Efficient method for estimating the number of communities in a network

While there exist a wide range of effective methods for community detection in networks, most of them require one to know in advance how many communities one is looking for. Here we present a method for estimating the number of communities in a network using a combination of Bayesian inference with a novel prior and an efficient Monte Carlo sampling scheme. We test the method extensively on both real and computer-generated networks, showing that it performs accurately and consistently, even in cases where groups are widely varying in size or structure.Comment: 13 pages, 4 figure

Signatures from a merging galaxy cluster and its AGN population : LOFAR observations of Abell 1682

Reproduced with permission from Astronomy & Astrophysics. © 2019 ESOWe present LOFAR data from 110-180 MHz of the merging galaxy cluster Abell 1682, alongside archival optical, radio, and X-ray data. Our images of 6 arcsec in resolution at low frequencies reveal new structures associated with numerous radio galaxies in the cluster. At a resolution of 20 arcsec we see diffuse emission throughout the cluster over hundreds of kiloparsecs, indicating particle acceleration mechanisms are in play as a result of the cluster merger event and powerful active galactic nuclei. We show that a significant part of the cluster emission is from an old radio galaxy with very steep spectrum emission (having a spectral index of α < -2.5). Furthermore, we identify a new region of diffuse steep-spectrum emission (α < -1.1) as a candidate for a radio halo which is co-spatial with the centre of the cluster merger. We suggest its origin as a population of old and mildly relativistic electrons left over from radio galaxies throughout the cluster which have been re-accelerated to higher energies by shocks and turbulence induced by the cluster merger event. We also note the discovery of six new giant radio galaxies in the vicinity of Abell 1682.Peer reviewedFinal Accepted Versio