Matching Items (51)
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- Creators: School of Mathematical and Statistical Sciences
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
Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.
ContributorsAnglin, Julia Mae (Author) / Middleton, James (Thesis director) / Vicich, James (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-12
Description
Bots tamper with social media networks by artificially inflating the popularity of certain topics. In this paper, we define what a bot is, we detail different motivations for bots, we describe previous work in bot detection and observation, and then we perform bot detection of our own. For our bot detection, we are interested in bots on Twitter that tweet Arabic extremist-like phrases. A testing dataset is collected using the honeypot method, and five different heuristics are measured for their effectiveness in detecting bots. The model underperformed, but we have laid the ground-work for a vastly untapped focus on bot detection: extremist ideal diffusion through bots.
ContributorsKarlsrud, Mark C. (Author) / Liu, Huan (Thesis director) / Morstatter, Fred (Committee member) / Barrett, The Honors College (Contributor) / Computing and Informatics Program (Contributor) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
The OMFIT (One Modeling Framework for Integrated Tasks) modeling environment and the BRAINFUSE module have been deployed on the PPPL (Princeton Plasma Physics Laboratory) computing cluster with modifications that have rendered the application of artificial neural networks (NNs) to the TRANSP databases for the JET (Joint European Torus), TFTR (Tokamak Fusion Test Reactor), and NSTX (National Spherical Torus Experiment) devices possible through their use. This development has facilitated the investigation of NNs for predicting heat transport profiles in JET, TFTR, and NSTX, and has promoted additional investigations to discover how else NNs may be of use to scientists at PPPL. In applying NNs to the aforementioned devices for predicting heat transport, the primary goal of this endeavor is to reproduce the success shown in Meneghini et al. in using NNs for heat transport prediction in DIII-D. Being able to reproduce the results from is important because this in turn would provide scientists at PPPL with a quick and efficient toolset for reliably predicting heat transport profiles much faster than any existing computational methods allow; the progress towards this goal is outlined in this report, and potential additional applications of the NN framework are presented.
ContributorsLuna, Christopher Joseph (Author) / Tang, Wenbo (Thesis director) / Treacy, Michael (Committee member) / Orso, Meneghini (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2015-05
Description
In this paper, I analyze representations of nature in popular film, using the feminist / deconstructionist concept of a dualism to structure my critique. Using Val Plumwood’s analysis of the logical structure of dualism and the 5 ‘features of a dualism’ that she identifies, I critique 5 popular movies – Star Wars, Lord of the Rings, Brave, Grizzly Man, and Planet Earth – by locating within each of them one of the 5 features and explaining how the movie functions to reinforce the Nature/Culture dualism . By showing how the Nature/Culture dualism shapes and is shaped by popular cinema, I show how “Nature” is a social construct, created as part of this very dualism, and reified through popular culture. I conclude with the introduction of a number of ‘subversive’ pieces of visual art that undermine and actively deconstruct the Nature/Culture dualism and show to the viewer a more honest presentation of the non-human world.
ContributorsBarton, Christopher Joseph (Author) / Broglio, Ron (Thesis director) / Minteer, Ben (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Geographical Sciences and Urban Planning (Contributor)
Created2015-05
Description
Twitter, the microblogging platform, has grown in prominence to the point that the topics that trend on the network are often the subject of the news and other traditional media. By predicting trends on Twitter, it could be possible to predict the next major topic of interest to the public. With this motivation, this paper develops a model for trends leveraging previous work with k-nearest-neighbors and dynamic time warping. The development of this model provides insight into the length and features of trends, and successfully generalizes to identify 74.3% of trends in the time period of interest. The model developed in this work provides understanding into why par- ticular words trend on Twitter.
