Matching Items (3)
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- All Subjects: Star Formation
- Creators: Gardner, Carl
Description
Predicting resistant prostate cancer is critical for lowering medical costs and improving the quality of life of advanced prostate cancer patients. I formulate, compare, and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). I accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). I demonstrate that the inverse problem of parameter estimation might be too complicated and simply relying on data fitting can give incorrect conclusions, since there is a large error in parameter values estimated and parameters might be unidentifiable. I provide confidence intervals to give estimate forecasts using data assimilation via an ensemble Kalman Filter. Using the ensemble Kalman Filter, I perform dual estimation of parameters and state variables to test the prediction accuracy of the models. Finally, I present a novel model with time delay and a delay-dependent parameter. I provide a geometric stability result to study the behavior of this model and show that the inclusion of time delay may improve the accuracy of predictions. Also, I demonstrate with clinical data that the inclusion of the delay-dependent parameter facilitates the identification and estimation of parameters.
ContributorsBaez, Javier (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric (Committee member) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2017
ContributorsPowell, Devon (Author) / Gardner, Carl (Thesis director) / Scannapieco, Evan (Committee member) / Windhorst, Rogier (Committee member) / Barrett, The Honors College (Contributor)
Created2012-05
Description
The purpose of this thesis is to accurately simulate the surface brightness in various spectral emission lines of the HH 901 jets in the Mystic Mountain Formation of the Carina Nebula. To accomplish this goal, we gathered relevant spectral emission line data for [Fe II] 12660 Å, Hα 6563 Å, and [S II] 6720 Å to compare with Hubble Space Telescope observations of the HH 901 jets presented in Reiter et al. (2016). We derived the emissivities for these lines from the spectral synthesis code Cloudy by Ferland et al. (2017). In addition, we used WENO simulations of density, temperature, and radiative cooling to model the jet. We found that the computed surface brightness values agreed with most of the observational surface brightness values. Thus, the 3D cylindrically symmetric simulations of surface brightness using the WENO code and Cloudy spectral emission models are accurate for jets like HH 901. After detailing these agreements, we discuss the next steps for the project, like adding an external ambient wind and performing the simulations in full 3D.
ContributorsMohan, Arun (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05