Madelung transform and variational asymptotics in Born-Oppenheimer molecular dynamics

While Born-Oppenheimer molecular dynamics (BOMD) has been widely studied by resorting to powerful methods in mathematical analysis, this paper presents a geometric formulation in terms of Hamilton's variational principle and Euler-Poincar\'{e} reduction by symmetry. Upon resorting to the Lagrangian hydrodynamic paths made available by the Madelung transform, we show how BOMD arises by applying asymptotic methods to the variational principles underlying different continuum models and their particle closure schemes. In particular, after focusing on the hydrodynamic form of the fully quantum dynamics, we show how the recently proposed bohmion scheme leads to an alternative implementation of BOMD. In addition, we extend our analysis to models of mixed quantum-classical dynamics.Comment: 13 pages, no figure. To appear in Lecture Notes in Comput. Sc

Colorings of oriented planar graphs avoiding a monochromatic subgraph

For a fixed simple digraph $F$ and a given simple digraph $D$, an $F$-free $k$-coloring of $D$ is a vertex-coloring in which no induced copy of $F$ in $D$ is monochromatic. We study the complexity of deciding for fixed $F$ and $k$ whether a given simple digraph admits an $F$-free $k$-coloring. Our main focus is on the restriction of the problem to planar input digraphs, where it is only interesting to study the cases $k \in \{2,3\}$. From known results it follows that for every fixed digraph $F$ whose underlying graph is not a forest, every planar digraph $D$ admits an $F$-free $2$-coloring, and that for every fixed digraph $F$ with $\Delta(F) \ge 3$, every oriented planar graph $D$ admits an $F$-free $3$-coloring. We show in contrast, that - if $F$ is an orientation of a path of length at least $2$, then it is NP-hard to decide whether an acyclic and planar input digraph $D$ admits an $F$-free $2$-coloring. - if $F$ is an orientation of a path of length at least $1$, then it is NP-hard to decide whether an acyclic and planar input digraph $D$ admits an $F$-free $3$-coloring

The Neighborhood Polynomial of Chordal Graphs

The neighborhood polynomial of a graph $G$ is the generating function of subsets of vertices in $G$ that have a common neighbor. In this paper we study the neighborhood polynomial and the complexity of its computation for chordal graphs. We will show that it is \NP-hard to compute the neighborhood polynomial on general chordal graphs. Furthermore we will introduce a parameter for chordal graphs called anchor width and an algorithm to compute the neighborhood polynomial which runs in polynomial time if the anchor width is polynomially bounded. Finally we will show that we can bound the anchor width for chordal comparability graphs and chordal graphs with bounded leafage. The leafage of a chordal graphs is the minimum number of leaves in the host tree of a subtree representation. In particular, interval graphs have leafage at most 2. This shows that the anchor width of interval graphs is at most quadratic

Bildende Kraft: religiöse Erwachsenenbildung heute

Dieser Beitrag versteht sich als ein Versuch, aus religionspädagogischer Sicht mit Hilfe eines Konzeptes der Salutogenese, das aus dem Gesundheitswesen kommt, einen neuen Impuls der Weiterentwicklung religiöser Erwachsenenbildung zu setzen. Dabei soll das Bildungspotenzial religiöser Erwachsenenbildung genauer betrachtet und nach neuen Schwerpunktsetzungen gefragt werden

Projekt "Evidenzbasierte Medizin Frankfurt"

Im Juli 2000 wurde die Arbeitsgruppe Evidenzbasierte Medizin Frankfurt von einer Gruppe Studierender an der Goethe-Universität gegründet, um die Anwendung der klinisch-wissenschaftlichen Medizin und deren Lehre mit Hilfe der Methoden der Evidenzbasierten Medizin zu verbessern. Aus den mittlerweile 21 freiwilligen zunächst studentischen Kursen in Evidenzbasierter Medizin sind deutschlandweit die ersten verpflichtenden Seminare in Evidenzbasierter Medizin entstanden. Aufgrund des Einsatzes neuer Lehrmethoden von Beginn an und der kontinuierlichen Verbesserung des Seminars sind sowohl formative als auch summative Evaluationen sehr gut. Die im Rahmen der Lehrforschung erhobenen Evaluationsdaten konnten hochrangig publiziert werden. ..