The Words are not Enough: An Investigation into the Viability of Textual Complexity as a Feature for Recommendation Systems

Reading is an essential skill for any child to learn, and finding enjoyment in it can greatly contribute to developing proper reading comprehension. Finding the books they like could prove to be difficult. Utilizing collaborative filtering recommender systems to recommend books to children is a tricky task, the lack of user feedback makes it...

Decreasing message complexity in Byzantine Fault Tolerant communications using Consistent-Broadcast

During this research we have replaced Bracha’s layer in the state-of-the-art Bracha-Dolev protocol to improve the performance by decreasing the message complexity of the protocol running on top of a given network topology so long as the requirements stated by Bracha and Dolev are met. Bracha-Dolev is an algorithm that is used to establish a...

Simplicial Neural Networks in a physical application

Artificial Intelligence in the form of neural networks is becoming wide spread. This report focuses on a specific form of neural networks, Simplicial Neural Networks. After presenting their advantages and how they were implemented in Python by using the code of [1], they are tested in 2 experiments to explore their applicability in solving...

First-order methods to recover the measurement operators and states of bipartite quantum correlations

In this thesis, we start with giving a mathematical description of bipartite quantum correlations and how they are built up in the Tensor model. This is needed because we want to recover the state and the operators when only the bipartite quantum correlation is known. In the literature, there are see-saw algorithms to...

Noiseless clusters and perturbations in networks of coupled quantum harmonic oscillators

In this thesis, networks of coupled quantum harmonic oscillators are studied. The dynamics of these networks are determined by single-frequency vibrations of the entire network called normal modes. We study the behavior of the nor- mal modes when the network is coupled to a thermodynamical heat bath by looking at the Lindblad Master Equation of...

Riemann's Explicit Formula and the Prime Number Theorem

This thesis presents an insight in the Riemann zeta function and the prime number theorem at an undergraduate mathematical level. The main goal is to construct an explicit formula for the prime counting function and to prove the prime number theorem using the zeta function and a Tauberian theorem. The Riemann zeta function can be continued...

Combining genetic regulatory network models and a random matrix approach to solve large biological networks

In this thesis we study genetic regulatory networks using a minimal nonlinear<br/>model from literature and extend this to multi-compartment gene-to-gene interaction networks using both numerical simulations and random matrix theory.<br/>When we add perturbations to a system of two interaction networks, the largest<br/>eigenvalue becomes larger,...

On discrete and continuous state adaptive network models: with an application to self-organisation in swarming systems

We consider adaptive network models with discrete and continuous state sets obeying dynamical rules that enable application to swarming systems. The 2-state adaptive network contains a supercritical pitchfork bifurcation in the transition between ordered and disordered stationary solutions. We derive an adaptive network model that works on a...

Het toepassen van complexe methodes voor het schatten van afgeleiden

It is possible to estimate derivatives of real functions with complex methods. These complex methods can increase speed or accuracy. The functions needs to be known to determine the derivative with a complex method.

The Borsuk-Ulam Theorem in Combinatorics

We examine and prove the Borsuk-Ulam theorem and its combinatorial equivalent Fan's lemma. The theory of simplicial complexes and triangulations plays an important role in this. The Borsuk-Ulam theorem and Fan's lemma will be used to provide proofs for the Brouwer fixed point theorem and the combinatorial Sperner's lemma. Lastly the Borsuk-Ulam...

Nulpunten van de Riemann zeta functie

Dit verslag geeft als eerste een overzicht van basis resultaten van de Riemann zeta functie. Vervolgens worden twee meer specifieke resultaten laten zien met betrekking tot de nulpunten van deze Riemann zeta functie.

Calibration Procedure for Complex Permittivity Extraction Using an Open-Ended Coaxial Probe

As a part of the development of a device for skin cancer tissue detection, this report is about the development of a new calibration procedure for measuring complex permittivity with an open-ended coaxial probe. The developed method is based on comparing the measured reflection coefficient to an array of reference coefficients for different...

De verschillende aspecten van Riemanns ?-functie

In dit verslag wordt de analytische uitbreiding van de ?-functie besproken, samen met nog drie andere alternatieve schrijfwijzen. Er worden een aantal eigenschappen van de ?-functie en haar nulpunten afgeleid, waaronder een formule van het aantal nulpunten N(T) met imaginair deel tussen 0 en T. Daarna wordt numeriek aangetoond dat de pair...

Eulers productformule voor de sinus

In dit Bachelor Eindproject is Eulers productformule voor de sinus bestudeerd. Allereerst worden er vier bewijzen van deze formule gegeven en daarna worden deze bewijzen vergeleken.

DE-XRT method to separate platinum ore

The Potgietersus Platinum mine is an open pit mine in the Bushveld Complex in South Africa. During the mining different rock types are mined, some of these are detrimental. The goal of the research done in this project is to assess the feasibility of Dual Energy X-ray Transmission (DE-XRT) to distinguish the detrimental ore types from the rest...