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The Dutch government compensates health insurance companies when insuring individuals who are estimated to have high health care costs. This is necessary to avoid insurers not offering services to certain groups or not providing them with a high quality of service. It is, however, unknown to what extent the differences in health care expenses by different groups of people are truly due to a poorer or better health status. We explore several statistical approaches that facilitate explaining the cause of these differences.

The paper analyses signals that have been measured by brain probes during surgery. First background noise is removed from the signals. The remaining signals are a superposition of spike trains which are subsequently assigned to different families. For this two techniques are used: classic PCA and code vectors. Both techniques confirm that amplitude is the distinguishing feature of spikes. Finally the presence of various types of periodicity in spike trains are examined using correlation and the interval shift histogram. The results allow the development of a visual aid for surgeons.

Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the electromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch. We investigate the present problem along two lines of attack. First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO. Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state.

The casting process of aluminum products involves the spatial distribution of alloying elements. It is essential that these elements are uniformly distributed in order to guarantee reliable and consistent products. This requires a good understanding of the main physical mechanisms that affect the solidification, in particular the thermodynamic description and its coupling to the transport processes of heat and mass that take place. The continuum modeling is reviewed and methods for handling the thermodynamics component of multi-element alloys are proposed. Savings in data-storage and computing costs on the order of 100 or more appear possible, when a combination of data-reduction and data-representation methods is used. To test the new approach a simplified model was proposed and shown to qualitatively capture the evolving solidification front.

Due to climate changes that are expected in the coming years, the characteristics of the rainfall will change. This can potentially cause flooding or have negative influences on agriculture and nature. In this research, we study the effects of this change in rainfall and investigate what can be done to reduce the undesirable consequences of these changes.

In this paper we consider the problem of shunting train units on a railway station. Train units arrive at and depart from the station according to a given train schedule and in between the units may have to be stored at the station. The assignment of arriving to departing train units (called matching) and the scheduling of the movements to realize this matching is called shunting. The goal is to realize the shunting using a minimal number of shunt movements. For a restricted version of this problem an ILP approach has been presented in the literature. In this paper, we consider the general shunting problem and derive a greedy heuristic approach and an exact solution method based on dynamic programming. Both methods are flexible in the sense that they allow the incorporation of practical planning rules and may be extended to cover additional requirements from practice.

Many processes in nature and engineering are governed by partial differential equations (PDEs). We focus on parabolic PDEs, that describe time-dependent phenomena like heat conduction, chemical concentration, and fluid flow. Even if we know that a unique solution exists, we can express it in closed form only under very strict circumstances. So, to understand what it looks like, we turn to numerical approximation. Historically, parabolic PDEs are solved using time-stepping. One first discretizes the PDE in space as to obtain a system of coupled ordinary differential equations in time. This system is then solved using the vast theory for ODEs. While efficient in terms of memory and computational cost, time-stepping schemes take global time steps, which are independent of spatial position. As a result, these methods cannot efficiently resolve details in localized regions of space and time. Moreover, being inherently sequential, they have limited possibilities for parallel computation. In this thesis, we take a different approach and reformulate the parabolic evolution equation as an equation posed in space and time simultaneously. Space-time methods mitigate the aforementioned issues, and moreover produce approximations to the unknown solution that are uniformly quasi-optimal. The focal point of this thesis is the space-time minimal residual (MR) method introduced by R. Andreev, that finds the approximation that minimizes both PDE- and initial error. We discuss its theoretical properties, provide numerical algorithms for its computation, and discuss its applicability in data assimilation (the problem of fusing measured data to its underlying PDE).

The goal of reflection seismic imaging is making images of the Earth subsurface using surface measurements of reflected seismic waves. Besides the position and orientation of subsurface reflecting interfaces it is a challenge to recover the size or amplitude of the discontinuities. We investigate two methods or techniques of reflection seismic imaging in order to improve the amplitude. First we study the \textsl{one-way wave equation} with attention to the amplitude of the waves. In our study of \textsl{reverse-time migration} the amplitude refers to the amplitude of the image. Though the approach in the thesis is formal, our results have practical implications for seismic imaging algorithms, which improve or correct the amplitudes. The one-way wave equation is a $1^{\rm st}$-order equation that describes wave propagation in a predetermined direction. We derive the equation and identify the steps that determine the wave amplitude. We introduce a \textsl{symmetric square root operator} and a wave field normalization operator and show that they provide the correct amplitude. The idea to use a symmetric square root is generally applicable. Our amplitude claims are numerically verified. The one-way wave equation is an application of \textsl{pseudo-differential operators}. \textsl{Reverse-time migration} (RTM) is an imaging method that uses simulations of the source and receiver wave fields through a slowly varying estimate of the subsurface medium. The receiver wave is an in reverse time continued field that matches the measurements. An \textsl{imaging condition} transforms the fields into an image of the small scale medium contrast. We investigate the linearized inverse problem and use the RTM procedure to reconstruct the perturbation of the medium. We model the scattering event by the scattering operator, which maps the medium perturbation to the scattered wave. We propose an approximate inverse of the scattering operator, derive a novel imaging condition and show that it yields a reconstruction of the perturbation with correct amplitude. The study extensively uses the theory of \textsl{Fourier integral operators} (FIO). Besides that we globally characterize the scattering operator as a FIO, we also obtain a local expression to calculate the amplitude explicitly. The claims are confirmed and illustrated by numerical simulations.