Quantifying the abundance of four large epiphytic fern species in remnant complex notophyll vine forest on the Atherton Tableland, north Queensland, Australia

Epiphytes are generally considered rare in complex forests on the western edge of the Atherton Tablelands, north Queensland. This assertion is based on comparisons with wetter forests in the Wet Tropics bioregion, but is of limited use in restoration projects where targets need to be quantified. We quantified ‘rarity’ for a subset of the epiphyte community in one of the largest remaining patches of Type 5b rainforest at Wongabel State Forest(17°18' S, 145°28' E). The bundance of large individuals of the epiphytic fern species Asplenium australasicum, Drynaria rigidula, Platycerium bifurcatum, and Platycerium superbum were recorded from 100 identified midstorey or canopy trees. Epiphytes were less rare than the canopy trees sampled, averaging 1.7 individuals per tree. A clumped distribution was suggested with large epiphytes only occurring on 57 of the 100 trees. As tree size increased so did the number of individuals and species of large epiphytes recorded; only trees taller than 20 m yielded more than one epiphyte. Trees from the Meliaceae and Rutaceae hosted the most epiphytes, but host tree specificity patterns were not conclusive. Techniques for including epiphytes in restoration planning and projects are considered, and a quantified restoration target for epiphyte communities in Type 5b plantings is outlined

Anticommuting Variables, Fermionic Path Integrals and Supersymmetry

(Replacement because mailer changed `hat' for supercript into something weird. The macro `\sp' has been used in place of the `hat' character in this revised version.) Fermionic Brownian paths are defined as paths in a space para\-metr\-ised by anticommuting variables. Stochastic calculus for these paths, in conjunction with classical Brownian paths, is described; Brownian paths on supermanifolds are developed and applied to establish a Feynman-Kac formula for the twisted Laplace-Beltrami operator on differential forms taking values in a vector bundle. This formula is used to give a proof of the Atiyah-Singer index theorem which is rigorous while being closely modelled on the supersymmetric proofs in the physics literature.Comment: 18 pages, KCL-TH-92-

Global Research Report – South and East Asia

Global Research Report – South and East Asia by Jonathan Adams, David Pendlebury, Gordon Rogers & Martin Szomszor. Published by Institute for Scientific Information, Web of Science Group

Britain’s EU referendum uncovers a key group – those who feel they have nothing to lose

Martin Rogers analyses the upcoming EU referendum and highlights that certain demographic groups may be pivotal to the outcome

Sheffield Brightside & Hillsborough: Can UKIP advance?

As voters go to the polls for the Sheffield, Brightside & Hillsborough by-election on the 5 May, Martin Rogers suggests that it the performance of The United Kingdom Independence Party (UKIP) which is of greatest interest

Oldham: post-election analysis

On 3 December Labour candidate Jim McMahon won the Oldham West and Royton by-election. After his prediction that Labour were likely to hold the seat but face a UKIP surge, Martin Rogers discusses the result and suggests that any findings should be treated with caution

Labour likely to hold Oldham but face UKIP surge

Martin Rogers discusses the possible outcome of the Oldham West & Royton by-election, suggesting that although Labour is likely to hold the seat, a decline in overall majority and UKIP gains may weaken Corbyn’s position as party leader

A mixed picture in the UK election results favours the Conservatives

The initial tale of the May 2016 ‘Super Thursday’ is an incredibly mixed picture so it is difficult to draw too many firm conclusions from the results. However, the failure of the Conservatives’ opponents, especially the Labour party, to make any significant gains means that the Conservative party had the best overall outcome from these elections

Geometric Langevin equations on submanifolds and applications to the stochastic melt-spinning process of nonwovens and biology

In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Leli\`evre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant absolute value. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. All our studies are strongly motivated by industrial applications in modeling the fiber lay-down dynamics in the production process of nonwovens. We light up the geometry occuring in these models and show up the connection with the spherical velocity version of the geometric Langevin process. Moreover, as a main point, we construct new smooth industrial relevant three-dimensional fiber lay-down models involving the spherical Langevin process. Finally, relations to a class of self-propelled interacting particle systems with roosting force are presented and further applications of the geometric Langevin equations are given