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Volumn 12, Issue 2, 2009, Pages 131-155

A spectral method for aggregating variables in linear dynamical systems with application to cellular automata renormalization

Author keywords

Aggregated linear dynamics; Aggregated Markov chains; Aggregation of variables; Cellular automata; Coarse graining; Lumpability; Quotient processes; Renormalization; State space reduction

Indexed keywords


EID: 67649291799     PISSN: 02195259     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219525909002155     Document Type: Article
Times cited : (18)

References (46)
  • 2
    • 0024895750 scopus 로고
    • A general analysis of exact lumping in chemical kinetics
    • Li, G. and Rabitz, H., A general analysis of exact lumping in chemical kinetics, Chem. Engin. Sci. 44(6) (1989) 1413-1430.
    • (1989) Chem. Engin. Sci , vol.44 , Issue.6 , pp. 1413-1430
    • Li, G.1    Rabitz, H.2
  • 3
    • 0031372071 scopus 로고    scopus 로고
    • The effect of lumping and expanding on kinetic differential equations
    • Tomlin, A., Li, G., Rabitz, H. and Toth, J., The effect of lumping and expanding on kinetic differential equations, SIAM J. Appl. Math. 57(6) (1997) 1531-1556.
    • (1997) SIAM J. Appl. Math , vol.57 , Issue.6 , pp. 1531-1556
    • Tomlin, A.1    Li, G.2    Rabitz, H.3    Toth, J.4
  • 5
    • 21844481805 scopus 로고    scopus 로고
    • Baker, G. A., The Markov property method applied to Ising model calculations, J. Stat. Phys. 77(5-6) (1994) 955-976.
    • Baker, G. A., The Markov property method applied to Ising model calculations, J. Stat. Phys. 77(5-6) (1994) 955-976.
  • 6
    • 0030457325 scopus 로고    scopus 로고
    • Aggregation and emergence in hierarchically organized systems: Population dynamics
    • Auger, P. and Poggiale, J., Aggregation and emergence in hierarchically organized systems: Population dynamics, Acta Biotheoretica 44(3-4) (1996) 301-316.
    • (1996) Acta Biotheoretica , vol.44 , Issue.3-4 , pp. 301-316
    • Auger, P.1    Poggiale, J.2
  • 7
    • 3142632025 scopus 로고    scopus 로고
    • Aggregation of variables and system decomposition: Applications to fitness landscape analysis
    • Shpak, M., Stadler, P., Wagner, G. and Hermisson, J., Aggregation of variables and system decomposition: Applications to fitness landscape analysis, Theory Biosci. 123(1) (2004) 33-68.
    • (2004) Theory Biosci , vol.123 , Issue.1 , pp. 33-68
    • Shpak, M.1    Stadler, P.2    Wagner, G.3    Hermisson, J.4
  • 8
    • 0037391104 scopus 로고    scopus 로고
    • An application of Markov chain Monte Carlo to community ecology
    • Cobb, G. and Chen, Y., An application of Markov chain Monte Carlo to community ecology, Am. Math. Monthly 110(4) (2003) 265-288.
    • (2003) Am. Math. Monthly , vol.110 , Issue.4 , pp. 265-288
    • Cobb, G.1    Chen, Y.2
  • 9
    • 26444609094 scopus 로고    scopus 로고
    • State aggregation and population dynamics in linear systems
    • Rowe, J. E., Vose, M. and Wright, A., State aggregation and population dynamics in linear systems, Artificial Life 11(4) (2005) 473-492.
    • (2005) Artificial Life , vol.11 , Issue.4 , pp. 473-492
    • Rowe, J.E.1    Vose, M.2    Wright, A.3
  • 12
    • 0032274141 scopus 로고    scopus 로고
    • State aggregation for solving Markov decision problems an application to mobile robotics
    • Laroche, P. and Charpillet, F., State aggregation for solving Markov decision problems an application to mobile robotics, in 10th IEEE Int. Conf. Tools with Artificial Intelligence, (1998), pp. 384-391.
    • (1998) 10th IEEE Int. Conf. Tools with Artificial Intelligence , pp. 384-391
    • Laroche, P.1    Charpillet, F.2
  • 13
    • 67649299362 scopus 로고
