Trace functions as Laplace transforms

We study trace functions on the form t\to\tr f(A+tB) where $f$ is a real function defined on the positive half-line, and $A$ and $B$ are matrices such that $A$ is positive definite and $B$ is positive semi-definite. If $f$ is non-negative and operator monotone decreasing, then such a trace function can be written as the Laplace transform of a positive measure. The question is related to the Bessis-Moussa-Villani conjecture. Key words: Trace functions, BMV-conjecture.Comment: Minor change of style, update of referenc

Cluster temperatures and non-extensive thermo-statistics

We propose a novel component to the understanding of the temperature structure of galaxy clusters which does not rely on any heating or cooling mechanism. The new ingredient is the use of non-extensive thermo-statistics which is based on the natural generalization of entropy for systems with long-range interactions. Such interactions include gravity and attraction or repulsion due to charges. We explain that there is growing theoretical indications for the need of this generalization for large cosmological structures. The observed pseudo temperature is generally different from the true thermodynamic temperature, and we clarify the connection between the two. We explain that this distinction is most important in the central part of the cluster where the density profile is most shallow. We show that the observed pseudo temperature may differ up to a factor 2/5 from the true thermodynamic temperature, either larger or smaller. In general the M-T and L-T relations will be affected, and the central DM slope derived through hydrostatic equilibrium may be either more shallow or steeper. We show how the true temperature can be extracted correctly either from the spectrum or from the shape of the Doppler broadening of spectral lines.Comment: 11 pages, 1 figur

Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem

We describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is described by a complete trinary symbolic dynamics for scaled energies larger then $\epsilon_c=0.328782\ldots$.Comment: 15 pages PostScript uuencoded with figure

Forecasting the consumption effect of taxing foods containing saturated fat

The purpose of the current paper is to explain how one can forecast the effect of an elected tax on saturated fat on the demand for butter. The tax is to take affect from the first of January 2010 in Denmark. The tax is supposed to affect the consumption of saturated fat and especially high consuming households are of interest. Quantile regression is thus better suited than mean regression. Interest centre on at risk groups with larger consumption, but we are also interested in a simple measure that measure the total effect of the tax change, i.e. the unconditional quantile. The former can easily be obtained from the quantile regression while it is proposed to use simulations in the latter case. In mean regression a close form formula for calculating the unconditional mean from the conditional mean exist; unfortunately this is not the case for quantile regression. Hence, simulations are needed. The principle in the proposed method is the same as the methodology used in a recent published paper for comparing labour income distributions. A refinement of this methodology is suggested.Quantile Regression, Simulation, Healthy Diet, Public Policy., Agricultural and Food Policy,

New developments in fruit and vegetables consumption in the period 1999-2004 in Denmark - A quantile regression approach

The development in the consumption of fruit and vegetables in the period 1999-2004 in Denmark was investigated using quantile regression and two previously overlooked problems were identified. First, the change in the ten percent quantile samples decreased. This could have been caused by changes in the distribution of covariates. Therefore, the counterfactual decomposition of Machado and Mata (2005) was used and the methodology established that the change was not caused by alterations in the distribution of covariates but by changes in the coefficients and therefore a change in behaviour. The reason for this development is probably due to low income groups becoming relatively more income constrained since the gap to the high income group have grown considerably at the lower end of the distribution. The second problem was that the education inducing gap became larger in 2004 indicating that uneducated people have not responded as well to the health related information flow. These results suggest that information campaigns have not been as successful as previously thought; more importantly the results indicate that information campaigns alone will do a poor job in solving the identified problems. Other instruments targeting uneducated and low income groups more directly are needed. Instruments which make fruit and vegetables relatively cheaper would undoubtedly have an effect on low income groups and send a strong signal to the uneducated population.Quantile regression, Counterfactual decomposition, Expenditure distribution, Food Consumption/Nutrition/Food Safety,

The behaviour of shape and velocity anisotropy in dark matter haloes

Dark matter haloes from cosmological N-body simulations typically have triaxial shapes and anisotropic velocity distributions. Recently it has been shown that the velocity anisotropy, beta, of cosmological haloes and major merger remnants depends on direction in such a way that beta is largest along the major axis and smallest along the minor axis. In this work we use a wide range of non-cosmological N-body simulations to examine halo shapes and direction-dependence of velocity anisotropy profiles. For each of our simulated haloes we define 48 cones pointing in different directions, and from the particles inside each cone we compute velocity anisotropy profiles. We find that elongated haloes can have very distinct velocity anisotropies. We group the behaviour of haloes into three different categories, that range from spherically symmetric profiles to a much more complex behaviour, where significant differences are found for beta along the major and minor axes. We encourage future studies of velocity anisotropies in haloes from cosmological simulations to calculate beta-profiles in cones, since it reveals information, which is hidden from a spherically averaged profile. Finally, we show that spherically averaged profiles often obey a linear relation between beta and the logarithmic density slope in the inner parts of haloes, but this relation is not necessarily obeyed, when properties are calculated in cones.Comment: 23 pages, 14 figures. Accepted for publication in JCA

Asymmetric velocity anisotropies in remnants of collisionless mergers

Dark matter haloes in cosmological N-body simulations are affected by processes such as mergers, accretion and the gravitational interaction with baryonic matter. Typically the analysis of dark matter haloes is performed in spherical or elliptical bins and the velocity distributions are often assumed to be constant within those bins. However, the velocity anisotropy, which describes differences between the radial and tangential velocity dispersion, has recently been show to have a strong dependence on direction in the triaxial halos formed in cosmological simulations. In this study we derive properties of particles in cones parallel or perpendicular to the collision axis of merger remnants. We find that the velocity anisotropy has a strong dependence on direction. The finding that the direction-dependence of the velocity anisotropy of a halo depends on the merger history, explains the existence of such trends in cosmological simulations. It also explains why a large diversity is seen in the velocity anisotropy profiles in the outer parts of high-resolution simulations of cosmological haloes.Comment: 19 pages, 15 figures, Resubmitted to JCAP after referee comment