The Rubik’s Cube is a familiar toy that has embedded itself into popular culture since its invention in 1974 by Ernő Rubik. It is especially popular among mathematicians, for good reason. In this paper, we will investigate some of the interesting mathematical structure underlying the Rubik’s Cube, which was documented by David Joyner in his book, Adventures in Group Theory [Joy]. Let us conside...

The precomputation of the different views of a data cube is critical to improving the response time of data cube queries for On-Line Analytical Processing (OLAP). However, the user is often not interested in the set of all views of the data cube but only in a certain subset of views. In this paper, we study the problem of computing the partial data cube, i.e. a subset of selected views in the l...

The cube attack is a powerful cryptanalytic technique and is especially powerful against stream ciphers. Since we need to analyze the complicated structure of a stream cipher in the cube attack, the cube attack basically analyzes it by regarding it as a blackbox. Therefore, the cube attack is an experimental attack, and we cannot evaluate the security when the size of cube exceeds an experiment...

We have studied the cerebral activity for the depth perception of the Necker cube by functional magnetic resonance imaging. Three types of line drawing figures were used as stimuli, the Necker cube, hidden line elimination cube and overlapping squares. Subjects were instructed to perceive both orientations of the depth of the Necker cube. They were instructed to shift their attention voluntaril...