The Alexander-Orbach conjecture holds in high dimensions

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

Pupil response hazard rates predict perceived gaze durations

We investigated the mechanisms for evaluating perceived gaze-shift duration. Timing relies on the accumulation of endogenous physiological signals. Here we focused on arousal, measured through pupil dilation, as a candidate timing signal. Participants timed gaze-shifts performed by face stimuli in a Standard/Probe comparison task. Pupil responses were binned according to “Longer/Shorter” judgements in trials where Standard and Probe were identical. This ensured that pupil responses reflected endogenous arousal fluctuations opposed to differences in stimulus content. We found that pupil hazard rates predicted the classification of sub-second intervals (steeper dilation =“Longer” classifications). This shows that the accumulation of endogenous arousal signals informs gaze-shift timing judgements. We also found that participants relied exclusively on the 2nd stimulus to perform the classification, providing insights into timing strategies under conditions of maximum uncertainty. We observed no dissociation in pupil responses when timing equivalent neutral spatial displacements, indicating that a stimulus-dependent timer exploits arousal to time gaze-shifts

Language attitudes, linguistic authority and independence in 21st century Catalonia

peer-reviewedIn a context of increasing linguistic and cultural diversity and political uncertainty in Catalonia, this article reports on a research project which set out to explore the attitudes of members of independence organisations operating in the city of Girona toward the Catalan and Spanish languages. This study approaches language attitudes through the theoretical lens of linguistic authority, in particular, the concepts of anonymity and authenticity. The data, gathered from six focus groups, provide an insight on the nature of linguistic authority in contemporary Catalonia. Two themes emerge in the informants’ discussion of Catalan and Spanish: ‘twenty-first Century Catalanisme’ and ‘Embracing Linguistic Diversity’. The comments of the respondents indicate that, against the backdrop of the independence process in the region, bilingualism and multilingualism have become highly valued in the territory. In addition, this study suggests that a fuller understanding of the situation in Catalonia may be facilitated by qualitative approaches, which explore attitudes in-depth