Transforming fixed-length self-avoiding walks into radial SLE_8/3

We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial SLE with kappa=8/3 in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and then apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial SLE. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial SLE, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values

Multiple drivers of decline in the global status of freshwater crayfish (Decapoda: Astacidea)

International audienceRates of biodiversity loss are higher in freshwater ecosystems than in most terrestrial or marine ecosystems, making freshwater conservation a priority. However, prioritization methods are impeded by insufficient knowledge on the distribution and conservation status of freshwater taxa, particularly invertebrates. We evaluated the extinction risk of the world's 590 freshwater crayfish species using the IUCN Categories and Criteria and found 32% of all species are threatened with extinction. The level of extinction risk differed between families, with proportionally more threatened species in the Parastacidae and Astacidae than in the Cambaridae. Four described species were Extinct and 21% were assessed as Data Deficient. There was geographical variation in the dominant threats affecting the main centres of crayfish diversity. The majority of threatened US and Mexican species face threats associated with urban development, pollution, damming and water management. Conversely, the majority of Australian threatened species are affected by climate change, harvesting, agriculture and invasive species. Only a small proportion of crayfish are found within the boundaries of protected areas, suggesting that alternative means of long-term protection will be required. Our study highlights many of the significant challenges yet to come for freshwater biodiversity unless conservation planning shifts from a reactive to proactive approach

Developing a predictive modelling capacity for a climate change-vulnerable blanket bog habitat: Assessing 1961-1990 baseline relationships

Aim: Understanding the spatial distribution of high priority habitats and developing predictive models using climate and environmental variables to replicate these distributions are desirable conservation goals. The aim of this study was to model and elucidate the contributions of climate and topography to the distribution of a priority blanket bog habitat in Ireland, and to examine how this might inform the development of a climate change predictive capacity for peat-lands in Ireland. Methods: Ten climatic and two topographic variables were recorded for grid cells with a spatial resolution of 1010 km, covering 87% of the mainland land surface of Ireland. Presence-absence data were matched to these variables and generalised linear models (GLMs) fitted to identify the main climatic and terrain predictor variables for occurrence of the habitat. Candidate predictor variables were screened for collinearity, and the accuracy of the final fitted GLM was evaluated using fourfold cross-validation based on the area under the curve (AUC) derived from a receiver operating characteristic (ROC) plot. The GLM predicted habitat occurrence probability maps were mapped against the actual distributions using GIS techniques. Results: Despite the apparent parsimony of the initial GLM using only climatic variables, further testing indicated collinearity among temperature and precipitation variables for example. Subsequent elimination of the collinear variables and inclusion of elevation data produced an excellent performance based on the AUC scores of the final GLM. Mean annual temperature and total mean annual precipitation in combination with elevation range were the most powerful explanatory variable group among those explored for the presence of blanket bog habitat. Main conclusions: The results confirm that this habitat distribution in general can be modelled well using the non-collinear climatic and terrain variables tested at the grid resolution used. Mapping the GLM-predicted distribution to the observed distribution produced useful results in replicating the projected occurrence of the habitat distribution over an extensive area. The methods developed will usefully inform future climate change predictive modelling for Irelan

Probing ferroic transitions in a multiferroic framework family: a neutron diffraction study of the ammonium transition metal formates

This study probes the magnetic and ferroelectric ordering of the NH4M(HCO2)3 (M = Mn2+, Fe2+, Co2+ and Ni2+) frameworks using neutron diffraction, improving the understanding of the origins of the properties of these fascinating multiferroics. This rare study of the magnetic structure of a family of metal-organic frameworks shows that all four compounds exhibit antiferromagnetic coupling between neighbouring cations bridged by formate ligands. The orientation of the spin, however, changes in a highly unusual way across the series with the spins aligned along the c-axis for the Fe2+ and Ni2+ frameworks but lying in the ab plane for the other members of the series. This work also sheds new light on the nature of the ferroelectric order-disorder transition in these materials; probing changes in the ammonium cation across the transition and also shows that the Ni2+ framework does not undergo a transition to the polar P63 phase due to the smaller size of the Ni2+ cation. Finally trends in their anisotropic negative thermal expansion, which potentially enhances their ferroic behaviour, are quantified