A close examination of cosmic microwave background mirror-parity after Planck

Previous claims of significant evidence for mirror-parity in the large-scale cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP) experiment have been recently echoed in the first study of isotropy and statistics of CMB data from Planck. We revisit these claims with a careful analysis of the latest data available. We construct statistical estimators in both harmonic and pixel space, test them on simulated data with and without mirror-parity symmetry, apply different Galactic masks, and study the dependence of the results on arbitrary choices of free parameters. We confirm that the data exhibit evidence for odd mirror-parity at a significance which reaches as high as ~ 99 per cent C.L., under some circumstances. However, given the inherent biases in the pixel-based statistic and the dependence of both pixel and harmonic space statistics on the particular form of Galactic masking and other a-posteriori choices, we conclude that these results are not in significant tension with the predictions of the concordance cosmological model.Comment: 9 pages, 5 figures, minor changes, as published in MNRA

The Kullback-Leibler Divergence as an Estimator of the Statistical Properties of CMB Maps

The identification of unsubtracted foreground residuals in the cosmic microwave background maps on large scales is of crucial importance for the analysis of polarization signals. These residuals add a non-Gaussian contribution to the data. We propose the Kullback-Leibler (KL) divergence as an effective, non-parametric test on the one-point probability distribution function of the data. With motivation in information theory, the KL divergence takes into account the entire range of the distribution and is highly non-local. We demonstrate its use by analyzing the large scales of the Planck 2013 SMICA temperature fluctuation map and find it consistent with the expected distribution at a level of 6%. Comparing the results to those obtained using the more popular Kolmogorov-Smirnov test, we find the two methods to be in general agreement.Comment: 12 pages, 5 figures, minor change, as published in JCA

Skewness and Kurtosis as Indicators of Non-Gaussianity in Galactic Foreground Maps

Observational cosmology is entering an era in which high precision will be required in both measurement and data analysis. Accuracy, however, can only be achieved with a thorough understanding of potential sources of contamination from foreground effects. Our primary focus will be on non- Gaussian effects in foregrounds. This issue will be crucial for coming experiments to determine B-mode polarization. We propose a novel method for investigating a data set in terms of skewness and kurtosis in locally defined regions that collectively cover the entire sky. The method is demonstrated on two sky maps: (i) the SMICA map of Cosmic Microwave Background fluctuations provided by the Planck Collaboration and (ii) a version of the Haslam map at 408 MHz that describes synchrotron radiation. We find that skewness and kurtosis can be evaluated in combination to reveal local physical information. In the present case, we demonstrate that the local properties of both maps are predominantly Gaussian. This result was expected for the SMICA map; that it also applies for the Haslam map is surprising. The approach described here has a generality and flexibility that should make it useful in a variety of astrophysical and cosmological contexts.Comment: 15 pages, 7 figures, minor change, as published in JCA

Parity in the CMB: Space Oddity

We search for a direction in the sky that exhibits parity symmetry under reflections through a plane. We use the natural estimator, which compares the power in even and odd $\ell+m$ multipoles, and apply minimal blind masking of outliers to the ILC map in order to avoid large errors in the reconstruction of multipoles. The multipoles of the cut sky are calculated both naively and by using the covariance inversion method and we estimate the significance of our results using $\Lambda$CDM simulations. Focusing on low multipoles, $2\leq \ell \leq \ell_{\max}$ with $\ell_{\max}=5,6$ or even 7, we find two perpendicular directions of even and odd parity in the map. While the even parity direction does not appear significant, the odd direction is quite significant -- at least a $3.6\sigma$ effect.Comment: 6 pages, 7 figures. Accepted for publication in The Astrophysical Journa

Understanding the Scope of Business Law Clinics: Perspectives from the United Kingdom, Israel and the United States

The impetus for the emergence of business law clinics across jurisdictions is remarkably similar: commercially orientated education and development of students combined with a reconceptualised social justice agenda which embraces entrepreneurial activity in all forms. Business law clinics face the challenge of balancing the interests of students and clients,of service provision versus learning environment, within a distinctly entrepreneurial environment. To achieve this, we must enter into a dialogue and embrace a common mission. This article addresses the gap in the literature with a comparative analysis of the Business and Commercial Law Clinic at Northumbria Law School, England; The Interdisciplinary Center Herzliya Legal Clinic for Start-Ups at Radzyner Law School, Israel; and BrooklynLaw Incubator & Policy Clinic at Brooklyn Law School, United States. We posit that business law clinics should be valued for their rich educational experience, the important assistance they provide and the wider benefits they bestow on teaching institutions

Giant Rings in the CMB Sky

We find a unique direction in the CMB sky around which giant rings have an anomalous mean temperature profile. This direction is in very close alignment with the afore measured anomalously large bulk flow direction. Using Monte Carlo simulations, we estimate the significance of the giant rings at the $3\sigma$ level and the alignment with the bulk flow at $2.5\sigma$. We argue that a cosmic defect seeded by a pre-inflationary particle could explain the giant rings, the large bulk flow and their alignment.Comment: 6 pages, 7 figures, accepted for publication in The Astrophysical Journa

Experimental Study of Parametric Autoresonance in Faraday Waves

The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of nonlinear waves in a dissipative system. The experiments presented are in excellent agreement with theory.Comment: 4 pages, 4 eps figures, to appear in Phys. Rev. Let