The number of people using online social networks in their everyday life is continuously growing at a pace never saw before. This new kind of communication has an enormous impact on opinions, cultural trends, information spreading and even in the commercial success of new products. More importantly, social online networks have revealed as a fundamental organizing mechanism in recent country-wide social movements. In this paper, we provide a quantitative analysis of the structural and dynamical patterns emerging from the activity of an online social network around the ongoing May 15th (15M) movement in Spain. Our network is made up by users that exchanged tweets in a time period of one month, which includes the birth and stabilization of the 15M movement. We characterize in depth the growth of such dynamical network and find that it is scale-free with communities at the mesoscale. We also find that its dynamics exhibits typical features of critical systems such as robustness and power-law distributions for several quantities. Remarkably, we report that the patterns characterizing the spreading dynamics are asymmetric, giving rise to a clear distinction between information sources and sinks. Our study represents a first step towards the use of data from online social media to comprehend modern societal dynamics.

Résumé. La dynamique oscillante d'un champ de vecteurs analytique en dimension trois s'organise autour d'un nombre fini d'axes de tourbillonnement lorsqu'elle ne se délocalise pas par deś eclatements de point.Abstract. The oscillating dynamics of an analytic vector field in dimension three is organized around a finite number of twister axis when it is localisable by point blowing-ups.

The Mediterranean diet (MD) is a dietary pattern with important benefits. The objectives of this study were to assess the adherence to the MD among pregnant women in Valencia (Spain) and characterize the pregnant women according to their level of adherence. Finally, we aimed to examine the role of MD adherence during pregnancy in the anthropometric development of the newborn. The study included 492 pregnant women who were followed at La Fe Hospital in 2017. The self-administered “Kidmed” questionnaire for data collection on dietary information evaluation was used and a clinical history review of mothers and newborns was performed. Two groups of mothers were identified: those with low adherence (LA) and optimal adherence (OA). The study revealed that 40.2% of the women showed LA to the MD. The newborns born to these women presented a higher risk of being small for gestational age (SGA) {adjusted odds ratio (aOR) = 1.68; 95% confidence interval (CI) 1.02–5.46} when adjusting for parental body mass index (BMI) and multiple gestation, but not when adjusting for all significant possible confounders (aOR = 2.32; 95% CI 0.69–7.78). The association between MD and SGA was not significantly affected by the use of iron and folic acid supplements (aOR = 2.65; 95% CI 0.66–10.65). The profile of the pregnant woman with LA is that of a young smoker, with a low level of education and a low daily intake of dairy products. These results suggest that LA to the MD is not associated with a higher risk of giving birth to a SGA newborn.

In this paper, an analysis is made of the evolution of Spanish urban structure during the period 1900-99. It is postulated that the size distribution of the cities follows a Pareto distribution, which is estimated on a yearly basis. At the same time, the hypothesis is adopted that the intradistribution dynamics can be modelled by means of a Markov chain. In this way, are deduced the so-called transition matrix and its associated vector or ergodic probabilities. This methodology allows two main results to be obtained. First, this evolution has not been homogeneous ; there has been a divergent pattern of growth during the period 1900-70; and a convergent pattern for the period 1970-99. Secondly, the intradistribution movements in the Spanish urban hierarchy have been very significant during the course of the 20th century. In addition, the existence of spatial correlation has also been detected for those cities that have either entered or exited from the sample of the 100 largest cities during the course of the century.

It is well known that the non‐spiraling leaves of real analytic foliations of codimension 1 all belong to the same o‐minimal structure. Naturally, the question arises of whether the same statement is true for non‐oscillating trajectories of real analytic vector fields. We show, under certain assumptions, that such a trajectory generates an o‐minimal and model‐complete structure together with the analytic functions. The proof uses the asymptotic theory of irregular singular ordinary differential equations in order to establish a quasi‐analyticity result from which the main theorem follows. As applications, we present an infinite family of o‐minimal structures such that any two of them do not admit a common extension, and we construct a non‐oscillating trajectory of a real analytic vector field in ℝ5 that is not definable in any o‐minimal extension of ℝ.