Estimating Third-Order Moments for an Absorber Catalog

Thanks to the recent availability of large surveys, there has been renewed interest in third-order correlation statistics. Measures of third-order clustering are sensitive to the structure of filaments and voids in the universe and are useful for studying large-scale structure. Thus, statistics of these third-order measures can be used to test and constrain parameters in cosmological models. Third-order measures such as the three-point correlation function are now commonly estimated for galaxy surveys. Studies of third-order clustering of absorption systems will complement these analyses. We define a statistic, which we denote K, that measures third-order clustering of a data set of point observations and focus on estimating this statistic for an absorber catalog. The statistic K can be considered a third-order version of the second-order Ripley K-function and allows one to study the abundance of various configurations of point triplets. In particular, configurations consisting of point triplets that lie close to a straight line can be examined. Studying third-order clustering of absorbers requires consideration of the absorbers as a three-dimensional process, observed on QSO lines of sight that extend radially in three-dimensional space from Earth. Since most of this three-dimensional space is not probed by the lines of sight, edge corrections become important. We use an analytical form of edge correction weights and construct an estimator of the statistic K for use with an absorber catalog. We show that with these weights, ratio-unbiased estimates of K can be obtained. Results from a simulation study also verify unbiasedness and provide information on the decrease of standard errors with increasing number of lines of sight.Comment: 19 pages, 4 figure

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

The SUMO-targeted ubiquitin ligase subunit Slx5 resides in nuclear foci and at sites of DNA breaks

The Slx5/Slx8 protein complex, a heterodimeric SUMO-targeted ubiquitin ligase, plays an important role in genomic integrity. Slx5/Slx8 is believed to interact with sumoylated proteins that reside in the nuclei of budding yeast cells. In this complex, Slx5, owing to at least two SUMO interacting motifs (SIMs), has been proposed to be the targeting subunit of the Slx8 ubiquitin ligase. However, little is known about the exact subnuclear localization and targets of Slx5/Slx8. In this study we show that Slx5, but not Slx8, forms prominent nuclear foci. The formation of these foci depends on SUMO and a SIM in Slx5. Therefore, we investigated the subnuclear localization and potential chromatin association of Slx5. Using co-localization studies in live cells and fixed chromatin, we were able to localize Slx5 to DNA damage induced foci of Rad52 and Rad9, two proteins involved in the cellular response to DNA damage. Subsequent chromatin immunoprecipitation (ChIP) studies revealed that Slx5 is associated with HO endonuclease induced chromosome breaks. Surprisingly, real-time PCR analysis of Slx5 ChIPs revealed that the level of Slx5 at HO breaks in an slx8 deletion background is reduced about 4-fold. These results indicate that the DNA-damage targeting of Slx5/Slx8 depends on formation of the heterodimer and that this occurs at a subset of nuclear foci also containing DNA damage repair and checkpoint factors

Reconstructing the shape of the correlation function

We develop an estimator for the correlation function which, in the ensemble average, returns the shape of the correlation function, even for signals that have significant correlations on the scale of the survey region. Our estimator is general and works in any number of dimensions. We develop versions of the estimator for both diffuse and discrete signals. As an application, we examine Monte Carlo simulations of X-ray background measurements. These include a realistic, spatially-inhomogeneous population of spurious detector events. We discuss applying the estimator to the averaging of correlation functions evaluated on several small fields, and to other cosmological applications.Comment: 10 pages, 5 figures, submitted to ApJS. Methods and results unchanged but text is expanded and significantly reordered in response to refere

Biased-estimations of the Variance and Skewness

Nonlinear combinations of direct observables are often used to estimate quantities of theoretical interest. Without sufficient caution, this could lead to biased estimations. An example of great interest is the skewness $S_3$ of the galaxy distribution, defined as the ratio of the third moment \xibar_3 and the variance squared \xibar_2^2. Suppose one is given unbiased estimators for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does not necessarily result in an unbiased estimator of $S_3$. Exactly such an estimation-bias affects most existing measurements of $S_3$. Furthermore, common estimators for \xibar_3 and \xibar_2 suffer also from this kind of estimation-bias themselves: for \xibar_2, it is equivalent to what is commonly known as the integral constraint. We present a unifying treatment allowing all these estimation-biases to be calculated analytically. They are in general negative, and decrease in significance as the survey volume increases, for a given smoothing scale. We present a re-analysis of some existing measurements of the variance and skewness and show that most of the well-known systematic discrepancies between surveys with similar selection criteria, but different sizes, can be attributed to the volume-dependent estimation-biases. This affects the inference of the galaxy-bias(es) from these surveys. Our methodology can be adapted to measurements of analogous quantities in quasar spectra and weak-lensing maps. We suggest methods to reduce the above estimation-biases, and point out other examples in LSS studies which might suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap

A study of white etching crack formation by compression-torsion experiments

In this study, an attempt was made to recreate the bearing damage phenomenon “White Etching Cracks” with a simplified testing setup. Rolling contact fatigue conditions were simulated with in-phase and out-ofphase cyclic compression-torsion experiments on 100Cr6 steel specimens. The results are compared in terms of microstructural change. Focused Ion Beam and metallographic analysis reveal that a fine-grained, white etching zone formed in the vicinity of the fatigue cracks of specimens tested with the in-phase load pattern. In contrast, no such structures were found after testing the out-of-phase load pattern. The properties of the white etching zone are characterised in more detail and compared with White Etching Cracks. KEYWORDS. White Etching Cracks; Multiaxial fatigue; Bearing steel

Pathogenic mutations in NUBPL affect complex I activity and cold tolerance in the yeast model Yarrowia lipolytica

Complex I deficiency is a common cause of mitochondrial disease, resulting from mutations in genes encoding structural subunits, assembly factors or defects in mitochondrial gene expression. Advances in genetic diagnostics and sequencing have led to identification of several variants in NUBPL (nucleotide binding protein-like), encoding an assembly factor of complex I, which are potentially pathogenic. To help assign pathogenicity and learn more about the function of NUBPL, amino acid substitutions were recreated in the homologous Ind1 protein of the yeast model Yarrowia lipolytica. Leu102Pro destabilized the Ind1 protein, leading to a null-mutant phenotype. Asp103Tyr, Leu191Phe and Gly285Cys affected complex I assembly to varying degrees, whereas Gly136Asp substitution in Ind1 did not impact on complex I levels nor dNADH:ubiquinone activity. Blue-native polyacrylamide gel electrophoresis and immunolabelling of the structural subunits NUBM and NUCM revealed that all Ind1 variants accumulated a Q module intermediate of complex I. In the Ind1 Asp103Tyr variant, the matrix arm intermediate was virtually absent, indicating a dominant effect. Dysfunction of Ind1, but not absence of complex I, rendered Y. lipolytica sensitive to cold. The Ind1 Gly285Cys variant was able to support complex I assembly at 28°C, but not at 10°C. Our results indicate that Ind1 is required for progression of assembly from the Q module to the full matrix arm. Cold sensitivity could be developed as a phenotype assay to demonstrate pathogenicity of NUBPL mutations and other complex I defects

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

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

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