2,447 research outputs found
Structure in the 3D Galaxy Distribution: I. Methods and Example Results
Three methods for detecting and characterizing structure in point data, such
as that generated by redshift surveys, are described: classification using
self-organizing maps, segmentation using Bayesian blocks, and density
estimation using adaptive kernels. The first two methods are new, and allow
detection and characterization of structures of arbitrary shape and at a wide
range of spatial scales. These methods should elucidate not only clusters, but
also the more distributed, wide-ranging filaments and sheets, and further allow
the possibility of detecting and characterizing an even broader class of
shapes. The methods are demonstrated and compared in application to three data
sets: a carefully selected volume-limited sample from the Sloan Digital Sky
Survey redshift data, a similarly selected sample from the Millennium
Simulation, and a set of points independently drawn from a uniform probability
distribution -- a so-called Poisson distribution. We demonstrate a few of the
many ways in which these methods elucidate large scale structure in the
distribution of galaxies in the nearby Universe.Comment: Re-posted after referee corrections along with partially re-written
introduction. 80 pages, 31 figures, ApJ in Press. For full sized figures
please download from: http://astrophysics.arc.nasa.gov/~mway/lss1.pd
Pseudolikelihood inference for Gibbsian T-tessellations ... and point processes
Recently a new class of planar tessellations, named T-tessellations, was
introduced. Splits, merges and a third local modification named flip where
shown to be sufficient for exploring the space of T-tessellations. Based on
these local transformations and by analogy with point process theory, tools
Campbell measures and a general simulation algorithm of
Metropolis-Hastings-Green type were translated for random T-tessellations.The
current report is concerned with parametric inference for Gibbs models of
T-tessellations. The estimation criterion referred to as the pseudolikelihood
is derived from Campbell measures of random T-tessellations and the
Kullback-Leibler divergence. A detailed algorithm for approximating the
pseudolikelihood maximum is provided. A simulation study seems to show that
bias and variability of the pseudolikelihood maximum decrease when the
tessellated domain grows in size.In the last part of the report, it is shown
that an analogous approach based on the Campbell measure and the KL divergence
when applied to point processes leads to the well-known pseudo-likelihood
introduced by Besag. More surprisingly, the binomial regression method recently
proposed by Baddeley and his co-authors for computing the pseudolikelihood
maximum can be derived using the same approach starting from a slight
modification of the Campbell measure
Elastic moduli of model random three-dimensional closed-cell cellular solids
Most cellular solids are random materials, while practically all theoretical
results are for periodic models. To be able to generate theoretical results for
random models, the finite element method (FEM) was used to study the elastic
properties of solids with a closed-cell cellular structure. We have computed
the density () and microstructure dependence of the Young's modulus ()
and Poisson's ratio (PR) for several different isotropic random models based on
Voronoi tessellations and level-cut Gaussian random fields. The effect of
partially open cells is also considered. The results, which are best described
by a power law (), show the influence of randomness
and isotropy on the properties of closed-cell cellular materials, and are found
to be in good agreement with experimental data.Comment: 13 pages, 13 figure
Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web
We study the topology of the Megaparsec Cosmic Web in terms of the
scale-dependent Betti numbers, which formalize the topological information
content of the cosmic mass distribution. While the Betti numbers do not fully
quantify topology, they extend the information beyond conventional cosmological
studies of topology in terms of genus and Euler characteristic. The richer
information content of Betti numbers goes along the availability of fast
algorithms to compute them.
For continuous density fields, we determine the scale-dependence of Betti
numbers by invoking the cosmologically familiar filtration of sublevel or
superlevel sets defined by density thresholds. For the discrete galaxy
distribution, however, the analysis is based on the alpha shapes of the
particles. These simplicial complexes constitute an ordered sequence of nested
subsets of the Delaunay tessellation, a filtration defined by the scale
parameter, . As they are homotopy equivalent to the sublevel sets of
the distance field, they are an excellent tool for assessing the topological
structure of a discrete point distribution. In order to develop an intuitive
understanding for the behavior of Betti numbers as a function of , and
their relation to the morphological patterns in the Cosmic Web, we first study
them within the context of simple heuristic Voronoi clustering models.
