A Short Introduction to Model Selection, Kolmogorov Complexity and Minimum Description Length (MDL)

The concept of overfitting in model selection is explained and demonstrated with an example. After providing some background information on information theory and Kolmogorov complexity, we provide a short explanation of Minimum Description Length and error minimization. We conclude with a discussion of the typical features of overfitting in model selection.Comment: 20 pages, Chapter 1 of The Paradox of Overfitting, Master's thesis, Rijksuniversiteit Groningen, 200

Convergence of Income Growth Rates in Evolutionary Agent-Based Economics

We consider a heterogeneous agent-based economic model where economic agents have strictly bounded rationality and where income allocation strategies evolve through selective imitation. Income is calculated by a Cobb-Douglas type production function, and selection of strategies for imitation depends on the income growth rate they generate. We show that under these conditions, when an agent adopts a new strategy, the effect on its income growth rate is immediately visible to other agents, which allows a group of imitating agents to quickly adapt their strategies when needed.Comment: 5 pages, 2 figure

Convergence of infinite element methods for scalar waveguide problems

We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both the Perfectly Matched Layer (PML) method and the Hardy space infinite element method in a unified framework. We treat both diffraction and resonance problems. The theoretical error bounds are compared with errors in numerical experiments

Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problems

The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Non-physical modes of the solution are identified by the position of poles of the solution's spatial Laplace transform in the complex plane. By requiring the Laplace transform to be analytic on some problem dependent complex half-plane, these modes can be suppressed. The resulting algorithm computes a finite number of coefficients of a series expansion of the Laplace transform, thereby providing an approximation to the exact boundary condition. The resulting error decays super-algebraically with the number of coefficients, so relatively few additional degrees of freedom are sufficient to reduce the error to the level of the discretization error in the interior of the computational domain. The approach shows good results for the Schr\"odinger and the drift-diffusion equation but, in contrast to the one-dimensional case, exhibits instabilities for the wave and Klein-Gordon equation. Numerical examples are shown that demonstrate the good performance in the former and the instabilities in the latter case