Shapes from point clouds arise in many application areas, such as chemistry, meshing or autonomous vehicles. Analysing such shapes requires efficient comparison methods which consider both geometry and topology. The researcher will show that such comparisons are easier for asymmetric shapes and develop efficient algorithms which exploit asymmetry. . .

In order to secure a sustainable future, it is crucial that consumers adopt more resource-efficient foods, such as soy butter, cultured beef and seaweed. One obvious marketing strategy is to position sustainable alternatives as the morally-superior choice. The main selling point of cultured beef, for instance, is its contribution to the collective good. But while such moral appeals could indeed boost demand, this proposal examines the notion that there are some important, previously unconsidered, social risks associated with moral appeals. Specifically, while compliance with moral appeals could satisfy consumers? internal need to be moral, it also calls the morality of fellow consumers into question. In response, fellow consumers may attempt to restore their threatened sense of morality by discrediting or rejecting moral outliers ? a phenomenon known as ?moral do-gooder derogation?. This social-psychological perspective on morality may have some important implications for the marketing of sustainable products, which I will examine in a series of lab and field studies. Project 1 takes the perspective of the observer. It documents defensive responses by consumers who witness others buying ?morally-superior? sustainable products. Importantly, I additionally propose that prospective buyers also anticipate such defensive responses. Project 2 therefore takes the perspective of the actor. It investigates the notion that consumers may avoid purchasing ?morally-superior? sustainable products in an attempt to avoid being perceived as a moral outlier. In doing so, this proposal introduces a new angle on the adoption of sustainable products: consumers want to be moral, but not be perceived as a moral outlier.

In the brain, neurons communicate across highly specialized contacts, synapses. The researchers will develop advanced microscopy techniques to visualize lipids in the synapse, and investigate how these cellular components contribute to synaptic communication. Disruptions in synapses underlie brain disorders, these studies will reveal insights in the development of these diseases.

Mixed continuous-discrete problems are hard non-linear optimization problems that occur in many application fields and are particularly difficult to solve. The variables of mixed type problems belong to different kind of search spaces, such as continuous (or real-valued) variables, ordinal discrete (or integer-valued) variables, and nominal discrete variables where the values have no order between them. The goal of this research project is to extend a class of meta-heuristic search algorithms - namely, Estimation of Distribution Algorithms (EDAs) - such that they can be applied to mixed continuous-discrete problems. EDAs have shown great success in both the purely continuous domain as well as in the purely discrete domain. We plan to study how novel EDA approaches can be applied to mixed continuous-discrete problems. To ensure that the techniques we develop are applicable to complex real world problems we intend to test our new meta-heuristic search algorithms on a difficult but representative problem, namely the transmission network expansion planning problem.

In theoretical computer science, we study algorithmic problems and their various levels of difficulty. The mostfamous level of difficulty is NP‐completeness. This proposal deals with algorithmic problems that are believedto be even more difficult than NP‐complete problems: the class of ER‐complete algorithmic problems. The diffi‐culty of ER‐complete problems stems from the inherent presence of continuous numbers in the solution. Manyprofound and important algorithmic problems are ER‐complete. The art gallery problem, geometric packing,real‐root‐finding, Nash‐equilibria, polytope realizability, and training neural networks are prominent examples.Methods to find solutions to those algorithmic problems generally fall into three categories: Algebraic methods,gradient descent, and discretization schemes. Algebraic methods are mathematically guaranteed to always re‐turn the optimal solution, but in practice take an infeasible amount of time. Gradient descent often convergesvery fast in experiments but has no guarantee on the quality of the solution or the time it takes to converge.This discrepancy between theoretical and practical methods forms an abyss in our understanding. Discretizationschemes have the potential to bridge this abyss. They are much faster than algebraic methods. Moreover, (usingadditional assumptions) they have the potential to provably terminate in finite amount of time. As a proof ofconcept, I developed a new discretization scheme for the art gallery problem. The discretization scheme is fasterthan any previously fully published algorithm on benchmark instances and it returns reliable solutions in prov‐ably finite time. I will develop new powerful discretization schemes for other central ER‐complete algorithmicproblems in this proposal. Furthermore, I will strengthen our theoretical understanding of ER‐completeness andbroaden its scope even further.