MATH Theses and Dissertations

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    Closed form expressions for the sums of infinite series
    (Wichita State University, 1958-06) Durbin, John R.; Buschman, R.G.
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    A general legendre transformation
    (Wichita State University, 1958-06) Damaskos, Nickander J.
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    Bernoulli polynomials of the first kind
    (Wichita State University, 1958-06) Bargen, Ralph K.; Buschman, R.G.
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    Bayesian adaptive lasso binary quantile regression with hybrid resampling for classification of imbalanced data
    (Wichita State University, 2023-07) Garcia, Fernando Rubio; Dao, Mai
    In this data-intensive era, analyzing datasets with imbalanced binary responses is an important yet challenging task due to the common presence of outliers, heteroskedasticity, and other data anomalies. This talk introduces a novel and robust solution to improve the classification accuracies at various quantiles, with special focus on rare event detection applications, such as customer churn prediction, that are highly valuable to strategic business decision-making and profit maximization. Our proposed method first employs a hybrid data resampling approach that combines the benefits of both oversampling and undersampling, then imposes a Bayesian adaptive Lasso penalization on each quantile regression coefficient to perform statistical inference and variable selection simultaneously. Our resampling layer coupled with the Metropolis-Hastings-within-Gibbs algorithm is efficient and easy to implement. Extensive simulation studies and real data analyses showcase our competitive performance in comparison with some existing Bayesian methods in the literature.
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    A exploratory study to create an anti-neutrino directional and ranging sensitive detector (NUDAR)
    (Wichita State University, 2023-07) Novak, Jarred C.; Solomey, Nickolas
    This research project set out to do an exploratory study to find a novel way to detect $\bar{\nu }$ for small reactor powered vessels and to analyze the potential capabilities within the realm of nuclear defense. A comprehensive study of the energy spectrum of $\bar{\nu }$ particles produced as byproducts of nuclear fission processes was performed. The study combines theoretical calculations and experimental observations from other experiments, to understand the complex dynamics of $\bar{\nu }$ interactions. In addition, this research explores the selection of isotopes with favorable __ cross-sections for detection purposes. The GENIE platform is used to analyze hundreds of isotopes, leading to the identification of $^{137}$Ba, $^{152}$Gd, and $^{183}$W as potential candidates. These isotopes exhibit suitable cross-sections and threshold energies for detecting $\bar{\nu }$ particles. Scintillator materials, such as $BaF_2, GAGG,$ and $NaPGaW$ are assessed for their performance in detecting $\bar{\nu }$ particles. As well, a comprehensive study was carried out to determine the total ranging capabilities of the detector, with the results indicating detection is possible at great lengths. Along with this a possible new $\bar{\nu }$ detecton method was modeled with a double pulse indicator based off of the excitation state of Tantalum. Furthermore, detector construction and simulations are conducted to study particle tracking mechanisms. Crystal structures and segmented scintillator plates are evaluated for their ability to track particles effectively. A proposed detector design involves assembling scintillator structures using optical glue and utilizing fiber-optic lines for light collection. Monte Carlo simulations using Geant4 provide insights into energy deposition, timing, and the potential for detecting low-energy gamma rays. This research paves the way for advancements in understanding of low energy $\bar{\nu }$ physics and offers insights into the development of next-generation detectors. The findings contribute to fundamental physics and have implications for nuclear deterrence, non-proliferation, and defense.
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