On the fractal patterns of language structures.

Natural Language Processing (NLP) makes use of Artificial Intelligence algorithms to extract meaningful information from unstructured texts, i.e., content that lacks metadata and cannot easily be indexed or mapped onto standard database fields. It has several applications, from sentiment analysis and text summary to automatic language translation. In this work, we use NLP to figure out similar structural linguistic patterns among several different languages. We apply the word2vec algorithm that creates a vector representation for the words in a multidimensional space that maintains the meaning relationship between the words. From a large corpus we built this vectorial representation in a 100-dimensional space for English, Portuguese, German, Spanish, Russian, French, Chinese, Japanese, Korean, Italian, Arabic, Hebrew, Basque, Dutch, Swedish, Finnish, and Estonian. Then, we calculated the fractal dimensions of the structure that represents each language. The structures are multi-fractals with two different dimensions that we use, in addition to the token-dictionary size rate of the languages, to represent the languages in a three-dimensional space. Finally, analyzing the distance among languages in this space, we conclude that the closeness there is tendentially related to the distance in the Phylogenetic tree that depicts the lines of evolutionary descent of the languages from a common ancestor.

Successive Pandemic Waves with Different Virulent Strains and the Effects of Vaccination for SARS-CoV-2.

One hundred years after the flu pandemic of 1918, the world faces an outbreak of a new severe acute respiratory syndrome, caused by a novel coronavirus. With a high transmissibility, the pandemic has spread worldwide, creating a scenario of devastation in many countries. By the middle of 2021, about 3% of the world population had been infected and more than 4 million people had died. Different from the H1N1 pandemic, which had a deadly wave and ceased, the new disease is maintained by successive waves, mainly produced by new virus variants and the small number of vaccinated people. In the present work, we create a version of the SIR model using the spatial localization of persons, their movements, and considering social isolation probabilities. We discuss the effects of virus variants, and the role of vaccination rate in the pandemic dynamics. We show that, unless a global vaccination is implemented, we will have continuous waves of infections.