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Description
A semi-implicit, fourth-order time-filtered leapfrog numerical scheme is investigated for accuracy and stability, and applied to several test cases, including one-dimensional advection and diffusion, the anelastic equations to simulate the Kelvin-Helmholtz instability, and the global shallow water spectral model to simulate the nonlinear evolution of twin tropical cyclones. The leapfrog scheme leads to computational modes in the solutions to highly nonlinear systems, and time-filters are often used to damp these modes. The proposed filter damps the computational modes without appreciably degrading the physical mode. Its performance in these metrics is superior to the second-order time-filtered leapfrog scheme developed by Robert and Asselin.
ContributorsBurke, Lee Matthew Moore (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Preventive maintenance is a practice that has become popular in recent years, largely due to the increased dependency on electronics and other mechanical systems in modern technologies. The main idea of preventive maintenance is to take care of maintenance-type issues before they fully appear or cause disruption of processes and daily operations. One of the most important parts is being able to predict and foreshadow failures in the system, in order to make sure that those are fixed before they turn into large issues. One specific area where preventive maintenance is a very big part of daily activity is the automotive industry. Automobile owners are encouraged to take their cars in for maintenance on a routine schedule (based on mileage or time), or when their car signals that there is an issue (low oil levels for example). Although this level of maintenance is enough when people are in charge of cars, the rise of autonomous vehicles, specifically self-driving cars, changes that. Now instead of a human being able to look at a car and diagnose any issues, the car needs to be able to do this itself. The objective of this project was to create such a system. The Electronics Preventive Maintenance System is an internal system that is designed to meet all these criteria and more. The EPMS system is comprised of a central computer which monitors all major electronic components in an autonomous vehicle through the use of standard off-the-shelf sensors. The central computer compiles the sensor data, and is able to sort and analyze the readings. The filtered data is run through several mathematical models, each of which diagnoses issues in different parts of the vehicle. The data for each component in the vehicle is compared to pre-set operating conditions. These operating conditions are set in order to encompass all normal ranges of output. If the sensor data is outside the margins, the warning and deviation are recorded and a severity level is calculated. In addition to the individual focus, there's also a vehicle-wide model, which predicts how necessary maintenance is for the vehicle. All of these results are analyzed by a simple heuristic algorithm and a decision is made for the vehicle's health status, which is sent out to the Fleet Management System. This system allows for accurate, effortless monitoring of all parts of an autonomous vehicle as well as predictive modeling that allows the system to determine maintenance needs. With this system, human inspectors are no longer necessary for a fleet of autonomous vehicles. Instead, the Fleet Management System is able to oversee inspections, and the system operator is able to set parameters to decide when to send cars for maintenance. All the models used for the sensor and component analysis are tailored specifically to the vehicle. The models and operating margins are created using empirical data collected during normal testing operations. The system is modular and can be used in a variety of different vehicle platforms, including underwater autonomous vehicles and aerial vehicles.
ContributorsMian, Sami T. (Author) / Collofello, James (Thesis director) / Chen, Yinong (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
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
Background: Noninvasive MRI methods that can accurately detect subtle brain changes are highly desirable when studying disease-modifying interventions. Texture analysis is a novel imaging technique which utilizes the extraction of a large number of image features with high specificity and predictive power. In this investigation, we use texture analysis to assess and classify age-related changes in the right and left hippocampal regions, the areas known to show some of the earliest change in Alzheimer's disease (AD). Apolipoprotein E (APOE)'s e4 allele confers an increased risk for AD, so studying differences in APOE e4 carriers may help to ascertain subtle brain changes before there has been an obvious change in behavior. We examined texture analysis measures that predict age-related changes, which reflect atrophy in a group of cognitively normal individuals. We hypothesized that the APOE e4 carriers would exhibit significant age-related differences in texture features compared to non-carriers, so that the predictive texture features hold promise for early assessment of AD. Methods: 120 normal adults between the ages of 32 and 90 were recruited for this neuroimaging study from a larger parent study at Mayo Clinic Arizona studying longitudinal cognitive functioning (Caselli et al., 2009). As part of the parent study, the participants were genotyped for APOE genetic polymorphisms and received comprehensive cognitive testing every two years, on average. Neuroimaging was done at Barrow Neurological Institute and a 3D T1-weighted magnetic resonance image was obtained during scanning that allowed for subsequent texture analysis processing. Voxel-based features of the appearance, structure, and arrangement of these regions of interest were extracted utilizing the Mayo Clinic Python Texture Analysis Pipeline (pyTAP). Algorithms applied in feature extraction included Grey-Level Co-Occurrence Matrix (GLCM), Gabor Filter Banks (GFB), Local Binary Patterns (LBP), Discrete Orthogonal Stockwell Transform (DOST), and Laplacian-of-Gaussian Histograms (LoGH). Principal component (PC) analysis was used to reduce the dimensionality of the algorithmically selected features to 13 PCs. A stepwise forward regression model was used to determine the effect of APOE status (APOE e4 carriers vs. noncarriers), and the texture feature principal components on age (as a continuous variable). After identification of 5 significant predictors of age in the model, the individual feature coefficients of those principal components were examined to determine which features contributed most significantly to the prediction of an aging brain. Results: 70 texture features were extracted for the two regions of interest in each participant's scan. The texture features were coded as 70 initial components andwere rotated to generate 13 principal components (PC) that contributed 75% of the variance in the dataset by scree plot analysis. The forward stepwise regression model used in this exploratory study significantly predicted age, accounting for approximately 40% of the variance in the data. The regression model revealed 5 significant regressors (2 right PC's, APOE status, and 2 left PC by APOE interactions). Finally, the specific texture features that contributed to each significant PCs were identified. Conclusion: Analysis of image texture features resulted in a statistical model that was able to detect subtle changes in brain integrity associated with age in a group of participants who are cognitively normal, but have an increased risk of developing AD based on the presence of the APOE e4 phenotype. This is an important finding, given that detecting subtle changes in regions vulnerable to the effects of AD in patients could allow certain texture features to serve as noninvasive, sensitive biomarkers predictive of AD. Even with only a small number of patients, the ability for us to determine sensitive imaging biomarkers could facilitate great improvement in speed of detection and effectiveness of AD interventions..
ContributorsSilva, Annelise Michelle (Author) / Baxter, Leslie (Thesis director) / McBeath, Michael (Committee member) / Presson, Clark (Committee member) / School of Life Sciences (Contributor) / Department of Psychology (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
Global Devils is an organization of students that are interested or have previously studied, lived, travelled or interned abroad. The members advocate for cultural and global experiences that academically, professionally and personally enhance collegiate experiences. This creative project details the conceptualization and establishment of this international education student run-organization. The activity reports outline the process of working closely with the Arizona State University Study Abroad Office, creating a constitution, forming pillars and organization purpose, establishing meeting structure and how to apply and receive funding. This documentation additionally includes the club constitution, the club pillars and the establishment of the executive board positions: President, Secretary, Events Coordinator, Marketing Specialist, Cultural Engagement Chair and Finance Officer. To ensure the longevity of this organization, online documentation, via Google Drive, is available to all executive board members. This creative project additionally outlines how to recruit members, the best practices for outreach, such as email communication, and the events that Global Devils tabled at to outreach to a targeted audience. Via SunDevilSync, all members have access to the club's purpose, receive updates regarding Global Devils meetings, access to documents and executive board contact information. Lastly, throughout the process, ideas for improvement were documented.
ContributorsMalkoon, Denise Patricia (Author) / Infurna, Frank (Thesis director) / McManus, Seth (Committee member) / School of International Letters and Cultures (Contributor) / Department of Psychology (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
In this study, potential differences in the manifestation and rates of eating disorders and symptoms (body dissatisfaction, weight and shape concerns, food restriction, and compensatory behaviors) in college women across sexual orientations were examined. The sociocultural model of eating disorders was also examined for these women across sexual orientations. The participants were organized into three different sexual orientation groups for analysis: heterosexual (group 1), bisexual, pansexual, and polysexual (group 2), and lesbian, gay, queer, transsexual, asexual, and other (group 3). Using cross-sectional data, it was revealed that there were significant group differences when comparing the three sexual orientation groups on loss of control over eating, but no significant group differences on body dissatisfaction, thin ideal internalization, and weight-related eating pathology, and total eating disorder symptoms scores. The sociocultural model was not predictive of eating disorder symptoms among non-heterosexual groups. Longitudinal analyses revealed that the sociocultural model of eating disorders prospectively predicts eating disorder symptoms among heterosexual women, but not non-heterosexual women. Both cross-sectional and longitudinal analyses indicate that non-heterosexual women may be protected from societal pressure to subscribe to the thin ideal and its subsequent internalization. However, the comparison group of heterosexual women in our study may not have been completely representative of undergraduate women in terms of total eating disorder symptoms or eating pathology. Additionally, regardless of sexual orientation, our sample reported more total eating disorder symptoms and emotional eating than previous studies. These findings have both clinical and research implications. Future research is needed to determine what risk factors and treatment target variables are relevant for non-heterosexual women.
ContributorsNorman, Elizabeth Blair (Author) / Perez, Marisol (Thesis director) / Presson, Clark (Committee member) / Cavanaugh Toft, Carolyn (Committee member) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05