A Survey of Counterexamples to Hilbert's Fourteenth Problem

We survey counterexamples to Hilbert’s Fourteenth Problem, beginning with those of Nagata in the late 1950s, and including recent counterexamples in low dimension constructed with locally nilpotent derivations. Historical framework and pertinent references are provided. We also include 8 important open questions.

Semantic Interpretation of 3D Point Clouds of Historical Objects

This paper presents the main concepts of a project under development concerning the analysis process of a scene containing a large number of objects, represented as unstructured point clouds. To achieve what we called the "optimal scene interpretation" (the shortest scene description satisfying the MDL principle) we follow an approach for managing 3-D objects based on a semantic framework based on ontologies for adding and sharing conceptual knowledge about spatial objects.