We reformulate a class of non-linear stochastic optimal control problems introduced by Todorov (in Advances in Neural Information Processing Systems, vol. 19, pp. 1369–1376, 2007) as a Kullback-Leibler (KL) minimization problem. As a result, the optimal control computation reduces to an inference computation and approximate inference methods can be applied to efficiently compute approximate optimal controls. We show how this KL control theory contains the path integral control method as a special case. We provide an example of a block stacking task and a multi-agent cooperative game where we demonstrate how approximate inference can be successfully applied to instances that are too complex for exact computation. We discuss the relation of the KL control approach to other inference approaches to control.

We analyze the social network emerging from the user comment activity on the website Slashdot. The network presents/ncommon features of traditional social networks such as a giant component, small average path length and high clustering, but differs from them showing moderate reciprocity and neutral assortativity by degree. Using Kolmogorov-Smirnov/nstatistical tests, we show that the degree distributions are better explained by log-normal instead of power-law distributions./nWe also study the structure of discussion threads using an intuitive radial tree representation. Threads show strong heterogeneity and self-similarity throughout the different nesting levels of a conversation. We use these results to propose a simple measure to evaluate the degree of controversy provoked by a post.We thank the reviewers for their valuable suggestions and Càtedra Telefònica de Producció Multimèdia for funding

With the irruption of ICTs and the crisis of political representation, many online platforms have been developed with the aim of improving participatory democratic processes. However, regarding platforms for online petitioning, previous research has not found examples of how to effectively introduce discussions, a crucial feature to promote deliberation. In this study we focus on the case of Decidim Barcelona, the online participatory-democracy platform launched by the City Council of Barcelona in which proposals can be discussed with an interface that combines threaded discussions and comment alignment with the proposal. This innovative approach allows to examine whether neutral, positive or negative comments are more likely to generate discussion cascades. The results reveal that, with this interface, comments marked as negatively aligned with the proposal were more likely to engage users in online discussions and, therefore, helped to promote deliberative decision making.

Online discussion threads are conversational cascades in the form of posted messages that can be generally found in social systems that comprise many-to-many interaction such as blogs, news aggregators or bulletin board systems. We propose a framework based on generative models of growing trees to analyse the structure and evolution of discussion threads. We consider the growth of a discussion to be determined by an interplay between popularity, novelty and a trend (or bias) to reply to the thread originator. The relevance of these features is estimated using a full likelihood approach and allows to characterise the habits and communication patterns of a given platform and/or community. We apply the proposed framework on four popular websites: Slashdot, Barrapunto (a Spanish version of Slashdot), Meneame (a Spanish Digg-clone) and the article discussion pages of the English Wikipedia. Our results provide significant insight into understanding how discussion cascades grow and have potential applications in broader contexts such as community management or design of communication platforms.

Online discussion in form of written comments is a core component of many social media platforms. It has attracted increasing attention from academia, mainly because theories from social sciences can be explored at an unprecedented scale. This interest has led to the development of statistical models which are able to characterize the dynamics of threaded online conversations.