Multi-fractal patterns occur widely in nature. In developing new algorithms to determine multi-fractal spectra of experimental data I am lead to the conclusion that generalised dimensions Dq of order q ≤ 0, including the Hausdorff dimension, are effectively irrelevant. The reason is that these dimensions are extraordinarily sensitive to regions of low density in the multi-fractal data. Instead,...

GEAMAS is a knowledge engineering environment for multi-agent simulation of complex systems. The basic architecture of GEAMAS is designed around three dimensions: MultiAgent Systems (MAS) software design, MAS knowledge abstraction and MAS services dimension. Each one of this third aspects, is implemented into several modular open software layers. First, the paper argues the benefits of a such a...

The Vapnik-Chervonenkis dimension of a set K in R n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This has a number of consequences, including the optimal Elton's theorem and a uniform central limit theorem in the real valued case.