Focused information criterion and model averaging for generalized additive partial linear models

We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability. Simulation experiments have provided evidence of the superiority of the proposed procedures. The approach is further applied to a real-world data example.Comment: Published in at http://dx.doi.org/10.1214/10-AOS832 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole

In this paper we discuss the supersymmetric localization of the 4D $\mathcal{N}=2$ off-shell gauged supergravity in the background of the $\textrm{AdS}_4$ neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary $\textrm{S}^1 \times \mathbb{H}^2$. We compute the large-$N$ expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.Comment: 34 pages, 1 figure; minor changes in v2; references added in v3, published version in JHE

On the Structure of Quasi-Universal Jets for Gamma-Ray Bursts

The idea that GRBs originate from uniform jets has been used to explain numerous observations of breaks in the GRB afterglow lightcurves. We explore the possibility that GRBs instead originate from a structured jet that may be quasi-universal, where the variation in the observed properties of GRBs is due to the variation in the observer viewing angle. We test how various models reproduce the jet data of Bloom, Frail, & Kulkarni (2003), which show a negative correlation between the isotropic energy output and the inferred jet opening angle (in a uniform jet configuration). We find, consistent with previous studies, that a power-law structure for the jet energy as a function of angle gives a good description. However, a Gaussian jet structure can also reproduce the data well, particularly if the parameters of the Gaussian are allowed some scatter. We place limits on the scatter of the parameters in both the Gaussian and power-law models needed to reproduce the data, and discuss how future observations will better distinguish between these models for the GRB jet structure. In particular, the Gaussian model predicts a turnover at small opening angles and in some cases a sharp cutoff at large angles, the former of which may already have been observed. We also discuss the predictions each model makes for the observed luminosity function of GRBs and compare these predictions with the existing data.Comment: 13 pages, including 10 figures; To appear in Ap

Homeostatic Elastic States and the Stability of Elastic Arteries

Vascular mechanics has undergone significant growth within the last 50 years owing to the rapid development of nonlinear continuum mechanics occurring roughly within the same period and motivated primarily by rubber materials. However, one important distinction of blood vessels, in contrast to typical engineering materials is that, through a variety of physiological mechanisms, they seek to maintain constant a preferred mechanical state (mechanical homeostasis) thereby exhibiting a remarkable mechanical stability in response to temporal evolution and alterations in blood pressure, vessel tethering forces and geometry and material properties. The mechanical state experienced by blood vessels plays a critical role in mechanical homeostasis and mechanical stability, and there remains a pressing need for mechanical/mathematical analysis to i) understand/predict the stretch/stress states within vessels and how they evolve with increasing blood pressure and tethering forces, ii) understand/predict the mechanical stability of arteries in response to diverse stimuli such as inhomogeneities in geometry and material properties. This dissertation seeks to add to this vibrant field by conducting a rigorous analysis of i) the mechanics of the homeostatic states of uniform circumferential stress and uniform stretch in an N-layer cylindrical artery subject to circumferential prestress, axial tethering force and the pressure of blood and ii) the local mechanical stability by imperfection growth in a solid body subject to inhomogeneities in geometry and material properties. In order to make these results relevant to a blood vessel, a micromechanics based constitutive relation is proposed based on the more or less regular architecture of a large elastic artery composed of collagen, elastin and vascular smooth muscle. Although the primary focus of the work is on the healthy artery, the effect on imperfection growth of diseased tissue constituents is accounted for in a simple model of damaged elastin and collagen