Global Monge-Ampere equation with asymptotically periodic data

Let $u$ be a convex solution to $\det(D^2u)=f$ in $\mathbb R^n$ where $f\in C^{1,\alpha}(\mathbb R^n)$ is asymptotically close to a periodic function $f_p$. We prove that the difference between $u$ and a parabola is asymptotically close to a periodic function at infinity, for dimension $n\ge 3$.Comment: 20 page

Radiation-induced magnetoresistance oscillation in a two-dimensional electron gas in Faraday geometry

Microwave-radiation induced giant magnetoresistance oscillations recently discovered in high-mobility two-dimensional electron systems in a magnetic field, are analyzed theoretically. Multiphoton-assisted impurity scatterings are shown to be the primary origin of the oscillation. Based on a model which considers the interaction of electrons with the electromagnetic fields in Faraday geometry, we are able not only to reproduce the correct period, phase and the negative resistivity of the main oscillation, but also to obtain secondary peaks and additional maxima and minima in the resistivity curve, some of which were already observed in the experiments.Comment: 4 pages, 1 figure, revised version to be published in Phys. Rev. Let

Direct-current control of radiation-induced differential magnetoresistance oscillations in two-dimensional electron systems

Magnetoresistance oscillations in two-dimensional electron systems driven simultaneously by a strong direct current and a microwave irradiation, are analyzed within a unified microscopic scheme treating both excitations on an equal footing. The microwave-induced resistance oscillations are described by a parameter $\epsilon_\omega$ proportional to the radiation frequency, while the dc-induced resistance oscillations are governed by a parameter $\epsilon_j$ proportional to the current density. In the presence of both a microwave radiation and a strong dc, the combined parameter $\epsilon_\omega+\epsilon_j$ is shown to control the main resistance oscillations, in agreement with the recent measurement [Zhang {\it et al.} Phys. Rev. Lett. {\bf 98}, 106804 (2007)]Comment: 4 pages, 2 figues, published versio

Bayesian methods to overcome the winner's curse in genetic studies

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in studies with low power. We investigate the performance of the method with simulations and applications to four real data examples.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS373 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

In vivo super-resolution photoacoustic computed tomography by localization of single dyed droplets

The spatial resolution of photoacoustic (PA) computed tomography (PACT) is limited by acoustic diffraction. Here, we report in vivo superresolution PACT, which breaks the acoustic diffraction limit by localizing the centers of single dyed droplets. The dyed droplets generate much stronger PA signals than blood and can flow smoothly in blood vessels; thus, they are excellent tracers for localization-based superresolution imaging. The flowing droplets were first localized, and then their center positions were used to construct a superresolution image that exhibits sharper features and more finely resolved vascular details. A 6-fold improvement in spatial resolution has been realized in vivo