We show how generalized Gibbs-Shannon entropies can provide new insights on the statistical properties of texts. The universal distribution of word frequencies (Zipf's law) implies that the generalized entropies, computed at the word level, are dominated by words in a specific range of frequencies. Here we show that this is the case not only for the generalized entropies but also for the generalized (Jensen-Shannon) divergences, used to compute the similarity between different texts. This finding allows us to identify the contribution of specific words (and word frequencies) for the different generalized entropies and also to estimate the size of the databases needed to obtain a reliable estimation of the divergences. We test our results in large databases of books (from the Google n-gram database) and scientific papers (indexed by Web of Science).
We use an information-theoretic measure of linguistic similarity to investigate the organization and evolution of scientific fields. An analysis of almost 20 M papers from the past three decades reveals that the linguistic similarity is related but different from experts and citation-based classifications, leading to an improved view on the organization of science. A temporal analysis of the similarity of fields shows that some fields (e.g. computer science) are becoming increasingly central, but that on average the similarity between pairs of disciplines has not changed in the last decades. This suggests that tendencies of convergence (e.g. multi-disciplinarity) and divergence (e.g. specialization) of disciplines are in balance.
In this work, we investigate the effects of torsion on electromagnetic fields. As a model spacetime, endowed with both curvature and torsion, we choose a generalization of the cosmic string, the cosmic dislocation. Maxwell's equations in the spacetime of a cosmic dislocation are then solved, considering both the case of a static, uniform, charge distribution along the string, and the case of a constant current flowing through the string. We find that the torsion associated to the defect affects only the magnetic field whereas curvature affects both electric and magnetic fields. Moreover, the magnetic field is found to spiral up around the defect axis.
Probe-tack measurements evaluate the adhesion strength of viscous fluids confined between parallel plates. This is done by recording the adhesion force that is required to lift the upper plate, while the lower plate is kept at rest. During the lifting process, it is known that the interface separating the confined fluids is deformed, causing the emergence of intricate interfacial fingering structures. Existing meticulous experiments and intensive numerical simulations indicate that fingering formation affects the lifting force, causing a decrease in intensity. In this work, we propose an analytical model that computes the lifting adhesion force by taking into account not only the effect of interfacial fingering, but also the action of wetting and viscous normal stresses. The role played by the system's spatial confinement is also considered. We show that the incorporation of all these physical ingredients is necessary to provide a better agreement between theoretical predictions and experiments.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.