mass spectrometry. The resulting glycan node-ratios represent the initial quantitative data that were used in this experiment.
For this experiment, two Sets of 50 µl blood plasma samples were provided by NYU Medical School. These samples were then analyzed by Dr. Borges’s lab so that they contained normalized biomarker levels from patients with stage 1 adenocarcinoma and control patients with matched age, smoking status, and gender were examined. An ROC curve was constructed under individual and paired conditions and AUC calculated in Wolfram Mathematica 10.2. Methods such as increasing size of training set, using hard vs. soft margins, and processing biomarkers together and individually were used in order to increase the AUC. Using a soft margin for this particular data set was proved to be most useful compared to the initial set hard margin, raising the AUC from 0.6013 to 0.6585. In regards to which biomarkers yielded the better value, 6-Glc/6-Man and 3,6-Gal glycan node ratios had the best with 0.7687 AUC and a sensitivity of .7684 and specificity of .6051. While this is not enough accuracy to become a primary diagnostic tool for diagnosing stage I adenocarcinoma, the methods examined in the paper should be evaluated further. . By comparison, the current clinical standard blood test for prostate cancer that has an AUC of only 0.67.
For this experiment, two Sets of 50 µl blood plasma samples were provided by NYU Medical School. These samples were then analyzed by Dr. Borges’s lab so that they contained normalized biomarker levels from patients with stage 1 adenocarcinoma and control patients with matched age, smoking status, and gender were examined. An ROC curve was constructed under individual and paired conditions and AUC calculated in Wolfram Mathematica 10.2. Methods such as increasing size of training set, using hard vs. soft margins, and processing biomarkers together and individually were used in order to increase the AUC. Using a soft margin for this particular data set was proved to be most useful compared to the initial set hard margin, raising the AUC from 0.6013 to 0.6585. In regards to which biomarkers yielded the better value, 6-Glc/6-Man and 3,6-Gal glycan node ratios had the best with 0.7687 AUC and a sensitivity of .7684 and specificity of .6051. While this is not enough accuracy to become a primary diagnostic tool for diagnosing stage I adenocarcinoma, the methods examined in the paper should be evaluated further. . By comparison, the current clinical standard blood test for prostate cancer that has an AUC of only 0.67.
ContributorsDe Jesus, Celine Spicer (Author) / Taylor, Thomas (Thesis director) / Borges, Chad (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local, discrete convolution kernels, but this is not possible when samples are measured directly in the frequency domain. The concentration factor edge detection method was therefore developed to realize an edge detector directly from spectral data. This thesis explores the possibilities of detecting edges from the phase of the spectral data, that is, without the magnitude of the sampled spectral data. Prior work has demonstrated that the spectral phase contains particularly important information about underlying features in a signal. Furthermore, the concentration factor method yields some insight into the detection of edges in spectral phase data. An iterative design approach was taken to realize an edge detector using only the spectral phase data, also allowing for the design of an edge detector when phase data are intermittent or corrupted. Problem formulations showing the power of the design approach are given throughout. A post-processing scheme relying on the difference of multiple edge approximations yields a strong edge detector which is shown to be resilient under noisy, intermittent phase data. Lastly, a thresholding technique is applied to give an explicit enhanced edge detector ready to be used. Examples throughout are demonstrate both on signals and images.
ContributorsReynolds, Alexander Bryce (Author) / Gelb, Anne (Thesis director) / Cochran, Douglas (Committee member) / Viswanathan, Adityavikram (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
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
A growing number of jobs in the US require a college degree or technical education, and the wage difference between jobs requiring a high school diploma and a college education has increased to over $17,000 per year. Enrollment levels in postsecondary education have been rising for at least the past decade, and this paper attempts to tease out how much of the increasing enrollment is due to changes in the demand by companies for workers. A Bartik Instrument, which is a measure of local area labor demand, for each county in the US was constructed from 2007 to 2014, and using multivariate linear regression the effect of changing labor demand on local postsecondary education enrollment rates was examined. A small positive effect was found, but the effect size in relation to the total change in enrollment levels was diminutive. From the start to the end of the recession (2007 to 2010), Bartik Instrument calculated unemployment increased from 5.3% nationally to 8.2%. This level of labor demand contraction would lead to a 0.42% increase in enrollment between 2008 and 2011. The true enrollment increase over this period was 7.6%, so the model calculated 5.5% of the enrollment increase was based on the changes in labor demand.
