We say that a population is perfectly polarized when divided in two groups of the same size and opposite opinions. In this paper, we propose a methodology to study and measure the emergence of polarization from social interactions. We begin by proposing a model to estimate opinions in which a minority of influential individuals propagate their opinions through a social network. The result of the model is an opinion probability density function. Next, we propose an index to quantify the extent to which the resulting distribution is polarized. Finally, we apply the proposed methodology to a Twitter conversation about the late Venezuelan president, Hugo Chávez, finding a good agreement between our results and offline data. Hence, we show that our methodology can detect different degrees of polarization, depending on the structure of the network.

Transmitting messages in the most efficient way as possible has always been one of politicians’ main concerns during electoral processes. Due to the rapidly growing number of users, online social networks have become ideal platforms for politicians to interact with their potential voters. Exploiting the available potential of these tools to maximize their influence over voters is one of politicians’ actual challenges. To step in this direction, we have analyzed the user activity in the online social network Twitter, during the 2011 Spanish Presidential electoral process, and found that such activity is correlated with the election results. We introduce a new measure to study political sentiment in Twitter, which we call the relative support. We have also characterized user behavior by analyzing the structural and dynamical patterns of the complex networks emergent from the mention and retweet networks. Our results suggest that the collective attention is driven by a very small fraction of users. Furthermore, we have analyzed the interactions taking place among politicians, observing a lack of debate. Finally, we develop a network growth model to reproduce the interactions taking place among politicians.

In this work we study Twitter data to understand influence dynamics in social networks. We define user efficiency on Twitter, as the ratio between the emergent spreading process and the activity employed by the user. We characterize this property by means of a quantitative analysis of the structural and dynamical patterns emergent from human interactions, and show it to be universal across several Twitter conversations

A general method to construct wave functions highly localized on a given periodic orbit, using the information contained in the short term quantum dynamics of the system, is presented. The relationship with the Husimi's quasiprobability distribution in phase space is also discussed.

An increase in the rates of activated processes with the coupling to the solvent has long been predicted through the phenomenological Langevin equation in the weak coupling regime. However, its direct observation in particle-based models has been elusive because the coupling typically places the processes in the spacial-diffusion limited regime wherein rates decrease with increasing friction. In this work, the forward and backward reaction rates of the $\mathrm{LiNC}\rightleftharpoons \mathrm{LiCN}$ isomerization reaction in a bath of argon atoms at various densities have been calculated directly using molecular dynamics trajectories. The so-called Kramers turnover in the rate with microscopic friction is clearly visible, thus providing direct and unambiguous evidence for the energy-diffusion regime in which rates increase with friction.