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in the early 2000s. For some systems that display a characteristic scale, a global optimization term could potentially be added that would then yield power law behavior. It has been used to generate and describe internet-like graphs,
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Zhou, Tong; Carlson, J. M.; Doyle, John (2002), "Mutation, specialization, and hypersensitivity in highly optimized tolerance",
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giving us a power law. The global optimization of minimizing the energy along with the power law dependence between
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650:; Doyle, John (August 1999), "Highly optimized tolerance: A mechanism for power laws in designed systems",
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Critical
Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools
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Zhou, Tong; Carlson, J. M. (2000), "Dynamics and changing environments in highly optimized tolerance",
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755:"Power Laws, Highly Optimized Tolerance, and Generalized Source Coding"
709:"Highly Optimized Tolerance: Robustness and Design in Complex Systems"
593:"Highly optimized tolerance: robustness and design in complex systems"
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Li, Lun; Alderson, David; Doyle, John C.; Willinger, Walter (2005),
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938:, Springer Series in Synergetics, Berlin: Springer-Verlag,
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Robert, Carl; Carlson, J. M.; Doyle, John (April 2001),
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189:. Furthermore, let’s assume for another parameter
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may be too technical for most readers to understand
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499:{\displaystyle p_{i}\propto x_{i}^{-(1+1/\beta )}}
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100:models and may also apply to biological systems.
801:"Untangling a web: The internet gets a new look"
1009:Proceedings of the National Academy of Sciences
421:{\displaystyle \sum _{i=0}^{N-1}r_{i}=\kappa }
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355:{\displaystyle L=\sum _{i=0}^{N-1}p_{i}x_{i}}
108:The following is taken from Sornette's book.
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707:Carlson, J. M.; Doyle, John (March 2000),
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59:Learn how and when to remove this message
43:, without removing the technical details.
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259:{\displaystyle x_{i}=r_{i}^{-\beta }}
41:make it understandable to non-experts
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83:behavior in systems by including a
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77:highly optimized tolerance (HOT)
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87:principle. It was developed by
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1:
1080:. You can help Knowledge by
289:. We then want to minimize
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738:10.1103/PhysRevLett.84.2529
620:10.1103/PhysRevLett.84.2529
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573:self-organized criticality
365:subject to the constraint
79:is a method of generating
1132:Applied mathematics stubs
1127:Mathematical optimization
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991:10.1103/PhysRevE.62.3197
684:10.1103/PhysRevE.60.1412
763:Physical Review Letters
717:Physical Review Letters
600:Physical Review Letters
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1076:-related article is a
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282:{\displaystyle \beta }
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1082:expanding it
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111:Consider a
98:forest fire
1121:Categories
579:References
93:John Doyle
628:1079-7114
489:β
469:−
456:∝
416:κ
395:−
377:∑
325:−
307:∑
277:β
252:β
249:−
81:power law
49:June 2012
1050:11842230
999:11088814
934:(2000),
924:11414976
792:10991018
746:11018927
692:11969901
636:11018927
567:See also
1018:Bibcode
979:Bibcode
962:1782504
904:Bibcode
870:2241756
827:4016836
772:Bibcode
726:Bibcode
700:2648280
672:Bibcode
608:Bibcode
104:Example
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596:(PDF)
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