Properties of a random attachment growing network

In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects 'k' possible partners from the existing network and joins them with probability delta by undirected edges. The 'activity' of the node ends here; it will get new partners only if it is selected by a newcomer. The model produces an infinite-order phase transition when a giant component appears at a specific value of delta, which depends on k. The average component size is discontinuous at the transition. In contrast, the network behaves significantly different for k=1. There is no giant component formed for any delta and thus in this sense there is no phase transition. However, the average component size diverges for delta greater or equal than one half.Comment: LaTeX, 19 pages, 6 figures. Discussion section, comments, a new figure and a new reference are added. Equations simplifie

The SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: final Emission Line Galaxy Target Selection

International audienceWe describe the algorithm used to select the emission line galaxy (ELG) sample at z ∼ 0.85 for the extended Baryon Oscillation Spectroscopic Survey of the Sloan Digital Sky Survey IV, using photometric data from the DECam Legacy Survey. Our selection is based on a selection box in the g − r versus r − z colour–colour space and a cut on the g-band magnitude, to favour galaxies in the desired redshift range with strong $$[{{\rm O}\,\small {II}}]$$ emission. It provides a target density of 200 deg^−2 on the North Galactic Cap and of 240 deg^−2 on the South Galactic Cap (SGC), where we use a larger selection box because of deeper imaging. We demonstrate that this selection passes the extended Baryon Oscillation Spectroscopic Survey requirements in terms of homogeneity. About 50 000 ELGs have been observed since the observations have started in 2016, September. These roughly match the expected redshift distribution, though the measured efficiency is slightly lower than expected. The efficiency can be increased by enlarging the redshift range and with incoming pipeline improvement. The cosmological forecast based on these first data predict $$\sigma _{D_V}/D_V = 0.023$$, in agreement with previous forecasts. Lastly, we present the stellar population properties of the ELG SGC sample. Once observations are completed, this sample will be suited to provide a cosmological analysis at z ∼ 0.85, and will pave the way for the next decade of massive spectroscopic cosmological surveys, which heavily rely on ELGs. The target catalogue over the SGC will be released along with DR14