Equality of bond percolation critical exponents for pairs of dual lattices

For a certain class of two-dimensional lattices, lattice-dual pairs are shown to have the same bond percolation critical exponents. A computational proof is given for the martini lattice and its dual to illustrate the method. The result is generalized to a class of lattices that allows the equality of bond percolation critical exponents for lattice-dual pairs to be concluded without performing the computations. The proof uses the substitution method, which involves stochastic ordering of probability measures on partially ordered sets. As a consequence, there is an infinite collection of infinite sets of two-dimensional lattices, such that all lattices in a set have the same critical exponents.Comment: 10 pages, 7 figure

The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices

We give a conditional derivation of the inhomogeneous critical percolation manifold of the bow-tie lattice with five different probabilities, a problem that does not appear at first to fall into any known solvable class. Although our argument is mathematically rigorous only on a region of the manifold, we conjecture that the formula is correct over its entire domain, and we provide a non-rigorous argument for this that employs the negative probability regime of the triangular lattice critical surface. We discuss how the rigorous portion of our result substantially broadens the range of lattices in the solvable class to include certain inhomogeneous and asymmetric bow-tie lattices, and that, if it could be put on a firm foundation, the negative probability portion of our method would extend this class to many further systems, including F Y Wu’s checkerboard formula for the square lattice. We conclude by showing that this latter problem can in fact be proved using a recent result of Grimmett and Manolescu for isoradial graphs, lending strong evidence in favor of our other conjectured results. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98528/1/1751-8121_45_49_494005.pd

The PREDICTS database: a global database of how local terrestrial biodiversity responds to human impacts

Biodiversity continues to decline in the face of increasing anthropogenic pressures such as habitat destruction, exploitation, pollution and introduction of alien species. Existing global databases of species’ threat status or population time series are dominated by charismatic species. The collation of datasets with broad taxonomic and biogeographic extents, and that support computation of a range of biodiversity indicators, is necessary to enable better understanding of historical declines and to project – and avert – future declines. We describe and assess a new database of more than 1.6 million samples from 78 countries representing over 28,000 species, collated from existing spatial comparisons of local-scale biodiversity exposed to different intensities and types of anthropogenic pressures, from terrestrial sites around the world. The database contains measurements taken in 208 (of 814) ecoregions, 13 (of 14) biomes, 25 (of 35) biodiversity hotspots and 16 (of 17) megadiverse countries. The database contains more than 1% of the total number of all species described, and more than 1% of the described species within many taxonomic groups – including flowering plants, gymnosperms, birds, mammals, reptiles, amphibians, beetles, lepidopterans and hymenopterans. The dataset, which is still being added to, is therefore already considerably larger and more representative than those used by previous quantitative models of biodiversity trends and responses. The database is being assembled as part of the PREDICTS project (Projecting Responses of Ecological Diversity In Changing Terrestrial Systems – www.predicts.org.uk). We make site-level summary data available alongside this article. The full database will be publicly available in 2015

A New Species of \u3ci\u3eIstiodactylus\u3c/i\u3e (Pterosauria, Pterodactyloidea) from the Lower Cretaceous of Liaoning, China

Istiodactylus sinensis, sp. nov., from the Jiufotang Formation of Liaoning, People\u27s Republic of China, is described on the basis of a single nearly complete and nearly osteologically adult specimen. This is the tenth pterosaur described from this formation and the eighteenth pterosaur species described from northeastern China in almost half as many years. The species is placed in the Istiodactylidae, which was previously a monospecific family of pterodactyloid pterosaurs known only from the Isle of Wight, England. The new form is distinct from the two other istiodactylid species. It is smaller, more plesiomorphic, and younger than Istiodactylus latidens, but larger and more derived than the contemporaneous Nurhachius ignaciobritoi. Istiodactylus sinensis is very similar to I. latidens, so that almost all of the previous autapomorphies of I. latidens are now synapomorphies of Istiodactylus. They differ most in that I. sinensis is much smaller than I. latidens. The length of the wingspan, skull, and most of the preserved limb elements of I. sinensis are about 63 percent of the wingspan and elements of I. latidens. This new specimen demonstrates that Istiodactylus is diagnosed by, among other characters, a dorsoventrally depressed but not laterally expanded rostrum, and the presence of a suborbital vacuity. A dorsal deflection of the alveolar margins of the jaws and a humerus between 55 percent and one and a half times the length of metacarpal IV are synapomorphies uniting the Istiodactylidae and the Anhangueridae

The database of the PREDICTS (Projecting Responses of Ecological Diversity In Changing Terrestrial Systems) project

The PREDICTS project—Projecting Responses of Ecological Diversity In Changing Terrestrial Systems (www.predicts.org.uk)—has collated from published studies a large, reasonably representative database of comparable samples of biodiversity from multiple sites that differ in the nature or intensity of human impacts relating to land use. We have used this evidence base to develop global and regional statistical models of how local biodiversity responds to these measures. We describe and make freely available this 2016 release of the database, containing more than 3.2 million records sampled at over 26,000 locations and representing over 47,000 species. We outline how the database can help in answering a range of questions in ecology and conservation biology. To our knowledge, this is the largest and most geographically and taxonomically representative database of spatial comparisons of biodiversity that has been collated to date; it will be useful to researchers and international efforts wishing to model and understand the global status of biodiversity