Finding Structures within Large Point Sets

We investigate two open problems in discrete geometry regarding how large subsets of sets of points need to be in order for certain structures to emerge. First of all there is the Erdős-Szekeres convex polygon problem, also known as the Happy Ending problem. Interestingly, there is a clear distinction between the number of points required to...

Analyzing the Neural Dynamics of Emotional Associative Memory Encoding through Data-Driven Modeling

Researchers have been interested in studying the connection between emotion and memory for decades but much remains unknown due to the elusive nature of the human brain. Furthering our understanding of the phenomenon is crucial for improving the treatment of neurological disorders associated with emotion dysregulation, as well as for enhancing...

A Note on Integrity: ILP Modelling and Analysis on Graph Families

This thesis provides a fresh perspective on the (vertex) integrity of graphs, serving as a measure of network robustness. The study begins by introducing fundamental concepts and methods for evaluating the integrity of different graph families. An Integer Linear Programming (ILP) model, specifically designed for assessing integrity, is then...

Real Equiangular Lines

A set of lines passing through the origin in Euclidean space is called equiangular if the angle between any two lines is the same. The question of finding the maximum number of such lines, N(d) in any dimension d is an extensively studied problem. Closely related, is the problem of finding the maximum number of lines, N_α(d), such that the...

The Connectivity Framework as a Tool to plan Nature Restoration Measures: A graph-theory approach to assess aquatic habitat connectivity of the Sliedrechtse Biesbosch

This study assesses the application of graph theory to examine the connectivity of aquatic habitat in the Sliedrechtse Biesbosch and preserve or improve the area’s ecological value. The study addresses the relation between hydrodynamics and ecology, and evaluates different definitions of connectivity. Graph theory provides a novel and promising...

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,...

Topological Properties of Semantic Networks

The main goal of this thesis is to understand the topological properties of semantic networks, to find language-specific patterns, and to investigate their connection principles. Interpreting unstructured texts in natural language is a crucial task for computers. Natural Language Processing (NLP) applications rely on semantic networks for...

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...

Temporal Analysis of Accessibility Using Complex Network Theory

Urban areas are evolving in terms of their growing population and their developing systems and infrastructure. This evolution brings about concerns regarding social equity, which refers to the fairness of distribution of certain attributes to groups or individuals. Transport equity is one of the dimensions of this issue, and accessibility...

A topological characterisation of looped drainage networks

Hydrodynamic models are used to analyse water networks (water distribution, drainage, surface water, district heating, etc.). The non-linear nature of water flows necessitates the use of iterative solution methods in hydraulic modelling. This requires a relatively large computational effort. To reduce this effort, networks, network forcing...

Reuse: On Evaluating the Fitness of Spatial Configurations Before & After Retrofitting for Reuse of Architectural Heritage

Focusing on the quality of reuse of buildings with respect to the efficiency of human movement patterns and the effectiveness of allocation of functional spaces with respect to their needs for social encounter and avoidance reveals the configurative nature and the human impact of architectural design. By comparing such functionality assessments...

Configraphics: Graph Theoretical Methods for Design and Analysis of Spatial Configurations

This dissertation reports a PhD research on mathematical-computational models, methods, and techniques for analysis, synthesis, and evaluation of spatial configurations in architecture and urban design. Spatial configuration is a technical term that refers to the particular way in which a set of spaces are connected to one another as a network....