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DTSTART;TZID=America/Chicago:20250807T140000
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DTSTAMP:20260417T220102
CREATED:20250725T141802Z
LAST-MODIFIED:20250730T151929Z
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SUMMARY:PhD Dissertation Defense: Mr. Joe Paulson
DESCRIPTION:Theory of Z_n – Structures\nMr. Joe Paulson\nGraduate Student\nUniversity of Wisconsin-Milwaukee \nIn this defense\, we discuss the boundaries of Type F_n groups; those being groups whose K(G\,1) complex has a finite n-skeleton. The boundaries we develop extend the notion of Z-boundaries to what we call Z_n-boundaries. This extension centers around groups no longer acting geometrically on contractible spaces\, but instead n-connected spaces. Immediately this means the major theorems of “Boundary Swapping” and “Shape Equivalence of Z-Boundaries” will need revision\, but a more subtle point to be discussed is that the category of spaces must also be generalized. \nAfter discussing the foundation work for a theory of Z_n-boundaries\, we end with an exploration how these new structures can be related to other well-known compactifications such as the one-point compactification\, end-point compactification\, and Z-compactifications. \nAdvisor:\nCraig Guilbault \nCommittee Members:\nBoris Okun\, Chris Hruska\, Jonah Gaster\, and Pamela Harris
URL:/math/event/phd-dissertation-defense-mr-joe-paulson/
LOCATION:EMS Building\, Room E408\, E408; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Defenses
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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CREATED:20250808T010452Z
LAST-MODIFIED:20250808T010452Z
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SUMMARY:PhD Dissertation Defense: Mr. Shenyan Pan
DESCRIPTION:Doubly Stochastic Model With Covariates For Replicated Poisson Point Processes\nMr. Shenyan Pan\nGraduate Student\nUniversity of Wisconsin-Milwaukee \nPoisson point processes (PPPs) are powerful tools for modeling random point occurrences in multidimensional spaces\, with applications across various fields. Although the traditional literature has focused on single realizations\, replicated point processes are becoming increasingly common due to the growing availability of complex data. This dissertation develops a doubly stochastic model for replicated PPPs that incorporates covariates\, extending latent component models to capture external effects. The proposed model expresses the log-intensity function as the sum of a mean function and latent component scores that vary with covariates. To ensure identifiability\, component scores are constrained to be zero-mean and uncorrelated via centering and orthogonality. Parameter estimation is performed using penalized maximum likelihood\, employing Newton–Raphson updates and the Laplace approximation for conditional distributions. Simulation studies assess the model’s stability across various covariate structures (linear and nonlinear)\, baseline rates\, and sample sizes. The results demonstrate decreasing error with increasing sample size\, confirming the estimators’ consistency. The model is applied to real data from the Divvy bicycle-sharing system in Chicago\, analyzing daily usage at a representative station. The results reveal a nonlinear relationship between temperature and ridership\, with peak usage occurring at moderate temperatures and declines observed under extreme heat or cold. This modeling framework improves the interpretability and predictive accuracy of PPPs with covariates\, offering practical insights for applications such as fleet allocation in bicycle-sharing systems. \nAdvisor:\nProf. Daniel Gervini \nCommittee Members:\nProf. Lei Wang\, Prof. Chao Zhu\, Prof. David Spade\, and Prof. Vytaras Brazauskas \nLink to Event
URL:/math/event/phd-dissertation-defense-mr-shenyan-pan/
CATEGORIES:Graduate Student Defenses
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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DTSTART;TZID=America/Chicago:20250811T133000
DTEND;TZID=America/Chicago:20250811T153000
DTSTAMP:20260417T220102
CREATED:20250730T140303Z
LAST-MODIFIED:20250730T140303Z
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SUMMARY:PhD Dissertation Defense: Mr. Marco Vaassen
DESCRIPTION:A Bootstrap Goodness-of-Fit Test for Parametric Survival Models\nMr. Marco Vaassen\nGraduate Student\nUniversity of Wisconsin-Milwaukee \nIn many scientific disciplines\, finding a suitable model compatible with real-world observations is the basis for statistical inference and prediction. In survival analysis\, this task is further complicated by censoring. This dissertation introduces a new bootstrap approach to goodness-of-fit testing for parametric survival models\, based on the Kaplan–Meier process with estimated parameters. The test statistic compares the nonparametric Kaplan–Meier estimator to a fitted parametric model\, quantifying deviations from the null via functionals that yield Kolmogorov–Smirnov or Cramér–von Mises-type tests. We establish the asymptotic correctness of our method by showing that the original and bootstrap test statistics have the same weak limit under the null. The result is a consistent\, easily implementable framework for assessing model fit in censored settings. \nAdvisor:\nProf. Richard Stockbridge\, Prof. Gerhard Dikta \nCommittee Members:\nProf. Richard Stockbridge\, Prof. Gerhard Dikta\, Prof. Chao Zhu\, Prof. David Spade\, and Prof. Vincent Larson
URL:/math/event/phd-dissertation-defense-mr-marco-vaassen/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Graduate Student Defenses
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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