In this thesis the Conjugate Gradient method used in the forecasting of the number of students in the Netherlands is investigated. The addition of international students to the forecasting led to mathematical problem of which a solution could not be computed. While the numerical method is working as intended, the work presented in this thesis shows that the unsolvability lies with a linear system that has no solution. The cause of this is attributed to the use of a selection process in the linear system. Leading to a hugely singular matrix and a forecasting problem without a solution. Several methods were tried to change the use of the selection process but without any results .

Phylogenetic networks are a type of directed acyclic graph used to represent evolutionary relationships that contain events such as hybridization or horizontal gene transfer. When a network
lacks such events it is a phylogenetic tree. Some phylogenetic networks that are not trees can
however be represented as a tree with additional linking arcs, e.g. representing transfer of genetic
materials. We have implemented an algorithm that can be used to determine whether a given
network is tree-based or not. Moreover if the network is not tree-based, the algorithm shows
how it can be made tree-based by adding a minimum number of additional leaves, representing
possible extinct or un-sampled species. We also describe the theory behind the algorithm and
apply it to several synthetic as well as biological datasets.