    • Note consolidation within a Leontieff system
    • Hatanaka, M., Note consolidation within a Leontieff system, Econometrica 20(2) (1952) 60-66.
    • (1952) Econometrica , vol.20 , Issue.2 , pp. 60-66
    • Hatanaka, M.1
  • 14
    • 0001633546 scopus 로고
    • Aggregation of variables in dynamical systems
    • Simon, H. and Ando, A., Aggregation of variables in dynamical systems, Econometrica 29(2) (1961) 111-138.
    • (1961) Econometrica , vol.29 , Issue.2 , pp. 111-138
    • Simon, H.1    Ando, A.2
  • 15
    • 0029244710 scopus 로고
    • Hierarchical Markovian models: Symmetries and reduction
    • Buchholz, P., Hierarchical Markovian models: Symmetries and reduction, Perf. Eval. 22(1) (1995) 93-110.
    • (1995) Perf. Eval , vol.22 , Issue.1 , pp. 93-110
    • Buchholz, P.1
  • 17
    • 44249091170 scopus 로고    scopus 로고
    • A method for inferring hierarchical dynamics in stochastic processes
    • Görnerup, O. and Nilsson Jacobi, M., A method for inferring hierarchical dynamics in stochastic processes, Adv. Complex Syst. 11(1) (2008) 1-16.
    • (2008) Adv. Complex Syst , vol.11 , Issue.1 , pp. 1-16
    • Görnerup, O.1    Nilsson Jacobi, M.2
  • 18
    • 85036847018 scopus 로고    scopus 로고
    • A dual eigenvector condition for strong lumpa-bility of Markov chains
    • Nilsson Jacobi, M., and Görnerup, O., A dual eigenvector condition for strong lumpa-bility of Markov chains, http://arxiv.org/abs/0710.1986 (2007).
    • (2007)
    • Nilsson Jacobi, M.1    Görnerup, O.2
  • 19
    • 33344472563 scopus 로고    scopus 로고
    • Coarse-graining of cellular automata, emergence, and the predictability of complex systems
    • Israeli, N. and Goldenfeld, N., Coarse-graining of cellular automata, emergence, and the predictability of complex systems, Phys. Rev. E 73(026203) (2006) 1-17.
    • (2006) Phys. Rev. E , vol.73 , pp. 026203
    • Israeli, N.1    Goldenfeld, N.2
  • 20
    • 0000779360 scopus 로고
    • Detecting strange attractors in turbulence
    • eds. Rand, D. and Young, L. S, Springer, Berlin
    • Takens, F., Detecting strange attractors in turbulence, in Dynamical Systems and Turbulence, Warwick 1980, eds. Rand, D. and Young, L. S. (Springer, Berlin, 1981), p. 366.
    • (1981) Dynamical Systems and Turbulence, Warwick 1980 , pp. 366
    • Takens, F.1
  • 22
    • 33751278790 scopus 로고    scopus 로고
    • Sauer, T., Yorke, J. A. and Casdagli, M., Embedolgy, J. Stat. Phys. 65 (1991) 579-616.
    • Sauer, T., Yorke, J. A. and Casdagli, M., Embedolgy, J. Stat. Phys. 65 (1991) 579-616.
  • 23
    • 85036804092 scopus 로고    scopus 로고
    • Shalizi, C. and Moore, C., What is a macrostate? Subjective observations and objective dynamics, http://www.citebase.org/abstract?id=oai:arXiv.org:cond- mat/0303625 (2003).
    • Shalizi, C. and Moore, C., What is a macrostate? Subjective observations and objective dynamics, http://www.citebase.org/abstract?id=oai:arXiv.org:cond- mat/0303625 (2003).
  • 24
    • 0021409415 scopus 로고
    • Nonequilibrium Statistical Mechanics (Oxford University Press, 2001). [25] Coxson, P., Lumpability and observability of linear systems
    • Zwanzig, R., Nonequilibrium Statistical Mechanics (Oxford University Press, 2001). [25] Coxson, P., Lumpability and observability of linear systems, J. Math. Anal. Appl. 99(22) (1984) 435-446.
    • (1984) J. Math. Anal. Appl , vol.99 , Issue.22 , pp. 435-446
    • Zwanzig, R.1
  • 25
    • 0021409415 scopus 로고
    • Lumpability and observability of linear systems
    • Coxson, P., Lumpability and observability of linear systems, J. Math. Anal. Appl. 99(22) (1984) 435-446.
    • (1984) J. Math. Anal. Appl , vol.99 , Issue.22 , pp. 435-446
    • Coxson, P.1
  • 29
    • 84904778756 scopus 로고
