Burn injuries present a significant global health challenge. Among the most severe long-term consequences are contractures, which can lead to functional impairments and disfigurement. Understanding and predicting the evolution of post-burn wounds is crucial for developing effective treatment strategies. Traditional mathematical models, while accurate, are often computationally expensive and time-consuming, limiting their practical application. Recent advancements in machine learning, particularly in deep learning, offer promising alternatives for accelerating these predictions. This study investigates the use of a deep operator network (DeepONet), a type of neural operator, as a surrogate model for finite element simulations for predicting post-burn wound evolution. We trained DeepONets on various wound shapes, enhancing the architecture by incorporating initial wound shape information and applying sine augmentation to enforce boundary conditions. The most sophisticated model achieved an R² score of 0.9960, indicating strong predictive accuracy. Additionally, the model generalised well to convex combinations of basic shapes, with an R² score of 0.9944, and provided reliable predictions over an extended period of up to one year. These findings suggest that DeepONets can effectively serve as a surrogate for traditional finite element methods in simulating post-burn wound evolution, with potential applications in medical treatment planning.

A common tool for exploring the space of phylogenetic networks is applying rearrangement moves, such as tail moves. Recently, it has been shown by Janssen et al that, given a rooted binary phylogenetic network, it is possible to generate any other alternative network, using only tail moves. The aim of this report is to translate this theory into a tail move rearrangement algorithm, that calculates a sequence of tail moves necessary to transform one network into another, and thus determines an upper bound on the tail distance between the two networks. Furthermore, the goal is to assess the quality of the upper bound as determined by the algorithm, and to try to improve it. To this end, four improvement proposals were made and tested. A comparison was made with the true tail distance for a range of 385 combinations of small networks. It was shown that the original algorithm gives adequate results. However, it was concluded that it generally cannot be predicted which version of the algorithm will perform best. In the case of small and relatively simple networks, the fourth improvement provides the best results.