Semantic Map Geometry: Two Approaches

Semantic Map Geometry: Two Approaches

Two Approaches to Non-Commutative Geometry

Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)—to Klein. We will see that they are not rivalling but are tied (by Galois). We also examine their modern life as philosophies of non-commutative geometry. Connections between different objects (see keywords) are discussed. ∗Support...

University_Of_Sheffield: Two Approaches to Semantic Text Similarity

This paper describes the University of Sheffield’s submission to SemEval-2012 Task 6: Semantic Text Similarity. Two approaches were developed. The first is an unsupervised technique based on the widely used vector space model and information from WordNet. The second method relies on supervised machine learning and represents each sentence as a set of n-grams. This approach also makes use of inf...

Understanding the semantic principles of a political map

The attempt to recognize phenomena and affairs has always been a concern of the human mind and has constantly sought to complete this knowledge. The correct recognition is also achieved when the real nature of phenomena is clear to man. The phenomena are based on their own philosophical foundations and, therefore, their understanding requires perception these philosophical foundations and using...

Geometry of Pinchuk’s map

Sergey Pinchuk found a polynomial map from the real plane to itself which is a local diffeomorphism but is not one-to-one. The aim of this paper is to give a geometric description of Pinchuk’s map.