Asymptotic behavior of Eigen's quasispecies model

We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to infinity and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove the convergence of the trajectories, as well as the convergence of the equilibrium solutions. We give the analogous results for a discrete-time version of Eigen's model, which coincides with a model proposed by Moran

Maltsev digraphs have a majority polymorphism

We prove that when a digraph $G$ has a Maltsev polymorphism, then $G$ also has a majority polymorphism. We consider the consequences of this result for the structure of Maltsev graphs and the complexity of the Constraint Satisfaction Problem.Comment: 8 pages, 4 figures; minor changes (stylistics, elsarticle LaTeX style, citations); submitted to European Journal of Combinatoric

Generalized Majority-Minority Operations are Tractable

Generalized majority-minority (GMM) operations are introduced as a common generalization of near unanimity operations and Mal'tsev operations on finite sets. We show that every instance of the constraint satisfaction problem (CSP), where all constraint relations are invariant under a (fixed) GMM operation, is solvable in polynomial time. This constitutes one of the largest tractable cases of the CSP