The source-lens clustering effect in the context of lensing tomography and its self-calibration

Cosmic shear can only be measured where there are galaxies. This source-lens clustering (SLC) effect has two sources, intrinsic source clustering and cosmic magnification (magnification/size bias). Lensing tomography can suppress the former. However, this reduction is limited by the existence of photo-z error and nonzero redshift bin width. Furthermore, SLC induced by cosmic magnification cannot be reduced by lensing tomography. Through N-body simulations, we quantify the impact of SLC on the lensing power spectrum in the context of lensing tomography. We consider both the standard estimator and the pixel-based estimator. We find that none of them can satisfactorily handle both sources of SLC. (1) For the standard estimator, SLC induced by both sources can bias the lensing power spectrum by O(1)-O(10)%. Intrinsic source clustering also increases statistical uncertainties in the measured lensing power spectrum. However, the standard estimator suppresses intrinsic source clustering in the cross-spectrum. (2) In contrast, the pixel-based estimator suppresses SLC through cosmic magnification. However, it fails to suppress SLC through intrinsic source clustering and the measured lensing power spectrum can be biased low by O(1)-O(10)%. In short, for typical photo-z errors (sigma_z/(1+z)=0.05) and photo-z bin sizes (Delta_z^P=0.2), SLC alters the lensing E-mode power spectrum by 1-10%, with ell~10^3$ and z_s~1 being of particular interest to weak lensing cosmology. Therefore the SLC is a severe systematic for cosmology in Stage-IV lensing surveys. We present useful scaling relations to self-calibrate the SLC effect.Comment: 13 pages, 10 figures, Accepted by AP

Gaussianizing the non-Gaussian lensing convergence field I: the performance of the Gaussianization

Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010, we proposed a Gaussianization transform to Gaussianize the non-Gaussian lensing convergence field $\kappa$. It performs a local monotonic transformation $\kappa\rightarrow y$ pixel by pixel to make the unsmoothed one-point probability distribution function of the new variable $y$ Gaussian. We tested whether the whole $y$ field is Gaussian against N-body simulations. (1) We found that the proposed Gaussianization suppresses the non-Gaussianity by orders of magnitude, in measures of the skewness, the kurtosis, the 5th- and 6th-order cumulants of the $y$ field smoothed over various angular scales relative to that of the corresponding smoothed $\kappa$ field. The residual non-Gaussianities are often consistent with zero within the statistical errors. (2) The Gaussianization significantly suppresses the bispectrum. Furthermore, the residual scatters around zero, depending on the configuration in the Fourier space. (3) The Gaussianization works with even better performance for the 2D fields of the matter density projected over \sim 300 \mpch distance interval centered at $z\in(0,2)$, which can be reconstructed from the weak lensing tomography. (4) We identified imperfectness and complexities of the proposed Gaussianization. We noticed weak residual non-Gaussianity in the $y$ field. We verified the widely used logarithmic transformation as a good approximation to the Gaussianization transformation. However, we also found noticeable deviations.Comment: 13 pages, 15 figures, accepted by PR

Exploring Green Innovation Practices: Content Analysis of the Fortune Global 500 Companies

Green innovation has been attracting increasing attention due to its contributions to the conservation of resources and environmental protection. However, in the process of exploring green innovation, the allocation of resources and the direction of innovation are often inaccurate, which leads to a low efficiency of green innovation. If we can learn the green innovation practices from successful companies, we can certainly provide reference strategies for those companies that are exploring green innovation. Therefore, taking the Fortune Global 500 companies as the analysis object, this research develops the criteria of green innovation practices and conducts a cluster analysis of these companies by using a content analysis method. Finally, this paper summarizes the green innovation practices of the six types of industries and provides corresponding countermeasures and suggestions, which provide a strong reference for relevant companies to carry out green innovation