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

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

Extension and estimation of correlations in Cold Dark Matter models

We discuss the large scale properties of standard cold dark matter cosmological models characterizing the main features of the power-spectrum, of the two-point correlation function and of the mass variance. Both the real-space statistics have a very well defined behavior on large enough scales, where their amplitudes become smaller than unity. The correlation function, in the range 0<\xi(r)<1, is characterized by a typical length-scale r_c, at which \xi(r_c)=0, which is fixed by the physics of the early universe: beyond this scale it becomes negative, going to zero with a tail proportional to -(r^{-4}). These anti-correlations represent thus an important observational challenge to verify models in real space. The same length scale r_c characterizes the behavior of the mass variance which decays, for r>r_c, as r^{-4}, the fastest decay for any mass distribution. The length-scale r_c defines the maximum extension of (positively correlated) structures in these models. These are the features expected for the dark matter field: galaxies, which represent a biased field, however may have differences with respect to these behaviors, which we analyze. We then discuss the detectability of these real space features by considering several estimators of the two-point correlation function. By making tests on numerical simulations we emphasize the important role of finite size effects which should always be controlled for careful measurements.Comment: 18 pages, 27 figures, accepted for publication in Astronomy and Astrophysic

Power law correlations in galaxy distribution and finite volume effects from the Sloan Digital Sky Survey Data Release Four

We discuss the estimation of galaxy correlation properties in several volume limited samples, in different sky regions, obtained from the Fourth Data Release of the Sloan Digital Sky Survey. The small scale properties are characterized through the determination of the nearest neighbor probability distribution. By using a very conservative statistical analysis, in the range of scales [0.5,~30] Mpc/h we detect power-law correlations in the conditional density in redshift space, with an exponent \gamma=1.0 \pm 0.1. This behavior is stable in all different samples we considered thus it does not depend on galaxy luminosity. In the range of scales [~30,~100] Mpc/h we find evidences for systematic unaveraged fluctuations and we discuss in detail the problems induced by finite volume effects on the determination of the conditional density. We conclude that in such range of scales there is an evidence for a smaller power-law index of the conditional density. However we cannot distinguish between two possibilities: (i) that a crossover to homogeneity (corresponding to \gamma=0 in the conditional density) occurs before 100 Mpc/h, (ii) that correlations extend to scales of order 100 Mpc/h (with a smaller exponent 0 < \gamma <1). We emphasize that galaxy distributions in these samples present large fluctuations at the largest scales probed, corresponding to the presence of large scale structures extending up to the boundaries of the present survey. Finally we discuss several differences between the behavior of the conditional density in mock galaxy catalogs built from cosmological N-body simulations and real data. We discuss some theoretical implications of such a fact considering also the super-homogeneous features of primordial density fields.Comment: 13 pages, 19 figures, to be publsihed in Astronomy and Astrophysic

Large scale correlations in galaxy clustering from the Two degree Field Galaxy Redshift Survey

We study galaxy correlations from samples extracted from the 2dFGRS final release. Statistical properties are characterized by studying the nearest neighbor probability density, the conditional density and the reduced two-point correlation function. The result is that the conditional density has a power-law behavior in redshift space described by an exponent \gamma=0.8 \pm 0.2 in the interval from about 1 Mpc/h, the average distance between nearest galaxies, up to about 40 Mpc/h, corresponding to radius of the largest sphere contained in the samples. These results are consistent with other studies of the conditional density and are useful to clarify the subtle role of finite-size effects on the determination of the two-point correlation function in redshift and real spaceComment: 11 pages, 14 figures. Accepted for publication in Astronomy and Astrophysic

Detecting Baryon Acoustic Oscillations

Baryon Acoustic Oscillations are a feature imprinted in the galaxy distribution by acoustic waves traveling in the plasma of the early universe. Their detection at the expected scale in large-scale structures strongly supports current cosmological models with a nearly linear evolution from redshift approximately 1000, and the existence of dark energy. Besides, BAOs provide a standard ruler for studying cosmic expansion. In this paper we focus on methods for BAO detection using the correlation function measurement. For each method, we want to understand the tested hypothesis (the hypothesis H0 to be rejected) and the underlying assumptions. We first present wavelet methods which are mildly model-dependent and mostly sensitive to the BAO feature. Then we turn to fully model-dependent methods. We present the most often used method based on the chi^2 statistic, but we find it has limitations. In general the assumptions of the chi^2 method are not verified, and it only gives a rough estimate of the significance. The estimate can become very wrong when considering more realistic hypotheses, where the covariance matrix of the measurement depends on cosmological parameters. Instead we propose to use a new method based on two modifications: we modify the procedure for computing the significance and make it rigorous, and we modify the statistic to obtain better results in the case of varying covariance matrix. We verify with simulations that correct significances are different from the ones obtained using the classical chi^2 procedure. We also test a simple example of varying covariance matrix. In this case we find that our modified statistic outperforms the classical chi^2 statistic when both significances are correctly computed. Finally we find that taking into account variations of the covariance matrix can change both BAO detection levels and cosmological parameter constraints

