The fitting of multifunctions : an approach to nonparametric multimodal regression.

In the last decades a lot of research has been devoted to smoothing in the sense of nonparametric regression. However, this work has nearly exclusively concentrated on fitting regression functions. When the conditional distribution of y|x is multimodal, the assumption of a functional relationship y = m(x) + noise might be too restrictive. We introduce a nonparametric approach to fit multifunctions, allowing to assign a set of output values to a given x. The concept is based on conditional mean shift, which is an easily implemented tool to detect the local maxima of a conditional density function. The methodology is illustrated by environmental data examples

Classical and all-floating FETI methods for the simulation of arterial tissues

High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is - as most other biological tissues - characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters.Comment: 29 page

Exact and Fast Numerical Algorithms for the Stochastic Wave Equation

On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense

The planetary nebula population in the halo of M87

We investigate the diffuse light in the outer regions of the nearby elliptical galaxy M87 in the Virgo cluster, using planetary nebulas (PNs) as tracers. The surveyed areas (0.43 squared degrees) cover M87 up to a radial distance of 150 kpc, in the ransition region between galaxy halo and intracluster light (ICL). All PNs are identified through the on-off band technique using automatic selection criteria based on the distribution of the detected sources in the colour-magnitude diagram and the properties of their point-spread function. We extract a catalogue of 688 objects down to m_5007=28.4, with an estimated residual contamination from foreground stars and background Lyalpha galaxies, which amounts to ~35% of the sample. This is one of the largest extragalactic PN samples in number of candidates, magnitude depth, and radial extent, which allows us to carry out an unprecedented photometric study of the PN population in the outer regions of M87. We find that the logarithmic density profile of the PN distribution is shallower than the surface brightness profile at large radii. This behaviour is consistent with the superposition of two components associated with the halo of M87 and with the ICL, which have different luminosity specific PN numbers, the ICL contributing three times more PNs per unit light. Because of the depth of this survey we are also able to study the shape of the PN luminosity function (PNLF) in the outer regions of M87. We find a slope for the PNLF that is steeper at fainter magnitudes than the standard analytical PNLF formula and adopt a generalised model that treats the slope as a free parameter. Comparing the PNLF of M87 and the M31 bulge, both normalised by the sampled luminosity, the M87 PNLF contains fewer bright PNs and has a steeper slope towards fainter magnitudes.Comment: 16 pages, 13 figures, 5 tables, accepted for publication in A&

Transition from antibunching to bunching in cavity QED

The photon statistics of the light emitted from an atomic ensemble into a single field mode of an optical cavity is investigated as a function of the number of atoms. The light is produced in a Raman transition driven by a pump laser and the cavity vacuum [M.Hennrich et al., Phys. Rev. Lett. 85, 4672 (2000)], and a recycling laser is employed to repeat this process continuously. For weak driving, a smooth transition from antibunching to bunching is found for about one intra-cavity atom. Remarkably, the bunching peak develops within the antibunching dip. For saturated driving and a growing number of atoms, the bunching amplitude decreases and the bunching duration increases, indicating the onset of Raman lasing.Comment: 4 pages, 4 figure

Detection, photometry and slitless radial velocities of 535 planetary nebulae in the flattened elliptical galaxy NGC 4697

We have detected 535 planetary nebulae (PNs) in NGC 4697, using the classic on-band, off-band filter technique with the Focal Reducer and Spectrograph (FORS) at the Cassegrain focus of the first 8-meter telescope unit of the ESO Very Large Telescope. From our photometry we have built the [O III] 5007 planetary nebula luminosity function (PNLF) of NGC 4697. It indicates a distance of 10.5 Mpc, substantially smaller than a previous estimate of 24 Mpc used in earlier dynamical studies. The PNLF also provides an estimate of the specific PN formation rate. Combining the information from on-band images with PN positions on dispersed, slitless grism images, we have obtained radial velocities for 531 of the 535 PNs. They provide kinematic information up to a distance of almost three effective radii from the nucleus. Some rotation is detected in the outer regions, but the rotation curve of this galaxy appears to drop beyond one effective radius. Assuming an isotropic velocity distribution, the velocity dispersion profile is consistent with no dark matter within three effective radii of the nucleus (however, some dark matter can be present if the velocity distribution is anisotropic). We obtain a blue mass-to-light ratio of 11. Earlier M/L ratios for NGC 4697 were too small, because of the too large distance used for their derivation.Comment: 52 pages, 24 Postscript figures, ApJ 2001, in pres

The stellar dynamics and mass of NGC 1316 using the radial velocities of planetary nebulae

We present a study of the kinematics of the outer regions of the early-type galaxy NGC 1316, based on radial velocity measurements of 43 planetary nebulae as well as deep integrated-light absorption line spectra. The smoothed velocity field of NGC 1316 indicates fast rotation at a distance of 16 kpc, possibly associated with an elongated feature orthogonal to the inner dust lanes. The mean square stellar velocity is approximately independent of radius, and the estimated total mass of the system is 2.6 x 10^11 M_sun within a radius of 16 kpc, implying an integrated mass-to-light ratio of M/L_B = 8.Comment: 39 pages, 14 figures, in press on The Astrophysical Journal n. 50

Infinite compressibility states in the Hierarchical Reference Theory of fluids. II. Numerical evidence

Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility kappa[T] we now turn to the available numerical evidence to elucidate the character of the partial differential equation: Of the three scenarios identified previously, only the assumption of the equations turning stiff when building up the divergence of kappa[T] allows for a satisfactory interpretation of the data. In addition to the asymptotic regime where the arguments of part I (cond-mat/0308467) directly apply, a similar mechanism is identified that gives rise to transient stiffness at intermediate cutoff for low enough temperature. Heuristic arguments point to a connection between the form of the Fourier transform of the perturbational part of the interaction potential and the cutoff where finite difference approximations of the differential equation cease to be applicable, and they highlight the rather special standing of the hard-core Yukawa potential as regards the severity of the computational difficulties.Comment: J. Stat. Phys., in press. Minor changes to match published versio

From algebra to logic: there and back again -- the story of a hierarchy

This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.Comment: Developments in Language Theory 2014, Ekaterinburg : Russian Federation (2014