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DTSTART;TZID=America/Chicago:20250807T140000
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DTSTAMP:20260614T181332
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:https://uwm.edu/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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DTSTAMP:20260614T181332
CREATED:20250808T010452Z
LAST-MODIFIED:20250808T010452Z
UID:10016232-1754661600-1754668800@uwm.edu
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:https://uwm.edu/math/event/phd-dissertation-defense-mr-shenyan-pan/
LOCATION:https://teams.microsoft.com/l/meetup-join/19%3aCQyl6Y73Ps7zxWXrM3dRP8rS7Q89Bvw2sceTNhSLlUw1%40thread.tacv2/1754451851629?context=%7b%22Tid%22%3a%220bca7ac3-fcb6-4efd-89eb-6de97603cf21%22%2c%22Oid%22%3a%2234947e74-60a7-40f3-ae30-4a6cd4dc57b7%22%7d
CATEGORIES:Graduate Student Defenses
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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