DOI: 10.1007/s11424-017-6117-5. Dynamical Criticality: Overview and Open Questions

Dynamical Criticality: Overview and Open Questions

10.1007/s11424-017-6117-5

Crossref journal-article

Springer Science and Business Media LLC

Journal of Systems Science and Complexity (297)

Bibliography

Roli, A., Villani, M., Filisetti, A., & Serra, R. (2017). Dynamical Criticality: Overview and Open Questions. Journal of Systems Science and Complexity, 31(3), 647â663.

Authors 4

Andrea Roli (first)
Marco Villani (additional)
Alessandro Filisetti (additional)
Roberto Serra (additional)

References 93 Referenced 63

Kauffman S A, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, Oxford, 1993. (10.1093/oso/9780195079517.001.0001) / The Origins of Order: Self-Organization and Selection in Evolution by S A Kauffman (1993)
Kauffman S A, At Home in the Universe, Oxford University Press, Oxford, 1996. / At Home in the Universe by S A Kauffman (1996)
Packard N H, Adaptation toward the edge of chaos, Dynamic Patterns in Complex Systems, 1988, 293–301. / Dynamic Patterns in Complex Systems by N H Packard (1988)
Langton C G, Computation at the edge of chaos: Phase transitions and emergent computation, Physica D, 1990, 42: 12–37. (10.1016/0167-2789(90)90064-V) / Physica D by C G Langton (1990)
Crutchfield J P and Young K, Computation at the Onset of Chaos, Complexity, Entropy, and Physics of Information, Addison Wesley, New Jersey, USA, 1990. / Computation at the Onset of Chaos, Complexity, Entropy, and Physics of Information by J P Crutchfield (1990)
Binney J J, Dowrick N J, Fisher A J, et al., The Theory of Critical Phenomena, OxfordUniversity Press, Oxford, 1992. (10.1093/oso/9780198513940.001.0001) / The Theory of Critical Phenomena by J J Binney (1992)
Solé R V, Manrubia S C, Luque B, et al., Phase transitions and complex systems: Simple, nonlinear models capture complex systems at the edge of chaos, Complexity, 1996, 1: 13–26. / nonlinear models capture complex systems at the edge of chaos, Complexity by R V Solé (1996)
Solé R V, Phase Transitions, Princeton University Press, Princeton, 2011. (10.2307/j.ctvcm4j0p) / Phase Transitions by R V Solé (2011)
Wissel C, A universal law of the characteristic return time near threshold, Oecologia, 1984, 65: 101–107. (10.1007/BF00384470) / Oecologia by C Wissel (1984)
Janke W, Johnston D A, and Kenna R, Information geometry and phase transitions, Physica A, 2004, 336: 181–186. (10.1016/j.physa.2004.01.023) / Physica A by W Janke (2004)
Wang X R, Lizier J T, and Prokopenko M, Fisher information at the edge of chaos in random boolean networks, Artificial Life, 2011, 17: 315–329. (10.1162/artl_a_00041) / Artificial Life by X R Wang (2011)
Prokopenko M, Lizier J T, Obst O, et al., Relating fisher information to order parameters, Phys. Rev. E, 2011, 84: 041116:1–11. / Phys. Rev. E by M Prokopenko (2011)
Prokopenko M, Information dynamics at the edge of chaos: Measures, examples, and principles, Proceedings of IEEE Symposium of Artificial Life — ALIFE 2013, 2013. / Proceedings of IEEE Symposium of Artificial Life — ALIFE by M Prokopenko (2013)
Bak P, Tang C, and Wiesenfeld K, Self-organized criticality: An explanation of 1/f noise, Phys. Rev. Lett., 1987, 59: 381–384. (10.1103/PhysRevLett.59.381) / Phys. Rev. Lett. by P Bak (1987)
Bak P, How Nature Works: The Science of Self-Organized Criticality, Springer-Verlag, New York, 1996. (10.1007/978-1-4757-5426-1) / How Nature Works: The Science of Self-Organized Criticality by P Bak (1996)
Jensen H J, Self-Organized Criticality, Cambridge University Press, Cambridge, 1998. (10.1017/CBO9780511622717) / Self-Organized Criticality by H J Jensen (1998)
Sornette D, Johansen A, and Dornic I, Mapping self-organized criticality onto criticality, J. Phys. I France, 1995, 5: 325–335. (10.1051/jp1:1995129) / J. Phys. I France by D Sornette (1995)
Dickman R, Mu˜noz M A, Vespignani A, et al., Paths to self-organized criticality, Brazilian Journal of Physics, 2000, 30: 27–41. (10.1590/S0103-97332000000100004) / Brazilian Journal of Physics by R Dickman (2000)
Bagnoli F, Palmerini P, and Rechtman R, Algorithmic mapping from criticality to self-organized criticality, Phys. Rev. E, 1997, 55: 3970–3976. (10.1103/PhysRevE.55.3970) / Phys. Rev. E by F Bagnoli (1997)
Luque B, Ballestreros J F, and Muro E M, Self-organized critical random boolean networks, Phys. Rev. E, 2001, 63: 051913:1–8. / Phys. Rev. E by B Luque (2001)
Strogatz S H, Nonlinear Dynamics and Chaos, Westview Press, Boulder, USA, 2001. / Nonlinear Dynamics and Chaos by S H Strogatz (2001)
Haken H, Synergetics — An Introduction, Springer-Verlag, Berlin, 1983. (10.1007/978-3-642-88338-5) / Synergetics — An Introduction by H Haken (1983)
Riauba L, Niaura G, Eicher-Lorka O, et al., Self-Organization in Nonequilibrium Systems, Wiley, New Jersey, USA, 1977. / Self-Organization in Nonequilibrium Systems by L Riauba (1977)
