Small clique number graphs with three trivial critical ideals

The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs for the set of graphs with at most three trivial critical ideals. Then we use these forbidden graphs to characterize the graphs with at most three trivial critical ideals and clique number equal to 2 and 3.Comment: 33 pages, 3 figure

Fusion11 Conference Summary

A summary account of the conference "Fusion11", held in Saint Malo, France, May 2-6, 2011.Comment: 10 pages, 13 figure

Wiggly tails: a gravitational wave signature of massive fields around black holes

Massive fields can exist in long-lived configurations around black holes. We examine how the gravitational wave signal of a perturbed black hole is affected by such `dirtiness' within linear theory. As a concrete example, we consider the gravitational radiation emitted by the infall of a massive scalar field into a Schwarzschild black hole. Whereas part of the scalar field is absorbed/scattered by the black hole and triggers gravitational wave emission, another part lingers in long-lived quasi-bound states. Solving numerically the Teukolsky master equation for gravitational perturbations coupled to the massive Klein-Gordon equation, we find a characteristic gravitational wave signal, composed by a quasi-normal ringing followed by a late time tail. In contrast to `clean' black holes, however, the late time tail contains small amplitude wiggles with the frequency of the dominating quasi-bound state. Additionally, an observer dependent beating pattern may also be seen. These features were already observed in fully non-linear studies; our analysis shows they are present at linear level, and, since it reduces to a 1+1 dimensional numerical problem, allows for cleaner numerical data. Moreover, we discuss the power law of the tail and that it only becomes universal sufficiently far away from the `dirty' black hole. The wiggly tails, by constrast, are a generic feature that may be used as a smoking gun for the presence of massive fields around black holes, either as a linear cloud or as fully non-linear hair.Comment: 6 pages, 4 figure

Plant functional constraints on foliar N:P ratios in a tropical forest landscape

Although large scale analyses of foliar N:P ratios suggest and overall pattern of P limitation in tropical forests, analyses within the biome are less indicative of a consistent pattern of nutrient limitation. High tree species diversity and soil heterogeneity are important factors driving the variability of foliar chemistry in the tropics; however, this variability could be reduced at the level of the functional characteristics of the species present at a site. In this study it is hypothesized that foliar N:P ratios would be more constrained when the species are grouped according to functional characteristics, and would reveal patterns of nutrient limitation. The study was conducted in a tropical forest landscape of the Porce region in Colombia, which consists of patches of primary and secondary forests of different ages. The functional groupings revealed consistent patterns of conservative N cycling in species present at young secondary sites, as well as conservative P cycling of the species present later in succession and in primary forests. Although the observed data have limitations in terms of capturing the overall variability for each functional group, the classification used here provided support for the proposed hypotheses. It is concluded that functional composition, rather than taxonomic composition, can potentially improve our understanding of nutrient cycling in tropical forests