Local Equivalence and Intrinsic Metrics between Reeb Graphs

As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for applications, where it matters to quantify the extent by which two given Reeb graphs differ. Recent contributions emphasize this aspect, proposing novel distances such as {\em functional distortion} or {\em interleaving} that are provably more discriminative than the so-called {\em bottleneck distance}, being true metrics whereas the latter is only a pseudo-metric. Their main drawback compared to the bottleneck distance is to be comparatively hard (if at all possible) to evaluate. Here we take the opposite view on the problem and show that the bottleneck distance is in fact good enough {\em locally}, in the sense that it is able to discriminate a Reeb graph from any other Reeb graph in a small enough neighborhood, as efficiently as the other metrics do. This suggests considering the {\em intrinsic metrics} induced by these distances, which turn out to be all {\em globally} equivalent. This novel viewpoint on the study of Reeb graphs has a potential impact on applications, where one may not only be interested in discriminating between data but also in interpolating between them

Do academics doubt their own research?

When do experts doubt or question their own previously published research and why? An online survey was designed and distributed across academic staff and postgraduate research students at different universities in Great Britain. Respondents (n = 202 - 244) identified the likelihoods of six different (quasi) hypothetical occurrences causing them to doubt or question work they have published in peer reviewed journals. They are: two objective and two semi-objective citation based metrics, plus two semi-objective metrics based on verbalised reactions. Only limited support is found from this study to suggest that the authors of primary research would agree with any judgements made by others about their research based on these metrics. The occurrence most likely to cause respondents to doubt or question their previously published research was where the majority of citing studies suggested mistakes in their work. In a multivariate context, only age and nationality are significant determinants of doubt beyond average likelihoods. Understanding and acknowledging what makes authors of primary research doubt their own research could increase the validity of those who pass judgement

Evaluating the provision of school performance information for school choice

We develop and implement a framework for determining the optimal performance metrics to help parents choose a school. This approach combines the three major critiques of the usefulness of performance tables into a natural metric. We implement this for 500,000 students in England for a range of performance measures. Using performance tables is strongly better than choosing at random: a child who attends the highest ex ante performing school within their choice set will ex post do better than the average outcome in their choice set twice as often as they will do worse

Exploring rationales for branding a university: Should we be seeking to measure branding in UK universities?

Although branding is now widespread among UK universities, the application of branding principles in the higher education sector is comparatively recent and may be controversial for internal audiences who question its suitability and efficiency. This paper seeks to investigate how and whether the effectiveness of branding activity in the higher education sector should be evaluated and measured, through exploratory interviews with those who often drive it; UK University marketing professionals. Conclusions suggest that university branding is inherently complex and therefore application of commercial approaches may be over simplistic. Whilst marketing professionals discuss challenges they do not necessarily have a consistent view of the objectives of branding activity although all were able to clearly articulate branding objectives for their university, including both qualitative and, to some extent, quantitative metrics. Some measures of the real value of branding activity are therefore suggested but a key debate is perhaps whether the objectives and role of branding in higher education needs to be clarified, and a more consistent view of appropriate metrics reached? Various challenges in implementing branding approaches are also highlighted

A Spin-Statistics Theorem for Certain Topological Geons

We review the mechanism in quantum gravity whereby topological geons, particles made from non-trivial spatial topology, are endowed with nontrivial spin and statistics. In a theory without topology change there is no obstruction to ``anomalous'' spin-statistics pairings for geons. However, in a sum-over-histories formulation including topology change, we show that non-chiral abelian geons do satisfy a spin-statistics correlation if they are described by a wave function which is given by a functional integral over metrics on a particular four-manifold. This manifold describes a topology changing process which creates a pair of geons from $R^3$.Comment: 21 pages, Plain TeX with harvmac, 3 figures included via eps