L2L^2-Stability of Traveling Wave Solutions to Nonlocal Evolution Equations

Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in $L^2$-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum norm. We prove that the linearization around the traveling wave solution satisfies a Lyapunov-type stability condition in a weighted space $L^2(\rho)$ for a naturally associated density $\rho$. The result can be applied to obtain stability of the traveling wave solution under stochastic perturbations of additive or multiplicative type. For small wave speeds, we also prove an alternative Lyapunov-type stability condition in $L^2(\mathfrak{m})$, where $\mathfrak{m}$ is the symmetrizing density for the traveling wave operator, which allows to derive a long-term stochastic stability result.Comment: in comparison to first version setting in subsection 3.3 changed to stochastic neural field equations with multiplicative nois

"Mutter Natur und Vater Staat": Zukunftsperspektiven und Gestaltungsansätze einer schwierigen Beziehung im Zeichen der Nachhaltigkeit

Vorwort: Das vorliegende Heft 4 der Beiträge und Berichte der VÖÖ setzt die Tradition der Dokumentation der jährlichen Tagungen der Vereinigung für Ökologische Ökonomie fort. Im Mittelpunkt dieser fünften Jahrestagung stand die Frage nach dem Rollen-verständnis des Staates in der Ökologischen Ökonomie. Mit der Wahl dieses The-mas wurde eine Perspektive aufgegriffen, die in den Diskussionen auf unseren bis-herigen Tagungen immer wieder eine Rolle spielte. Zumeist wurden dabei die „staat-lichen Rahmenbedingungen“ als Voraussetzung, Bedingung oder Hemmnis einer nachhaltigen Entwicklung in Frage gestellt oder deren Veränderung eingefordert..

Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations

Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under the assumption that each population in the network is large, the activity is described in terms of a population average. The discrete network is then approximated by a continuum. In this article we make the two approximation steps explicit. Extending a model by Bressloff and Newby, we describe the evolution of the activity in a discrete network of finite populations by a Markov chain. In order to determine finite-size effects - deviations from the mean field limit due to the finite size of the populations in the network - we analyze the fluctuations of this Markov chain and set up an approximating system of diffusion processes. We show that a well-posed stochastic neural field equation with a noise term accounting for finite-size effects on traveling wave solutions is obtained as the strong continuum limit

Function estimation with locally adaptive dynamic models

We present a nonparametric Bayesian method for fitting unsmooth and highly oscillating functions, which is based on a locally adaptive hierarchical extension of standard dynamic or state space models. The main idea is to introduce locally varying variances in the state equations and to add a further smoothness prior for this variance function. Estimation is fully Bayesian and carried out by recent MCMC techniques. The whole approach can be understood as an alternative to other nonparametric function estimators, such as local or penalized regression with variable bandwidth or smoothing parameter selection. Performance is illustrated with simulated data, including unsmooth examples constructed for wavelet shrinkage, and by an application to sales data. Although the approach is developed for classical Gaussian nonparametric regression, it can be extended to more complex regression problems

Levels of Pesticides and Their Metabolites in Wistar Rat Amniotic Fluids and Maternal Urine upon Gestational Exposure.

Concentrations of pesticides and selected metabolites in rat urine and amniotic fluid were determined as biomarker upon oral administration of Wistar rats to two pesticide mixtures consisting of three to five pesticides (bitertanol, propiconazole, cypermethrin, malathion, and terbuthylazine). The pesticides and their metabolites were found in rat amniotic fluid and urine, generally in dose-response concentrations in relation to dosage. The measurement of the substances in the amniotic fluid indicated that the fetus was exposed to the pesticides as well as their metabolites. Moreover, the pesticides detected in urine demonstrated the exposure as well as the ability of the rat to excrete these compounds