    • Aggregation of systems described by Markov chains
    • Tsertsvadze, G. N., Aggregation of systems described by Markov chains, Autom. Remote Cont. 5 (1989) 628-636.
    • (1989) Autom. Remote Cont , vol.5 , pp. 628-636
    • Tsertsvadze, G.N.1
  • 30
    • 0020179285 scopus 로고    scopus 로고
    • Abdel-Moneim, A. and Leysieffer, F., Weak lumpability in finite Markov chains, J. Appl. Prob. 19 (1982) 685-691.
    • Abdel-Moneim, A. and Leysieffer, F., Weak lumpability in finite Markov chains, J. Appl. Prob. 19 (1982) 685-691.
  • 31
    • 0001581760 scopus 로고
    • On weak lumpability in Markov chains
    • Rubino, G. and Sericola, B., On weak lumpability in Markov chains, J. Appl. Prob. 26 (1989) 446-457.
    • (1989) J. Appl. Prob , vol.26 , pp. 446-457
    • Rubino, G.1    Sericola, B.2
  • 32
    • 0041360023 scopus 로고
    • On weak lumpability of denumerable Markov chains
    • Ledoux, C., On weak lumpability of denumerable Markov chains, Stat. Prob. Lett. 25(4) (1995) 329-339.
    • (1995) Stat. Prob. Lett , vol.25 , Issue.4 , pp. 329-339
    • Ledoux, C.1
  • 37
    • 0034370539 scopus 로고    scopus 로고
    • Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains
    • Deuflhard, P., Huisinga, W., Fischer, A. and Schiitte, Ch., Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains, Lin. Alg. Appl. 315(1-3) (2000) 39-59.
    • (2000) Lin. Alg. Appl , vol.315 , Issue.1-3 , pp. 39-59
    • Deuflhard, P.1    Huisinga, W.2    Fischer, A.3    Schiitte, C.4
  • 39
    • 0000812783 scopus 로고
    • Partitioning sparse matrices with eigenvectors of graphs
    • Pothen, A., Simon, H. and Liou, K.-P., Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal. Appl. 11(3) (1990) 430-452.
    • (1990) SIAM J. Matrix Anal. Appl , vol.11 , Issue.3 , pp. 430-452
    • Pothen, A.1    Simon, H.2    Liou, K.-P.3
  • 40
    • 33745012299 scopus 로고    scopus 로고
    • Modularity and community structure in networks
    • Newman, M., Modularity and community structure in networks, Proc. Natl. Acad. Sci. 103(23) (2006) 8577-8582.
    • (2006) Proc. Natl. Acad. Sci , vol.103 , Issue.23 , pp. 8577-8582
    • Newman, M.1
  • 42
    • 0020495993 scopus 로고
    • Universality and complexity in cellular automata
    • Wolfram, S., Universality and complexity in cellular automata, Physica, D 10 (1984) 1-35.
    • (1984) Physica, D , vol.10 , pp. 1-35
    • Wolfram, S.1
  • 43
    • 8744267587 scopus 로고    scopus 로고
    • Universality in elementary cellular automata
    • Cook, M., Universality in elementary cellular automata, Complex Syst. 5(1) (2004) 1-40.
    • (2004) Complex Syst , vol.5 , Issue.1 , pp. 1-40
    • Cook, M.1
  • 44
    • 21344495486 scopus 로고
    • Renormalization group for Markov chains and application to metasta-bility
    • Scoppola, E., Renormalization group for Markov chains and application to metasta-bility, J. Stat. Phys. 73(1-2), 1993.
    • (1993) J. Stat. Phys , vol.73 , Issue.1-2
    • Scoppola, E.1
  • 45
    • 0003609775 scopus 로고    scopus 로고
    • An Introduction to Chaos in Nonequilibrium Statistical Mechanics
    • Cambridge, Cambridge University press
    • Dorfman, J. R., An Introduction to Chaos in Nonequilibrium Statistical Mechanics, Cambridge Lecture Notes in Physics (Cambridge University press, 1999).
    • (1999) Lecture Notes in Physics
    • Dorfman, J.R.1
  • 46
    • 1542352856 scopus 로고
    • Approximate eigenfunctions of the liouville operator in classical many-body systems
    • Zwanzig, R., Approximate eigenfunctions of the liouville operator in classical many-body systems, Phys. Rev. 140 (1966) 170-177.
    • (1966) Phys. Rev , vol.140 , pp. 170-177
    • Zwanzig, R.1


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