Effect of Coriaria arborea on seed banks during primary succession on Mt Tarawera, New Zealand

An experiment was conducted over two years to investigate the effect of Coriaria arborea, a native nitrogen-fixing shrub, on soil seed banks at sites representing a post-volcanic successional sequence on Mt Tarawera, New Zealand. The sites ranged from bare volcanic ash and lapilli substrate, through low-growing pre-Coriaria vegetation, to dense stands of Coriaria scrub. Soils (to a depth of 50 mm) under recently established Coriaria and older stands had more seedlings (1096 and 1585 seedlings 0.4 m-2, respectively) and species (37 and 45 species 0.4 m-2, respectively) emerge than where there was no Coriaria (243-320 seedlings 0.4 m-2, 14-25 species 0.4 m-2) and were the only soils with Coriaria seedlings. In total, 3488 seedlings representing 63 taxa were recorded. Seeds were still germinating after 24 months but rates declined markedly in the second year. For example, Coriaria reached a germination peak at 8 weeks but continued to germinate sporadically over the 2-year period. Tree species present in young forest within 0.5 km of the sites were absent. Establishment of Coriaria greatly accelerated an underlying trend of gradually increasing abundance and diversity of seeds in the soil with vegetation age. Adventive, wind-dispersed, and annual species were over-represented in the seed banks compared with the regional evergreen forest-dominated flora. These proportions are expected to decline as succession to forest gradually occurs

Soliton Solutions to the Einstein Equations in Five Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological constant that asymptotically approach AdS$_{5}/\Gamma$, but have less energy than AdS$_{5}/\Gamma$. We present evidence that these solutions are the lowest-energy states within their asymptotic class.Comment: 9 pages, Latex; Final version that appeared in Phys. Rev. Lett; title changed by journal from original title "Eguchi-Hanson Solitons

Eguchi-Hanson Solitons in Odd Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dS$_{d+1}/Z_p$. In the AdS case their energy is negative relative to that of pure AdS. We present perturbative evidence in 5 dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.Comment: 26 pages, Late

1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations

We use the, covariant and gauge-invariant, 1+1+2 formalism developed by Clarkson and Barrett, and develop new techniques, to decouple electromagnetic (EM) perturbations on arbitrary locally rotationally symmetric (LRS) space-times. Ultimately, we derive 3 decoupled complex equations governing 3 complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized for LRS space-times, whereas the remaining two are new generalizations of the Bardeen-Press (BP) equations. This is achieved by first using linear algebra techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2 form which is conducive to decoupling. This new complex system immediately yields the generalized RW equation, and furthermore, we also derive a decoupled equation governing a newly defined complex EM 2-vector. Subsequently, a further decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed, allowing us to decompose the complex EM 2-vector, and its governing equations, into spin-weighted scalars, giving rise to the generalized BP equations

1+1+2 Electromagnetic perturbations on non-vacuum LRS class II space-times: Decoupling scalar and 2-vector harmonic amplitudes

We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and Barrett \cite{Clarkson2003} to analyze electromagnetic (EM) perturbations on non-vacuum {\it locally rotationally symmetric} (LRS) class II space-times. Ultimately, we show how to derive six real decoupled equations governing the total of six EM scalar and 2-vector harmonic amplitudes. Four of these are new, and result from expanding the complex EM 2-vector which we defined in \cite{Burston2007} in terms of EM 2-vector harmonic amplitudes. We are then able to show that there are four precise combinations of the amplitudes that decouple, two of these are polar perturbations whereas the remaining two are axial. The remaining two decoupled equations are the generalized Regge-Wheeler equations which were developed previously in \cite{Betschart2004}, and these govern the two EM scalar harmonic amplitudes. However, our analysis generalizes this by including a full description and classification of energy-momentum sources, such as charges and currents.Comment: 9 page

Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method

Quantifying Information Flow with Beliefs

To reason about information flow, a new model is developed that describes how attacker beliefs change due to the attacker's observation of the execution of a probabilistic (or deterministic) program. The model enables compositional reasoning about information flow from attacks involving sequences of interactions. The model also supports a new metric for quantitative information flow that measures accuracy of an attacker's beliefs. Applying this new metric reveals inadequacies of traditional information flow metrics, which are based on reduction of uncertainty. However, the new metric is sufficiently general that it can be instantiated to measure either accuracy or uncertainty. The new metric can also be used to reason about misinformation; deterministic programs are shown to be incapable of producing misinformation. Additionally, programs in which nondeterministic choices are made by insiders, who collude with attackers, can be analyzed

Halting indigenous biodiversity decline: ambiguity, equity, and outcomes in RMA assessment of significance

In New Zealand, assessment of ‘significance’ is undertaken to give effect to a legal requirement for local authorities to provide for protection of significant sites under the Resource Management Act (1991). The ambiguity of the statute enables different interests to define significance according to their goals: vested interests (developers), local authorities, and non-vested interests in pursuit of protection of environmental public goods may advance different definitions. We examine two sets of criteria used for assessment of significance for biological diversity under the Act. Criteria adapted from the 1980s Protected Natural Areas Programme are inadequate to achieve the maintenance of biological diversity if ranking is used to identify only highest priority sites. Norton and Roper-Lindsay (2004) propose a narrow definition of significance and criteria that identify only a few high-quality sites as significant. Both sets are likely to serve the interests of developers and local authorities, but place the penalty of uncertainty on non-vested interests seeking to maintain biological diversity, and are likely to exacerbate the decline of biological diversity and the loss of landscape-scale processes required for its persistence. When adopting criteria for assessment of significance, we suggest local authorities should consider whose interests are served by different criteria sets, and who will bear the penalty of uncertainty regarding biological diversity outcomes. They should also ask whether significance criteria are adequate, and sufficiently robust to the uncertainty inherent in the assessment of natural values, to halt the decline of indigenous biological diversity