Bayesian Contrastive Learning on Topological Structures

In this thesis we develop a Bayesian approach to graph contrastive learning and propose a new uncertainty measure based on the disagreement in likelihood due to different positive samples. Moreover, we extend contrastive learning to simplicial complexes and show that it can be used to generate high-quality representations of edge flow data.

Classes of Semi-binary Phylogenetic Networks encoded by μ-representations

This thesis is on the subject of phylogenetic networks. These are schematic<br/>visualisations used mainly to investigate the evolutionary history of species,<br/>but which can be used for any set of distinguishable elements which have diverged from a common ancestor through some evolutionary process. The research specifically focuses on a way...

Optimising OR planning: Sequencing surgery groups while levelling bed occupancy

This research is conducted in collaboration with the Sophia Children's Hospital (SCH). The hospital wants to provide their patients with more detailed information about when a patient is approximately scheduled to have a surgery. The first step is to create a model which optimises the operation room (OR) schedule and indicates when different...

QAOA Mixing Hamiltonians for MinVertexCover

The minimum vertex cover problem (MinVertexCover) is an important optimization problem in graph theory, with applications in numerous fields outside of mathematics. As MinVertexCover is an NP-hard problem, there currently exists no efficient algorithm to find an optimal solution on arbitrary graphs. We consider quantum optimization algorithms,...

A MaxSAT Approach to Solving Frequency Conflicts within Cyclic Train Timetables

ILP-based solvers that intake a line planning, an infrastructure and a set of constraints and then output a cyclic train timetable have been researched extensively in the world of trains. However, these types of solvers are not able to automatically output a timetable when the problem gets overconstrained and no feasible solution exists.<br/><br...

Optimizing Urban Multi-Energy Systems using Column Generation

The "Number Hides Game" on a Tree: A bachelor thesis in game theory

The "Number Hides Game" (NHG) is 2-player game played on a board that consists of a row of p consecutive coins. Player I and player II simultaneously choose subsets of m and n consecutive coins respectively. Player II pays the number of coins that lie in the intersection of the subsets to player I. This thesis introduces basic knowledge from the...

Matter Distributions of Galaxy Clusters in Modified Newtonian Dynamics

Over the past century various different discrepancies in the expected and observed behaviour of galaxies and galaxy clusters were found. Together this is called the missing mass problem and the most well known theory trying to explain these differences states that there is additional undetectable mass in the form of dark matter. Modified...

Applying the Pebble Motion problem: studying the feasibility of the Train Unit Shunting Problem

Shunting yards are the locations where trains, which are not included in the train schedule at a certain time, are parked until they are required again. Managing the parking of the trains such that all trains can leave at the desired time is a complicated task, and results in the problem formally known as the Train Unit Shunting Problem (TUSP)....

Constructing the medial axis of a discrete level-set curve

In (mathematical) physics one can encounter problems with a fase change, the so called Stefan problems. Numerical methods to solve these problems often use a level-set function which indicates the distance to the fase boundary. Problems can arise in the medial axis points of the zero set. Therefore it can be usefull to calculate this medial axis...

Het voorspellen van de verspreiding van het COVID-19 in Nederland aan de hand van het Ensemble Kalman Filter

Al ruim een half jaar houdt het de hele wereld in zijn greep: het Corona virus. Waar we dachten dat het allemaal begon als een onschuldige griep, werd al snel duidelijk dat er meer aan de hand was. Wuhan kampte al een tijdje met dit onbekende virus en op 23 januari 2020 werd het zelfs zo serieus dat de Chineese overheid een lockdown afkondigde...

De verstrooiing van het licht berekend voor het Asahi-U substraat

In dit project is gewerkt aan een manier om de reflectie van het licht op de textuur van een zonnecel te berekenen. Deze reflectie is berekenend voor de verschillende hoeken van inval en uitval en omgezet in een reflectie matrix. In dit<br/>project is verder gewerkt aan een al bestaand wiskundig model. Dat model was<br/>in staat het door de...

Identifying the most relevant cost-functions for radiotherapy treatment planning with multicriteria optimisation

Cancer is a disease that one of every three people will get in The Netherlands. One of the treatment methods for this disease is radiotherapy. Approximately half of all cancer patients will get radiotherapy at some point of their treatment. During radiotherapy cancer cells are destroyed with ionizing radiation, but healthy cells get destroyed...

Multi-Machine Scheduling Lower Bounds Using Decision Diagrams

We investigate the use of relaxed decision diagrams for obtaining lower bounds on multi-machine scheduling problems. The type of scheduling problem we consider models a railway service site where maintenance jobs are performed, but is sufficiently general to potentially have wider applicability.<br/>We find that our decision diagram formulation...

Decision diagrams for decomposed mixed integer linear programs

A recent development in the field of discrete optimization is the combined use of (binary) decision diagrams (DD) and branch and bound for optimization. This method has been shown to outperform integer linear programming on several classic problems. The performance of DDs in integer optimization raises the question if this method can be extended...