This thesis aims to improve the current risk classification for (company) car insurance at Achmea, focusing on WAM and ARD coverages. By using cluster analysis, specifically K-prototypes and spectral clustering, policyholders are grouped based on zip codes and license plates to enhance the current claim frequency models (and thus premium pricing models). The application of spectral clustering (with U-SPEC as the observation reduction technique) led to significant improvement of the current claim frequency GLM for the ARD coverage. This thesis highlights the potential of cluster analysis in actuarial science, offering new methods for mixed data types and high-dimensional clustering, thus providing a foundation for more accurate claim frequency models. The time stabilities and stabilities with respect to the number of observations of the clusters are also investigated.

Extreme Ultraviolet lithography is a vital step in the production of cutting edge computer chips that drive emergent technologies like AI, VR and the internet of things [1]. Careful control of Ultraviolet light beams by EUV machine modules such as the Unicom, Uniformity correction module, enable extremely precise printing of nano-scale structures on these chips. This thesis focuses on the construction of a model that predicts the impact of the Unicom on EUV illumination in ASML's lithography machines. Such a model could be used in a predictive maintenance scheme to prevent a fraction of unscheduled machine downtime, which can be estimated to cost ASML's customers around 38 million dollars per machine per year [2-4]. Similar problems have been tackled before [5, 6], but both existing models disregard multiple properties of the EUV machine and are incompatible with the type of measurements obtained by ASML. Therefore, the question remains how an accurate Unicom model can be constructed.
In this thesis, a physics based Unicom model was developed that can be fine-tuned to machine specific measurements. Significant reductions of up to 90.3% of prediction errors were obtained by using the model. Overall, making use of the model provided better or equivalent predictions when compared to not using the model for all but one of the investigated indicators of prediction quality. For the latter indicator errors remained within the desired bound, but further investigation is needed to discover why the Unicom model adversely affected this indicator. With an average execution time of 31.4 s, the created Unicom model in general enables swift and substantial accuracy gains.

This paper primarily employs Item Response Theory (IRT) to estimate item characteristics and the proficiency levels of students as reflected in the exam results. The process includes the application of algorithms for item characteristic parameter estimation and the utilization of statistical techniques for item selection from an item pool. Additionally, Classical Test Theory (CTT) is also used to gain insights into the item characteristics. The mathematical frameworks behind every algorithm and model will be introduced in detail. Our ultimate objective is to create an item bank that unifies all items from various exam versions onto a common scale. The technique to put items from different versions on the same scale is the test equating technique, and it will also be described in detail.

After a comprehensive analysis to determine the appropriate model within the framework of Item Response Theory (IRT), the Rasch model has been selected for all versions of the exams. One item from version 9 has been removed from the item pool due to its unsatisfactory item fit. Based on the Item-Map plot, the conclusion can be made that all three exam versions appear to be relatively easy for students to answer, as evidenced by the high bar of the exams. Ultimately, the item bank has been successfully established through the application of two test-equating methods, with results indicating its reliability.

We introduce a method of designing NMR pulse sequences, with a specific focus toward complete decoupling of carbon-13 spin qubits coupled to a nitrogen-vacancy (NV) center in diamond. Using Average Hamiltonian Theory, we calculate different intermediate Hamiltonians corresponding to different rotations implemented by NMR pulses. Two novel pulse sequences are obtained containing 24 and 12 evolution periods respectively. Assuming ideal and instantaneous pulses, performance for both sequences is better than the WAHUHA + echo sequence for total evolution times of less than 5 ms and comparable for greater evolution times. Analysis of sensitivity points toward non-robustness for angle errors in the applied pulses when the direction of pulses is not taken into account, however this can be corrected for using chirality sums. Suggestions for further research include the study of non-globally applied pulses and application of the design method to non-zero effective Hamiltonians.

