Reinforcement Learning for minimizing the total waiting time of passengers in a Taxi Dispatch Problem

A Taxi Dispatch Problem involves assigning taxis to requests of passengers who are waiting at different locations for a trip. In today's economy and society, the Taxi Dispatch Problem and other transport problems can be found everywhere. Not only in transporting people, but also in food delivery from restaurants and package delivery for all kind...

Duality in interacting particle systems out of equilibrium

In this thesis we study a class of interacting particle systems sharing a duality property. This class includes the Symmetric Inclusion Process (SIP(2k)), the Symmetric Exclusion Process (SEP(2j)) and the Independent Random Walkers (IRW). When these systems are in equilibrium (namely they are isolated from the exterior) they admit stationary...

Non-imaging optics: Using Laplacian magic windows and Zernike polynomials

In this report a semi-analytic solution to the Laplacian magic window is proposed. The Laplacian magic window is a term recently introduced in 2017[2]. When a uniform wavefront hits a refractive surface, it creates an illumination distribution behind the surface. When the curvature of the surface is sufficiently small, it can be related linearly...

Exoplanet surface mapping

In this thesis we consider the reconstruction of albedo maps of exoplanets. This is done with a new variant of spin-orbit tomography that has been described in [Cowan and Agol, 2008] and more in depth in [Fujii and Kawahara, 2012]. This method reconstructs the albedo map from the reflected-light curve, the total intensity of the light that...

Akiyama's Nim

Akiyama’s Nim is een 3d versie van een onpartijdig combinatorisch spel genaamd Wythoffs Nim. Het spel van Wythoff kan met twee stapels munten gespeeld worden. Elke positie in dit spel komt overeen met een getal dat als temperatuur te zien is waarbij posities met temperatuur 0 koud genoemd worden. Er is een makkelijke formule voor de koude...

Cleavage and unbinding times of CRISPR associated proteins

In this thesis the CRISPR-Cas9 mechanism, a promising mechanism for geneediting, is considered. Closed form expressions are derived for the probability and time to cleave or unbind for the associated Cas9 protein. The mechanism can be modelled mathematically by a birth and death process, therefore the expressions could be derived using Markov...

Ambulancelocaties bepalen met een benadering van het hypercube model

De locaties van ambulancestations zijn van belang bij het redden van levens. Dit onderzoek beschrijft een Mixed Integer Lineair Programming (MILP) model die de optimale locaties van ambulances bepaald zodat het dekkingsniveau maximaal is. Het dekkingsniveau is het percentage van het totale aantal oproepen waarbij een ambulance binnen een...

Quantum Algorithms and their Implementation on Quantum Computer Simulators

Quantum computation is becoming an increasingly interesting field, especially with the rise of real quantum computers. However, current quantum processors contain a few tens of error-prone qubits and the realization of large-scale quantum computers is still very challenging. Therefore, quantum computer simulators are particularly suitable for...

The Brachistochrone Problem: From Euler to Quantum

In this thesis I take a look at various aspects of the brachistochrone problem. In the first half I consider the classical brachistochrone problem, without friction, after which I generalize to also consider drag; friction proportional to the squared speed. I do this numerically, with the shooting method, and following some papers, which Euler...