An alternate proof of Wise's Malnormal Special Quotient Theorem

We give an alternate proof of Wise's Malnormal Special Quotient Theorem (MSQT), avoiding cubical small cancellation theory. We also show how to deduce Wise's Quasiconvex Hierarchy Theorem from the MSQT and theorems of Hsu--Wise and Haglund--Wise.Comment: 42 pages, 10 figures. Version 2 contains minor changes, addressing referee comments. To appear in Forum of Mathematics, P

Machine Learning for Physiological Time Series: Representing and Controlling Blood Glucose for Diabetes Management

Type 1 diabetes is a chronic health condition affecting over one million patients in the US, where blood glucose (sugar) levels are not well regulated by the body. Researchers have sought to use physiological data (e.g., blood glucose measurements) collected from wearable devices to manage this disease, either by forecasting future blood glucose levels for predictive alarms, or by automating insulin delivery for blood glucose management. However, the application of machine learning (ML) to these data is hampered by latent context, limited supervision and complex temporal dependencies. To address these challenges, we develop and evaluate novel ML approaches in the context of i) representing physiological time series, particularly for forecasting blood glucose values and ii) decision making for when and how much insulin to deliver. When learning representations, we leverage the structure of the physiological sequence as an implicit information stream. In particular, we a) incorporate latent context when predicting adverse events by jointly modeling patterns in the data and the context those patterns occurred under, b) propose novel types of self-supervision to handle limited data and c) propose deep models that predict functions underlying trajectories to encode temporal dependencies. In the context of decision making, we use reinforcement learning (RL) for blood glucose management. Through the use of an FDA-approved simulator of the glucoregulatory system, we achieve strong performance using deep RL with and without human intervention. However, the success of RL typically depends on realistic simulators or experimental real-world deployment, neither of which are currently practical for problems in health. Thus, we propose techniques for leveraging imperfect simulators and observational data. Beyond diabetes, representing and managing physiological signals is an important problem. By adapting techniques to better leverage the structure inherent in the data we can help overcome these challenges.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163134/1/ifox_1.pd

The Devolution of Man: Mental and Social “Madness” Throughout Literature

Examines portrayals of madness in a selection of literature Essay and annotated bibliography from the 2012 University of Puget Sound Book Collecting Contest

Residual finiteness, QCERF, and fillings of hyperbolic groups

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.Comment: (v1) 22 pages, 2 figures. (v2) 24 pages, 2 figures. An error in the proof and statement of the main technical lemma was corrected, and some other small corrections and clarifications were mad

Hunting the Dark Knight: Books on the Batman

My essay and annotate bibliography explores the many facets of Batman as both a cultural icon and as a morally and politically complicated character. I explore the merits of comics and superheroes as a modern mythology that deserves serious academic study. Ultimately this is the expression of my personal growth by learning about the Batman and hope that others will pursue their respective passions

Strengthening the Passivity Default

In The Prudence of Passivity, Bryon Harmon and Laura Fisher (hereafter HF) argue that passive management become the default approach for the investment of trust funds, to be abandoned only when circumstances specifically dictate the use of active management. \u27 In this comment we argue that their thesis could be strengthened (i) by more clearly distinguishing between default law and default investment practices, (ii) by more clearly articulating their favored altering rules