Subsequently, we address the topology of structures emerging in the standard
LCDM scenario and in cosmological scenarios with alternative dark energy
content. The evolution and scale-dependence of the Betti numbers is shown to
reflect the hierarchical evolution of the Cosmic Web and yields a promising
measure of cosmological parameters. We also discuss the expected Betti numbers
as a function of the density threshold for superlevel sets of a Gaussian random
field.Comment: 42 pages, 14 figure
Voronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe
The spatial cosmic matter distribution on scales of a few up to more than a
hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi
tessellations are a versatile and flexible mathematical model for such weblike
spatial patterns. They would be the natural asymptotic result of an evolution
in which low-density expanding void regions dictate the spatial organization of
the Megaparsec Universe, while matter assembles in high-density filamentary and
wall-like interstices between the voids. We describe the results of ongoing
investigations of a variety of aspects of cosmologically relevant spatial
distributions and statistics within the framework of Voronoi tessellations.
Particularly enticing is the finding of a profound scaling of both clustering
strength and clustering extent for the distribution of tessellation nodes,
suggestive for the clustering properties of galaxy clusters. Cellular patterns
may be the source of an intrinsic ``geometrically biased'' clustering.Comment: 10 pages, 9 figures, accepted for publication as long paper in
proceedings Fourth International Symposium on Voronoi Diagrams in Science and
Engineering (ISVD 2007), ed. C. Gold, IEEE Computer Society, July 2007. For
high-res version see
http://www.astro.rug.nl/~weygaert/tim1publication/vorwey.isvd07.pd
The oscillating behavior of the pair correlation function in galaxies
The pair correlation function (PCF) for galaxies presents typical
oscillations in the range 20-200 Mpc/h which are named baryon acoustic
oscillation (BAO). We first review and test the oscillations of the PCF when
the 2D/3D vertexes of the Poissonian Voronoi Tessellation (PVT) are considered.
We then model the behavior of the PCF at a small scale in the presence of an
auto gravitating medium having a line/plane of symmetry in 2D/3D. The analysis
of the PCF in an astrophysical context was split into two, adopting a
non-Poissonian Voronoi Tessellation (NPVT). We first analyzed the case of a 2D
cut which covers few voids and a 2D cut which covers approximately 50 voids.
The obtained PCF in the case of many voids was then discussed in comparison to
the bootstrap predictions for a PVT process and the observed PCF for an
astronomical catalog. An approximated formula which connects the averaged
radius of the cosmic voids to the first minimum of the PCF is given.Comment: 19 pages 14 figure
Statistics of cross sections of Voronoi tessellations
In this paper we investigate relationships between the volumes of cells of
three-dimensional Voronoi tessellations and the lengths and areas of sections
obtained by intersecting the tessellation with a randomly oriented plane. Here,
in order to obtain analytical results, Voronoi cells are approximated to
spheres. First, the probability density function for the lengths of the radii
of the sections is derived and it is shown that it is related to the Meijer
-function; its properties are discussed and comparisons are made with the
numerical results. Next the probability density function for the areas of cross
sections is computed and compared with the results of numerical simulations.Comment: 10 pages and 6 figure
The VOISE Algorithm: a Versatile Tool for Automatic Segmentation of Astronomical Images
The auroras on Jupiter and Saturn can be studied with a high sensitivity and
resolution by the Hubble Space Telescope (HST) ultraviolet (UV) and
far-ultraviolet (FUV) Space Telescope spectrograph (STIS) and Advanced Camera
for Surveys (ACS) instruments. We present results of automatic detection and
segmentation of Jupiter's auroral emissions as observed by HST ACS instrument
with VOronoi Image SEgmentation (VOISE). VOISE is a dynamic algorithm for
partitioning the underlying pixel grid of an image into regions according to a
prescribed homogeneity criterion. The algorithm consists of an iterative
procedure that dynamically constructs a tessellation of the image plane based
on a Voronoi Diagram, until the intensity of the underlying image within each
region is classified as homogeneous. The computed tessellations allow the
extraction of quantitative information about the auroral features such as mean
intensity, latitudinal and longitudinal extents and length scales. These
outputs thus represent a more automated and objective method of characterising
auroral emissions than manual inspection.Comment: 9 pages, 7 figures; accepted for publication in MNRA
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