1,347 research outputs found
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 of phase space. The leading term is proportional to
the area of the billiard times the phase-space fraction of . The
boundary term is proportional to the fraction of the boundary where parallel
trajectories belong to . 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 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 (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
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