The thesis by Lisa Maria Kreusser is very comprehensive and voluminous. The overarching mathematical technique used in the thesis is nonlinear partial differential equations. Moreover, dynamic modelling approaches on graphs are used. While much work had been done earlier on isotropic models, Dr. Kreusser’s thesis is about anisotropic models, which makes it even more demanding. Another special feature is that nonlocal interaction models are established, which describe the collective behavior of large numbers of individuals where each of them can interact not only with its nearest neighbours but also with individuals far away.
The thesis deals with several applications of the above-mentioned techniques. Part 1 of the thesis is about simulation and prediction of human fingerprint patterns and, thus, bears forensic and biometric applications. Anisotropy enters the scene by a stress field. In Part 2 of the thesis, biological transportation networks are analysed, which describe leaf venation in plants, blood circulatory systems, and neural networks. Here, a distinction is made between the energy requirement for pumping material through the networks and the metabolic costs for maintaining the network. By sophisticated methods, branching of vessels and leaf veins could nicely be predicted.
In summary, Kreusser’s thesis is very beautiful work, especially on the maths side, and is outstanding both in quality and quantity. Each of the two parts would have been excellent PhD theses on their own. The dissertation is appealing by its mathematical depth, exact and detailed presentation, and the biological applications and interpretation.