We present quantitative models for the selection pressure of cellular evolutionary algorithms structured in two dimensional regular lattices. We derive models based on probabilistic difference equations for synchronous and several asynchronous cell update policies. Theoretical results are in agreement with experimental values and show that the selection intensity can be controlled by using diff...

We present quantitative models for the selection pressure on cellular evolutionary algorithms structured as a ring of cells. We obtain results for synchronous and asynchronous cell update policies. Theoretical results are in agreement with experimental values and show that the selection intensity can be controlled by using different update methods.

Here we will use results of Cox, Durrett, and Perkins [56] for voter model perturbations to study spatial evolutionary games on Zd, d ≥ 3 when the interaction kernel is finite range, symmetric, and has covariance matrix σ2I. The games we consider have payoff matrices of the form 1 + wG where 1 is matrix of all 1’s and w is small and positive. Since our population size N = ∞, we call our selecti...

We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klymik, we develop a tree-method approach for those intertwining functions. We also give a group theoretic proof of the relation between Hahn polynomials and Clebesh-Gordan coefficients, give...

We introduce a general and efficient method to recover piecewise constant coefficients occurring in elliptic partial differential equations as well as the interface where these coefficients have jump discontinuities. For this purpose, we use an output least squares approach with level set and augmented Lagrangian methods. Our formulation incorporates the inherent nature of the piecewise constan...