The permeability of random two‐dimensional Poisson fracture networks can be studied using a model based on percolation theory and equivalent media theory. Such theories are usually applied on regular lattices where the lattice elements are present with probability p. In order to apply these theories to random systems, we (1) define the equivalent to the case where p = 1, (2) define p in terms of the statistical parameters of the random network, and (3) define the equivalent of the coordination number z. An upper bound for permeability equivalent to the case of p = 1 is found by calculating the permeability of the fracture network with the same linear fracture frequency and infinitely long fractures. The permeability of networks with the same linear fracture frequency and finite fractures can be normalized by this maximum. An equivalent for p is found as a function of the connectivity ζ, which is defined as the average number of intersections per fracture. This number can be calculated from the fracture density and distributions of fracture length and orientation. Then the equivalent p is defined by equating the average run length for a random network as a function of ζ to the average run length for a lattice as a function of p. The average run length in a random system is the average number of segments that a fracture is divided into by intersections with other fractures. In a lattice, it is the average number of bonds contiguous to a given bond. Also, an average coordination number can be calculated for the random systems as a function of ζ. Given these definitions of p and z, expressions for permeability are found based on percolation theory and equivalent media theory on regular lattices. When the expression for p is used to calculate the correlation length from percolation theory, an empirical formula for the size of the REV can be developed. To apply the models to random length systems, the expression for ζ must be modified to remove short fractures which do not contribute to flow. This leads to a quantitative prediction of how permeability decreases as one removes shorter fractures from a network. Numerical studies provide strong support for these models. These results also apply to the analogous electrical conduction problem.

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Feature selection is an important challenge in many classification problems, especially if the number of features greatly exceeds the number of examples available. We have developed a procedure--GenForest--which controls feature selection in random forests of decision trees by using a genetic algorithm. This approach was tested through our entry into the Comparative Evaluation of Prediction Algorithms 2006 (CoEPrA) competition (accessible online at: http://www.coepra.org). CoEPrA was a modeling competition organized to provide an objective testing for various classification and regression algorithms via the process of blind prediction. In the competition GenForest ranked 10/23, 5/16 and 9/16 on CoEPrA classification problems 1, 3 and 4, respectively, which involved the classification of type I MHC nonapeptides i.e. peptides containing nine amino acids. These problems each involved the classification of different sets of nonapeptides. Associated with each amino acid was a set of 643 features for a total of 5787 features per peptide. The method, its application to the CoEPrA datasets, and its performance in the competition are described.