The nature of assembly bias - III. Observational properties

We analyse galaxies in groups in the Sloan Digital Sky Survey (SDSS) and find a weak but significant assembly-type bias, where old central galaxies have a higher clustering amplitude (61 $\pm$ 9 per cent) at scales > 1 Mpc than young central galaxies of equal host halo mass ($M_{h} \sim 10^{11.8} h^{-1}$ $M_{\odot}$). The observational sample is volume-limited out to z=0.1 with $M_r -$ 5 log$(h) \le -19.6$. We construct a mock catalogue of galaxies that shows a similar signal of assembly bias (46 $\pm$ 9 per cent) at the same halo mass. We then adapt the model presented by Lacerna & Padilla (Paper I) to redefine the overdensity peak height, which traces the assembly bias such that galaxies in equal density peaks show the same clustering regardless of their stellar age, but this time using observational features such as a flux limit. The proxy for peak height, which is proposed as a better alternative than the virial mass, consists in the total mass given by the mass of neighbour host haloes in cylinders centred at each central galaxy. The radius of the cylinder is parametrized as a function of stellar age and virial mass. The best-fitting set of parameters that make the assembly bias signal lower than 5$-$15 per cent for both SDSS and mock central galaxies are similar. The idea behind the parametrization is not to minimize the bias, but it is to use this method to understand the physical features that produce the assembly bias effect. Even though the tracers of the density field used here differ significantly from those used in paper I, our analysis of the simulated catalogue indicates that the different tracers produce correlated proxies, and therefore the reason behind this assembly bias is the crowding of peaks in both simulations and the SDSS.Comment: 12 pages, 11 figures. Accepted for publication in MNRA

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

The Spine of the Cosmic Web

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version: http://skysrv.pha.jhu.edu/~miguel/SpineWeb