Nicolis G and Prigogine I, Exploring Complexity, Freeman and Company, New York, 1989. / Exploring Complexity by G Nicolis (1989)
Polani D, Foundations and formalizations of self-organization, Advances in Applied Self- Organizing Systems, Springer, 2007, 19–37. / Advances in Applied Self- Organizing Systems by D Polani (2007)
Wolfram S, Universality and complexity in cellular automata, Physica D, 1984, 10: 1–35. (10.1016/0167-2789(84)90245-8) / Physica D by S Wolfram (1984)
Cook M, Universality in elementary cellular automata, Complex Systems, 2004, 15: 1–40. (10.25088/ComplexSystems.15.1.1) / Complex Systems by M Cook (2004)
Mitchell M, Crutchfield J P, and Hraber P T, Dynamics, computation, and the “edge of chaos”: A re-examination. Complexity: Metaphors, Models, and Reality, 1994, 497–513. / Complexity: Metaphors, Models, and Reality by M Mitchell (1994)
Hordijk W, The EvCA project: A brief history, Complexity, 2013, 18: 15–19. (10.1002/cplx.21445) / Complexity by W Hordijk (2013)
Solé R V and Miramontes O, Information at the edge of chaos in fluid neural networks, Physica D, 1995, 80: 171–180. (10.1016/0167-2789(95)90075-6) / Physica D by R V Solé (1995)
Cover T M and Thomas J A, Elements of Information Theory, Wiley and Sons, New Jersey, USA, 2006. / Elements of Information Theory by T M Cover (2006)
Kauffman S A, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theor. Biol., 1969, 22: 437–467. (10.1016/0022-5193(69)90015-0) / J. Theor. Biol. by S A Kauffman (1969)
Derrida B and Pomeau Y, Random networks of automata: A simple annealed approximation, Europhys. Lett., 1986, 1: 45–49. (10.1209/0295-5075/1/2/001) / Europhys. Lett. by B Derrida (1986)
Shmulevich I and Kauffman S A, Activities and sensitivities in boolean network models, Phys. Rev. Lett., 2004, 93: 048701:1–8. / Phys. Rev. Lett. by I Shmulevich (2004)
Rämö P, Kauffman S A, Kesseli J, et al., Measures for information propagation in boolean networks, Physica D, 2006a, 227: 100–104. (10.1016/j.physd.2006.12.005) / Physica D by P Rämö (2006)
Ribeiro A S, Kauffman S A, Lloyd-Price J, et al., Mutual information in random boolean models of regulatory networks, Physical Review E, 2008, 77: 011901:1–10. / Physical Review E by A S Ribeiro (2008)
Krawitz P and Shmulevich I, Basin entropy in boolean network ensembles, Phys. Rev. Lett., 2007, 98: 158701:1–4. (10.1103/PhysRevLett.98.158701)
Galas D J, Nykter M, Carter G W, et al., Biological information as set-based complexity, IEEE Tran. on Information Theory, 2010, 56: 667–677. (10.1109/TIT.2009.2037046) / IEEE Tran. on Information Theory by D J Galas (2010)
Mäki-Marttunen T, Kesseli J, Kauffman S A, et al., Of the complexity of boolean network state trajectories, Proc. of WCSB 2011, 2011. / Proc. of WCSB by T Mäki-Marttunen (2011)
Lizier J T, The Local Information Dynamics of Distributed Computation in Complex Systems, Springer Theses Series, Springer, 2013. (10.1007/978-3-642-32952-4) / The Local Information Dynamics of Distributed Computation in Complex Systems by J T Lizier (2013)
Lizier J T, Prokopenko M, and Zomaya A Y, The information dynamics of phase transitions in random boolean networks, Proceedings of Artificial Life XI, 2008, 374–381. / Proceedings of Artificial Life XI by J T Lizier (2008)
Kinouchi O and Copelli M, Optimal dynamical range of excitable networks at criticality, Nature Physics, 2006, 2: 348–351. (10.1038/nphys289) / Nature Physics by O Kinouchi (2006)
Bertschinger N and Natschläger T, Real-time computation at the edge of chaos in recurrent neural networks, Neural Computation, 2004, 16: 1413–1436. (10.1162/089976604323057443) / Neural Computation by N Bertschinger (2004)
Legenstein R and Maass W, Edge of chaos and prediction of computational performance for neural circuit models, Neural Networks, 2007, 20: 323–334. (10.1016/j.neunet.2007.04.017) / Neural Networks by R Legenstein (2007)
Macready W G, Siapas A G, and Kauffman S A, Criticality and parallelism in combinatorial optimization, Science, 1996, 5: 56–59. (10.1126/science.271.5245.56) / Science by W G Macready (1996)
Kauffman S A and Macready W, Technological evolution and adaptive organizations, Complexity, 1995, 26: 26–43. (10.1002/cplx.6130010208) / Complexity by S A Kauffman (1995)
Roli A, Criticality and parallelism in GSAT, Electronic Notes in Discrete Mathematics, 2001, 9: 150–161. (10.1016/S1571-0653(04)00319-1) / Electronic Notes in Discrete Mathematics by A Roli (2001)
Kauffman S A, Reinventing the Sacred — A New View of Science, Reason and Religion, Basic Books, 2008. / Reinventing the Sacred — A New View of Science, Reason and Religion by S A Kauffman (2008)
