In multi-armed trials, adaptive designs are a popular way to increase estimation efficiency or identify optimal treatments. Many recent papers have proposed adaptive methods for minimizing the error of unbiased estimators that consider each treatment arm in isolation. This approach may be inefficient, because it fails to borrow shared information across the treatment arms. We […]
A Belyĭ pair \bigl( S,\, z(w) \bigr) is a compact, connected Riemann surface S together with a rational function z \colon S \to \mathbb{P}^1(\mathbb{C}) which has at most three critical values […]
A wide variety of medical imaging methods exist for research and diagnostic procedures on the Central Nervous System (CNS), among them Magnetic Resonance Imaging (MRI) and Optical Imaging. Mathematical modeling […]
Political scientists forecast elections, not primarily to satisfy public interest, but to validate statistical models used for estimating quantities of scholarly interest. Although scholars have learned a great deal from these models, they can be embarrassingly overconfident: Events that should occur once in 10,000 elections occur almost every year, and even those that should occur […]
This paper examines how initial conditions shape the long-run impact of large temporary shocks on economic geography. Using WWII supply contracts in the United States, we show that temporary spending had persistent effects on population and manufacturing employment only in counties with low initial manufacturing development. Motivated by these findings, we develop a multisector economic […]
Large language models (LLMs) can use examples provided in a prompt to make predictions for new queries without updating their parameters, a capability known as in-context learning. In this talk, I will explore how transformers, the architectural backbone of many LLMs, can perform nonlinear kernel ridge regression (KRR). I will first present numerical observations showing […]
