Mathematics Theses and Dissertations
http://hdl.handle.net/1903/2793
Thu, 21 Sep 2017 08:51:22 GMT2017-09-21T08:51:22ZApplication of Mathematical and Computational Models to Mitigate the Overutilization of Healthcare Systems
http://hdl.handle.net/1903/20003
Application of Mathematical and Computational Models to Mitigate the Overutilization of Healthcare Systems
Hu, Xia
The overutilization of the healthcare system has been a significant issue financially and politically, placing burdens on the government, patients, providers and individual payers. In this dissertation, we study how mathematical models and computational models can be utilized to support healthcare decision-making and generate effective interventions for healthcare overcrowding. We focus on applying operations research and data mining methods to mitigate the overutilization of emergency department and inpatient services in four scenarios. Firstly, we systematically review research articles that apply analytical queueing models to the study of the emergency department, with an additional focus on comparing simulation models with queueing models when applied to similar research questions. Secondly, we present an agent-based simulation model of epidemic and bioterrorism transmission, and develop a prediction scheme to differentiate the simulated transmission patterns during the initial stage of the event. Thirdly, we develop a machine learning framework for effectively selecting enrollees for case management based on Medicaid claims data, and demonstrate the importance of enrolling current infrequent users whose utilization of emergency visits might increase significantly in the future. Lastly, we study the role of temporal features in predicting future health outcomes for diabetes patients, and identify the levels to which the aggregation can be most informative.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1903/200032017-01-01T00:00:00ZParabolic Higgs bundles and the Deligne-Simpson Problem for loxodromic conjugacy classes in PU(n,1)
http://hdl.handle.net/1903/19998
Parabolic Higgs bundles and the Deligne-Simpson Problem for loxodromic conjugacy classes in PU(n,1)
Maschal Jr, Robert Allan
In this thesis we study the Deligne-Simpson problem of finding matrices $A_j\in C_j$ such that $A_1A_2\ldots A_k = I$ for $k\geq 3$ fixed loxodromic conjugacy classes $C_1,\ldots,C_k$ in $PU(n,1)$. Solutions to this problem are equivalent to representations of the $k$ punctured sphere into $PU(n,1)$, where the monodromy around the punctures are in the $C_j$. By Simpson's correspondence \cite{s1}, irreducible such representations correspond to stable parabolic $U(n,1)$-Higgs bundles of parabolic degree 0. A parabolic $U(n,1)$-Higgs bundle can be decomposed into a parabolic $U(1,1)$-Higgs bundle and a $U(n-1)$ bundle by quotienting out by the rank $n-1$ kernel of the Higgs field. In the case that the $U(1,1)$-Higgs bundle is of loxodromic type, this construction can be reversed, with the added consequence that the stability conditions of the resulting $U(n,1)$-Higgs bundle are determined only by the kernel of $\Phi$, the number of marked points, and the degree of the $U(1,1)$-Higgs bundle. With this result, we prove our main theorem, which says that when the log eigenvalues of lifts $\widetilde{C}_j$ of the $C_j$ to $U(n,1)$ satisfy the inequalities in \cite{biswas} for the existence of a stable parabolic bundle, then there is a stable parabolic $U(n,1)$-Higgs bundle whose monodromies around the marked points are in $\widetilde{C}_j$. This new approach using Higgs bundle techniques generalizes the result of Falbel and Wentworth in \cite{fw1} for fixed loxodromic conjugacy classes in $PU(2,1)$.
This new result gives sufficient, but not necessary, conditions for the existence of an irreducible solution to the Deligne-Simpson problem for fixed loxodromic conjugacy classes in $PU(n,1)$. The stability assumption cannot be dropped from our proof since no universal characterization of unstable bundles exists. In the last chapter, we explore what happens when we change the weights of the stable kernel in the special case of three fixed loxodromic conjugacy classes in $PU(3,1)$. Using the techniques from \cite{fw2}, \cite{fw1}, and \cite{paupert}, we can show that our construction implies the existence of many other solutions to the problem.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1903/199982017-01-01T00:00:00ZDESCRIBING URGENT EVENT DIFFUSION ON TWITTER USING NETWORK STATISTICS
http://hdl.handle.net/1903/19997
DESCRIBING URGENT EVENT DIFFUSION ON TWITTER USING NETWORK STATISTICS
Sun, Hechao
In this dissertation, I develop a novel framework to study the diffusion of urgent events through the popular social media platformâ€”Twitter. Based on my literature review, this is the first comprehensive study on urgent event diffusion through Twitter. I observe similar diffusion patterns among different data sets and adopt the "cross prediction" mode to handle the early time prediction problem. I show that the statistics from the network of Twitter retweets can not only provide profound insights about event diffusion, but also can be used to effectively predict user influence and topic popularity. The above findings are consistent across various experiment settings. I also demonstrate that linear models consistently outperform state-of-art nonlinear ones in both user and hashtag prediction tasks, possibly implying the strong log-linear relationship between selected prediction features and the responses, which potentially could be a general phenomenon in the case of urgent event diffusion.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1903/199972017-01-01T00:00:00ZSTATISTICAL LEARNING WITH APPLICATIONS IN HIGH DIMENSIONAL DATA AND HEALTH CARE ANALYTICS
http://hdl.handle.net/1903/19996
STATISTICAL LEARNING WITH APPLICATIONS IN HIGH DIMENSIONAL DATA AND HEALTH CARE ANALYTICS
Fan, Yimei
Statistical learning has been applied in business and health care analytics. Predictive models are fit using hierarchically structured data: common characteristics of products and customers are represented as categorical variables, and each category can be split up into multiple subcategories at a lower level of the hierarchy. Hundreds of thousands of binary variables may be required to model the hierarchy, necessitating the use of variable selection to screen out large numbers of irrelevant or insignificant features. We propose a new dynamic screening method, based on the distance correlation criterion, designed for hierarchical binary data. Our method can screen out large parts of the hierarchy at the higher levels, avoiding the need to explore many lower-level features and greatly reducing the computational cost of screening. The practical potential of the method is demonstrated in a case application involving a large volume of B2B transaction data.
While statistical inference has been widely used for decision and policy making in health care, we particularly focused on how providers get paid for some common procedures. We explored a few rich datasets and discovered large variations among providers for how much payers/insurers have paid, aka allowed payment. Then we proposed to incorporate available providers' attributes with regression model to explain the possible reasons for those payment variations.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1903/199962017-01-01T00:00:00Z