Reconstructing a minimum reticulation network from phylogenetic trees is used in evolutionary studies. In this thesis, we focus on finding temporal networks using cherry-picking sequences for binary trees with all taxa. Finding such a minimum reticulation temporal network is NP-hard.

We introduce an algorithm to find a minimum reticulation network with a running time of O(2^n poly(n,t)). In addition, this study explores potential enhancements to the algorithm through the utilisation of branch and bound.

Additionally, we introduce a similar algorithm to determine the existence of a temporal phylogenetic network. This algorithm is improved upon by integrating a new concept called cherry growing. This leads to a notable speed-up in performance.

Furthermore, we examine the application of Graph Neural Networks (GNN) in heuristics to find a cherry-picking sequence which can be used to construct a network. This is done by classifying leaves into good, which leads to optimal solutions, and bad leaves. To assess this, two types of data were employed: one simulating evolutionary models and the other employing a fully random approach. The best-performing GNN model has a 97.4% accuracy for evolution-based data and a 79.1% accuracy for random-based data.

The GNN models are implemented as predictors in two classes of heuristics. The first generates a cherry-picking sequence by repeatedly picking leaves. The second class of heuristics is based on a tree search heuristic. This tree-search-based heuristic outperforms the cherry-picking-based heuristic. Furthermore, the GNN heuristics outperform their random variant, even for problems substantially larger than the GNN was trained on.

We also examine the use of GNN in predicting the existence of a phylogenetic temporal network given a set of trees. The best-performing GNN found for this problem has an accuracy of 80.3%.

Steel is commonly coated to protect it from corrosion. One method of applying this is by using Physical Vapor Deposition, which can be done by using multiple jets. In this process jets next to each other interact. This paper's main aim is to investigate the interaction effect of two rarefied two-dimensional vapor jets in vacuum and how this is influenced by the distance between jets and inlet density. Furthermore, the analytical solution for the collisionless case for a single jet is extended to dual jets. Additionally, the objective is to maximize the processing speed for the use of coating, with a certain uniformity for the parameters researched in this paper and finding an optimal method in doing so. This study is done by using the Direct Simulation Monte Carlo (DSMC) method.
The analytical solution gave the same results as the collisionless DSMC method for both single and dual jets. Simulations with a strong interaction effect resulted in a shock. These behaved similar compared to three-dimensional jets, in the plane of the jets. The shock results in a secondary jet, which has a lower density in the middle. The interaction effect depends primarily on the inlet density. Multiple regimes are observed for different inlet density ranging from small change in properties to a shock wave, with a transitional regime inbetween. The influence of the distance between the jets is found to result in a higher density at the axis of the inlet behind the shock, for bigger distance between jets. However, for very small distances between jets compared to the inlet size the shock is weak. For the optimization, it resulted in the conclusion that the optimal coating in general is applied with the smallest distance between jets. This generally gives a better uniform coating and increased performance. However, this is not always the case when constraining the distance between the jets and sheet, as it only holds if the shock between the jets for this distance. Furthermore, an approximation is found for the optimization, which results in fewer simulations needed.