A comparison of estimators for the two-point correlation function

Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion. The indicators were extracted from over 500 subsamples of the Virgo Hubble Volume simulation cluster catalog. The ``real'' correlation function was determined from the full survey in a 3000Mpc/h periodic cube. The estimators were ranked by the cumulative probability of returning a value within a certain tolerance of the real correlation function. This criterion takes into account bias and variance, and it is independent of the possibly non-Gaussian nature of the error statistics. As a result for astrophysical applications a clear recommendation has emerged: the Landy & Szalay (1993) estimator, in its original or grid version Szapudi & Szalay (1998), are preferred in comparison to the other indicators examined, with a performance almost indistinguishable from the Hamilton (1993) estimator.Comment: aastex, 10 pages, 1 table, 1 figure, revised version, accepted in ApJ

Minkowski Functionals of Abell/ACO Clusters

We determine the Minkowski functionals for a sample of Abell/ACO clusters, 401 with measured and 16 with estimated redshifts. The four Minkowski functionals (including the void probability function and the mean genus) deliver a global description of the spatial distribution of clusters on scales from $10$ to 60\hMpc with a clear geometric interpretation. Comparisons with mock catalogues of N--body simulations using different variants of the CDM model demonstrate the discriminative power of the description. The standard CDM model and the model with tilted perturbation spectrum cannot generate the Minkowski functionals of the cluster data, while a model with a cosmological constant and a model with breaking of the scale invariance of perturbations (BSI) yield compatible results.Comment: 10 pages, 13 Postscript figures, uses epsf.sty and mn.sty (included), submitted to MNRA

A global descriptor of spatial pattern interaction in the galaxy distribution

We present the function J as a morphological descriptor for point patterns formed by the distribution of galaxies in the Universe. This function was recently introduced in the field of spatial statistics, and is based on the nearest neighbor distribution and the void probability function. The J descriptor allows to distinguish clustered (i.e. correlated) from ``regular'' (i.e. anti-correlated) point distributions. We outline the theoretical foundations of the method, perform tests with a Matern cluster process as an idealised model of galaxy clustering, and apply the descriptor to galaxies and loose groups in the Perseus-Pisces Survey. A comparison with mock-samples extracted from a mixed dark matter simulation shows that the J descriptor can be profitably used to constrain (in this case reject) viable models of cosmic structure formation.Comment: Significantly enhanced version, 14 pages, LaTeX using epsf, aaspp4, 7 eps-figures, accepted for publication in the Astrophysical Journa

The Angular Three-Point Correlation Function in the Quasilinear Regime

We calculate the normalized angular three-point correlation function (3PCF), $q$, as well as the normalized angular skewness, $s_3$, assuming the small-angle approximation, for a biased mass distribution in flat and open cold-dark-matter (CDM) models with Gaussian initial conditions. The leading-order perturbative results incorporate the explicit dependence on the cosmological parameters, the shape of the CDM transfer function, the linear evolution of the power spectrum, the form of redshift distribution function, and linear and nonlinear biasing, which may be evolving. Results are presented for different redshift distributions, including that appropriate for the APM Galaxy Survey, as well as for a survey with a mean redshift of $\bar{z} \simeq 1$ (such as the VLA FIRST Survey). Qualitatively, many of the results found for $s_3$ and $q$ are similar to those obtained in a related treatment of the spatial skewness and 3PCF (Buchalter & Kamionkowski 1999), such as a leading-order correction to the standard result for $s_3$ in the case of nonlinear bias (as defined for unsmoothed density fields), and the sensitivity of the configuration dependence of $q$ to both cosmological and biasing models. We show that since angular CFs are sensitive to clustering over a range of redshifts, the various evolutionary dependences included in our predictions imply that measurements of $q$ in a deep survey might better discriminate between models with different histories, such as evolving vs. non-evolving bias, that can have similar spatial CFs at low redshift. Our calculations employ a derived equation---valid for open, closed, and flat models---for obtaining the angular bispectrum from the spatial bispectrum in the small-angle approximation.Comment: 45 pages, including 11 Figures, submitted to the Astrophysical Journa

Luminosity- and morphology-dependent clustering of galaxies

How does the clustering of galaxies depend on their inner properties like morphological type and luminosity? We address this question in the mathematical framework of marked point processes and clarify the notion of luminosity and morphological segregation. A number of test quantities such as conditional mark-weighted two-point correlation functions are introduced. These descriptors allow for a scale-dependent analysis of luminosity and morphology segregation. Moreover, they break the degeneracy between an inhomogeneous fractal point set and actual present luminosity segregation. Using the Southern Sky Redshift Survey~2 (da Costa et al. 1998, SSRS2) we find both luminosity and morphological segregation at a high level of significance, confirming claims by previous works using these data (Benoist et al. 1996, Willmer et al. 1998). Specifically, the average luminosity and the fluctuations in the luminosity of pairs of galaxies are enhanced out to separations of 15Mpc/h. On scales smaller than 3Mpc/h the luminosities on galaxy pairs show a tight correlation. A comparison with the random-field model indicates that galaxy luminosities depend on the spatial distribution and galaxy-galaxy interactions. Early-type galaxies are also more strongly correlated, indicating morphological segregation. The galaxies in the PSCz catalog (Saunders et al. 2000) do not show significant luminosity segregation. This again illustrates that mainly early-type galaxies contribute to luminosity segregation. However, based on several independent investigations we show that the observed luminosity segregation can not be explained by the morphology-density relation alone.Comment: aastex, emulateapj5, 20 pages, 13 figures, several clarifying comments added, ApJ accepte

