Non-Hamiltonian symmetries of a Boussinesq equation

For a class of Hamiltonian systems there exist infinite series of non-Hamiltonian symmetries. Some properties of these series are illustrated using a Boussinesq equation. It is shown that the recursion operators generated by these non-Hamiltonian symmetries are powers of the original recursion operator. A class of recursion formulas for the constants of the motion (not for the corresponding symmetries!) is given

Simulated evolution of mass conserving reaction networks

With the rise of systems biology, the systematic analysis and construction of behavioral mechanisms in both natural and artificial biochemical networks has become a vital part of understanding and predicting the inner workings of intracellular signaling networks. As a modeling platform, artificial chemistries are commonly adopted to study and construct artificial reaction network motifs that exhibit complex computational behaviors. Here, we present a genetic algorithm to evolve networks that can compute elementary mathematical functions by transforming initial input molecules into the steady state concentrations of output molecules. Morespecifically, the proposed algorithm implicitly guarantees mass conservation through an atom based description of the molecules and reaction networks. We discuss the adopted approach for the artificial evolution of these chemical networks, evolve networks to compute the square root function. Finally,we provide an extensive deterministic and stochastic analysis of a core square root network motif present in these resulting networks, confirming that the motif is indeed capable of computing the square root function