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

Budding Yeast Protein Extraction and Purification for the Study of Function, Interactions, and Post-translational Modifications

Homogenization by bead beating is a fast and efficient way to release DNA, RNA, proteins, and metabolites from budding yeast cells, which are notoriously hard to disrupt. Here we describe the use of a bead mill homogenizer for the extraction of proteins into buffers optimized to maintain the functions, interactions and post-translational modifications of proteins. Logarithmically growing cells expressing the protein of interest are grown in a liquid growth media of choice. The growth media may be supplemented with reagents to induce protein expression from inducible promoters (e.g. galactose), synchronize cell cycle stage (e.g. nocodazole), or inhibit proteasome function (e.g. MG132). Cells are then pelleted and resuspended in a suitable buffer containing protease and/or phosphatase inhibitors and are either processed immediately or frozen in liquid nitrogen for later use. Homogenization is accomplished by six cycles of 20 sec bead-beating (5.5 m/sec), each followed by one minute incubation on ice. The resulting homogenate is cleared by centrifugation and small particulates can be removed by filtration. The resulting cleared whole cell extract (WCE) is precipitated using 20% TCA for direct analysis of total proteins by SDS-PAGE followed by Western blotting. Extracts are also suitable for affinity purification of specific proteins, the detection of post-translational modifications, or the analysis of co-purifying proteins. As is the case for most protein purification protocols, some enzymes and proteins may require unique conditions or buffer compositions for their purification and others may be unstable or insoluble under the conditions stated. In the latter case, the protocol presented may provide a useful starting point to empirically determine the best bead-beating strategy for protein extraction and purification. We show the extraction and purification of an epitope-tagged SUMO E3 ligase, Siz1, a cell cycle regulated protein that becomes both sumoylated and phosphorylated, as well as a SUMO-targeted ubiquitin ligase subunit, Slx5

Luminosity segregation versus fractal scaling in the galaxy distribution

In this letter I present results from a correlation analysis of three galaxy redshift catalogs: the SSRS2, the CfA2 and the PSCz. I will focus on the observation that the amplitude of the two--point correlation function rises if the depth of the sample is increased. There are two competing explanations for this observation, one in terms of a fractal scaling, the other based on luminosity segregation. I will show that there is strong evidence that the observed growth is due to a luminosity dependent clustering of the galaxies.Comment: 7 pages, EPL in pres

Shape Statistics of Sloan Digital Survey superclusters

We study the supercluster shape properties of the recently compiled SDSS cluster catalog using an approach based on differential geometry. We detect superclusters by applying the percolation algorithm to observed cluster populations, extended out to $z_{\rm max}\leq 0.23$ in order to avoid selection biases. We utilize a set of shapefinders in order to study the morphological features of superclusters with $\geq 8$ cluster members and find that filamentary morphology is the dominant supercluster shape feature, in agreement with previous studies.Comment: 6 pages, 6 figures, accepted for publication in the MNRAS, (minor changes

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

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

On the abundance of collapsed objects

The redshift dependence of the abundance of collapsed objects places strong constraints on cosmological models of structure formation. We apply a recently proposed model describing the anisotropic collapse of inhomogeneous spatial domains. Compared with the spherical top-hat model, this generic model leads to significantly more collapsed objects at high redshifts: at redshift one and on the scale of rich clusters a factor of 65. Furthermore, for a fixed normalization of the initial fluctuation spectrum (\sigma_8=1), we predict four times as much presently collapsed objects on the mass-scale of rich clusters within the standard CDM cosmogony, compared to the spherical collapse.Comment: 4 pages, 2 figures, revised version accepted in the ApJ

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

Viscosity and Surface Tension of Benzene at Saturation Conditions from Surface Light Scattering

In the present study, the liquid viscosity and surface tension of benzene was determined at saturation conditions from surface light scattering (SLS) experiments between (283 and 393) K. Based on the application of the hydrodynamic theory for surface fluctuations at the vapor–liquid phase boundary which was successfully validated by the measurements, a simultaneous determination of liquid viscosity and surface tension with average relative expanded uncertainties (k = 2) of (1.0 and 0.8)% was achieved. Agreement between the measurement data and reference values available in the literature was found for the viscosity and in general also for the surface tension, where benzene constitutes a recommended reference material of relatively moderate surface tension values. All these findings demonstrate for a repeated time that SLS is a suitable method for the investigation of fluids including reference fluids such as benzene, which enables a sound representation of its surface tension, presumably as a result of a rather random molecular orientation at the surface. Overall, the experimental results from this work could contribute to an improved data situation for benzene, in particular with respect to providing viscosities and surface tensions at true saturation conditions