Comparing Implicit, Differential, Dimensional and BPHZ Renormalisation

We compare a momentum space implicit regularisation (IR) framework with other renormalisation methods which may be applied to dimension specific theories, namely Differential Renormalisation (DfR) and the BPHZ formalism. In particular, we define what is meant by minimal subtraction in IR in connection with DfR and dimensional renormalisation (DR) .We illustrate with the calculation of the gluon self energy a procedure by which a constrained version of IR automatically ensures gauge invariance at one loop level and handles infrared divergences in a straightforward fashion. Moreover, using the $\phi^4_4$ theory setting sun diagram as an example and comparing explicitly with the BPHZ framework, we show that IR directly displays the finite part of the amplitudes. We then construct a parametrization for the ambiguity in separating the infinite and finite parts whose parameter serves as renormalisation group scale for the Callan-Symanzik equation. Finally we argue that constrained IR, constrained DfR and dimensional reduction are equivalent within one loop order.Comment: 21 pages, 2 figures, late

Echinoderms from Todos os Santos Bay and Aratu Bay (Bahia, Brazil)

Neste trabalho são registrados os equinodermos (exceto Holothuroidea) obtidos durante a execução do projeto "Marine Environmental Evaluation of the Todos os Santos Bay-MAREMBA" em julho/agosto de 1996 e durante o projeto "Geoecologia das comunidades bentônicas infralitorais da Baía de Todos os Santos (BTS), BA, Brasil: diversidade biótica e sedimentológica", (1997). Um total de 33 espécies pertencentes a 15 famílias foram registradas e re-descritas. A distribuição de Ophiactis brasiliensis Manso, 1988 e Amphiodia trychna H.L. Clark, 1918 é estendida para a região nordeste do Brasil. A classe Ophiuroidea foi dominante nas amostragens em termos de abundância e freqüência de ocorrência, em particular as espécies Amphiodia atra Stimpson, 1852, Amphipholis subtilis (Ljungman, 1867), Ophiactislymani Ljungman, 1871 e Ophiostigma isocanthum (Say, 1825). O asteróide Oreaster reticulatus (Linnaeus, 1758) é considerado vulnerável à exploração humana e foi escasso durante as coletas. Outras espécies encontradas na BTS, tais como os asteroides Luidia clathrata (Say, 1825) e L. senegalensis (Lamarck, 1816) e o equinóide Eucidaristribuloides (Lamarck, 1816) figuram na lista nacional de espécies de invertebrados aquáticos ameaçados de extinção._______________________________________________________________________________ ABSTRACT: We present the results of the studies on biodiversity of Echinodermata (except Holothuroidea) from the Projects "Marine Environmental Evaluation of the Todos os Santos Bay - MAREMBA" (July/August 1996) and "Geoecology of the Benthic Infralitoral Communities of Todos os Santos Bay (BTS), Bahia, Brazil" (1997). A total of 33 species from 15 families were registered and re-described. The distribution of Ophiactis brasiliensis Manso, 1988 and Amphiodia trychna H.L. Clark, 1918 is extended to northwestern Brazil. The class Ophiuroidea was dominant in samples in terms of abundance and frequency of occurrence, in particular Amphiodia atra Stimpson, 1852, Amphipholis subtilis (Ljungman, 1867), Ophiactislymani Ljungman, 1871and Ophiostigma isocanthum (Say, 1825). The asteroid Oreaster reticulatus (Linnaeus, 1758) is considered vulnerable to human exploration and was scarce during the surveys. Other species found at BTS, such the asteroids Luidia clathrata (Say, 1825) and L. senegalensis (Lamarck, 1816) and the echinoid Eucidaristribuloides (Lamarck, 1816)are included in the national list of threatened invertebrate species

Mapping density, diversity and species-richness of the Amazon tree flora

Using 2.046 botanically-inventoried tree plots across the largest tropical forest on Earth, we mapped tree species-diversity and tree species-richness at 0.1-degree resolution, and investigated drivers for diversity and richness. Using only location, stratified by forest type, as predictor, our spatial model, to the best of our knowledge, provides the most accurate map of tree diversity in Amazonia to date, explaining approximately 70% of the tree diversity and species-richness. Large soil-forest combinations determine a significant percentage of the variation in tree species-richness and tree alpha-diversity in Amazonian forest-plots. We suggest that the size and fragmentation of these systems drive their large-scale diversity patterns and hence local diversity. A model not using location but cumulative water deficit, tree density, and temperature seasonality explains 47% of the tree species-richness in the terra-firme forest in Amazonia. Over large areas across Amazonia, residuals of this relationship are small and poorly spatially structured, suggesting that much of the residual variation may be local. The Guyana Shield area has consistently negative residuals, showing that this area has lower tree species-richness than expected by our models. We provide extensive plot meta-data, including tree density, tree alpha-diversity and tree species-richness results and gridded maps at 0.1-degree resolution