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|Title:||Percolation and depinning transitions in cut-and-paste models of adaptation|
|Keywords:||Condensed matter;Statistical mechanics|
|Citation:||Physica A, 308(1): 443-459(17), May 2002|
|Abstract:||We show that a cut-and-paste model to mimic a trial-and-error process of adaptation displays two pairs of percolation and depinning transitions, one for persistence and the other for efficiency. The percolation transition signals the onset of a property and the depinning transition, the growth of the same property. Despite its simplicity, the cut-and-paste model is qualitatively the same as the Minority Game. A majority cut-and-paste model is also introduced, to mimic the spread of a trend. When both models are iterated, the majority model reaches a frozen state while the minority model converges towards an alternate state. We show that a transition from the frozen to the alternate state occurs in the limit of a non-adaptive system.|
|Appears in Collections:||Mathematical Physics|
Dept of Mathematics Research Papers
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