476 research outputs found

    Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time

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    For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (2007). This improvement finally settles a conjecture by Aizenman (1997) about the role of boundary conditions in critical high-dimensional percolation, and it is a key step in deriving further properties of critical percolation on the torus. Indeed, a criterion of Nachmias and Peres (2008) implies appropriate bounds on diameter and mixing time of the largest clusters. We further prove that the volume bounds apply also to any finite number of the largest clusters. The main conclusion of the paper is that the behavior of critical percolation on the high-dimensional torus is the same as for critical Erdos-Renyi random graphs. In this updated version we incorporate an erratum to be published in a forthcoming issue of Probab. Theory Relat. Fields. This results in a modification of Theorem 1.2 as well as Proposition 3.1.Comment: 16 pages. v4 incorporates an erratum to be published in a forthcoming issue of Probab. Theory Relat. Field

    Graduate employability, skills development and the UK’s Universities Business Challenge (UBC) competition: a self-determined learning perspective

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    Drawing on elements of self-determined learning or heutagogy, the graduate employability impact of the UK’s leading Universities Business Challenge (UBC) competition is investigated over a five year period of from 2012-17. A central research question was addressed, namely: what do inter-university business simulations, such as the UBC, contribute to developing self-determined learner skills and graduate employability? A mixed-methods research approach combined structured equation modelling (SEM) results of 2 student surveys from over 50 (UK) universities, with qualitative analysis of 7 student focus-groups and 15 semi-structured interviews. The article contributes to new knowledge about the role of UBC as an example of an inter-university business simulation. It models the direct and indirect effects of personal/managerial skills development and reflective learning capacity (as mediator) on perceived employability impact. There is fresh evidence to support the claim that reflective learning is important in the study of self-determined learning and graduate employability

    The Alexander-Orbach conjecture holds in high dimensions

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    We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

    Supplier qualification for high value goods and services in Nigeria: A comparison of qualified and non-qualified suppliers

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    This study set out to understand the capabilities of suppliers of high value products and services in Nigeria. Supplier capability data was collected from almost 500 potential suppliers across 28 product categories. The findings indicate that only a small minority of potential suppliers achieved the required levels of performance and that very few companies have suitable operational capabilities or corporate citizenship behaviour. Furthermore, significant differences were found between service suppliers and product suppliers with regard to performance. The findings suggest that the majority of suppliers of products and services in Nigeria need to improve their operational capabilities and corporate citizenship behaviours or else risk losing their ability to compete in a changing market place with new barriers to entry

    A generation apart? Youth and political participation in Britain

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    Conventional wisdom holds that young people in Britain are alienated from politics, with some claiming that this reflects a wider crisis of legitimacy that should be met by initiatives to increase citizenship. This article addresses these areas, presenting both panel survey and focus group data from first-time voters. It concludes that, contrary to the findings from many predominantly quantitative studies of political participation, young people are interested in political matters, and do support the democratic process. However they feel a sense of anti-climax having voted for the first time, and are critical of those who have been elected to positions of political power. If they are a generation apart, this is less to do with apathy, and more to do with their engaged scepticism about ‘formal’ politics in Britain
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