Icosahedral clusters: towards understanding the nature of the formation of quasicrystals

This thesis aims to enhance the understanding of quasicrystal formation by integrating global geometry optimization and atomic simulations using the Oscillating Pair Potential (OPP). Quasicrystals, with non-periodic long-range order and forbidden rotational symmetries, have captivated scientists since their discovery. This research combines the...

Analysis of Runge-Kutta methods using Butcher tableaus

This Bachelor thesis provides an analysis of Runge-Kutta methods using Butcher tableaus. Runge-Kutta method are numerical methods used for approximating initial value problems. A Runge-Kutta method can be classified as either an explicit or an implicit method. A special kind of implicit methods are diagonally implicit methods. The type of method...

Robust Tail Assignment: Incorporating Delay Predictions into a Tail Assignment Model to Decrease Flight Operation Costs

In this thesis a novel model is proposed to solve the Robust Tail Assignment problem. The Robust Tail Assignment problem aims to assign aircraft to flights, while minimize expected costs of operating a flight schedule, including expected delay costs. This problem is difficult, because delays can propagate between successive flights in the...

Data driven simulation of clouds using Markov Chain models with spatial dependence

Thanks to increasing computational resources, the grid sizes of global climate and weather prediction models are decreasing to scales at which subgrid processes, especially the evolution of clouds, can become spatially too variable for traditional deterministic parameterization approaches. We propose a stochastic parameterization in which clouds...

Multivariate generalisations of classical hypergeometric polynomials from Lie theory

In this thesis, we will be studying Lie groups and their connection to certain orthogonal polynomials. We will look into the classical Krawtchouk, Meixner and Laguerre polynomials, and the multivariate Krawtchouk and Meixner polynomials as defined by Iliev. Using representations of the Lie groups SU(2) and SU(1,1), it will be shown that the...

Een analytische en algebraïsche beschouwing van de Wilson- en Racahpolynomen

De Wilson- en Racahpolynomen zijn hypergeometrische orthogonale polynomen die helemaal bovenaan staan in het Askey-schema. Deze polynomen zijn de meest algemene hypergeometrische orthogonale polynomen in één variabele en generaliseren de andere hypergeometrische orthogonale polynomen in het Askey-schema.<br/><br/>In deze scriptie wordt ingegaan...

A comparison of the Hull-White model and BGM model: on the EPE of a swap portfolio

Interest rate products form a large segment of over-the-counter derivatives. When the interest rate became negative, for the first time, in July 2009, interest rate models needed to adjust. Where first a log-normal model, as the Brace Gatarek Musiela (BGM) model, might have seemed logical for interest-rate products, as they were<br/>bounded by...

GAN Driven Audio Synthesis: On using adversarial training for data driven audio generation

In this study, we investigate the usage of generative adversarial networks for modelling a collection of sounds. The proposed method incites an interpretation of musical sound synthesis based on audio collections rather than synthesizer component controls. This promises the generation of arbitrarily complex sounds without the restrictions of...

Determinacy of Infinite Games

This paper introduces the notion of infinite games, i.e., games in which two players take turns playing moves ad infinitum, so that player I wins if the sequence of moves is in a predetermined payoff set. Theorems are then provided about whether a player in such games can have a winning strategy. The first theorem, Gale-Stewart, shows that games...

Stochastic Genetics

In this bachelor thesis we use a stochastic model to aspire to explain biodiversity patterns in different ecosystems with selection advantage. The stochastic model we use is an extension of the mean­-field voter model where we include a selection factor. In the model individuals with two different types of alleles in two different ecosystems are...

Exploring Convolutional Neural Networks

In this thesis we have looked into the complexity of neural networks. Especially convolutional neural networks (CNNs), which are useful for image recognition, are looked into. In order to better understand the process in the neural networks, in the first half of this report a mathematical foundation for neural networks and CNNs is constructed....

Creating adaptive master Applied Mathematics graduates: Closing the gap between programme and professional career

We live in a fast-changing world, where higher engineering education focusses on creating engineers that will deal with upcoming technological innovations. It is important to think ahead and educate engineers that could work on these problems and develop technological solutions for them, and are adaptable to deal with the changes in the world....

Assessing the impact of wrong-way risk on valuation adjustments of a portfolio of interest rate swaps

We study the impact of wrong-way risk (WWR) on the credit valuation adjustment (CVA) of a portfolio of interest rate swaps (IRSs), using an intensity-based reduced form model. To model WWR in IRSs we create a dependence between he underlying market risk factor of the IRS and the survival probability of the <br/>counterparty. The focus lies on...

A Novel Method for Solving High-Dimensional Backward Stochastic Differential Equations Using Malliavin Calculus and Deep Learning

Backward stochastic differential equations (BSDE) are known to be a powerful tool in mathematical modeling due to their inherent connection with second-order parabolic partial differential equations (PDE) established by the non-linear Feynman-Kac relations. The fundamental power of BSDEs lies in the fact that with them one does not merely obtain...

Music Genre Detection: with Neural Networks

In this thesis we classify samples of music according to the genre that the music belongs to using neural networks. We divide this task into four parts. In the first part, we prepare the audio files to be used as input to a neural network. Specifically, we examine ways to create spectrograms. We then optimise the spectrograms by reducing and...

Elaboration on Kwapien's theorem: Representing bounded mean zero functions f as coboundary f = g ◦ T − g

In [8] Kwapien proved that every mean zero function f ∈ L∞[0, 1] we can<br/> write as f = g ◦ T − g for some g ∈ L∞[0, 1] and some measure preserving<br/> transformation T of [0, 1]. However, as was discovered in [4] there is a gap<br/> in the proof for the case that f is not continuous. The aim of this bachelor<br/> thesis...