Phylogenetic networks are a generalization of evolutionary trees that can be used to represent reticulate events. Level-k phylogenetic networks are such networks, but with a at most k reticulations per biconnected component of the network. For level-1 networks there exists an algorithm, called TriLoNet (Trinet Level-one Network algorithm), that constructs these networks directly from sequence alignments which works by piecing together smaller level-1 networks on three taxa. Here, we introduce TriL2Net (Trinet Level-2 Network algorithm), an algorithm similar to TriLoNet that works for the larger class of level-2 networks. More specifically, TriL2Net constructs a level-2 phylogenetic network from a set of level-2 trinets. We show that TriL2Net performs better on sampled level-2 networks than TriLoNet performs om sampled level-1 networks. We hypothesize that this result is either due to the different ways the data is sampled, or the difference in heuristics used. Moreover, we applied TriL2Net to level-1 trinet sets derived from real sequence data involving recombination. When comparing the networks generated by TriL2Net from these data sets to the networks generated by TriLoNet from these same data sets, we found that TriL2Net’s networks are at least as consistent with the input as TriLoNet’s networks. TriL2Net has been implemented in Python and is freely available at https://github.com/KSjors/TriL2Net.

In this report, the rain-wind induced vibrations of cables are studied. This is done by modeling the cable cross-section as a mass-spring system with two time-varying masses. Thereafter, the solution of this model is approximated using a multiple timescale perturbation method. Lastly, for some choices
of the time-varying masses the eigenfrequencies are analyzed, stability properties are derived, and approximations of the solutions are given.