Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.

Advancing impact prediction and hypothesis testing in invasion ecology using a comparative functional response approach

Invasion ecology urgently requires predictive methodologies that can forecast the ecological impacts of existing, emerging and potential invasive species. We argue that many ecologically damaging invaders are characterised by their more efficient use of resources. Consequently, comparison of the classical ‘functional response’ (relationship between resource use and availability) between invasive and trophically analogous native species may allow prediction of invader ecological impact. We review the utility of species trait comparisons and the history and context of the use of functional responses in invasion ecology, then present our framework for the use of comparative functional responses. We show that functional response analyses, by describing the resource use of species over a range of resource availabilities, avoids many pitfalls of ‘snapshot’ assessments of resource use. Our framework demonstrates how comparisons of invader and native functional responses, within and between Type II and III functional responses, allow testing of the likely population-level outcomes of invasions for affected species. Furthermore, we describe how recent studies support the predictive capacity of this method; for example, the invasive ‘bloody red shrimp’ Hemimysis anomala shows higher Type II functional responses than native mysids and this corroborates, and could have predicted, actual invader impacts in the field. The comparative functional response method can also be used to examine differences in the impact of two or more invaders, two or more populations of the same invader, and the abiotic (e.g. temperature) and biotic (e.g. parasitism) context-dependencies of invader impacts. Our framework may also address the previous lack of rigour in testing major hypotheses in invasion ecology, such as the ‘enemy release’ and ‘biotic resistance’ hypotheses, as our approach explicitly considers demographic consequences for impacted resources, such as native and invasive prey species. We also identify potential challenges in the application of comparative functional responses in invasion ecology. These include incorporation of numerical responses, multiple predator effects and trait-mediated indirect interactions, replacement versus non-replacement study designs and the inclusion of functional responses in risk assessment frameworks. In future, the generation of sufficient case studies for a meta-analysis could test the overall hypothesis that comparative functional responses can indeed predict invasive species impacts.

Existing and emerging high impact invasive species are characterized by higher functional responses than natives

Predicting ecological impacts of invasive species and identifying potentially damaging future invaders are research priorities. Since damage by invaders is characterized by their depletion of resources, comparisons of the ‘functional response’ (FR; resource uptake rate as a function of resource density) of invaders and natives might predict invader impact. We tested this by comparing FRs of the ecologically damaging ‘world's worst’ invasive fish, the largemouth bass (Micropterus salmoides), with a native equivalent, the Cape kurper (Sandelia capensis), and an emerging invader, the sharptooth catfish (Clarias gariepinus), with the native river goby (Glossogobius callidus), in South Africa, a global invasion hotspot. Using tadpoles (Hyperolius marmoratus) as prey, we found that the invaders consumed significantly more than natives. Attack rates at low prey densities within invader/native comparisons reflected similarities in predatory strategies; however, both invasive species displayed significantly higher Type II FRs than the native comparators. This was driven by significantly lower prey handling times by invaders, resulting in significantly higher maximum feeding rates. The higher FRs of these invaders are thus congruent with, and can predict, their impacts on native communities. Comparative FRs may be a rapid and reliable method for predicting ecological impacts of emerging and future invasive species.

Reconstructing the quantum state of oscillator networks with a single qubit

We introduce a scheme to reconstruct arbitrary states of networks composed of quantum oscillators-e. g., the motionalstate of trapped ions or the radiation state of coupled cavities. The scheme involves minimal resources and minimal access, in the sense that it (i) requires only the interaction between a one-qubit probe and a single node of the network; (ii) provides the Weyl characteristic function of the network directly from the data, avoiding any tomographic transformation; (iii) involves the tuning of only one coupling parameter. In addition, we show that a number of quantum properties can be extracted without full reconstruction of the state. The scheme can be used for probing quantum simulations of anharmonic many-body systems and quantum computations with continuous variables. Experimental implementation with trapped ions is also discussed and shown to be within reach of current technology.

Tackling Invasive Alien Species in Europe: the Top 20 Issues

Globally, Invasive Alien Species (IAS) are considered to be one of the major threats to native biodiversity, with the World Conservation Union (IUCN) citing their impacts as ?immense, insidious, and usually irreversible?. It is estimated that 11% of the c. 12,000 alien species in Europe are invasive, causing environmental, economic and social damage; and it is reasonable to expect that the rate of biological invasions into Europe will increase in the coming years. In order to assess the current position regarding IAS in Europe and to determine the issues that were deemed to be most important or critical regarding these damaging species, the international Freshwater Invasives - Networking for Strategy (FINS) conference was convened in Ireland in April 2013. Delegates from throughout Europe and invited speakers from around the world were brought together for the conference. These comprised academics, applied scientists, policy makers, politicians, practitioners and representative stakeholder groups. A horizon scanning and issue prioritization approach was used by in excess of 100 expert delegates in a workshop setting to elucidate the Top 20 IAS issues in Europe. These issues do not focus solely on freshwater habitats and taxa but relate also to marine and terrestrial situations. The Top 20 issues that resulted represent a tool for IAS management and should also be used to support policy makers as they prepare European IAS legislation.

Habitat simplification increases the impact of a freshwater invasive fish

Biodiversity continues to decline at a range of spatial scales and there is an urgent requirement to understand how multiple drivers interact in causing such declines. Further, we require methodologies that can facilitate predictions of the effects of such drivers in the future. Habitat degradation and biological invasions are two of the most important threats to biodiversity and here we investigate their combined effects, both in terms of understanding and predicting impacts on native species. The predatory largemouth bass Micropterus salmoides is one of the World’s Worst Invaders, causing declines in native prey species, and its introduction often coincides with habitat simplification. We investigated the predatory functional response, as a measure of ecological impact, of juvenile largemouth bass in artificial vegetation over a range of habitat complexities (high, intermediate, low and zero). Prey, the female guppy Poecilia reticulata, were representative of native fish. As habitats became less complex, significantly more prey were consumed, since, even although attack rates declined, reduced handling times resulted in higher maximum feeding rates by bass. At all levels of habitat complexity, bass exhibited potentially population destabilising Type II functional responses, with no emergence of more stabilising Type III functional responses as often occurs in predator-prey relationships in complex habitats. Thus, habitat degradation and simplification potentially exacerbate the impact of this invasive species, but even highly complex habitats may ultimately not protect native species. The utilisation of functional responses under varying environmental contexts provides a method for the understanding and prediction of invasive species impacts.

Classifying Rational G-Spectra for Finite G

We give a new proof that for a finite group G, the category of rational G-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G, as H runs over the conjugacy classes of subgroups of G. Furthermore, the Quillen equivalences of our proof are all symmetric monoidal. Thus we can understand categories of algebras or modules over a ring spectrum in terms of the algebraic model.