The aim of this thesis is to simulate quantum spin chains at a finite temperature. This has been achieved by using purification to write the incoherent thermal states of the spin chain as pure states, after which the matrix product state (MPS) formalism to simulate the spin chain. The influence of temperature on the spin chain has been tested by comparing chain magnetization to the strength of the external magnetic field at different temperatures. Real time evolution has also been applied under the assumption that the time evolution is adiabatic. The results have been compared to the analytical solution found by directly calculating the density matrix. The model is very accurate for imaginary time evolution, which is required to evolve the system to the desired temperature. During real time evolution the results oscillate slightly around the analytical solution, which remains constant. This oscillation is a consequence of model truncation and the Suzuki-Trotter approximation. The effect of allocating more numerical resources to limit this phenomenon is explored, and a method to increase reachable timescales by decreasing entanglement growth in the chain over time is tested and verified.

The potato is a plant that can grow from another potato tuber. Farmers and producers have to contend with the declining quality of soil and are producing less vital potato tubers. The differences in emergence speed between batches of the same variety of potato tubers cannot be explained. This is why Project ‘Flight to Vitality’ (FtV) is developing a diagnostic test to make predictions about the vitality of different varieties of potato tubers, with various measurements. One of these measurements consists of hyperspectral images taken from potato tubers, prior to planting. Another measurement is the actual growth of the potato plants, which was recorded after emerging. This thesis attempts to relate both measurements by means of regression. After grouping both data sets on each batch of tubers, we are left with an explanatory matrix that has more columns than rows. This causes an ordinary least squares model to overfit new data. Therefore an alternative regression model is proposed, which is Partial Least Squares (PLS). The goal of PLS is to find latent variables, that maximizes the covariance between both sets, to explain the variance in the explanatory space as good as possible, and to provide good predictions on the response space. The predictive performance of PLS, which is for the most part measured with the Mean Squared Error, relies on the number of latent variables used. Cross-validation is performed for finding this number. By splitting the data into training and testing sets, we evaluate PLS and find that some of the variances are explained well with PLS. This model is extended by including variable selection on the explanatory variables, which are the frequency bands taken from hyperspectral imaging. With this extension, the same experiment was rerun and we saw that the predictive performance can increase. However, the number of variables omitted seem to be inconsistent across different experiments. We have also found that the performance can slightly decrease, but the number of omitted variables remain much more consistent (and were overlapping across different experiments). With this established baseline model, we have also looked at the predictive information on different tuber parts. By conducting a similar experiment, it appears that the model is capable of explaining almost all variance and performs outstanding. We have also looked at leaving one tuber variety out before training the model. This variety is then used for evaluation. From this experiment, it seems that there is a strong variety-dependent component found in the FtV data, which makes it impossible to predict the relative vitality of the tubers. Finally, we compare PLS with another model that belongs to the same Krylov Subspace method, which is LSQR. The same experiment is conducted on both models and it seems like PLS and LSQR are not identical in terms of finding the number of latent variables used. Regardless, as an independent regression estimator, LSQR is much faster than PLS.

Ammonia (NH3) is an important chemical compound in the nitrogen cycle. Ammonia is an essential nutrient and an important part of fertilizer, which in soil leads to increased growth of crops. However, the current excess of NH3 emissions is a hazard to environmental and human health. While ammonia
emissions need to be reduced, the emission estimates are still highly uncertain.
In this study, a method is developed to combine the chemical transport model LOTOS-EUROS with measured ammonia concentrations to improve the ammonia emission estimates in the Netherlands and the surrounding regions. The measurements used are generated by the miniDOAS instruments on LML stations and the IRS instrument on board the future MTG-S satellite. The proposed method is an adjoint-free 4DVar method. The 4DVar method aims to retrieve the emission parameters for which the LOTOS-EUROS model determines NH3 concentrations that resemble the measurements while keeping the emissions fairly similar to the original inventories. A linear approximate model has been developed, which uses the near-linearity of the NH3 concentrations in terms
of the NH3 emissions. When using the approximate model, the 4DVar
method can be solved without using an adjoint model, making the method adjoint-free. Subsequently, the 4DVar cost function is rewritten to allow the emission parameters to have a lognormal prior distribution. A maximum likelihood approach is developed to estimate the parameters of both the prior distribution of the emissions and the likelihood of the measured observations. Last, a preconditioner in reduced space has been considered, to estimate emissions on a fine spatial resolution, while keeping the computational cost
feasible. This preconditioner uses the property that the emission parameters are correlated in space. First, the methodology has been tested in an identical twin experiment where the emissions vary only in time and strength, using the LML observations. It was concluded that the methodology worked well
for short periods (less than 30 days), but the results were dominated by observational noise. When using the real observations in the 4DVar
method, the results seem unrealistic Second, the method has been tested in an identical twin experiment where emissions vary in space, as well as in time and strength. Here, synthetic IRS observations of the future MTG-S satellite are
used. The optimized emissions did resemble the true emissions of the twin experiment. Observational noise appeared to no longer be an issue. However, the results were not perfect. The regions with the highest emission increase appeared to be underestimated, low emission areas appeared to have large
relative estimation errors, and estimates for coastal regions seemed to be incorrect. Hence, on a local scale, the emission estimates can be imperfect, but overall the adjoint-free 4DVar method does greatly improve the emission inventories.

