Optimal static and dynamic recycling of defective binary devices

The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular, the region in the parameter space where there is almost surely at least one fully-working subset. Dynamic recycling of a flux of imperfect binary components leads to zero wastage.Comment: 14 pages, 15 figure

On the strategy frequency problem in batch Minority Games

Ergodic stationary states of Minority Games with S strategies per agent can be characterised in terms of the asymptotic probabilities $\phi_a$ with which an agent uses $a$ of his strategies. We propose here a simple and general method to calculate these quantities in batch canonical and grand-canonical models. Known analytic theories are easily recovered as limiting cases and, as a further application, the strategy frequency problem for the batch grand-canonical Minority Game with S=2 is solved. The generalization of these ideas to multi-asset models is also presented. Though similarly based on response function techniques, our approach is alternative to the one recently employed by Shayeghi and Coolen for canonical batch Minority Games with arbitrary number of strategies.Comment: 17 page