Serra R, Villani M, and Semeria A, Genetic network models and statistical properties of gene expression data in knock-out experiments, J. Theor. Biol., 2004, 227: 149–157. (10.1016/j.jtbi.2003.10.018) / J. Theor. Biol. by R Serra (2004)
Serra R, Villani M, Graudenzi A, et al., Why a simple model of genetic regulatory network describes the distribution of avalanches in gene expression data, J. Theor. Biol., 2007, 246: 449–460. (10.1016/j.jtbi.2007.01.012) / J. Theor. Biol. by R Serra (2007)
Roli A, Vernocchi F, and Serra R, Continuous Network Models of Gene Expression in Knock Out Experiments: A Preliminary Study, Artificial Life and Evolutionary computation, World Scientific Publishing, 2010. / Continuous Network Models of Gene Expression in Knock Out Experiments: A Preliminary Study by A Roli (2010)
Shmulevich I, Kauffman S A, and Aldana M, Eukaryotic cells are dynamically ordered or critical but not chaotic, PNAS, 2005, 102(38): 13439–13444. (10.1073/pnas.0506771102) / PNAS by I Shmulevich (2005)
Rämö P, Kesseli J, and Yli-Harja O, Perturbation avalanches and criticality in gene regulatory networks. J. Theor. Biol., 2006, 242: 164–170. (10.1016/j.jtbi.2006.02.011) / J. Theor. Biol. by P Rämö (2006)
Nykter M, Price N D, Aldana M, et al., Gene expression dynamics in the macrophage exhibit criticality, PNAS, 2008a, 105: 1897–1900. (10.1073/pnas.0711525105) / PNAS by M Nykter (2008)
Balleza E, Alvarez-Buylla E R, Chaos A, et al., Critical dynamics in genetic regulatory networks: Examples from four kingdoms, PLoS ONE, 2008, 3: e2456:1–10. / PLoS ONE by E Balleza (2008)
Chowdhury S, Lloyd-Price J, Smolander O P, et al., Information propagation within the genetic network of Saccharomyces cerevisiae, BMC Systems Biology, 2010, 4: 1–10. (10.1186/1752-0509-4-143) / BMC Systems Biology by S Chowdhury (2010)
Di Stefano M L, Villani M, La Rocca L, et al., Dynamically critical systems and power-law distributions: Avalanches revisited, Advances in Artificial Life, Evolutionary Computation and Systems Chemistry, 2016, 29–39. (10.1007/978-3-319-32695-5_3) / Advances in Artificial Life, Evolutionary Computation and Systems Chemistry by M L Stefano Di (2016)
Lempel A and Ziv J, On the complexity of finite sequence, IEEE Trans. on Info. Theory, 1976, 22(1): 75–81. (10.1109/TIT.1976.1055501) / IEEE Trans. on Info. Theory by A Lempel (1976)
Li M, Chen X, Li X, et al., The similarity metric, IEEE Trans. on Info. Theory, 2004, 50(12): 3250–3264. (10.1109/TIT.2004.838101) / IEEE Trans. on Info. Theory by M Li (2004)
Darabos C, Giacobini M, Tomassini M, et al., Are cells really operating at the edge of chaos? Darwin Meets von Neumann, Volume 5777 of Lecture Notes in Computer Science, Springer, 2011, 281–288. / Volume 5777 of Lecture Notes in Computer Science by C Darabos (2011)
Hanel R, Pöchacker M, and Thurner S, Living on the edge of chaos: Minimally nonlinear models of genetic regulatory dynamics, Phil. Trans. R. Soc. A, 2010, 368: 5583–5596. (10.1098/rsta.2010.0267) / Phil. Trans. R. Soc. A by R Hanel (2010)
Kaneko K, Life: An Introduction to Complex Systems Biology, Springer, Berlin Heidelberg, 2006. (10.1007/978-3-540-32667-0) / Life: An Introduction to Complex Systems Biology by K Kaneko (2006)
Beggs J M, The criticality hypothesis: How local cortical networks might optimize information processing, Phil. Trans. R. Soc. A, 2008, 366: 329–343. (10.1098/rsta.2007.2092) / Phil. Trans. R. Soc. A by J M Beggs (2008)
Chialvo D R, Emergent complex neural dynamics, Nature Physics, 2010, 6: 744–750. (10.1038/nphys1803) / Nature Physics by D R Chialvo (2010)
Friedman N, Ito S, Brinkman B A W, et al., Universal critical dynamics in high resolution neuronal avalanche data, Phys. Rev. Letters, 2012, 108: 208102:1–5. / Phys. Rev. Letters by N Friedman (2012)
Tagliazucchi E and Chialvo D R, Brain complexity born out of criticality, “Physics, Computation and the Mind — Advances and Challenges at Interfaces”, AIP Conf., 2013. / “Physics, Computation and the Mind — Advances and Challenges at Interfaces”, AIP Conf. by E Tagliazucchi (2013)
Beggs J M and Timme N, Being critical of criticality in the brain, Frontiers in Physiology, 2012, 3: 163:1–14. / Frontiers in Physiology by J M Beggs (2012)
Mora T and Bialek W, Are biological systems poised at criticality? J. Stat. Phys., 2011, 144: 268–302. (10.1007/s10955-011-0229-4) / J. Stat. Phys. by T Mora (2011)
Krotov D, et al., Morphogenesis at criticality, PNAS, 2014, 111: 3683–3688. (10.1073/pnas.1324186111) / PNAS by D Krotov (2014)
Bailly F and Longo G, Extended critical situations: The physical singularity of life phenomena, J. Biol. Syst., 2008, 16: 309–336. (10.1142/S0218339008002514) / J. Biol. Syst. by F Bailly (2008)
Aldana M, Balleza E, Kauffman S A, et al., Robustness and evolvability in genetic regulatory networks, J. Theor. Bio., 2007, 245: 433–448. (10.1016/j.jtbi.2006.10.027) / J. Theor. Bio. by M Aldana (2007)
