04456nam 22007215 450 991025461350332120200702214059.03-319-24877-410.1007/978-3-319-24877-6(CKB)3710000000541926(SSID)ssj0001599551(PQKBManifestationID)16306140(PQKBTitleCode)TC0001599551(PQKBWorkID)14892273(PQKB)11002393(DE-He213)978-3-319-24877-6(MiAaPQ)EBC6288134(MiAaPQ)EBC5592552(Au-PeEL)EBL5592552(OCoLC)1066177239(PPN)190885807(EXLCZ)99371000000054192620151221d2016 u| 0engurnn|008mamaatxtccrMarkov Chain Aggregation for Agent-Based Models /by Sven Banisch1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XIV, 195 p. 83 illus., 18 illus. in color.) Understanding Complex Systems,1860-0832Bibliographic Level Mode of Issuance: Monograph3-319-24875-8 Introduction -- Background and Concepts -- Agent-based Models as Markov Chains -- The Voter Model with Homogeneous Mixing -- From Network Symmetries to Markov Projections -- Application to the Contrarian Voter Model -- Information-Theoretic Measures for the Non-Markovian Case -- Overlapping Versus Non-Overlapping Generations -- Aggretion and Emergence: A Synthesis -- Conclusion.This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting “micro-chain” including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the updating rule and governs the dynamics at a Markovian level, plays a crucial part in the analysis of “voter-like” models used in population genetics, evolutionary game theory and social dynamics. The book demonstrates that the problem of aggregation in ABMs - and the lumpability conditions in particular - can be embedded into a more general framework that employs information theory in order to identify different levels and relevant scales in complex dynamical systems.Understanding Complex Systems,1860-0832Statistical physicsSystem theoryPhysicsComputational complexityApplications of Nonlinear Dynamics and Chaos Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P33020Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/M13090Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Complexityhttps://scigraph.springernature.com/ontologies/product-market-codes/T11022Statistical physics.System theory.Physics.Computational complexity.Applications of Nonlinear Dynamics and Chaos Theory.Complex Systems.Mathematical Methods in Physics.Complexity.519.233Banisch Svenauthttp://id.loc.gov/vocabulary/relators/aut805579MiAaPQMiAaPQMiAaPQBOOK9910254613503321Markov Chain Aggregation for Agent-Based Models1808125UNINA