Harnessing technology: the learner and their context: choosing to use technology: how learners construct their learning lives in their own contexts: key findings from the first year of research

This report covers the findings from the first year of the learners and their context research and highlights emerging findings including; choosing to use technology and how learners construct their learning lives in their own contexts

On the omega-limit sets of tent maps

For a continuous map f on a compact metric space (X,d), a subset D of X is internally chain transitive if for every x and y in D and every delta > 0 there is a sequence of points {x=x_0,x_1, ...,x_n=y} such that d(f(x_i),x_{i+1}) < delta for i=0,1, ...,n-1. It is known that every omega-limit set is internally chain transitive; in earlier work it was shown that for X a shift of finite type, a closed subset D of X is internally chain transitive if and only if D is an omega-limit set for some point in X, and that the same is also true for the tent map with slope equal to 2. In this paper, we prove that for tent maps whose critical point c=1/2 is periodic, every closed, internally chain transitive set is necessarily an omega-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed, internally chain transitive set which is not an omega-limit set. Together, these results lead us to conjecture that for those tent maps with shadowing (or pseudo-orbit tracing), the omega-limit sets are precisely those sets having internal chain transitivity.Comment: 17 page

How Far Does Economic Theory Explain Competitive Nonlinear Pricing in Practice?

Liberalisation of the British electricity market, in which previously monopolised regional markets were exposed to large-scale entry, is used to test the propositions of several recent theoretical papers on oligopolistic nonlinear pricing. Consistent with those theories, each oligopolist offered a single two-part electricity tariff, and a lump sum discount to consumers who purchased both electricity and gas. However, inconsistent with those theories, firms’ two-part tariffs are heterogeneous in ways that cannot be attributed to cost. We establish a series of stylised facts about the nature of these asymmetries between firms and use them to confront established theory

Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks

We present a novel Bayesian nonparametric regression model for covariates X and continuous, real response variable Y. The model is parametrized in terms of marginal distributions for Y and X and a regression function which tunes the stochastic ordering of the conditional distributions F(y|x). By adopting an approximate composite likelihood approach, we show that the resulting posterior inference can be decoupled for the separate components of the model. This procedure can scale to very large datasets and allows for the use of standard, existing, software from Bayesian nonparametric density estimation and Plackett-Luce ranking estimation to be applied. As an illustration, we show an application of our approach to a US Census dataset, with over 1,300,000 data points and more than 100 covariates

Social Change and the Family

This paper explores the social change of the past 40 years through reporting the results of a restudy. It argues that social change can be understood, culturally, as involving a process of de-institutionalisation and, structurally, as involving differentiation within elementary family groups as well as within extended family networks. Family change is set in the context of changes in the housing and labour markets and the demographic, industrial and occupational changes of the past 40 years. These changes are associated with increases in women\'s economic activity rates and a decrease in their \'degree of domesticity\'. They are also associated with increasing differentiation within families such that occupational heterogeneity is now found at the heart of the elementary family as well as within kinship groupings as was the case 40 years ago. Thus the trend towards increased differentiation identified in the original study (Rosser and Harris: The Family and Social Change) has continued into the 21st century. This is associated with a de-institutionalisation of family life and an increasing need for partners to negotiate participation in both productive and reproductive work.De-Institutionalisation, Social Change, Restudy, Occupational Differentiation, Extended Family

Transport properties for liquid silicon-oxygen-iron mixtures at Earth's core conditions

We report on the thermal and electrical conductivities of two liquid silicon-oxygen-iron mixtures (Fe$_{0.82}$Si$_{0.10}$O$_{0.08}$ and Fe$_{0.79}$Si$_{0.08}$O$_{0.13}$), representative of the composition of the Earth's outer core at the relevant pressure-temperature conditions, obtained from density functional theory calculations with the Kubo-Greenwood formulation. We find thermal conductivities $k$ =100 (160) W m$^{-1}$ K$^{-1}$, and electrical conductivities $\sigma = 1.1 (1.3) \times 10^6 \Omega^{-1}$ m$^{-1}$ at the top (bottom) of the outer core. These new values are between 2 and 3 times higher than previous estimates, and have profound implications for our understanding of the Earth's thermal history and the functioning of the Earth's magnetic field, including rapid cooling rate for the whole core or high level of radiogenic elements in the core. We also show results for a number of structural and dynamic properties of the mixtures, including the partial radial distribution functions, mean square displacements, viscosities and speeds of sound.Comment: 16 pages, 12 figure