tokens: ACKNOWLEDGEMENTS I thank P. Behroozi and C. Pacifici for the inspiring discussions to work on this, to B. Diemer, G. Lemson, Y. Feng for help in various steps of obtaining and analysing the data, and many others for conversations, comments, and questions, including S. Alam, M. van Daalen, N. Dalal, R. Dave, and A. Kravtsov. I also thank other participants at the Santa Barbara Galaxy-Halo connection workshop in June 2017, members of the Royal Observatory of Edinburgh, and participants at the Berkeley Center for Cosmological physics workshop and Nordita workshop in July 2017 for the opportunity to talk on this work and for their feedback and suggestions, and the Royal Observatory and Nordita for their kind hospitality. B. Diemer and C. Pacifici generously provided many helpful suggestions and criticisms of an earlier draft. I am especially grateful to M. White for innumerable discussions and suggestions, as well as encouragement. I also thank the referee for many helpful suggestions and questions. The Millennium simulation data bases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory (GAVO).
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