Redshift-Space Enhancement of Line-of-Sight Baryon Acoustic Oscillations in the SDSS Main-Galaxy Sample

We show that redshift-space distortions of galaxy correlations have a strong effect on correlation functions with distinct, localized features, like the signature of the baryon acoustic oscillations (BAO). Near the line of sight, the features become sharper as a result of redshift-space distortions. We demonstrate this effect by measuring the correlation function in Gaussian simulations and the Millennium Simulation. We also analyze the SDSS DR7 main-galaxy sample (MGS), splitting the sample into slices 2.5 degrees on the sky in various rotations. Measuring 2D correlation functions in each slice, we do see a sharp bump along the line of sight. Using Mexican-hat wavelets, we localize it to (110 +/- 10) Mpc/h. Averaging only along the line of sight, we estimate its significance at a particular wavelet scale and location at 2.2 sigma. In a flat angular weighting in the (pi,r_p) coordinate system, the noise level is suppressed, pushing the bump's significance to 4 sigma. We estimate that there is about a 0.2% chance of getting such a signal anywhere in the vicinity of the BAO scale from a power spectrum lacking a BAO feature. However, these estimates of the significances make some use of idealized Gaussian simulations, and thus are likely a bit optimistic.Comment: 17 pages, 27 figures. Minor changes to match final version accepted to Ap

Perturbative Analysis of Adaptive Smoothing Methods in Quantifying Large-Scale Structure

Smoothing operation to make continuous density field from observed point-like distribution of galaxies is crucially important for topological or morphological analysis of the large-scale structure, such as, the genus statistics or the area statistics (equivalently the level crossing statistics). It has been pointed out that the adaptive smoothing filters are more efficient tools to resolve cosmic structures than the traditional spatially fixed filters. We study weakly nonlinear effects caused by two representative adaptive methods often used in smoothed hydrodynamical particle (SPH) simulations. Using framework of second-order perturbation theory, we calculate the generalized skewness parameters for the adaptive methods in the case of initially power-law fluctuations. Then we apply the multidimensional Edgeworth expansion method and investigate weakly nonlinear evolution of the genus statistics and the area statistics. Isodensity contour surfaces are often parameterized by the volume fraction of the regions above a given density threshold. We also discuss this parameterization method in perturbative manner.Comment: 42 pages including 9 figure, ApJ 537 in pres

Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?

In this paper, we investigate the utility of Minkowski Functionals as a probe of cold/hot disk-like structures in the CMB. In order to construct an accurate estimator, we resolve a long-standing issue with the use of Minkowski Functionals as probes of the CMB sky -- namely that of systematic differences ("residuals") when numerical and analytical MF are compared. We show that such residuals are in fact by-products of binning, and not caused by pixelation or masking as originally thought. We then derive a map-independent estimator that encodes the effects of binning, applicable to beyond our present work. Using this residual-free estimator, we show that small disk-like effects (as claimed by Vielva et al.) can be detected only when a large sample of such maps are averaged over. In other words, our estimator is noise-dominated for small disk sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to the WMAP7 data to obtain a null result.Comment: 15 pages, 13 figure

Mark correlations: relating physical properties to spatial distributions

Mark correlations provide a systematic approach to look at objects both distributed in space and bearing intrinsic information, for instance on physical properties. The interplay of the objects' properties (marks) with the spatial clustering is of vivid interest for many applications; are, e.g., galaxies with high luminosities more strongly clustered than dim ones? Do neighbored pores in a sandstone have similar sizes? How does the shape of impact craters on a planet depend on the geological surface properties? In this article, we give an introduction into the appropriate mathematical framework to deal with such questions, i.e. the theory of marked point processes. After having clarified the notion of segregation effects, we define universal test quantities applicable to realizations of a marked point processes. We show their power using concrete data sets in analyzing the luminosity-dependence of the galaxy clustering, the alignment of dark matter halos in gravitational $N$-body simulations, the morphology- and diameter-dependence of the Martian crater distribution and the size correlations of pores in sandstone. In order to understand our data in more detail, we discuss the Boolean depletion model, the random field model and the Cox random field model. The first model describes depletion effects in the distribution of Martian craters and pores in sandstone, whereas the last one accounts at least qualitatively for the observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics, second Wuppertal conference "Spatial statistics and statistical physics

The C-Type Lectin Receptor CLECSF8/CLEC4D Is a Key Component of Anti-Mycobacterial Immunity

Open Access funded by Wellcome Trust: Under a Creative Commons license Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved. Acknowledgments We would like to thank S. Hardison, P. Redelinghuys, J. Taylor, C. Wallace, A. Richmond, S. Hadebe, A. Plato, F. Abbass, L. Fick, N. Allie, R. Wilkinson, K. Wilkinson, S. Cooper, D. Lang, and V. Kumar for reagents and assistance, and the animal facility staff for the care of our animals. This work was supported by the MRC (UK) and Wellcome Trust (G.D.B.); MRC (South Africa) and Sydney Brenner Fellowship (M.J.M.); Vici (M.G.N.), Vidi (R.v.C.), and Veni grants (T.S.P.) from the Netherlands Organization for Scientific Research; the Royal Netherlands Academy of Arts and Sciences (T.H.M.O.); EC FP7 projects (NEWTBVAC, ADITEC; T.H.M.O.); Carnegie Corporation and CIDRI (J.C.H.); and the University of Aberdeen (B.K.).Peer reviewedPublisher PD