Torres-Sosa C, Huang S, and Aldana M, Criticality is an emergent property of genetic networks that exhibit evolvability, PLOS Computational Biology, 2012, 8: 1–18. (10.1371/journal.pcbi.1002669) / PLOS Computational Biology by C Torres-Sosa (2012)
Nykter M, Price N D, Larjo A, et al., Critical networks exhibit maximal information diversity in structure-dynamics relationships, Phys. Rev. Lett., 2008b, 100: 058702:1–4. / Phys. Rev. Lett. by M Nykter (2008)
Roli A, Benedettini S, Serra R, et al., Analysis of attractor distances in random boolean networks, Neural Nets — WIRN10, 2011. / Neural Nets — WIRN by A Roli (2011)
Kauffman S A and Smith R G, Adaptive automata based on darwinian selection, Physica D, 1986, 22: 68–82. (10.1016/0167-2789(86)90234-4) / Physica D by S A Kauffman (1986)
Benedettini S, Villani M, Roli A, et al., Dynamical regimes and learning properties of evolved boolean networks, Neurocomputing, 2013, 99: 111–123. (10.1016/j.neucom.2012.05.023) / Neurocomputing by S Benedettini (2013)
Kauffman S A, Antichaos and Adaptation, Scientific American, August 1991, 1991. / Antichaos and Adaptation by S A Kauffman (1991)
Kauffman S A and Johnsen S, Coevolution at the edge of chaos: Coupled fitness landscapes, poised states, and coevolutionary avalanches, J. Theor. Biol., 1991, 149: 467–505. (10.1016/S0022-5193(05)80094-3) / poised states, and coevolutionary avalanches, J. Theor. Biol. by S A Kauffman (1991)
Christensen K, Donangelo R, Koiller B, et al. Evolution of random networks, Physical Rev. Lett., 1998, 81: 2380–2383. (10.1103/PhysRevLett.81.2380) / Physical Rev. Lett. by K Christensen (1998)
Bak P and Sneppen K, Punctuated equilibrium and criticality in a simple model of evolution, Phys. Rev. Lett., 1993, 71: 4083–4086. (10.1103/PhysRevLett.71.4083) / Phys. Rev. Lett. by P Bak (1993)
Bornholdt S and Rohlf T, Topological evolution of dynamical networks: Global criticality from local dynamics, Phys. Rev. Lett., 2000, 84: 6114–6117. (10.1103/PhysRevLett.84.6114) / Phys. Rev. Lett. by S Bornholdt (2000)
Liu M and Bassler K E, Emergent criticality from coevolution in random boolean networks, Physical Review E, 2006, 74: 041910:1–5. / Physical Review E by M Liu (2006)
Goudarzi A, Teuscher C, Gulbahce N, et al., Emergent criticality through adaptive information processing in boolean networks, Phys. Rev. Lett., 2012, 108: 128702:1–5. / Phys. Rev. Lett. by A Goudarzi (2012)
Hidalgo J, Grilli J, Suweis S, et al., Information-based fitness and the emergence of criticality in living systems, PNAS, 2014, 111: 10095–10100. (10.1073/pnas.1319166111) / PNAS by J Hidalgo (2014)
Campioli D, Villani M, Poli I, et al., Dynamical stability in random boolean networks, Neural nets WIRN11, Volume 234 of Frontiers in Artificial Intelligence and Applications, IOS Press, 2011. / Neural nets WIRN11, Volume 234 of Frontiers in Artificial Intelligence and Applications by D Campioli (2011)
Villani M, Campioli D, Damiani C, et al., Dynamical regimes in non-ergodic random boolean networks, Natural Computing, 2017, 353–363. / Natural Computing by M Villani (2017)
Sperati V, Trianni V, and Nolfi S, Evolving coordinated group behaviour through maximization of mean mutual information, Swarm Intelligence Journal, 2008, 2: 73–95. (10.1007/s11721-008-0017-1) / Swarm Intelligence Journal by V Sperati (2008)
Edlund J A, Chaumont N, Hintze A, et al., Integrated information increases with fitness in the evolution of animats, PLOS Comp. Biol., 2011, 7: e1002236:1–13. / PLOS Comp. Biol. by J A Edlund (2011)
Joshi N J, Tononi G, and Koch C, The minimal complexity of adapting agents increases with fitness, PLOS Comp. Biol., 2013, 9: e1003111:1–10. / PLOS Comp. Biol. by N J Joshi (2013)
Roli A, Benedettini S, Birattari M, et al., Robustness, evolvability and complexity in Boolean network robots, Proceedings of ECCS2011 — European Conference on Complex Systems, 2011a. / Proceedings of ECCS2011 — European Conference on Complex Systems by A Roli (2011)
Villani M, Roli A, Filisetti A, et al., The search for candidate relevant subsets of variables in complex systems, Artificial life, 2015, 412–431. / Artificial life by M Villani (2015)
Filisetti A, Villani M, Roli A, et al., Exploring the organisation of complex systems through the dynamical interactions among their relevant subsets, Proceedings of the European Conference on Artificial Life 2015 — ECAL2015, 2015, 286–293. / Proceedings of the European Conference on Artificial Life by A Filisetti (2015)
Villani M, Carra P, Roli A, et al., On the robustness of the detection of relevant sets in complex dynamical systems, Advances in Artificial Life, Evolutionary Computation and Systems Chemistry, Springer, 2016, 15–28. (10.1007/978-3-319-32695-5_2) / Advances in Artificial Life, Evolutionary Computation and Systems Chemistry by M Villani (2016)