Magnetic resonance imaging (MRI) scanners are a crucial diagnostic tool for radiologists. They are able to render two­ and three­dimensional images of the body without exposure to harmful radiation. MRI systems are, however, costly to build and maintain. This adversely impacts access to these scanners in developing regions. In an effort to combat this problem, a low­field MRI scanner is being developed. Conventional MRI scanners utilize a superconducting solenoid to generate the main magnetic field. The low­field scanner, on the other hand, induces the main magnetic field through a Hallbach array of permanent neodymium magnets. While beneficial for production and maintenance costs, as well as portability, the Hallbach array is not able to generate a perfectly homogeneous magnetic field. The inhomogeneities present in the main magnetic field result in distortion of the images when reconstructed using conventional fast Fourier transform (FFT) methods. To counteract this, a reconstruction method that utilizes field information needs to be employed. In this thesis, existing methods to determine and utilize the field information to correct image distortion are explored. From this analysis, it is evident that model­based (MB) methods are most suitable for reconstruction of data from the low­field scanner. Current MB methods are only implemented for two­dimensional reconstruction. The goal of this thesis is to expand these methods to three­dimensional reconstruction. A novel MB method for three­dimensional reconstruction is presented. This new method is able to circumvent memory constraints that arise from reconstruction of large data sets. Though the new method requires several hours to reconstruct a 128 × 128 × 30 data set, visual inspection indicates that an accurate result is achieved.

In the fight against money laundering, demand for data-driven Anti-Money Laundering (AML) solutions is growing. Particularly anomaly detection algorithms have proven effective in the detection of suspicious customer behaviour, as well as observing patterns otherwise hidden in customer transaction data. In this thesis, the Isolation Forest anomaly detection algorithm is studied in combination with the model-specific local explanation method, Multiple Indicator Local Depth-based Isolation Forest Feature Importance (MI-Local-DIFFI). To expand Isolation Forest to mixed-attribute data sets, the incorporation of nominal features is explored in more detail. This analysis resulted in the introduction of Isolation Forest with Categorical Sampling (iForestCS ), a methodology that directly incorporates nominal attributes into an isolation tree without the need of encoding it onto a numerical scale. This method is tested against different encoding strategies and Isolation Forest Conditional Anomaly Detection (iForestCAD) using different synthetic data sets. The method shows improved performance to the utilization of encoding strategies for different parameters of the underlying synthetic data. Furthermore, this thesis explores the potential of ternary Isolation Forest, in which the branching strategy of an isolation tree is expanded to produce three child nodes. It is demonstrated using synthetic data, that particularly the performance of MI-Local-DIFFI reduces when applied to a ternary Isolation Forest. Finally, the research considers a practical use-case. Using customer transaction data from Triodos Bank, the locally explainable Isolation Forest is applied to mixed-attribute customer transaction data. This has provided useful insight and resulted in the detection of suspicious customer behaviour and the introduction of new rules into business practices. Although the most interesting customer behaviour did not directly emanate from the nominal attributes, the method of incorporating nominal features resulted in differences when considering the anomalies with the highest anomaly scores.

