LEADER 04456nam 22007215 450 001 9910254613503321 005 20200702214059.0 010 $a3-319-24877-4 024 7 $a10.1007/978-3-319-24877-6 035 $a(CKB)3710000000541926 035 $a(SSID)ssj0001599551 035 $a(PQKBManifestationID)16306140 035 $a(PQKBTitleCode)TC0001599551 035 $a(PQKBWorkID)14892273 035 $a(PQKB)11002393 035 $a(DE-He213)978-3-319-24877-6 035 $a(MiAaPQ)EBC6288134 035 $a(MiAaPQ)EBC5592552 035 $a(Au-PeEL)EBL5592552 035 $a(OCoLC)1066177239 035 $a(PPN)190885807 035 $a(EXLCZ)993710000000541926 100 $a20151221d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMarkov Chain Aggregation for Agent-Based Models /$fby Sven Banisch 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIV, 195 p. 83 illus., 18 illus. in color.) 225 1 $aUnderstanding Complex Systems,$x1860-0832 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-24875-8 327 $aIntroduction -- 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. 330 $aThis self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting ?micro-chain? including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the updating rule and governs the dynamics at a Markovian level, plays a crucial part in the analysis of ?voter-like? models used in population genetics, evolutionary game theory and social dynamics. The book demonstrates that the problem of aggregation in ABMs - and the lumpability conditions in particular - can be embedded into a more general framework that employs information theory in order to identify different levels and relevant scales in complex dynamical systems. 410 0$aUnderstanding Complex Systems,$x1860-0832 606 $aStatistical physics 606 $aSystem theory 606 $aPhysics 606 $aComputational complexity 606 $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M13090 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aComplexity$3https://scigraph.springernature.com/ontologies/product-market-codes/T11022 615 0$aStatistical physics. 615 0$aSystem theory. 615 0$aPhysics. 615 0$aComputational complexity. 615 14$aApplications of Nonlinear Dynamics and Chaos Theory. 615 24$aComplex Systems. 615 24$aMathematical Methods in Physics. 615 24$aComplexity. 676 $a519.233 700 $aBanisch$b Sven$4aut$4http://id.loc.gov/vocabulary/relators/aut$0805579 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254613503321 996 $aMarkov Chain Aggregation for Agent-Based Models$91808125 997 $aUNINA