Dates

Type	When
Created	7 years, 9 months ago (Nov. 20, 2017, 7:47 p.m.)
Deposited	2 months ago (June 27, 2025, 1:21 a.m.)
Indexed	2 months ago (June 27, 2025, 1:40 a.m.)
Issued	7 years, 9 months ago (Nov. 17, 2017)
Published	7 years, 9 months ago (Nov. 17, 2017)
Published Online	7 years, 9 months ago (Nov. 17, 2017)
Published Print	7 years, 2 months ago (June 1, 2018)

Funders 0

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BibTeX

@article{Roli_2017, title={Dynamical Criticality: Overview and Open Questions}, volume={31}, ISSN={1559-7067}, url={http://dx.doi.org/10.1007/s11424-017-6117-5}, DOI={10.1007/s11424-017-6117-5}, number={3}, journal={Journal of Systems Science and Complexity}, publisher={Springer Science and Business Media LLC}, author={Roli, Andrea and Villani, Marco and Filisetti, Alessandro and Serra, Roberto}, year={2017}, month=nov, pages={647–663} }

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      "doi-asserted-by": "publisher",
      "first-page": "101",
      "DOI": "10.1007/BF00384470",
      "volume": "65",
      "author": "C Wissel",
      "year": "1984",
      "unstructured": "Wissel C, A universal law of the characteristic return time near threshold, Oecologia, 1984, 65: 101\u2013107.",
      "journal-title": "Oecologia"
    },
    {
      "key": "6117_CR10",
      "doi-asserted-by": "publisher",
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      "year": "2004",
      "unstructured": "Janke W, Johnston D A, and Kenna R, Information geometry and phase transitions, Physica A, 2004, 336: 181\u2013186.",
      "journal-title": "Physica A"
    },
    {
      "key": "6117_CR11",
      "doi-asserted-by": "publisher",
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      "author": "X R Wang",
      "year": "2011",
      "unstructured": "Wang X R, Lizier J T, and Prokopenko M, Fisher information at the edge of chaos in random boolean networks, Artificial Life, 2011, 17: 315\u2013329.",
      "journal-title": "Artificial Life"
    },
    {
      "issue": "041116",
      "key": "6117_CR12",
      "first-page": "1",
      "volume": "84",
      "author": "M Prokopenko",
      "year": "2011",
      "unstructured": "Prokopenko M, Lizier J T, Obst O, et al., Relating fisher information to order parameters, Phys. Rev. E, 2011, 84: 041116:1\u201311.",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "6117_CR13",
      "volume-title": "Proceedings of IEEE Symposium of Artificial Life \u2014 ALIFE",
      "author": "M Prokopenko",
      "year": "2013",
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      "key": "6117_CR14",
      "doi-asserted-by": "publisher",
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      "DOI": "10.1103/PhysRevLett.59.381",
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      "author": "P Bak",
      "year": "1987",
      "unstructured": "Bak P, Tang C, and Wiesenfeld K, Self-organized criticality: An explanation of 1/f noise, Phys. Rev. Lett., 1987, 59: 381\u2013384.",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6117_CR15",
      "doi-asserted-by": "publisher",
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      "volume-title": "How Nature Works: The Science of Self-Organized Criticality",
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      "year": "1996",
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    {
      "key": "6117_CR16",
      "doi-asserted-by": "publisher",
      "DOI": "10.1017/CBO9780511622717",
      "volume-title": "Self-Organized Criticality",
      "author": "H J Jensen",
      "year": "1998",
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    },
    {
      "key": "6117_CR17",
      "doi-asserted-by": "publisher",
      "first-page": "325",
      "DOI": "10.1051/jp1:1995129",
      "volume": "5",
      "author": "D Sornette",
      "year": "1995",
      "unstructured": "Sornette D, Johansen A, and Dornic I, Mapping self-organized criticality onto criticality, J. Phys. I France, 1995, 5: 325\u2013335.",
      "journal-title": "J. Phys. I France"
    },
    {
      "key": "6117_CR18",
      "doi-asserted-by": "publisher",
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      "DOI": "10.1590/S0103-97332000000100004",
      "volume": "30",
      "author": "R Dickman",
      "year": "2000",
      "unstructured": "Dickman R, Mu\u02dcnoz M A, Vespignani A, et al., Paths to self-organized criticality, Brazilian Journal of Physics, 2000, 30: 27\u201341.",
      "journal-title": "Brazilian Journal of Physics"
    },
    {
      "key": "6117_CR19",
      "doi-asserted-by": "publisher",
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      "volume": "55",
      "author": "F Bagnoli",
      "year": "1997",
      "unstructured": "Bagnoli F, Palmerini P, and Rechtman R, Algorithmic mapping from criticality to self-organized criticality, Phys. Rev. E, 1997, 55: 3970\u20133976.",
      "journal-title": "Phys. Rev. E"
    },
    {
      "issue": "051913",
      "key": "6117_CR20",
      "first-page": "1",
      "volume": "63",
      "author": "B Luque",
      "year": "2001",
