123,581 research outputs found
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
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measurements of the growth of structure and expansion rate at z=0.57 from anisotropic clustering
We analyze the anisotropic clustering of massive galaxies from the Sloan
Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (BOSS) Data
Release 9 (DR9) sample, which consists of 264,283 galaxies in the redshift
range 0.43 < z < 0.7 spanning 3,275 square degrees. Both peculiar velocities
and errors in the assumed redshift-distance relation ("Alcock-Paczynski
effect") generate correlations between clustering amplitude and orientation
with respect to the line-of-sight. Together with the sharp baryon acoustic
oscillation (BAO) standard ruler, our measurements of the broadband shape of
the monopole and quadrupole correlation functions simultaneously constrain the
comoving angular diameter distance (2190 +/- 61 Mpc) to z=0.57, the Hubble
expansion rate at z=0.57 (92.4 +/- 4.5 km/s/Mpc), and the growth rate of
structure at that same redshift (d sigma8/d ln a = 0.43 +/- 0.069). Our
analysis provides the best current direct determination of both DA and H in
galaxy clustering data using this technique. If we further assume a LCDM
expansion history, our growth constraint tightens to d sigma8/d ln a = 0.415
+/- 0.034. In combination with the cosmic microwave background, our
measurements of DA, H, and growth all separately require dark energy at z >
0.57, and when combined imply \Omega_{\Lambda} = 0.74 +/- 0.016, independent of
the Universe's evolution at z<0.57. In our companion paper (Samushia et al.
prep), we explore further cosmological implications of these observations.Comment: 19 pages, 11 figures, submitted to MNRAS, comments welcom
Clustering Time Series from Mixture Polynomial Models with Discretised Data
Clustering time series is an active research area with applications in many fields. One common feature of time series is the likely presence of outliers. These uncharacteristic data can significantly effect the quality of clusters formed. This paper evaluates a method of over-coming the detrimental effects of outliers. We describe some of the alternative approaches to clustering time series, then specify a particular class of model for experimentation with k-means clustering and a correlation based distance metric. For data derived from this class of model we demonstrate that discretising the data into a binary series of above and below the median improves the clustering when the data has outliers. More specifically, we show that firstly discretisation does not significantly effect the accuracy of the clusters when there are no outliers and secondly it significantly increases the accuracy in the presence of outliers, even when the probability of outlier is very low
Techniques for clustering gene expression data
Many clustering techniques have been proposed for the analysis of gene expression data obtained from microarray experiments. However, choice of suitable method(s) for a given experimental dataset is not straightforward. Common approaches do not translate well and fail to take account of the data profile. This review paper surveys state of the art applications which recognises these limitations and implements procedures to overcome them. It provides a framework for the evaluation of clustering in gene expression analyses. The nature of microarray data is discussed briefly. Selected examples are presented for the clustering methods considered
Socially Constrained Structural Learning for Groups Detection in Crowd
Modern crowd theories agree that collective behavior is the result of the
underlying interactions among small groups of individuals. In this work, we
propose a novel algorithm for detecting social groups in crowds by means of a
Correlation Clustering procedure on people trajectories. The affinity between
crowd members is learned through an online formulation of the Structural SVM
framework and a set of specifically designed features characterizing both their
physical and social identity, inspired by Proxemic theory, Granger causality,
DTW and Heat-maps. To adhere to sociological observations, we introduce a loss
function (G-MITRE) able to deal with the complexity of evaluating group
detection performances. We show our algorithm achieves state-of-the-art results
when relying on both ground truth trajectories and tracklets previously
extracted by available detector/tracker systems
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