Approximation und Berechnung von Zufallsgrößen anhand der Finite-Elemente-Methode

Es wird ein Verfahren vorgestellt, mit dem stetige Zufallsgrößen rechnerunterstützt dargestellt und miteinander verknüpft werden können. Die Verteilungsfunktionen der Zufallsgrößen werden mit einem Finite-Elemente-Ansatz in einem endlichen Intervall [tmin; tmax] approximiert. Die Addition zweier Zufallsgrößen wird durch numerische Berechnung des Faltungsintegrals durchgeführt.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Family business: Multiple members of major phytohormone classes orchestrate plant stress responses

Low-molecular-weight compounds such as jasmonic, abscisic and salicylic acids are commonly thought to be regulators of plant stress responses. However, it is becoming clear that these molecules, often referred to as phytohormones, are only a part of bigger groups of compounds with biological activity. We propose that the concept of "hormone families" may help to better understand plant physiological responses by taking into account not only the alleged main regulators, but also their precursors, conjugates and catabolites. Novel approaches to profile potentially active compounds in plants are discussed.

Gibbs point process approximation: Total variation bounds using Stein's method

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's method. We construct an explicit coupling between two spatial birth-death processes to obtain Stein factors, and employ the Georgii-Nguyen-Zessin equation for the total bound.

Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

Classes of multichannel EEG microstates in light and deep hypnotic conditions

The study assessed the brain electric mechanisms of light and deep hypnotic conditions in the framework of EEG temporal microstates. Multichannel EEG of healthy volunteers during initial resting, light hypnosis, deep hypnosis, and eventual recovery was analyzed into temporal EEG microstates of four classes. Microstates are defined by the spatial configuration of their potential distribution maps ([Symbol: see text]potential landscapes') on the head surface. Because different potential landscapes must have been generated by different active neural assemblies, it is reasonable to assume that they also incorporate different brain functions. The observed four microstate classes were very similar to the four standard microstate classes A, B, C, D [Koenig, T. et al. Neuroimage, 2002;16: 41-8] and were labeled correspondingly. We expected a progression of microstate characteristics from initial resting to light to deep hypnosis. But, all three microstate parameters (duration, occurrence/second and %time coverage) yielded values for initial resting and final recovery that were between those of the two hypnotic conditions of light and deep hypnosis. Microstates of the classes B and D showed decreased duration, occurrence/second and %time coverage in deep hypnosis compared to light hypnosis; this was contrary to microstates of classes A and C which showed increased values of all three parameters. Reviewing the available information about microstates in other conditions, the changes from resting to light hypnosis in certain respects are reminiscent of changes to meditation states, and changes to deep hypnosis of those in schizophrenic states.