We analyze the differential relation corresponding to integrability of almost complex structures, reformulated as a directed immersion by Demailly and Gaussier. Using recent results Clemente from 2020 in combination with this analysis, we show following two statements: first, there are no formal obstructions structure, sense h-principle. Second, for an manifold arbitrary metric (X,J,g), ϵ>0, ex...

Linguistic insight in the form of high-level relationships and rules text builds basis our understanding language. However, data-driven generation such structures often lacks labeled resources that can be used as training data for supervised machine learning. The creation ground-truth is a time-consuming process requires domain expertise to resolve ambiguities characterize linguistic phenomena....

Human language is characterized by variability in that the way in which language is used varies depending, for example, on facts about the identity of the speaker or author, the social context, and surrounding linguistic material. Variability poses formidable challenges to the systems underlying language comprehension, which are known to exploit statistical contingencies in the input to overcom...

So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky’s work). However, some linguistic phenomena do not cope properly with trees. In a former paper, we showed the benefit of encoding linguistic structures by graphs and of using graph rewriting rules to compute on those stru...

The main purpose of this note is to construct almost complex or structures on certain isoparametric hypersurfaces in unit spheres. As a consequence, S1 × S7 S6, and S3 S2 with vanishing first Chern class, are built.