Determination of a consistent viscosity distribution in the Earth's mantle beneath northern and Central Europe

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Partial Weyl Law for Billiards

For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region $\Gamma$ of phase space. The leading term is proportional to the area of the billiard times the phase-space fraction of $\Gamma$. The boundary term is proportional to the fraction of the boundary where parallel trajectories belong to $\Gamma$. Our result is numerically confirmed for the mushroom billiard and the generic cosine billiard, where we count the number of chaotic and regular states, and for the elliptical billiard, where we consider rotating and oscillating states.Comment: 5 pages, 3 figures, derivation extended, cosine billiard adde

Conjugate gradient acceleration of iteratively re-weighted least squares methods

Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic functions. This transformation suggests an algorithmic scheme that solves a sequence of quadratic problems to be tackled efficiently by tools of numerical linear algebra. Its general scope and its usually simple implementation, transforming the initial non-convex and non-smooth minimization problem into a more familiar and easily solvable quadratic optimization problem, make it a versatile algorithm. However, despite its simplicity, versatility, and elegant analysis, the complexity of IRLS strongly depends on the way the solution of the successive quadratic optimizations is addressed. For the important special case of $\textit{compressed sensing}$ and sparse recovery problems in signal processing, we investigate theoretically and numerically how accurately one needs to solve the quadratic problems by means of the $\textit{conjugate gradient}$ (CG) method in each iteration in order to guarantee convergence. The use of the CG method may significantly speed-up the numerical solution of the quadratic subproblems, in particular, when fast matrix-vector multiplication (exploiting for instance the FFT) is available for the matrix involved. In addition, we study convergence rates. Our modified IRLS method outperforms state of the art first order methods such as Iterative Hard Thresholding (IHT) or Fast Iterative Soft-Thresholding Algorithm (FISTA) in many situations, especially in large dimensions. Moreover, IRLS is often able to recover sparse vectors from fewer measurements than required for IHT and FISTA.Comment: 40 page

Do women behave more reciprocally than men? Gender differences in real effort dictator games

We analyze dictator allocation decisions in an experiment where the recipients have to earn the pot to be divided with a real-effort task. As the recipients move before the dictators, their effort decisions resemble the first move in a trust game. Depending on the recipients' performance, the size of the pot is either high or low. We compare this real-effort treatment to a baseline treatment where the pot is a windfall gain and where a lottery determines the pot size. In the baseline treatment, reciprocity cannot play a role. We find that female dictators show reciprocity and decrease their taking-rates significantly in the real-effort treatment. This treatment effect is larger when female dictators make a decision on recipients who successfully generated a large pot compared to the case where the recipients performed poorly. By contrast, there is no treatment effect with male dictators, who generally exhibit more sefish behavior. --Gender,Reciprocity,Dictator Game,Real Effort

Are there gambling effects in incentive-compatible elicitations of reservation prices? An empirical analysis of the BDM-mechanism

Pricing research suggests incentive compatible evaluations of separate products in so-called monadic designs when consumers\u27 situation-specific WTP is to be elicited in a monopolistic purchase setting. In our study, the lottery-based BDM-mechanism is applied for measuring subjects\u27 WTP for a fast moving consumer good in binding one-on-one interviews at the point of purchase. In previous studies, the validity of elicited WTP measures is commonly checked within subjects with respect to indicators of face and criterion validity (such as interest in buying, preference ratings, compliance rates). In addition, we observed real purchases of a separate validation sample at the point of purchase, thus checking external validity between subjects. As a result, the BDM-based WTPs reveal a sufficient degree of internal face validity. However, the external validity in terms of a goodness of fit between WTP-based predictions and purchases of the validation sample is significantly reduced. Specifically, we observed a substantial underestimation of shares of non-buyers. Hence, a potential bias is indicated, leading to an overrating of consumers\u27 true WTP in the lottery-based BDM-mechanism in the setting of our survey

Gassmann triples with special cycle types and applications

We show that if one of various cycle types occurs in the permutation action of a finite group on the cosets of a given subgroup, then every almost conjugate subgroup is conjugate. As a number theoretic application, corresponding decomposition types of primes effect that a number field is determined by the Dedekind zeta function. As a geometric application, coverings of Riemannian manifolds with certain geodesic lifting behaviors must be isometric.Comment: 11 page

Are there gambling effects in incentive-compatible elicitations of reservation prices? An empirical analysis of the BDM-mechanism

Pricing research suggests incentive compatible evaluations of separate products in so-called monadic designs when consumers' situation-specific WTP is to be elicited in a monopolistic purchase setting. In our study, the lottery-based BDM-mechanism is applied for measuring subjects' WTP for a fast moving consumer good in binding one-on-one interviews at the point of purchase. In previous studies, the validity of elicited WTP measures is commonly checked within subjects with respect to indicators of face and criterion validity (such as interest in buying, preference ratings, compliance rates). In addition, we observed real purchases of a separate validation sample at the point of purchase, thus checking external validity between subjects. As a result, the BDM-based WTPs reveal a sufficient degree of internal face validity. However, the external validity in terms of a goodness of fit between WTP-based predictions and purchases of the validation sample is significantly reduced. Specifically, we observed a substantial underestimation of shares of non-buyers. Hence, a potential bias is indicated, leading to an overrating of consumers' true WTP in the lottery-based BDM-mechanism in the setting of our survey.Pricing, Willingness to Pay (WTP), BDM-mechanism, Validation