Reduced convergence and the local smoothness parameter: bridging two different descriptions of weak lensing amplification

Weak gravitational lensing due to the inhomogeneous matter distribution in the universe is an important systematic uncertainty in the use of standard candles in cosmology. There are two different descriptions of weak lensing amplification, one uses a local smoothness parameter $\tilde{\alpha}$, the other uses reduced convergence $\eta= 1+ \kappa/|\kappa_{min}|$ (where $\kappa$ is convergence). The $\tilde{\alpha}$ description involves Dyer-Roeder distance $D_A(\tilde{\alpha}|z)$ ($\tilde{\alpha}=1$ corresponds to a smooth universe); it is simple and convenient, and has been used by the community to illustrate the effect of weak lensing on point sources such as type Ia supernovae. Wang (1999) has shown that the $\tilde{\alpha}$ description can be made realistic by allowing $\tilde{\alpha}$ to be a local variable, the local smoothness parameter. The $\eta$ description has been used by Wang, Holz, & Munshi (2002) to derive a universal probability distribution (UPDF) for weak lensing amplification. In this paper, we bridge the two different descriptions of weak lensing amplification by relating the reduced convergence $\eta$ and the local smoothness parameter $\tilde{\alpha}$. We give the variance of $\tilde{\alpha}$ in terms of the matter power spectrum, thus providing a quantitative guidance to the use of Dyer-Roeder distances in illustrating the effect of weak lensing. The by-products of this work include a corrected definition of the reduced convergence, and simple and accurate analytical expressions for $D_A(\tilde{\alpha}|z)$. Our results should be very useful in studying the weak lensing of standard candles.Comment: Revised and expanded version. ApJ accepte

Predicting H{\alpha} emission line galaxy counts for future galaxy redshift surveys

Knowledge of the number density of H$\alpha$ emitting galaxies is vital for assessing the scientific impact of the Euclid and WFIRST missions. In this work we present predictions from a galaxy formation model, Galacticus, for the cumulative number counts of H$\alpha$-emitting galaxies. We couple Galacticus to three different dust attenuation methods and examine the counts using each method. A $\chi^2$ minimisation approach is used to compare the model predictions to observed galaxy counts and calibrate the dust parameters. We find that weak dust attenuation is required for the Galacticus counts to be broadly consistent with the observations, though the optimum dust parameters return large values for $\chi^2$, suggesting that further calibration of Galacticus is necessary. The model predictions are also consistent with observed estimates for the optical depth and the H$\alpha$ luminosity function. Finally we present forecasts for the redshift distributions and number counts for two Euclid-like and one WFIRST-like survey. For a Euclid-like survey with redshift range $0.9\leqslant z\leqslant 1.8$ and H$\alpha+{\rm [NII]}$ blended flux limit of $2\times 10^{-16}{\rm erg}\,{\rm s}^{-1}\,{\rm cm}^{-2}$ we predict a number density between 3900--4800 galaxies per square degree. For a WFIRST-like survey with redshift range $1\leqslant z\leqslant 2$ and blended flux limit of $1\times 10^{-16}{\rm erg}\,{\rm s}^{-1}\,{\rm cm}^{-2}$ we predict a number density between 10400--15200 galaxies per square degree.Comment: 21 pages (including appendix), 12 figures, 6 tables. Accepted b

Illuminating the dark universe with a very high density galaxy redshift survey over a wide area

The nature of dark energy remains a profound mystery 20 years after the discovery of cosmic acceleration. A very high number density galaxy redshift survey over a wide area (HD GRS Wide) spanning the redshift range of 0.5<z<4 using the same tracer, carried out using massively parallel wide field multi-object slit spectroscopy from space, will provide definitive dark energy measurements with minimal observational systematics by design. The HD GRS Wide will illuminate the nature of dark energy, and lead to revolutionary advances in particle physics and cosmology. It will also trace the cosmic web of dark matter and provide key insight into large-scale structure in the Universe. The required observational facility can be established as part of the probe portfolio by NASA within the next decade

Faculty Recital: Horn and Clarinet Faculty Recital

State University University School of Music presents Horn and Clarinet Faculty Recital featuring Jason Eklund on horn, John Warren on clarinet, and Soohyun Yun on piano.https://digitalcommons.kennesaw.edu/musicprograms/1072/thumbnail.jp

The WFIRST Galaxy Survey Exposure Time Calculator

This document describes the exposure time calculator for the Wide-Field Infrared Survey Telescope (WFIRST) high-latitude survey. The calculator works in both imaging and spectroscopic modes. In addition to the standard ETC functions (e.g. background and S/N determination), the calculator integrates over the galaxy population and forecasts the density and redshift distribution of galaxy shapes usable for weak lensing (in imaging mode) and the detected emission lines (in spectroscopic mode). The source code is made available for public use.Comment: 44 pages. The current C source code and version history can be found at http://www.tapir.caltech.edu/~chirata/web/software/space-etc/ ; IPAC maintains a web interface at http://wfirst-web.ipac.caltech.edu/wfDepc/wfDepc.js

2014 Kennesaw State University Concert Band Invitational

Kennesaw State University School of Music presents 2014 Concert Band Invitational.https://digitalcommons.kennesaw.edu/musicprograms/1382/thumbnail.jp

Ferroelectric and octahedral tilt twin disorder and the lead-free piezoelectric, sodium potassium niobate system

Using electron diffraction, trends in the local structural behaviour of the KxNa1-xNbO3 (KNN x) 'solid solution' system are investigated and interpreted using an order/disorder based theoretical framework. At room temperature, electron diffraction shows a single plane of transverse polarised, diffuse intensity perpendicular to [0 1 0]p (p for parent sub-structure) across the entire phase diagram, indicative of ferroelectric disorder along the [0 1 0]p direction co-existing with long range ferroelectric order along the orthogonal [1 0 0]p and [0 0 1]p directions. An additional characteristic pattern of diffuse scattering is also observed, involving rods of diffuse intensity running along the [1 0 0]p (*) and [0 0 1]p (*) directions of the perovskite sub-structure and indicative of octahedral tilt disorder about the [1 0 0]p and [0 0 1]p axes co-existing with long range ordered octahedral tilting around the [0 1 0]p direction. A possible crystal chemical explanation for the existence of this latter octahedral tilt disorder is explored through bond valence sum calculations. The possible influence of both types of disorder on the previously refined, room temperature space group/s and average crystal structure/s is examined

Distributed Estimation for Principal Component Analysis: an Enlarged Eigenspace Analysis

The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine learning problem, principal component analysis (PCA). Despite the massive literature on top eigenvector estimation, much less is presented for the top-$L$-dim ($L>1$) eigenspace estimation, especially in a distributed manner. We propose a novel multi-round algorithm for constructing top-$L$-dim eigenspace for distributed data. Our algorithm takes advantage of shift-and-invert preconditioning and convex optimization. Our estimator is communication-efficient and achieves a fast convergence rate. In contrast to the existing divide-and-conquer algorithm, our approach has no restriction on the number of machines. Theoretically, the traditional Davis-Kahan theorem requires the explicit eigengap assumption to estimate the top-$L$-dim eigenspace. To abandon this eigengap assumption, we consider a new route in our analysis: instead of exactly identifying the top-$L$-dim eigenspace, we show that our estimator is able to cover the targeted top-$L$-dim population eigenspace. Our distributed algorithm can be applied to a wide range of statistical problems based on PCA, such as principal component regression and single index model. Finally, We provide simulation studies to demonstrate the performance of the proposed distributed estimator