Optimal topological simplification of discrete functions on surfaces

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with persistence less than 2{\delta}, constructively proving the tightness of a lower bound on the number of critical points given by the stability theorem of persistent homology in dimension two for any input function. We also show that an optimal solution can be computed in linear time after persistence pairs have been computed.Comment: 27 pages, 8 figure

The violence of narrative: embodying responsibility for poverty-related distress

This is the final version. Available on open access from Wiley via the DOI in this record.Narratives of self-responsibility are pervasive in neo-liberally oriented contexts, and have been found to engender feelings of shame and failure amongst those affected by poverty. Here we use findings from research in two low-income communities in south-west England to examine how these narratives become embodied within people’s daily lives when they intersect with systems of welfare support and the current political drive to upscale treatment for common mental health conditions. Drawing on Bourdieu’s notion of symbolic violence, we examine how narratives of self-responsibility and associated welfare reform strategies impact on the mental health of people living in economic hardship. The data show how such narratives inflict, sustain and exacerbate mental distress and suffering, and how they become naturalised and normalised by individuals themselves. We demonstrate how this situation pushes people to seek support from General Practitioners, and how clinical interactions can normalise, and in turn, medicalise, poverty-related distress. Whilst some people actively resist dominant narratives around self-responsibility, we argue that this is insufficient under broader socio- cultural and political circumstances, to free themselves from the harms perpetuated by symbolic violence.Economic and Social Research Council (ESRC

Geographic Visualisation: Lessons for Learning and Teaching.

This paper outlines a pedagogic project funded by the former GEES Learning and Teaching Development Fund, exploring students’ attitudes to, and learning through, visualisation as a method of assessment in a core undergraduate geography module. Student expectations and experiences of this assessment, together with reflections on learning and teaching methods more widely, were investigated using participatory appraisal, and follow-up face-to-face feedback. Student perceptions of visualisation as assessment mixed an uncertainty about what was expected, with a sense that visual work might be comparatively ‘easier’. Responses after the assessment recognised the difficulty of the method, the focus on data and the ability to address complex topics. Students also compared their experiences with visualisation to other assessment methods, with many finding the visual approach stimulating and effective for their learning, and module marks were higher than in previous years. We have retained the assessment in the module and extended some of the lessons, especially the use of show-and-tell critique sessions for formative feedback, to other modules