The complex dynamics of products and its asymptotic properties

PopRank: Ranking pages' impact and users' engagement on Facebook

The advent of social networks revolutionized the way people access to information sources. Understanding the complex relationship between these sources and users is crucial. We introduce an algorithm, that we call PopRank, to assess both the Impact of Facebook pages as well as users’ Engagement on the basis of their mutual interactions. The ideas behind the PopRank are that i) high impact pages attract many users with a low engagement, which means that they receive comments from users that rarely comment, and ii) high engagement users interact with high impact pages, that is they mostly comment pages with a high popularity. The resulting ranking of pages can predict the number of comments a page will receive and the number of its future posts. Pages’ impact turns out to be slightly dependent on the quality of pages’ informative content (e.g., science vs conspiracy) but independent of users’ polarization.

Complexity of Products: The Effect of Data Regularisation

Among several developments, the field of Economic Complexity (EC) has notably seen the introduction of two new techniques. One is the Bootstrapped Selective Predictability Scheme (SPSb), which can provide quantitative forecasts of the Gross Domestic Product of countries. The other, Hidden Markov Model (HMM) regularisation, denoises the datasets typically employed in the literature. We contribute to EC along three different directions. First, we prove the convergence of the SPSb algorithm to a well-known statistical learning technique known as Nadaraya-Watson Kernel regression. The latter has significantly lower time complexity, produces deterministic results, and it is interchangeable with SPSb for the purpose of making predictions. Second, we study the effects of HMM regularization on the Product Complexity and logPRODY metrics, for which a model of time evolution has been recently proposed. We find confirmation for the original interpretation of the logPRODY model as describing the change in the global market structure of products with new insights allowing a new interpretation of the Complexity measure, for which we propose a modification. Third, we explore new effects of regularisation on the data. We find that it reduces noise, and observe for the first time that it increases nestedness in the export network adjacency matrix.

Correction: The complex dynamics of products and its asymptotic properties

[This corrects the article DOI: 10.1371/journal.pone.0177360.].