Geometric Representations of Language Taxonomies

Geometric representations of language taxonomies

A Markov chain analysis of a network generated by the matrix of lexical distances allows for representing complex relationships between different languages in a language family geometrically, in terms of distances and angles. The fully automated method for construction of language taxonomy is tested on a sample of fifty languages of the Indo-European language group and applied to a sample of fi...

Concept Lattice Representations of Annotated Taxonomies

We show how the concept of an annotated ordered set can be used to model large taxonomically structured ontologies such as the Gene Ontology. By constructing a formal context consistent with a given annotated ordered set, their concept lattice representations are derived. We develop the fundamental mathematical relations present in this formulation, in particular deriving a conceptual pre-order...

Geometric Representations of Graphs

The study of geometrically defined graphs, and of the reverse question, the construction of geometric representations of graphs, leads to unexpected connections between geometry and graph theory. We survey the surprisingly large variety of graph properties related to geometric representations, construction methods for geometric representations, and their applications in proofs and algorithms.

Geometric Representations and Transformations

Geometric Representations of Interacting Maps

Motivated by phenomena in molecular biology, in [K3] we have formulated an interaction system by use of families of maps on intervals, which consistes of infinte families of compositions between them. By wasting detailed and extracting more rough information by use of projections, one can produce some integrable systems of automata. This enables one to see some patterns which correspond to more...