Abstract
We show that for a specific class of random matching Edgeworthian economies, the expectation of the limiting equilibrium price coincides with the equilibrium price of the related Walrasian economies. This result extends to the study of economies in the presence of uncertainty within the multi-period Arrow-Debreu model, allowing to understand the dynamics of how beliefs survive and propagate through the market.

Abstract
The von Mises-Fisher distribution is widely used for modelling directional data. In this paper we propose goodness-of-fit methods for a concentrated von Mises-Fisher distribution and we analyse by simulation some questions concerning the application of these tests. We analyse the empirical power of the Kolmogorov-Smirnov test for several dimensions of the sphere, supposing as alternative hypothesis a mixture of two von Mises-Fisher distributions with known parameters. We also compare the empirical power of the Kolmogorov-Smirnov test with the Rao's score test for data on the sphere, supposing as alternative hypothesis, a mixture of two Fisher distributions with unknown parameters replaced by their maximum likelihood estimates or a 5-parameter Fisher-Bingham distribution. Finally, we give an example with real spherical data.

Abstract
We analyse the dynamics and evolution of the corporate restructuring process in the Portuguese banking sector, where 10 banks were privatised during the period 1989-1996. We apply a novel methodological approach in this context, using a multidimensional measure of restructuring that links product and labour market variables. We find evidence of considerable heterogeneity in the restructuring process, where firms adjust at different speeds and intensities. We also find that the wage level is by far the firm attribute that changed more, which is shown to reflect substantial changes in terms of composition, and not size, of the workforce. Our empirical evidence also suggests that privatisation is associated with a higher level of rent sharing. © 2011 Elsevier B.V.

Abstract
Epidemiological spreading does not only happen from person to neighbouring person but often over wide distances, when infected but asymptomatic persons travel and carry infection to others over wide distances. Superdiffusion has been suggested to model such spreading in spatially restriced contact networks, i.e. there is still a notion of geographical distance, but spreading happens with high probability proportional to large distances. From fractional calculus several ways of describing superdiffusion are know. Here we investigate the representation in Fourier space and which is easily generalizable to higher dimensional space in order to compare with stochastic models of epidemiological spreading.

Abstract
In this paper we analyze the stochastic version of a minimalistic multi-strain model, which captures essential differences between primary and secondary infections in dengue fever epidemiology, and investigate the interplay between stochasticity, seasonality and import. The introduction of stochasticity is needed to explain the fluctuations observed in some of the available data sets, revealing a scenario where noise and complex deterministic skeleton strongly interact. For large enough population size, the stochastic system can be well described by the deterministic skeleton gaining insight on the relevant parameter values purely on topological information of the dynamics, rather than classical parameter estimation of which application is in general restricted to fairly simple dynamical scenarios.

Abstract
Our study aimed to assess the impact of a six-months nutrition program, taught by trained teachers, on fruit and vegetable consumption among children in grades 1 to 4. Four hundred and sixty-four children (239 female), 6 to 12 years old, from seven elementary schools were assigned to this randomized trial. Teachers were trained by researchers over six months, according to the following topics: nutrition, healthy eating, and strategies to increase physical activity. After each session, teachers were encouraged to develop activities in the classroom on the topics learned. Children's sociodemographic, anthropometric, dietary, and physical activity data were assessed at baseline and at the end of the intervention. The effect sizes ranged between small (Cohen's d=0.12 on "other vegetables") to medium (0.56 on "fruit and vegetable"), and intervened children reported a significantly higher consumption of vegetables and fruit. Interventions involving trained teachers offer promise to increase consumption of fruit and vegetable in children. © 2012 Rafaela Rosário et al.