The explicit solutions of the Bogomolny equations for $N$ vortices on a sphere of radius $R^2\mathrm{>N}$ are not known. In particular, this has prevented the use of the geodesic approximation to describe the low energy vortex dynamics. In this article we introduce an approximate general solution of the equations, valid for $R^2\mathrm{\gtrsim N,}$ which has many properties of the true solutions, including the same moduli space ${\mathbb{CP}}^N.$ Within the framework of the geodesic approximation, the metric on the moduli space is then computed to be proportional to the Fubini–Study metric, which leads to a complete description of the particle dynamics.

Sharing data in the form of text is important for a wide range of activities but it also raises a concern about privacy when sharing data that could be sensitive. Automated text anonymization is a solution for removing all the sensitive information from documents. However, this is a challenging task due to the unstructured form of textual data and the ambiguity of natural language. In this work, we present our implementation of an automated anonymization system, built in a modular structure, for documents written in Portuguese. Four different methods of anonymization are evaluated and compared. Two methods replace the sensitive information by artificial labels: suppression and tagging. The other two methods replace the information by textual expressions: random substitution and generalization. Evaluation showed that the use of the tagging and the generalization methods facilitates the reading of an anonymized text while preventing some semantic drifts caused by the remotion of the original information.

RESUMO Este artigo apresenta uma análise da utilização de diferentes modalidades de ensino no ensino superior, considerando o contexto atual provocado pela COVID-19. O estudo baseia-se em uma revisão da literatura sobre o tema e questionário aplicado a 225 estudantes e professores universitários do Brasil e de Portugal, dos quais 144 tiveram suas aulas presenciais substituídas por aulas a distância. A maioria dos respondentes considera o ensino a distância pior do que o presencial, a comunicação pior, a avaliação mais difícil, a exigência maior e a aprendizagem pior. Além disso, os professores julgam empregar muito mais de seu tempo e dedicação para o ensino a distância, enquanto os alunos parecem dedicar-se menos. Ao serem questionados sobre o futuro do ensino superior, a maioria acredita que a modalidade de ensino mais utilizada será a híbrida. Apesar de o ensino a distância proporcionar diversas vantagens, os participantes sentem falta da interação face a face.