Curves in the Minkowski plane and their contact with pseudo-circles

We study the caustic, evolute, Minkowski symmetry set and parallels of a smooth and regular curve in the Minkowski plane.

Identification of literary movements using complex networks to represent texts

The use of statistical methods to analyze large databases of text has been useful in unveiling patterns of human behavior and establishing historical links between cultures and languages. In this study, we identified literary movements by treating books published from 1590 to 1922 as complex networks, whose metrics were analyzed with multivariate techniques to generate six clusters of books. The latter correspond to time periods coinciding with relevant literary movements over the last five centuries. The most important factor contributing to the distinctions between different literary styles was the average shortest path length, in particular the asymmetry of its distribution. Furthermore, over time there has emerged a trend toward larger average shortest path lengths, which is correlated with increased syntactic complexity, and a more uniform use of the words reflected in a smaller power-law coefficient for the distribution of word frequency. Changes in literary style were also found to be driven by opposition to earlier writing styles, as revealed by the analysis performed with geometrical concepts. The approaches adopted here are generic and may be extended to analyze a number of features of languages and cultures.