Worldwide bilateral geopolitical interactions network inferred from national disciplinary profiles

A disciplinary profile of a country is defined as the versor whose components are the number of papers produced in a given discipline divided by the overall production of the country. Starting from the Essential Science Indicators (ESI) schema of classification of subject areas, we obtained the yearly disciplinary profiles of a worldwide graph, where on each node sits a country, in the two time intervals 1988-1988 and 1992-2017, the fall of the Berlin Wall being the watershed. We analyze the empirical pairwise cross-correlation matrices of the time series of disciplinary profiles. The contrast with random matrix theory proves that, beyond measurement noise, the empirical cross-correlation matrices bring genuine information. Arising from the Shannon theorem as the least-structured model consistent with the measured pairwise correlations, the stationary probability distribution of disciplinary profiles can be described by a Boltzmann distribution related to a generalized nd-dimensional Heisenberg model. The set of network interactions of the Heisenberg model has been inferred and to it, two clusterization methods, hierarchical clustering, and principal component analysis have been applied. This allows obtaining a characterization of the worldwide bilateral interactions based on physical modeling. A simple geopolitical analysis reveals the consistency of the results obtained and gives a boost to a deeper historical analysis. In order to obtain the optimal set of pairwise interactions, we used a pseudolikelihood approach. We analytically computed the pseudolikelihood and its gradient. The analytical computations deserve interest in whatever inference Bayesian problem involving an nd-dimensional Heisenberg model.