Realising the cup product of local Tate duality

We present an explicit description, in terms of central simple algebras, of a cup product map which occurs in the statement of local Tate duality for Galois modules of prime cardinality p. Given cocycles f and g, we construct a central simple algebra of dimension p^2 whose class in the Brauer group gives the cup product f\cup g. This algebra is as small as possible.

Formal linguistic approaches to heritage language acquisition: bridges for pedagogically oriented research

The goal of this chapter is to lay out the central themes of heritage language acquisition research adopting a formal/theoretical linguistic perspective.  Specifically, we aim to provide a detailed discussion of the nature of heritage language grammars. In doing so, we will address the debates on how to explain heritage speaker competence differences from monolingual baselines and more. This chapter will not be limited to discussions of Spanish as a heritage language, but rather will highlight the important role that Spanish has played and will continue to play in the development of heritage language acquisition studies. Finally, we will offer some comments/insights on how the information covered regarding the formal linguistic properties of heritage speaker knowledge should be considered for and implemented in heritage language pedagogies and thus dealing with heritage speakers in the classroom setting.

Building collaborative partnerships for climate change action in Maputo, Mozambique

The authors examine partnerships as a policy strategy for climate change governance in cities in the Global South. Partnerships offer the opportunity to link the actions of diverse actors operating at different scales and, thus, they may be flexible enough to deal with uncertain futures and changing development demands. However, simultaneously, partnerships may lack effectiveness in delivering action at the local level, and may constitute a strategy for some actors to legitimate their objectives in spite of the interests of other partners. Engaging with the specific example of urban governance in Maputo, Mozambique, the authors present an analysis of potential partnerships in this context, in relation to the actors that are willing and able to intervene to deliver climate change action. What, they ask, are the challenges to achieving common objectives in partnerships from the perspective of local residents in informal settlements? The analysis describes a changing context of climate change governance in the city, in which the prospects of access to international finance for climate change adaptation are moving institutional actors towards engaging with participatory processes at the local level. However, the analysis suggests a question about the extent to which local communities are actually perceived as actors with legitimate interests who can intervene in partnerships, and whether their interests are recognised.

Bayesian analysis of uncertainty in the GlobCover 2009 land cover product at climate model grid scale

Land cover data derived from satellites are commonly used to prescribe inputs to models of the land surface. Since such data inevitably contains errors, quantifying how uncertainties in the data affect a model’s output is important. To do so, a spatial distribution of possible land cover values is required to propagate through the model’s simulation. However, at large scales, such as those required for climate models, such spatial modelling can be difficult. Also, computer models often require land cover proportions at sites larger than the original map scale as inputs, and it is the uncertainty in these proportions that this article discusses. This paper describes a Monte Carlo sampling scheme that generates realisations of land cover proportions from the posterior distribution as implied by a Bayesian analysis that combines spatial information in the land cover map and its associated confusion matrix. The technique is computationally simple and has been applied previously to the Land Cover Map 2000 for the region of England and Wales. This article demonstrates the ability of the technique to scale up to large (global) satellite derived land cover maps and reports its application to the GlobCover 2009 data product. The results show that, in general, the GlobCover data possesses only small biases, with the largest belonging to non–vegetated surfaces. In vegetated surfaces, the most prominent area of uncertainty is Southern Africa, which represents a complex heterogeneous landscape. It is also clear from this study that greater resources need to be devoted to the construction of comprehensive confusion matrices.