To regulate pollution emission of $\text{NO}_2$ and greenhouse gasses like carbon dioxide and methane, satellite images of the TROPOspheric Monitoring Instrument (TROPOMI) are used to map the spread of air pollution. This instrument delivers near-daily 'snapshots' of the $\text{NO}_2$ concentration over the whole Earth. In this report, first, the spread of $\text{NO}_2$ pollution is modelled using a so called convection-diffusion equation. This equation is constructed from a convection term, which contributes to how much the wind transports matter, and a diffusion term which described the natural mixing of gases. Next, $\text{NO}_2$ pollution sources were reconstructed using the inverse of the time propagation of the model. Thus, known $\text{NO}_2$ concentrations are used to reconstruct temporal information. By finding out what is missing between data snapshots, sources can be reconstructed. The verification of the algorithm was first performed on artificial data, after which it was applied to experimental data.

The convection-diffusion equation that was used is a two dimensional equation, using longitude and latitude as Cartesian coordinates. The equation was solved by the method of lines, i.e. first a spatial discretisation was made using the Finite Volume Method, after which time integration methods were used to propagate the problem in time. In this report two time integration methods formed the basis for the time propagation and two source reconstruction algorithms. The algorithms take two $\text{NO}_2$ snapshots $\textbf{y}_n$ and $\textbf{y}_{n+m}$, with $m$ time steps in between. First the inverse form of Forward Euler is used, which performed well on artificial data on a small time scale. Afterwards the Backward Euler method is used to define the inverse problem of finding the source function. This algorithm performed well on artificial data with 24 hours between snapshots. The algorithms were found to be sensitive to noise and to be influenced greatly by the second $\text{NO}_2$ snapshot. After applying the algorithm to experimental data it was found that the algorithm is able to localise extended sources of emissions, but is not capable of pin-pointing individual point sources. In addition, sources with low emission rates were left undetected due to information being lost in the noise. Emission rates were not reconstructed accurately either, although it was able to find the main sources of emissions. The performance of the algorithm will take advantage from more frequent data. With this improvement, this method is a viable option for finding not only $\text{NO}_2$ sources, but can also be applied to other tropospheric gases.

Magnetic Resonance Imaging is one of the most widely used imaging modalities nowadays and it performs especially well imaging human organs such as the brain and liver. One of its main limitations is the relatively long imaging times, to overcome this issue and speed up the data acquisition, several techniques such as Parallel Imaging or PI have been developed. These techniques require advanced hardware and software to be able to decrease the acquisition time. On the hardware side, a highly efficient insert gradient coil has been designed and built at the University Medical Center Utrecht. Specialized software has to be implemented to optimally make use of this hardware. One of the recently proposed PI methods called Wave-CAIPI has been proved to achieve a ninth fold acceleration factor without compromising image quality. This project aims to investigate the time gain that can be achieved when combing the insert gradient coil with a Wave-CAIPI strategy. Two main aspects are reviewed. The first one is the maximum achievable under-sampling factor that does not compromise image quality. The second one is the decrease in acquisition time that can be obtained when using the insert gradient coil compared to conventional gradient systems while maintaining image quality. To do so, the strategy has been implemented and extensive simulations have been performed to optimize the MR acquisition parameters. To prove the results from the simulations, the Wave-CAIPI sequence was implemented in a 7T scanner at the UMCU, where the acquired data was retrospectively under-sampled, obtaining the wave image to be further reconstructed. Limitations of previous works on Wave-CAIPI have been the gradient specifications, which can be overcome by the high-efficiency coil. It has been concluded that shorter acquisition times without compromising image quality are possible when using the insert coil compared with conventional systems. The time gain can be up to a factor of five, and sixteen fold under-sampling factors could be possible. The time gain can be especially useful for Echo Planar Imaging sequences, where switching faster gradients allows to acquire more signals in less time. The next steps for this research are to prospectively under-sample the data in a Wave-CAIPI fashion with a sixteen under-sampling factor and corroborate if sequences such as Echo Planar Imaging can be benefited with the time gain.

