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Abstract We compute families of solutions to the Einstein vacuum equations of the type of Brill waves, but with slow fall-off towards spatial infinity. We prove existence and uniqueness of solutions for physical data and numerically construct some representative solutions. We numerically construct an explicit example with slow-off which does not exhibit antipodal symmetry at spatial infinity. 

Abstract Background and Aims The success of invasive plants can be attributed to many traits including the ability to adapt to variable environmental conditions. Whether by adaptation, acclimation or phenotypic plasticity, these plants often increase their resource-use efficiency and, consequently, their fitness. The goal of this study was to examine the hydraulic and eco-physiological attributes of sun and shade populations of Pteridium aquilinum, a weedy fern, to determine whether the presence of vessels and other hydraulic attributes affects its success under a variety of light conditions. Methods Hydraulic traits such as cavitation resistance, hydraulic conductivity, photosynthesis and water potential at turgor loss point were measured on fronds from sun and shade populations. Anatomical and structural traits such as conduit diameter and length, stomatal density and vein density were also recorded. Diurnal measures of leaf water potential and stomatal conductance complement these data. Key Results Gas exchange was nearly double in the sun plants, as was water-use efficiency, leaf-specific conductivity, and stomatal and vein density. This was largely achieved by a decrease in leaf area, coupled with higher xylem content. There was no significant difference in petiole cavitation resistance between the sun and shade leaves, nor in xylem-specific conductivity. Hydraulic conduit diameters were nearly equivalent in the two leaf types. Conclusions Shifts in leaf area and xylem content allow P. aquilinum to occupy habitats with full sun, and to adjust its physiology accordingly. High rates of photosynthesis explain in part the success of this fern in disturbed habitats, although no change was observed in intrinsic xylem qualities such as cavitation resistance or conduit length. This suggests that P. aquilinum is constrained by its fundamental body plan, in contrast to seed plants, which show greater capacity for hydraulic adjustment.