RESUMO
In recent decades, the field of statistical linguistics has made significant strides, which have been fueled by the availability of data. Leveraging Twitter data, this paper explores the English and Spanish languages, investigating their rank diversity across different scales: temporal intervals (ranging from 3 to 96 h), spatial radii (spanning 3 km to over 3000 km), and grammatical word ngrams (ranging from 1-grams to 5-grams). The analysis focuses on word ngrams, examining a time period of 1 year (2014) and eight different countries. Our findings highlight the relevance of all three scales with the most substantial changes observed at the grammatical level. Specifically, at the monogram level, rank diversity curves exhibit remarkable similarity across languages, countries, and temporal or spatial scales. However, as the grammatical scale expands, variations in rank diversity become more pronounced and influenced by temporal, spatial, linguistic, and national factors. Additionally, we investigate the statistical characteristics of Twitter-specific tokens, including emojis, hashtags, and user mentions, revealing a sigmoid pattern in their rank diversity function. These insights contribute to quantifying universal language statistics while also identifying potential sources of variation.
RESUMO
Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality-a balance between change and stability, order and chaos-is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks-a general model of discrete dynamical systems-we show that heterogeneity-in time, structure, and function-can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.