This thesis covers the power load flow problem and three numerical methods which can be used as a solution. We firstly discuss the concepts from electrical engineering required to discribe the problem. This includes alternating current and voltage and admittances of various electrical elements. We then use these concepts to derive a set of equations that govern how power flows through a network. To solve these equations, we consider the Newton-Raphson, line-search and trust-region algorithms. For these methods, we also look at its convergence and the amount of computational power required. We conclude in the cases where the parameters of the electrical network are within reasonable bounds, the Newton-Raphson algorithm is sufficient in precision and requires the least computational power. Otherwise, one of the other two methods may be tried.

In cases that the voltage source is made of multiple cos’s and we can compensate the current, it is always possible with the first Cauer form. This is caused by the shape of the found transfer function Z(s). This transfer function is a fraction where the odd powers of s are in the numerator, while in the denominator are only even powers of s. In this way the conditions 1 and 3 in chapter 4.2 are satisfied. For this special type of Z(s) satisfying condition 2, is having positive coefficients in the First Cauer form, hence the conclusion. In the tables in this thesis, it seems that when the first Cauer form works, the other forms areworking as well. It seems that the method used in this thesis to find a controller only works for small R, L and C. In the example the improved PF is optimal, like one would expect. I conclude that the method used in this thesis is working fine.

Danieli Corus supplies tailor-made solutions for the global steel industry. Cameras are used in tuyeres of blast furnaces to detect physical aspects and irregularities. No operator could monitor those videos all day, which is why video analyses are needed. A program is written to analyse a test video and give information about the temperature, the injection of pulverized coal and the movement of rocks. The mathematical background of these calculations is presented, which depend on the transport of light from the blast furnace to the camera through the tuyere. Also the implementation of the calculations can be found. The results are interpreted and discussed and further improvements are suggested.

In this thesis the stability type of y=0 is being considered for the delay differential equation y''(t) + ay(t) + by(t-1) = 0 with a and b real numbers. It is already known that y=0 is stable when b=0 and a>0 and unstable when b=0 and a<0. The aim of this project is to determine the stability of y=0 for all values of a and b. First, the general stability theory for delay differential equations was highlighted before giving an in-depth stability analysis of the equation y''(t) + ay(t) + by(t-1) = 0. It turns out that a theorem of Pontryagin (1908 -1988) is really helpful for answering these stability questions. Due to this theorem all values for a and b are determined such that y=0 is asymptotically stable for y''(t) + ay(t) + by(t-1) = 0. However, this does not cover the stability type of y=0 for all values of a and b. So more analysis was done in order to give a full answer of the stability problem. The full answer was not achieved as there are still values for a and b where the stability is unknown. Finally, numerical solutions of y''(t) + ay(t) + by(t-1) = 0 are shown to confirm the results that are obtained.

The theory of active contours is applied to microscopic images of cells. A model is developed that approximates cell borders by dynamic curves. This model is based on gradient vector flow (GVF), an external force that acts on the contours. Both active contours and the GVF force field are defined as functions that minimize certain functionals. The corresponding Euler-Lagrange equations are derived and analyzed theoretically. A number of auxiliary algorithms are designed to aid the performance of the main snake algorithm, including a preprocessing algorithm, a method for detecting cell centers and an algorithm that detects areas devoid of cells. Results of the snake algorithm are presented, along with practical considerations regarding parameter choice. Finally, statistical methods are applied to the results to demonstrate their usefulness.

In this thesis we apply the numerical method of Morphological Geometric Active Contours as proposed by Alvarez, Baumela and Marquez-Neila to microscopic images of plant cells. The goal is to find all plant cells in the images, and then to find their cell walls. This is done in order to calculate certain properties of these cells automatically, such as area, perimeter and ellipticity. As the name suggests, mathematical morphology plays a big part in morphological GAC. This thesis describes the theory behind morphological GAC, mathematical morphology and the implementation in Python of the actual algorithm. We made two adaptations compared to the original model. These are a change in the conditions of the balloon force, and an extra step at the end of each iteration. The change in the balloon force was made to keep edges stronger. The extra step was added to improve smoothness of the contours, since the smoothing parameter had no effect.

In this paper two ways of modeling the secondary electron yields of an insula-
tor under electron irradiation, are discussed and coupled. The drift-diusion-
reaction model is used to investigate the secondary yields and charging eects.