The Geography of Scientific Productivity: Scaling in U.S. Computer Science

Here we extract the geographical addresses of authors in the Citeseer database of computer science papers. We show that the productivity of research centres in the United States follows a power-law regime, apart from the most productive centres for which we do not have enough data to reach definite conclusions. To investigate the spatial distribution of computer science research centres in the United States, we compute the two-point correlation function of the spatial point process and show that the observed power-laws do not disappear even when we change the physical representation from geographical space to cartogram space. Our work suggests that the effect of physical location poses a challenge to ongoing efforts to develop realistic models of scientific productivity. We propose that the introduction of a fine scale geography may lead to more sophisticated indicators of scientific output.Comment: 6 pages, 3 figures; minor change

Pathophysiology of elevated ascites fluid cholesterol in malignant ascites

The existence of marked elevations of ascitic fluid cholesterol has been observed in patients with peritoneal carcinomatosis compared to patients with cirrhosis and has been found useful in differential diagnosis. This finding could be caused by an enhanced movement of plasma lipoproteins into the peritoneal cavity. To test this hypothesis we determined the fasting concentrations of total, high density lipoprotein (HDL)- and low density lipoprotein (LDL)-cholesterol, apolipoprotein-A1 (apo-A1) and apolipoprotein-B (apo-B) in serum and ascites of 17 patients with cirrhosis and 16 patients with peritoneal carcinomatosis. The movement of proteins from plasma to ascites was calculated from the ascites/serum concentration ratios of six different sized proteins with a molecular mass ranging from 54 kDa to 971 kDa. Mean values (mg/dl) for total cholesterol (92.6 vs. 21.0), HDL-cholesterol (15.6 vs. 1.8), LDL-cholesterol (63.4 vs. 16.1), apo-A1 (50.2 vs. 13.6) and apo-B (41.2 vs. 12.9) in ascites were significantly higher in peritoneal carcinomatosis than in cirrhosis. These differences could only partially be explained by the higher serum concentrations of these parameters in peritoneal carcinomatosis, but were mainly due to a lower selectivity for the movement of plasma proteins and lipoproteins into ascites (mean ascites/serum (A/S) ratio: 0.30–0.77) in peritoneal carcinomatosis as compared to cirrhosis (mean ascites/serum ratio: 0.11–0.21). In both groups about 85% of the total cholesterol in serum and ascites consisted of HDL- and LDL-cholesterol. These findings support the hypothesis that elevations in ascitic cholesterol in peritoneal carcinomatosis compared to cirrhosis are mainly caused by the increased movement of plasma HDL and LDL into the peritoneal cavity

SUMO targeting of a stress-tolerant Ulp1 SUMO protease

SUMO proteases of the SENP/Ulp family are master regulators of both sumoylation and desumoylation and regulate SUMO homeostasis in eukaryotic cells. SUMO conjugates rapidly increase in response to cellular stress, including nutrient starvation, hypoxia, osmotic stress, DNA damage, heat shock, and other proteotoxic stressors. Nevertheless, little is known about the regulation and targeting of SUMO proteases during stress. To this end we have undertaken a detailed comparison of the SUMO-binding activity of the budding yeast protein Ulp1 (ScUlp1) and its ortholog in the thermotolerant yeast Kluyveromyces marxianus, KmUlp1. We find that the catalytic UD domains of both ScUlp1 and KmUlp1 show a high degree of sequence conservation, complement a ulp1 Delta mutant in vivo, and process a SUMO precursor in vitro. Next, to compare the SUMO-trapping features of both SUMO proteases we produced catalytically inactive recombinant fragments of the UD domains of ScUlp1 and KmUlp1, termed ScUTAG and KmUTAG respectively. Both ScUTAG and KmUTAG were able to efficiently bind a variety of purified SUMO isoforms and bound immobilized SUMO1 with nanomolar affinity. However, KmUTAG showed a greatly enhanced ability to bind SUMO and SUMO-modified proteins in the presence of oxidative, temperature and other stressors that induce protein misfolding. We also investigated whether a SUMO-interacting motif (SIM) in the UD domain of KmULP1 that is not conserved in ScUlp1 may contribute to the SUMO-binding properties of KmUTAG. In summary, our data reveal important details about how SUMO proteases target and bind their sumoylated substrates, especially under stress conditions. We also show that the robust pan-SUMO binding features of KmUTAG can be exploited to detect and study SUMO-modified proteins in cell culture systems