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

Hyperfine structure and homogeneous broadening in Pr3+: KY(WO4)(2)

As part of a search for suitable materials for coherent quantum operations, relaxation times and hyperfine structure of the D-1(2)(1)-H-3(4)(1) transition in Pr3+:KY(WO4)(2) (0.29 at. %) at 4 K have been obtained using photon-echo and spectral hole burning techniques. The homogeneous linewidth and the effect of excitation-induced dephasing were measured using two-pulse photon-echo techniques. Linewidths of 23.4+/-1.0 and 17.6+/-0.9 kHz were obtained in the absence and presence of an external magnetic field of about 9 mT. The radiative lifetime (T-1) of the D-1(2) state was measured to be 43+/-2 mus using time-resolved laser-induced fluorescence and three-pulse photon-echo measurements. The transmission hole spectra were measured and directly yielded the quadrupole level splitting in the D-1(2) (3.77+/-0.03 and 4.58+/-0.04 MHz) and H-3(4) (17.1+/-0.1 and 33.2+/-0.3 MHz) states. The spectral hole lifetime due to population redistribution between the ground-state nuclear levels was also determined to be 70+/-10 ms. A strong dipole-dipole interaction observed in this crystal opens for potential applications in quantum computing schemes for performing quantum logic operations, but the short dephasing time makes it less useful in data storage applications

Modeling crack patterns by modified stit tessellations

Indexación: Scopus.Random planar tessellations are presented which are generated by subsequent division of their polygonal cells. The purpose is to develop parametric models for crack patterns appearing at length scales which can change by orders of magnitude in areas such as nanotechnology, materials science, soft matter, and geology. Using the STIT tessellation as a reference model and comparing with phenomena in real crack patterns, three modifications of STIT are suggested. For all these models a simulation tool, which also yields several statistics for the tessellation cells, is provided on the web. The software is freely available via a link given in the bibliography of this article. The present paper contains results of a simulation study indicating some essential features of the models. Finally, an example of a real fracture pattern is considered which is obtained using the deposition of a thin metallic film onto an elastomer material-the results of this are compared to the predictions of the model.https://www.ias-iss.org/ojs/IAS/article/view/224

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

Long-Range Autocorrelations of CpG Islands in the Human Genome

In this paper, we use a statistical estimator developed in astrophysics to study the distribution and organization of features of the human genome. Using the human reference sequence we quantify the global distribution of CpG islands (CGI) in each chromosome and demonstrate that the organization of the CGI across a chromosome is non-random, exhibits surprisingly long range correlations (10 Mb) and varies significantly among chromosomes. These correlations of CGI summarize functional properties of the genome that are not captured when considering variation in any particular separate (and local) feature. The demonstration of the proposed methods to quantify the organization of CGI in the human genome forms the basis of future studies. The most illuminating of these will assess the potential impact on phenotypic variation of inter-individual variation in the organization of the functional features of the genome within and among chromosomes, and among individuals for particular chromosomes

Design of acoustic trim based on geometric modeling and flow simulation for non-woven

In order to optimize the acoustic properties of a stacked fiber non-woven, the microstructure of the non-woven is modeled by a macroscopically homogeneous random system of straight cylinders (tubes). That is, the fibers are modeled by a spatially stationary random system of lines (Poisson line process), dilated by a sphere. Pressing the non-woven causes anisotropy. In our model, this anisotropy is described by a one parametric distribution of the direction of the fibers. In the present application, the anisotropy parameter has to be estimated from 2d reflected light microscopic images of microsections of the non-woven. After fitting the model, the flow is computed in digitized realizations of the stochastic geometric model using the lattice Boltzmann method. Based on the flow resistivity, the formulas of Delany and Bazley predict the frequency-dependent acoustic absorption of the non-woven in the impedance tube. Using the geometric model, the description of a non-woven with improved acoustic absorption properties is obtained in the following way: First, the fiber thicknesses, porosity and anisotropy of the fiber system are modified. Then the flow and acoustics simulations are performed in the new sample. These two steps are repeatedc for various sets of parameters. Finally, the set of parameters for the geometric model leading to the best acoustic absorption is chosen