Phylogenetic relationships of African Caecilians (Amphibia: Gymnophiona): insights from mitochondrial rRNA gene sequences

Africa (excluding the Seychelles) has a diverse caecilian fauna, including the endemic family Scolecomorphidae and six endemic genera of the more cosmopolitan Caeciliidae. Previous molecular phylogenetic studies have not included any caecilians from the African mainland. Partial 12S and 16S mitochondrial gene sequences were obtained for two species of the endemic African Scolecomorphidae and five species and four genera of African Caeciliids, aligned against previously reported sequences for 16 caecilian species, and analysed using parsimony, maximum likelihood, Bayesian and distance methods. Results are in agreement with traditional taxonomy in providing support for the monophyly of the African Caeciliid genera Boulengerula and Schistometopum and for the Scolecomorphidae. They disagree in indicating that the Caeciliidae is paraphyletic with respect to the Scolecomorphidae. Although more data from morphology and/or molecules will be required to resolve details of the interrelationships of the African caecilian genera, the data provide strong support for at least two origins of caecilians in which the eye is reduced and covered with bone, and do not support the hypotheses that the caecilian assemblages of Africa, and of East and of West Africa are monophyletic

The horofunction boundary of the Hilbert geometry

We investigate the horofunction boundary of the Hilbert geometry defined on an arbitrary finite-dimensional bounded convex domain D. We determine its set of Busemann points, which are those points that are the limits of `almost-geodesics'. In addition, we show that any sequence of points converging to a point in the horofunction boundary also converges in the usual sense to a point in the Euclidean boundary of D. We prove that all horofunctions are Busemann points if and only if the set of extreme sets of the polar of D is closed in the Painleve-Kuratowski topology.Comment: 24 pages, 2 figures; minor changes, examples adde

Education for democratic citizenship

Lecture delivered on the occasion of the awarding of the degree of Doctor Honoris Causa at the Institute of Social Studies, The Hague, The Netherlands, 9 March, 200

Existence of positive solutions of a superlinear boundary value problem with indefinite weight

We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case $g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.Comment: 12 pages, 4 PNG figure

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur

Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc graphs, proper circular-arc graphs and convex-round graphs.Comment: 25 pages, 9 figure