      "unstructured": "Luque B, Ballestreros J F, and Muro E M, Self-organized critical random boolean networks, Phys. Rev. E, 2001, 63: 051913:1\u20138.",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "6117_CR21",
      "volume-title": "Nonlinear Dynamics and Chaos",
      "author": "S H Strogatz",
      "year": "2001",
      "unstructured": "Strogatz S H, Nonlinear Dynamics and Chaos, Westview Press, Boulder, USA, 2001."
    },
    {
      "key": "6117_CR22",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/978-3-642-88338-5",
      "volume-title": "Synergetics \u2014 An Introduction",
      "author": "H Haken",
      "year": "1983",
      "unstructured": "Haken H, Synergetics \u2014 An Introduction, Springer-Verlag, Berlin, 1983."
    },
    {
      "key": "6117_CR23",
      "volume-title": "Self-Organization in Nonequilibrium Systems",
      "author": "L Riauba",
      "year": "1977",
      "unstructured": "Riauba L, Niaura G, Eicher-Lorka O, et al., Self-Organization in Nonequilibrium Systems, Wiley, New Jersey, USA, 1977."
    },
    {
      "key": "6117_CR24",
      "volume-title": "Exploring Complexity",
      "author": "G Nicolis",
      "year": "1989",
      "unstructured": "Nicolis G and Prigogine I, Exploring Complexity, Freeman and Company, New York, 1989."
    },
    {
      "key": "6117_CR25",
      "first-page": "19",
      "volume-title": "Advances in Applied Self- Organizing Systems",
      "author": "D Polani",
      "year": "2007",
      "unstructured": "Polani D, Foundations and formalizations of self-organization, Advances in Applied Self- Organizing Systems, Springer, 2007, 19\u201337."
    },
    {
      "key": "6117_CR26",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1016/0167-2789(84)90245-8",
      "volume": "10",
      "author": "S Wolfram",
      "year": "1984",
      "unstructured": "Wolfram S, Universality and complexity in cellular automata, Physica D, 1984, 10: 1\u201335.",
      "journal-title": "Physica D"
    },
    {
      "key": "6117_CR27",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.25088/ComplexSystems.15.1.1",
      "volume": "15",
      "author": "M Cook",
      "year": "2004",
      "unstructured": "Cook M, Universality in elementary cellular automata, Complex Systems, 2004, 15: 1\u201340.",
      "journal-title": "Complex Systems"
    },
    {
      "key": "6117_CR28",
      "first-page": "497",
      "volume-title": "Complexity: Metaphors, Models, and Reality",
      "author": "M Mitchell",
      "year": "1994",
      "unstructured": "Mitchell M, Crutchfield J P, and Hraber P T, Dynamics, computation, and the \u201cedge of chaos\u201d: A re-examination. Complexity: Metaphors, Models, and Reality, 1994, 497\u2013513."
    },
    {
      "key": "6117_CR29",
      "doi-asserted-by": "publisher",
      "first-page": "15",
      "DOI": "10.1002/cplx.21445",
      "volume": "18",
      "author": "W Hordijk",
      "year": "2013",
      "unstructured": "Hordijk W, The EvCA project: A brief history, Complexity, 2013, 18: 15\u201319.",
      "journal-title": "Complexity"
    },
    {
      "key": "6117_CR30",
      "doi-asserted-by": "publisher",
      "first-page": "171",
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      "volume": "80",
      "author": "R V Sol\u00e9",
      "year": "1995",
      "unstructured": "Sol\u00e9 R V and Miramontes O, Information at the edge of chaos in fluid neural networks, Physica D, 1995, 80: 171\u2013180.",
      "journal-title": "Physica D"
    },
    {
      "key": "6117_CR31",
      "volume-title": "Elements of Information Theory",
      "author": "T M Cover",
      "year": "2006",
      "unstructured": "Cover T M and Thomas J A, Elements of Information Theory, Wiley and Sons, New Jersey, USA, 2006."
    },
    {
      "key": "6117_CR32",
      "doi-asserted-by": "publisher",
      "first-page": "437",
      "DOI": "10.1016/0022-5193(69)90015-0",
      "volume": "22",
      "author": "S A Kauffman",
      "year": "1969",
      "unstructured": "Kauffman S A, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theor. Biol., 1969, 22: 437\u2013467.",
      "journal-title": "J. Theor. Biol."
    },
    {
      "key": "6117_CR33",
      "doi-asserted-by": "publisher",
      "first-page": "45",
      "DOI": "10.1209/0295-5075/1/2/001",
      "volume": "1",
      "author": "B Derrida",
      "year": "1986",
      "unstructured": "Derrida B and Pomeau Y, Random networks of automata: A simple annealed approximation, Europhys. Lett., 1986, 1: 45\u201349.",
      "journal-title": "Europhys. Lett."
    },
    {
      "issue": "048701",
      "key": "6117_CR34",
      "first-page": "1",
      "volume": "93",
      "author": "I Shmulevich",
      "year": "2004",
      "unstructured": "Shmulevich I and Kauffman S A, Activities and sensitivities in boolean network models, Phys. Rev. Lett., 2004, 93: 048701:1\u20138.",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6117_CR35",
      "doi-asserted-by": "publisher",
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      "author": "P R\u00e4m\u00f6",
      "year": "2006",
      "unstructured": "R\u00e4m\u00f6 P, Kauffman S A, Kesseli J, et al., Measures for information propagation in boolean networks, Physica D, 2006a, 227: 100\u2013104.",
