The Ellipticity and Orientation of Clusters of Galaxies from N-Body Experiments

In this study we use simulations of 128$^3$ particles to study the ellipticity and orientation of clusters of galaxies in N-body simulations of differing power-law initial spectra (P(k) \propto k^n ,n = +1, 0, -1, -2$), and density parameters ($\Omega_0 = 0.2$to 1.0). Furthermore, unlike most theoretical studies we mimic most observers by removing all particles which lie at distances greater than 2 1/h Mpc from the cluster center of mass. We computed the axial ratio and the principal axes using the inertia tensor of each cluster. The mean ellipticity of clusters increases strongly with increasing$n$. We also find that clusters tend to become more spherical at smaller radii. We compared the orientation of a cluster to the orientation of neighboring clusters as a function of distance (correlation). In addition, we considered whether a cluster's major axis tends to lie along the line connecting it to a neighboring cluster, as a function of distance (alignment). Both alignments and correlations were computed in three dimensions and in projection to mimic observational surveys. Our results show that significant alignments exist for all spectra at small separations ($D < 15 h^{-1}$Mpc) but drops off at larger distance in a strongly$n-$dependent way.Comment: 22 pages, requires aaspp4.sty, flushrt.sty, and epsf.sty Revised manuscript, accepted for publication in Ap

Correspondence matching with modal clusters

The modal correspondence method of Shapiro and Brady aims to match point-sets by comparing the eigenvectors of a pairwise point proximity matrix. Although elegant by means of its matrix representation, the method is notoriously susceptible to differences in the relational structure of the point-sets under consideration. In this paper, we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. To do this, we place the modal matching problem in a probabilistic setting in which the correspondences between pairwise clusters can be used to constrain the individual point correspondences. We demonstrate the utility of the method on a number of synthetic and real-world point-pattern matching problems

Feature Trajectory Dynamic Time Warping for Clustering of Speech Segments

Dynamic time warping (DTW) can be used to compute the similarity between two sequences of generally differing length. We propose a modification to DTW that performs individual and independent pairwise alignment of feature trajectories. The modified technique, termed feature trajectory dynamic time warping (FTDTW), is applied as a similarity measure in the agglomerative hierarchical clustering of speech segments. Experiments using MFCC and PLP parametrisations extracted from TIMIT and from the Spoken Arabic Digit Dataset (SADD) show consistent and statistically significant improvements in the quality of the resulting clusters in terms of F-measure and normalised mutual information (NMI).Comment: 10 page

HST, radio and infrared observations of 28 3CR radio galaxies at redshift z ~ 1: I. Old stellar populations in central cluster galaxies

Hubble Space Telescope images of 3CR radio galaxies at redshifts 0.6 < z < 1.8 have shown a remarkable variety of structures, generally aligned along the radio axis, indicating that the radio source strongly influences the optical appearance of these galaxies. In this paper we investigate the host galaxies underlying this aligned emission, combining the HST data with ground-based infrared images. An investigation of the spectral energy distributions of the galaxies shows that the contribution of the aligned blue component to the K--band light is generally small (about 10%). The radial intensity profiles of the galaxies are well matched at radii <~ 35 kpc by de Vaucouleurs' law, demonstrating that the K--band light is dominated by that of an elliptical galaxy. There is no evidence for a nuclear point source, in addition to the de Vaucouleurs profile, with a contribution >~15% of the total K--band flux density, except in two cases, 3C22 and 3C41. Large characteristic radii are derived, indicating that the 3CR galaxies must be highly evolved dynamically, even at a redshift of one. At radii > 35 kpc, a combined galaxy profile clearly shows an excess of emission reminiscent of cD--type halos. This supports other independent evidence for the hypothesis that the distant 3CR galaxies lie in moderately rich (proto--)clusters. Since the nearby FR II galaxies in the 3CR catalogue lie in more diffuse environments and do not possess cD halos, the galactic environments of the 3CR galaxies must change with redshift. The K-z relation of the 3CR galaxies cannot, therefore, be interpreted using a standard `closed-box, passive stellar evolution' model. We offer a new interpretation, and compare the model with the K-z relations of lower power radio galaxies and brightest cluster galaxies. (abridged)Comment: 21 pages including 13 figures, LaTeX. To appear in MNRA