tokens: Acknowledgments WW is grateful for useful discussions of merger trees with John Helly and Yan Qu. WW also thank Azadeh Fattahi and Shi Shao about the useful information of apostle . This work was supported by the European Research Council [GA 267291] COSMIWAY and Science and Technology Facilities Council Durham Consolidated Grant [ST/F001166/1,ST/L00075X/1]. WW acknowledges a Durham Junior Research Fellowship (RF040353). The simulations for the Aquarius project were carried out at the Leibniz Computing Centre, Garching, Germany, at the Computing Centre of the Max-Planck-Society in Garching, at the Institute for Computational Cosmology in Durham and on the STELLA supercomputer of the LOFAR experiment at the University of Groningen. apostle project used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ), and also resources provided by WestGrid ( www.westgrid.ca ) and Compute Canada ( www.computecanada.ca ). The DiRAC system was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. Kavli IPMU was established by World Premier International Research Center Initiative (WPI), MEXT, Japan. This work was supported by JSPS KAKENHI Grant Number JP17K14271.
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