Expectations for the Difference Between Local and Global Measurements of the Hubble Constant

There are irreducible differences between the Hubble constant measured locally and the global value. They are due to density perturbations and finite sample volume (cosmic variance) and finite number of objects in the sample (sampling variance). We quantify these differences for a suite of COBE-normalized CDM models that are consistent with the observed large-scale structure. For small samples of objects that only extend out to 10,000 km/sec, the variance can approach 4%. For the largest samples of Type Ia supernovae (SNeIa), which include about 40 objects and extend out to almost 40,000 km/sec, the variance is 1-2% and is dominated by sampling variance. Sampling and cosmic variance may be an important consideration in comparing local determinations of the Hubble constant with precision determinations of the global value that will be made from high-resolution maps of CBR anisotropy.Comment: 10 pages, Latex, 2 figures, version accepted for Ap.

Coherent control of Snell's law

We demonstrate coherent control of the generalized Snell's law in ultrathin gradient metasurfaces constructed by an array of V-shaped slot nanoantennas

The late Mesozoic-Cenozoic tectonic evolution of the South China Sea: A petrologic perspective

This paper presents a review of available petrological, geochonological and geochemical data for late Mesozoic to Recent igneous rocks in the South China Sea (SCS) and adjacent regions and a discussion of their petrogeneses and tectonic implications. The integration of these data with available geophysical and other geologic information led to the following tectono-magmatic model for the evolution of the SCS region. The geochemical characteristics of late Mesozoic granitic rocks in the Pearl River Mouth Basin (PRMB), micro-blocks in the SCS, the offshore continental shelf and Dalat zone in southern Vietnam, and the Schwaner Mountains in West Kalimantan, Borneo indicate that these are mainly I-type granites plus a small amount of S-type granites in the PRMB. These granitoids were formed in a continental arc tectonic setting, consistent with the ideas proposed by Holloway (1982) and Taylor and Hayes (1980, 1983), that there existed an Andean-type volcanic arc during later Mesozoic era in the SCS region. The geochonological and geochemical characteristics of the volcanics indicate an early period of bimodal volcanism (60-43. Ma or 32. Ma) at the northern margin of the SCS, followed by a period of relatively passive style volcanism during Cenozoic seafloor spreading (37 or 30-16. Ma) within the SCS, and post-spreading volcanism (tholeiitic series at 17-8. Ma, followed by alkali series from 8. Ma to present) in the entire SCS region. The geodynamic setting of the earlier volcanics was an extensional regime, which resulted from the collision between India and Eurasian plates since the earliest Cenozoic, and that of the post-spreading volcanics may be related to mantle plume magmatism in Hainan Island. In addition, the nascent Hainan plume may have played a significant role in the extension along the northern margin and seafloor spreading in the SCS. © 2014 Elsevier Ltd

Relations between three-point configuration space shear and convergence statistics

With the growing interest in and ability of using weak lensing studies to probe the non-Gaussian properties of the matter density field, there is an increasing need for the study of suitable statistical measures, e.g. shear three-point statistics. In this paper we establish the relations between the three-point configuration space shear and convergence statistics, which are an important missing link between different weak lensing three-point statistics and provide an alternative way of relating observation and theory. The method we use also allows us to derive the relations between other two- and three-point correlation functions. We show the consistency of the relations obtained with already established results and demonstrate how they can be evaluated numerically. As a direct application, we use these relations to formulate the condition for E/B-mode decomposition of lensing three-point statistics, which is the basis for constructing new three-point statistics which allow for exact E/B-mode separation. Our work applies also to other two-dimensional polarization fields such as that of the Cosmic Microwave Background.Comment: 17 pages, 5 figures, submitted to A&

Approximating Cross-validatory Predictive P-values with Integrated IS for Disease Mapping Models

An important statistical task in disease mapping problems is to identify out- lier/divergent regions with unusually high or low residual risk of disease. Leave-one-out cross-validatory (LOOCV) model assessment is a gold standard for computing predictive p-value that can flag such outliers. However, actual LOOCV is time-consuming because one needs to re-simulate a Markov chain for each posterior distribution in which an observation is held out as a test case. This paper introduces a new method, called iIS, for approximating LOOCV with only Markov chain samples simulated from a posterior based on a full data set. iIS is based on importance sampling (IS). iIS integrates the p-value and the likelihood of the test observation with respect to the distribution of the latent variable without reference to the actual observation. The predictive p-values computed with iIS can be proved to be equivalent to the LOOCV predictive p-values, following the general theory for IS. We com- pare iIS and other three existing methods in the literature with a lip cancer dataset collected in Scotland. Our empirical results show that iIS provides predictive p-values that are al- most identical to the actual LOOCV predictive p-values and outperforms the existing three methods, including the recently proposed ghosting method by Marshall and Spiegelhalter (2007).Comment: 21 page

Numerical simulation of vortex breakdown

The breakdown of an isolated axisymmetric vortex embedded in an unbounded uniform flow is examined by numerical integration of the complete Navier-Stokes equations for unsteady axisymmetric flow. Results show that if the vortex strength is small, the solution approaches a steady flow and the vortex is stable. If the strength is large enough, the solution remains unsteady and a recirculating zone will appear near the axis, its form and internal structure resembling those of the axisymmetric breakdown bubbles with multi-cells observed by Faler and Leibovich (1978). For apppropriate combinations of flow parameters, the flow reveals quasi-periodicity. Parallel calculations with the quasi-cylindrical approximation indicate that so far as predicting of breakdown is concerned, its results coincide quite well with the results mentioned above. Both show that the vortex breakdown has little concern with the Reynolds number or with the critical classification of the upstream flow, at least for the lower range of Reynolds numbers