The New B-Word

I get all of my career advice from Cosmopolitan magazine. Okay, maybe not all of it. But sitting in the airport this past weekend, I breezed through articles about Khloé Kardashian and confessions about why guys cheat, and, somewhere in the middle, stumbled on an article called “Like a Boss.” It was written by Sheryl Sandberg, COO of Facebook and author of Lean In, and described an issue I had never really given much thought to: why female leaders are, seemingly more often than male leaders, described as bossy. As a woman with a leadership position on campus, the topic stewed in my mind for a bit. Yeah, I’ve been called bossy, but it hasn’t really bothered me. Should it

Muslim Women and United States Healthcare: Challenges to Access and Navigation

This paper offers an analysis of the interactions of Muslim women in the US healthcare system in order to unpack challenges and propose potential accommodations. Islam may inform values or considerations in the context of other cultural factors or present Muslim women with specific challenges in seeking healthcare based on Islamic teachings or social constructs. This paper examines these factors by elaborating on an overview of Muslim interpretations of healthcare using religious authorities, text from the Qur’an, and social norms. It then delves into challenges faced by Muslim women in the US healthcare system and the implications of those challenges and finally proposes improvements to help Muslim women to gain access to fair and equal healthcare in the US

Restriction of Fourier transforms to curves, II: Some classes with vanishing torsion

We consider the Fourier restriction operators associated to certain degenerate curves in R^d for which the highest torsion vanishes. We prove estimates with respect to affine arclength and with respect to the Euclidean arclength measure on the curve. The estimates have certain uniform features, and the affine arclength results cover families of flat curves.Comment: 26 pages, Final version to appear in the Journal of the Australian Mathematical Societ

Restriction of Fourier transforms to curves and related oscillatory integrals

We prove sharp endpoint results for the Fourier restriction operator associated to nondegenerate curves in $\Bbb R^d$, $d\ge 3$, and related estimates for oscillatory integral operators. Moreover, for some larger classes of curves in $\Bbb R^d$ we obtain sharp uniform $L^p\to L^q$ bounds with respect to affine arclength measure, thereby resolving a problem of Drury and Marshall.Comment: Minor changes in the version to appear in American Journal of Mathematic

Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design

Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GP-UCB compares favorably with other heuristical GP optimization approaches