We look at the evolution through rewiring of the degree distribution of a network so the number edges is constant. This is exactly equivalent to the evolution of probability distributions in models of cultural transmission with drift and innovation, or models of homogeneity in genes in the presence of mutation. We show that the mean field equations in the literature are incomplete and provide the full equations. We then give an exact solution for both their long time solution and for their approach to equilibrium. Numerical results show these are excellent approximations and confirm the characteristic simple inverse power law distributions with a large scale cutoff under certain conditions. The alternative is that we reach a completely homogeneous solution. We consider how such processes may arise in practice, using a recent Minority Game study as an example.
When LLMs Play the Telephone Game: Cultural Attractors as Conceptual Tools to Evaluate LLMs in Multi-turn Settings
Inria（法国国家信息与自动化研究所）；Université de Bordeaux（波尔多大学）；MIT（麻省理工学院）；Computational Cognitive Science Lab（计算认知科学实验室）；University of California, Berkeley（加州大学伯克利分校）；Institute for Advanced Study in Toulouse（图卢兹高级研究学院）
Information and motor constraints shape melodic diversity across cultures
Center for Algorithmic；Robotized Synthesis, Institute for Basic Science, Ulsan 44919, South Korea；School of Business Administration, Ulsan National Institute of Science；Department of Molecular Life Science, Tokai University School of Medicine, Kanagawa, Japan；Department of Biomedical Engineering, Ulsan National Institute of Science；Cognitive Science Research Group, School of Electronic Engineering \& Computer Science, Queen Mary University of London, London, United Kingdom；Department of Clinical Medicine, Aarhus University, Aarhus, Denmark；Center for Soft；Living Matter, Institute for Basic Science, Ulsan 44919, South Korea；Departments of Physics；Chemistry, Ulsan National Institute of Science