ContributorsHerder, Daniel Steven (Author) / Dillon, Eleanor (Thesis director) / Schoellman, Todd (Committee member) / Economics Program in CLAS (Contributor) / Department of Psychology (Contributor) / Sandra Day O'Connor College of Law (Contributor) / School of Politics and Global Studies (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Honey bees (Apis mellifera) are responsible for pollinating nearly 80\% of all pollinated plants, meaning humans depend on honey bees to pollinate many staple crops. The success or failure of a colony is vital to global food production. There are various complex factors that can contribute to a colony's failure, including pesticides. Neonicotoids are a popular pesticide that have been used in recent times. In this study we concern ourselves with pesticides and its impact on honey bee colonies. Previous investigations that we draw significant inspiration from include Khoury et Al's \emph{A Quantitative Model of Honey Bee Colony Population Dynamics}, Henry et Al's \emph{A Common Pesticide Decreases Foraging Success and Survival in Honey Bees}, and Brown's \emph{ Mathematical Models of Honey Bee Populations: Rapid Population Decline}. In this project we extend a mathematical model to investigate the impact of pesticides on a honey bee colony, with birth rates and death rates being dependent on pesticides, and we see how these death rates influence the growth of a colony. Our studies have found an equilibrium point that depends on pesticides. Trace amounts of pesticide are detrimental as they not only affect death rates, but birth rates as well.
ContributorsSalinas, Armando (Author) / Vaz, Paul (Thesis director) / Jones, Donald (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
A Guide to Financial Mathematics is a comprehensive and easy-to-use study guide for students studying for the one of the first actuarial exams, Exam FM. While there are many resources available to students to study for these exams, this study is free to the students and offers an approach to the material similar to that of which is presented in class at ASU. The guide is available to students and professors in the new Actuarial Science degree program offered by ASU. There are twelve chapters, including financial calculator tips, detailed notes, examples, and practice exercises. Included at the end of the guide is a list of referenced material.
ContributorsDougher, Caroline Marie (Author) / Milovanovic, Jelena (Thesis director) / Boggess, May (Committee member) / Barrett, The Honors College (Contributor) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Often learning new skills, such as how to throw a basketball or how to play the piano, are better accomplished practicing with another than from self-practice. Why? We propose that during joint action, partners learn to adjust their behavior to each other. For example, when dancing with a partner, we must adjust the timing, the force, and the spatial locations of movements to those of the partner. We call these adjustments a joint body schema (JBS). That is, the locations of our own effectors and our own movements are adapted by interaction with the partner. Furthermore, we propose that after a JBS is established, learning new motor skills can be enhanced by the learner's attunement to the specifics of the partner's actions. We test this proposal by having partners engage in a motor task requiring cooperation (to develop the JBS). Then we determined whether a) the JBS enhances the coordination on an unrelated task, and b) whether the JBS enhances the learning of a new motor skill. In fact, participants who established a JBS showed stronger coordination with a partner and better motor learning from the partner than did control participants. Several applications of this finding are discussed.
ContributorsMunion, Amanda Kathleen (Author) / Glenberg, Arthur (Thesis director) / Knight, George (Committee member) / McBeath, Michael (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Psychology (Contributor)
Created2015-05
Description
This paper explores how marginalist economics defines and inevitably constrains Victorian sensation fiction's content and composition. I argue that economic intuition implies that sensationalist heroes and antagonists, writers and readers all pursued a fundamental, "rational" aim: the attainment of pleasure. So although "sensationalism" took on connotations of moral impropriety in the Victorian age, sensation fiction primarily involves experiences of pain on the page that excite the reader's pleasure. As such, sensationalism as a whole can be seen as a conformist product, one which mirrors the effects of all commodities on the market, rather than as a rebellious one. Indeed, contrary to modern and contemporary critics' assumptions, sensation fiction may not be as scandalous as it seems.
ContributorsFischer, Brett Andrew (Author) / Bivona, Daniel (Thesis director) / Looser, Devoney (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Economics Program in CLAS (Contributor) / School of Politics and Global Studies (Contributor) / Department of English (Contributor)
Created2014-12
DescriptionThis is a project to create an electric field sensing system which is fully portable. This system should provide accurate electric field readings from transmission lines allowing abstraction to find the voltage on the transmission line.
ContributorsScowen, Kegan (Co-author) / Vora, Sandeep (Co-author) / Ye, Weidong (Co-author) / Sciacca, Jacob (Co-author) / Allee, David (Thesis director) / Karady, George (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Electrical Engineering Program (Contributor)
Created2014-12