Highly optimized tolerance
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In applied mathematics, highly optimized tolerance (HOT) is a method of generating power law behavior in systems by including a global optimization principle. It was developed by Jean M. Carlson and John Doyle in the early 2000s.[1] 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, forest fire models and may also apply to biological systems.
![]() | This article may be too technical for most readers to understand. (June 2012) |
Example
Summarize
Perspective
The following is taken from Sornette's book.
Consider a random variable, , that takes on values with probability . Furthermore, let’s assume for another parameter
for some fixed . We then want to minimize
subject to the constraint
Using Lagrange multipliers, this gives
giving us a power law. The global optimization of minimizing the energy along with the power law dependence between and gives us a power law distribution in probability.
See also
References
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