576 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

    Interviewer: 'Are women and girls ever responsible for the domestic violence they encounter?' Student: 'No, well, unless they did something really, really bad 
'

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    Research shows the ‘gendered nature’ of domestic violence, with Women’s Aid (a UK-based charity) estimating that 1 in 4 women are affected (2014). This paper reports on a project - funded by Comic Relief, completed by Nottinghamshire Domestic Violence Forum (now known as Equation) and evaluated by Nottingham Trent University. The project adopts a Whole School Approach in seeking to prevent domestic violence. Students at three secondary schools attended between one and five blocks of work, and special events. There is evidence of positive developments - with young people showing understanding of domestic violence as well as the margins between healthy and unhealthy relationships. However, not all students could reply ‘never’ to the question of ‘are women and girls to blame for the domestic violence they experience?’, remarking that if the woman had done something ‘really, really bad’ then violence might be justified. We argue that young people’s uncertainties need to be situated within the gender-unequal socio-contexts of contemporary society, and further call for a WSA to domestic violence prevention to be a compulsory part of the UK national curriculum

    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
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