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http://bura.brunel.ac.uk/handle/2438/308
Title: | Percolation and depinning transitions in cut-and-paste models of adaptation |
Authors: | D'Hulst, R Rodgers, GJ |
Keywords: | Condensed matter;Statistical mechanics |
Issue Date: | 2001 |
Publisher: | Elsevier Science |
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. |
URI: | http://www.ingentaconnect.com/content/els/03784371 http://bura.brunel.ac.uk/handle/2438/308 |
Appears in Collections: | Mathematical Physics Dept of Mathematics Research Papers Mathematical Sciences |
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