      "journal-title": "Physica D"
    },
    {
      "issue": "011901",
      "key": "6117_CR36",
      "first-page": "1",
      "volume": "77",
      "author": "A S Ribeiro",
      "year": "2008",
      "unstructured": "Ribeiro A S, Kauffman S A, Lloyd-Price J, et al., Mutual information in random boolean models of regulatory networks, Physical Review E, 2008, 77: 011901:1\u201310.",
      "journal-title": "Physical Review E"
    },
    {
      "key": "6117_CR37",
      "doi-asserted-by": "crossref",
      "unstructured": "Krawitz P and Shmulevich I, Basin entropy in boolean network ensembles, Phys. Rev. Lett., 2007, 98: 158701:1\u20134.",
      "DOI": "10.1103/PhysRevLett.98.158701"
    },
    {
      "key": "6117_CR38",
      "doi-asserted-by": "publisher",
      "first-page": "667",
      "DOI": "10.1109/TIT.2009.2037046",
      "volume": "56",
      "author": "D J Galas",
      "year": "2010",
      "unstructured": "Galas D J, Nykter M, Carter G W, et al., Biological information as set-based complexity, IEEE Tran. on Information Theory, 2010, 56: 667\u2013677.",
      "journal-title": "IEEE Tran. on Information Theory"
    },
    {
      "key": "6117_CR39",
      "volume-title": "Proc. of WCSB",
      "author": "T M\u00e4ki-Marttunen",
      "year": "2011",
      "unstructured": "M\u00e4ki-Marttunen T, Kesseli J, Kauffman S A, et al., Of the complexity of boolean network state trajectories, Proc. of WCSB 2011, 2011."
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    {
      "key": "6117_CR40",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/978-3-642-32952-4",
      "volume-title": "The Local Information Dynamics of Distributed Computation in Complex Systems",
      "author": "J T Lizier",
      "year": "2013",
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    {
      "key": "6117_CR41",
      "first-page": "374",
      "volume-title": "Proceedings of Artificial Life XI",
      "author": "J T Lizier",
      "year": "2008",
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    },
    {
      "key": "6117_CR42",
      "doi-asserted-by": "publisher",
      "first-page": "348",
      "DOI": "10.1038/nphys289",
      "volume": "2",
      "author": "O Kinouchi",
      "year": "2006",
      "unstructured": "Kinouchi O and Copelli M, Optimal dynamical range of excitable networks at criticality, Nature Physics, 2006, 2: 348\u2013351.",
      "journal-title": "Nature Physics"
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    {
      "key": "6117_CR43",
      "doi-asserted-by": "publisher",
      "first-page": "1413",
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      "author": "N Bertschinger",
      "year": "2004",
      "unstructured": "Bertschinger N and Natschl\u00e4ger T, Real-time computation at the edge of chaos in recurrent neural networks, Neural Computation, 2004, 16: 1413\u20131436.",
      "journal-title": "Neural Computation"
    },
    {
      "key": "6117_CR44",
      "doi-asserted-by": "publisher",
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      "author": "R Legenstein",
      "year": "2007",
      "unstructured": "Legenstein R and Maass W, Edge of chaos and prediction of computational performance for neural circuit models, Neural Networks, 2007, 20: 323\u2013334.",
      "journal-title": "Neural Networks"
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      "key": "6117_CR45",
      "doi-asserted-by": "publisher",
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      "volume": "5",
      "author": "W G Macready",
      "year": "1996",
      "unstructured": "Macready W G, Siapas A G, and Kauffman S A, Criticality and parallelism in combinatorial optimization, Science, 1996, 5: 56\u201359.",
      "journal-title": "Science"
    },
    {
      "key": "6117_CR46",
      "doi-asserted-by": "publisher",
      "first-page": "26",
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      "volume": "26",
      "author": "S A Kauffman",
      "year": "1995",
      "unstructured": "Kauffman S A and Macready W, Technological evolution and adaptive organizations, Complexity, 1995, 26: 26\u201343.",
      "journal-title": "Complexity"
    },
    {
      "key": "6117_CR47",
      "doi-asserted-by": "publisher",
      "first-page": "150",
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      "volume": "9",
      "author": "A Roli",
      "year": "2001",
      "unstructured": "Roli A, Criticality and parallelism in GSAT, Electronic Notes in Discrete Mathematics, 2001, 9: 150\u2013161.",
      "journal-title": "Electronic Notes in Discrete Mathematics"
    },
    {
      "key": "6117_CR48",
      "volume-title": "Reinventing the Sacred \u2014 A New View of Science, Reason and Religion",
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      "year": "2008",
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      "doi-asserted-by": "publisher",
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      "year": "2004",
      "unstructured": "Serra R, Villani M, and Semeria A, Genetic network models and statistical properties of gene expression data in knock-out experiments, J. Theor. Biol., 2004, 227: 149\u2013157.",
      "journal-title": "J. Theor. Biol."