ContributorsMarshall, Grant A (Author) / Liu, Huan (Thesis director) / Morstatter, Fred (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
A model has been developed to modify Euler-Bernoulli beam theory for wooden beams, using visible properties of wood knot-defects. Treating knots in a beam as a system of two ellipses that change the local bending stiffness has been shown to improve the fit of a theoretical beam displacement function to edge-line deflection data extracted from digital imagery of experimentally loaded beams. In addition, an Ellipse Logistic Model (ELM) has been proposed, using L1-regularized logistic regression, to predict the impact of a knot on the displacement of a beam. By classifying a knot as severely positive or negative, vs. mildly positive or negative, ELM can classify knots that lead to large changes to beam deflection, while not over-emphasizing knots that may not be a problem. Using ELM with a regression-fit Young's Modulus on three-point bending of Douglass Fir, it is possible estimate the effects a knot will have on the shape of the resulting displacement curve.
ContributorsSexton, Thurston Bryant (Author) / Takahashi, Timothy (Thesis director) / Jones, Donald (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2015-05
Description
Despite the 40-year war on cancer, very limited progress has been made in developing a cure for the disease. This failure has prompted the reevaluation of the causes and development of cancer. One resulting model, coined the atavistic model of cancer, posits that cancer is a default phenotype of the cells of multicellular organisms which arises when the cell is subjected to an unusual amount of stress. Since this default phenotype is similar across cell types and even organisms, it seems it must be an evolutionarily ancestral phenotype. We take a phylostratigraphical approach, but systematically add species divergence time data to estimate gene ages numerically and use these ages to investigate the ages of genes involved in cancer. We find that ancient disease-recessive cancer genes are significantly enriched for DNA repair and SOS activity, which seems to imply that a core component of cancer development is not the regulation of growth, but the regulation of mutation. Verification of this finding could drastically improve cancer treatment and prevention.
ContributorsOrr, Adam James (Author) / Davies, Paul (Thesis director) / Bussey, Kimberly (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
Magnetic resonance imaging (MRI) data of metastatic brain cancer patients at the Barrow Neurological Institute sparked interest in the radiology department due to the possibility that tumor size distributions might mimic a power law or an exponential distribution. In order to consider the question regarding the growth trends of metastatic brain tumors, this thesis analyzes the volume measurements of the tumor sizes from the BNI data and attempts to explain such size distributions through mathematical models. More specifically, a basic stochastic cellular automaton model is used and has three-dimensional results that show similar size distributions of those of the BNI data. Results of the models are investigated using the likelihood ratio test suggesting that, when the tumor volumes are measured based on assuming tumor sphericity, the tumor size distributions significantly mimic the power law over an exponential distribution.
ContributorsFreed, Rebecca (Co-author) / Snopko, Morgan (Co-author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / WPC Graduate Programs (Contributor) / School of Accountancy (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
From 2007 to 2017, the state of California experienced two major droughts that required significant governmental action to decrease urban water demand. The purpose of this project is to isolate and explore the effects of these policy changes on water use during and after these droughts, and to see how these policies interact with hydroclimatic variability. As explanatory variables in multiple linear regression (MLR) models, water use policies were found to be significant at both the zip code and city levels. Policies that specifically target behavioral changes were significant mathematical drivers of water use in city-level models. Policy data was aggregated into a timeline and coded based on categories including user type, whether the policy was voluntary or mandatory, the targeted water use type, and whether the change in question concerns active or passive conservation. The analyzed policies include but are not limited to state drought declarations, regulatory municipal ordinances, and incentive programs for household appliances. Spatial averages of available hydroclimatic data have been computed and validated using inverse distance weighting methods. The data was aggregated at the zip code level to be comparable to the available water use data for use in MLR models. Factors already known to affect water use, such as temperature, precipitation, income, and water stress, were brought into the MLR models as explanatory variables. After controlling for these factors, the timeline policies were brought into the model as coded variables to test their effect on water demand during the years 2000-2017. Clearly identifying which policy traits are effective will inform future policymaking in cities aiming to conserve water. The findings suggest that drought-related policies impact per capita urban water use. The results of the city level MLR models indicate that implementation of mandatory policies that target water use behaviors effectively reduce water use. Temperature, income, unemployment, and the WaSSI were also observed to be mathematical drivers of water use. Interaction effects between policies and the WaSSI were statistically significant at both model scales.
ContributorsHjelmstad, Annika Margaret (Author) / Garcia, Margaret (Thesis director) / Larson, Kelli (Committee member) / Civil, Environmental and Sustainable Eng Program (Contributor, Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12