Standard methods in non-linear analysis are used to indicate that there exists a parabolic branching of solutions of the LichnerowiczYork equation with an unscaled source. We also apply these methods to the extended conformal thin sandwich formulation and, by assuming that the linearised system develops a kernel solution for sufficiently large initial data, we reproduce the parabolic solution curves for the conformal factor, lapse and shift found numerically by Pfeiffer and York.

Motivated by in vitro time–lapse images of ovarian cancer spheroids inducing mesothelial cell clearance, the traditional agent–based model of cell migration, based on simple volume exclusion, was extended to include the possibility that a cell seeking to move into an occupied location may push the resident cell, and any cells neighbouring it, out of the way to occupy that location. In traditional discrete models of motile cells with volume exclusion such a move would be aborted. We introduce a new shoving mechanism which allows cells to choose the direction to shove cells that expends the least amount of shoving effort (to account for the likely resistance of cells to being pushed). We call this motility rule ‘smart shoving’. We examine whether agent–based simulations of different shoving mechanisms can be distinguished on the basis of single realisations and averages over many realisations. We emphasise the difficulty in distinguishing cell mechanisms from cellular automata simulations based on snap–shots of cell distributions, site–occupancy averages and the evolution of the number of cells of each species averaged over many realisations. This difficulty suggests the need for higher resolution cell tracking.

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Previous studies have shown impaired memory for faces following restricted sleep. However, it is not known whether lack of sleep impairs performance on face identification tasks that do not rely on recognition memory, despite these tasks being more prevalent in security and forensic professions—for example, in photo-ID checks at national borders. Here we tested whether poor sleep affects accuracy on a standard test of face-matching ability that does not place demands on memory: the Glasgow Face-Matching Task (GFMT). In Experiment 1, participants who reported sleep disturbance consistent with insomnia disorder show impaired accuracy on the GFMT when compared with participants reporting normal sleep behaviour. In Experiment 2, we then used a sleep diary method to compare GFMT accuracy in a control group to participants reporting poor sleep on three consecutive nights—and again found lower accuracy scores in the short sleep group. In both experiments, reduced face-matching accuracy in those with poorer sleep was not associated with lower confidence in their decisions, carrying implications for occupational settings where identification errors made with high confidence can have serious outcomes. These results suggest that sleep-related impairments in face memory reflect difficulties in perceptual encoding of identity, and point towards metacognitive impairment in face matching following poor sleep.

This paper compares retail and wholesale electricity prices in SEM, the market of the island of Ireland, and BETTA in Great Britain. Estimated wholesale costs are much lower in BETTA. We show that this is mostly because the wholesale price in BETTA is set too low to cover generation costs, although it is compensated by large retail margins. The need for substantial new investment in generation in Great Britain suggests that returns to generators will have to increase. This should be accompanied by a decrease in retail margins to avoid overburdening final consumers. Renewable support in Great Britain appears very expensive when compared to Ireland.