    },
    {
      "key": "6117_CR50",
      "doi-asserted-by": "publisher",
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      "year": "2007",
      "unstructured": "Serra R, Villani M, Graudenzi A, et al., Why a simple model of genetic regulatory network describes the distribution of avalanches in gene expression data, J. Theor. Biol., 2007, 246: 449\u2013460.",
      "journal-title": "J. Theor. Biol."
    },
    {
      "key": "6117_CR51",
      "volume-title": "Continuous Network Models of Gene Expression in Knock Out Experiments: A Preliminary Study",
      "author": "A Roli",
      "year": "2010",
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      "doi-asserted-by": "publisher",
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      "author": "I Shmulevich",
      "year": "2005",
      "unstructured": "Shmulevich I, Kauffman S A, and Aldana M, Eukaryotic cells are dynamically ordered or critical but not chaotic, PNAS, 2005, 102(38): 13439\u201313444.",
      "journal-title": "PNAS"
    },
    {
      "key": "6117_CR53",
      "doi-asserted-by": "publisher",
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      "year": "2006",
      "unstructured": "R\u00e4m\u00f6 P, Kesseli J, and Yli-Harja O, Perturbation avalanches and criticality in gene regulatory networks. J. Theor. Biol., 2006, 242: 164\u2013170.",
      "journal-title": "J. Theor. Biol."
    },
    {
      "key": "6117_CR54",
      "doi-asserted-by": "publisher",
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      "year": "2008",
      "unstructured": "Nykter M, Price N D, Aldana M, et al., Gene expression dynamics in the macrophage exhibit criticality, PNAS, 2008a, 105: 1897\u20131900.",
      "journal-title": "PNAS"
    },
    {
      "issue": "e2456",
      "key": "6117_CR55",
      "first-page": "1",
      "volume": "3",
      "author": "E Balleza",
      "year": "2008",
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      "journal-title": "PLoS ONE"
    },
    {
      "key": "6117_CR56",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1186/1752-0509-4-143",
      "volume": "4",
      "author": "S Chowdhury",
      "year": "2010",
      "unstructured": "Chowdhury S, Lloyd-Price J, Smolander O P, et al., Information propagation within the genetic network of Saccharomyces cerevisiae, BMC Systems Biology, 2010, 4: 1\u201310.",
      "journal-title": "BMC Systems Biology"
    },
    {
      "key": "6117_CR57",
      "doi-asserted-by": "publisher",
      "first-page": "29",
      "DOI": "10.1007/978-3-319-32695-5_3",
      "volume-title": "Advances in Artificial Life, Evolutionary Computation and Systems Chemistry",
      "author": "M L Stefano Di",
      "year": "2016",
      "unstructured": "Di Stefano M L, Villani M, La Rocca L, et al., Dynamically critical systems and power-law distributions: Avalanches revisited, Advances in Artificial Life, Evolutionary Computation and Systems Chemistry, 2016, 29\u201339."
    },
    {
      "issue": "1",
      "key": "6117_CR58",
      "doi-asserted-by": "publisher",
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      "DOI": "10.1109/TIT.1976.1055501",
      "volume": "22",
      "author": "A Lempel",
      "year": "1976",
      "unstructured": "Lempel A and Ziv J, On the complexity of finite sequence, IEEE Trans. on Info. Theory, 1976, 22(1): 75\u201381.",
      "journal-title": "IEEE Trans. on Info. Theory"
    },
    {
      "issue": "12",
      "key": "6117_CR59",
      "doi-asserted-by": "publisher",
      "first-page": "3250",
      "DOI": "10.1109/TIT.2004.838101",
      "volume": "50",
      "author": "M Li",
      "year": "2004",
      "unstructured": "Li M, Chen X, Li X, et al., The similarity metric, IEEE Trans. on Info. Theory, 2004, 50(12): 3250\u20133264.",
      "journal-title": "IEEE Trans. on Info. Theory"
    },
    {
      "key": "6117_CR60",
      "first-page": "281",
      "volume-title": "Volume 5777 of Lecture Notes in Computer Science",
      "author": "C Darabos",
      "year": "2011",
      "unstructured": "Darabos C, Giacobini M, Tomassini M, et al., Are cells really operating at the edge of chaos? Darwin Meets von Neumann, Volume 5777 of Lecture Notes in Computer Science, Springer, 2011, 281\u2013288."
    },
    {
      "key": "6117_CR61",
      "doi-asserted-by": "publisher",
      "first-page": "5583",
      "DOI": "10.1098/rsta.2010.0267",
      "volume": "368",
      "author": "R Hanel",
      "year": "2010",
      "unstructured": "Hanel R, P\u00f6chacker M, and Thurner S, Living on the edge of chaos: Minimally nonlinear models of genetic regulatory dynamics, Phil. Trans. R. Soc. A, 2010, 368: 5583\u20135596.",
      "journal-title": "Phil. Trans. R. Soc. A"
    },
    {
      "key": "6117_CR62",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/978-3-540-32667-0",
      "volume-title": "Life: An Introduction to Complex Systems Biology",
      "author": "K Kaneko",
      "year": "2006",
      "unstructured": "Kaneko K, Life: An Introduction to Complex Systems Biology, Springer, Berlin Heidelberg, 2006."
    },
    {
      "key": "6117_CR63",
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