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

Pollination ecology of New Zealand orchids : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Ecology at Massey University

The New Zealand orchid flora comprises twenty-five genera and at least 100 species occurring throughout the country. Although the number of endemic species is high (69%) only four genera are endemic to New Zealand. The main physical threats to orchid survival in New Zealand are habitat destruction, modification and fragmentation. The effect of the disruption of interactions with their pollinators has never been considered. This study concentrates on this mutualistic interaction, by assessing the breeding system, pollination syndromes and pollinator-dependence of four widespread terrestrial (Gastrodia cunninghamii, Thelymitra longifolia, Pterostylis alobula and P. patens) and four widespread epiphytic orchids (Earina autumnalis, E. aestivalis, E. mucronata and Winika cunninghamii) occurring in the southern portion of the North Island. In order to determine the breeding system and the presence of self-incompatibility, hand-pollination treatments were conducted in all eight orchid species during the flowering seasons of 2001 and 2002. Pollen grains and ovules numbers, pollen:ovule ratio and presence of floral scent glands were assessed. In those nectariferous species (E. autumnalis, E. aestivalis, E. mucronata and W. cunninghamii), the nectar standing crop was determined using the anthrone colorimetric assay for total carbohydrates. The activity of pollinator was observed both in the field and in captivity. Insects observed foraging in these orchids were identified and ranked according to their likely pollination effectiveness. Finally, measurements of pollination success and pollinia removal and deposition were used to assess whether fruit-set is pollen limited in these species and explore the effect contrasting rewarding strategies (nectar v/s deception) has on the pollination success of these orchids. Pollination treatments in three terrestrial (T. longifolia, P. alobula and P. patens) and two epiphytic (E. autumnalis and E. mucronata) orchids confirmed the absence of genetic incompatibility. Despite these five orchids being self-compatible, their reproduction relies on contrasting reproductive strategies. T. longifolia is predominantly self-pollinated, whereas Pterostylis and Earina species are incapable of autonomous selfing and completely dependent on pollinators. The epiphytic species E. aestivalis and W. cunninghamii are partially self-incompatible and also completely dependent on pollinators. Agamospermy is likely to occur in G. cunninghamii but not involved in seed-production in any of the remaining seven orchids. Both terrestrial and epiphytic species showed a positive reaction to neutral red except E. autumnalis. This indicated the presence of scent glands, mainly located around the column, lip and sepal tips. Pollen:ovule ratios calculated for these species ranged from 20:1 in E. mucronata and E. aestivalis to 320: 1 in P. alobula. Of the four terrestrial orchids studied, insect visitation was observed only in P. alobula. This orchid is pollinated by male fungus gnats of the genus Zygomyia (Diptera: Mycetophilidae). Pollination by sexual deception is likely to occur in species of this genus. Numerous insects were recorded visiting the nectariferous epiphytic orchids (3 orders, 13 families). Insects considered as "probable pollinator" were Eristalis tenax (Diptera: Syrphidae) for Earina autumnalis, Dilophus nigrostigmus (Diptera: Bibionidae) for E. mucronata, and Melangyna novaezealandiae (Diptera: Syrphidae), Calliphora quadrimaculata (Diptera: Calliphoridae), the Ichneumonid wasp Aucklandella sp. (Hymenoptera: Ichneumonidae), Hylaeus sp. (Hymenoptera: Colletidae) and an unidentified weevil (Coleoptera: Curculionidae) for E. aestivalis. In W. cunninghamii the species Apis mellifera and the native syrphid flies Helophilus antipodus and M. novaezealandiae were considered as "probable pollinators". Levels of natural fruit-set were similarly low in rewarding and non-rewarding species fluctuating from 4.3% (P. alobula) to 40% (P. patens). Fruiting in these orchids is pollen limited, as supplementary hand-pollinations increased fruit set above 40% in all species except P. patens. The degree of pollen limitation varied from 0.32 (P. patens) and 0.94 (P. alobula and E. mucronata). Pollen limitation in these orchids may be caused by the simplicity of their flowers, the poor efficiency of their pollinators in depositing pollinia and the use of species-specific pollination systems (e.g. Pterostylis). The survival capability and conservation requirements of these orchids are discussed in the light of the specific reproductive requirements revealed by this study

Theory summary. Hard Probes 2012

I provide a summary of the theoretical talks in Hard Probes 2012 together with some personal thoughts about the present and the future of the field.Comment: 8 pages. Proceedings of the conference Hard Probes 2012 - Sardinia - Italy - May 27 -June 1 2012 --- Comments welcom