Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Contrasting effects of changing rhythm and content on auditory distraction in immediate memory

Across five experiments, the temporal regularity and content of an irrelevant speech stream were varied and their effects on a serial recall task examined. Variations of the content, but not the rhythm, of the irrelevant speech stimuli reliably disrupted serial recall performance in all experiments. Bayesian analyses supported the null hypothesis over the hypothesis that irregular rhythms would disrupt memory to a greater extent than regular rhythms. Pooling the data in a combined analysis revealed that regular presentation of the irrelevant speech was significantly more disruptive to serial recall than irregular presentation. These results are consistent with the idea that auditory distraction is sensitive to both intra-item and inter-item relations and challenge an orienting-based account of auditory distraction.

Working with legal pluralism: widowhood, property inheritance and poverty alleviation in urban Senegal

This article explores the role of women's inheritance and ownership of property in urban Senegal. It shows how being able to inherit and own property promotes the economic and emotional security of widows and their children in urban areas, and discusses the challenges posed by legal pluralism in working on poverty alleviation and social protection in the city.

Emotional responses to Hindustani raga music: the role of musical structure

In Indian classical music, ragas constitute specific combinations of tonic intervals potentially capable of evoking distinct emotions. A raga composition is typically presented in two modes, namely, alaap and gat. Alaap is the note by note delineation of a raga bound by a slow tempo, but not bound by a rhythmic cycle. Gat on the other hand is rendered at a faster tempo and follows a rhythmic cycle. Our primary objective was to (1) discriminate the emotions experienced across alaap and gat of ragas, (2) investigate the association of tonic intervals, tempo and rhythmic regularity with emotional response. 122 participants rated their experienced emotion across alaap and gat of 12 ragas. Analysis of the emotional responses revealed that (1) ragas elicit distinct emotions across the two presentation modes, and (2) specific tonic intervals are robust predictors of emotional response. Specifically, our results showed that the ‘minor second’ is a direct predictor of negative valence. (3) Tonality determines the emotion experienced for a raga where as rhythmic regularity and tempo modulate levels of arousal. Our findings provide new insights into the emotional response to Indian ragas and the impact of tempo, rhythmic regularity and tonality on it.

Serial clustering of extratropical cyclones in a multi-model ensemble of historical and future simulations

This study has investigated serial (temporal) clustering of extra-tropical cyclones simulated by 17 climate models that participated in CMIP5. Clustering was estimated by calculating the dispersion (ratio of variance to mean) of 30 December-February counts of Atlantic storm tracks passing nearby each grid point. Results from single historical simulations of 1975-2005 were compared to those from historical ERA40 reanalyses from 1958-2001 ERA40 and single future model projections of 2069-2099 under the RCP4.5 climate change scenario. Models were generally able to capture the broad features in reanalyses reported previously: underdispersion/regularity (i.e. variance less than mean) in the western core of the Atlantic storm track surrounded by overdispersion/clustering (i.e. variance greater than mean) to the north and south and over western Europe. Regression of counts onto North Atlantic Oscillation (NAO) indices revealed that much of the overdispersion in the historical reanalyses and model simulations can be accounted for by NAO variability. Future changes in dispersion were generally found to be small and not consistent across models. The overdispersion statistic, for any 30 year sample, is prone to large amounts of sampling uncertainty that obscures the climate change signal. For example, the projected increase in dispersion for storm counts near London in the CNRMCM5 model is 0.1 compared to a standard deviation of 0.25. Projected changes in the mean and variance of NAO are insufficient to create changes in overdispersion that are discernible above natural sampling variations.

Gendered struggles over land: shifting inheritance practices among the Serer in rural Senegal

Although women's land rights are often affirmed unequivocally in constitutions and international human rights conventions in many African countries, customary practices usually prevail on the ground and often deny women's land inheritance. Yet land inheritance often goes unnoticed in wider policy and development initiatives to promote women's equal access to land. This paper draws on feminist ethnographic research among the Serer ethnic group in two contrasting rural communities in Senegal. Through analysis of land governance, power relations and 'technologies of the self', this article shows how land inheritance rights are contingent on the specific effects of intersectionality in particular places. The contradictions of legal pluralism, greater adherence to Islam and decentralisation led to greater application of patrilineal inheritance practices. Gender, religion and ethnicity intersected with individuals' marital position, status, generation and socio-ecological change to constrain land inheritance rights for women, particularly daughters, and widows who had been in polygamous unions and who remarried. Although some women were aware that they were legally entitled to inherit a share of the land, they tended not to 'demand their rights'. In participatory workshops, micro-scale shifts in women's and men's positionings reveal a recognition of the gender discriminatory nature of customary and Islamic law and a desire to 'change with the times'. While the effects of 'reverse' discourses are ambiguous and potentially reinforce prevailing patriarchal power regimes, 'counter' discourses, which emerged in participatory spaces, may challenge customary practices and move closer to a rights-based approach to gender equality and women's land inheritance.