52 research outputs found
Self-similar disk packings as model spatial scale-free networks
The network of contacts in space-filling disk packings, such as the
Apollonian packing, are examined. These networks provide an interesting example
of spatial scale-free networks, where the topology reflects the broad
distribution of disk areas. A wide variety of topological and spatial
properties of these systems are characterized. Their potential as models for
networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of
higher-dimensional packing
Power Law Distribution of Wealth in a Money-Based Model
A money-based model for the power law distribution (PLD) of wealth in an
economically interacting population is introduced. The basic feature of our
model is concentrating on the capital movements and avoiding the complexity of
micro behaviors of individuals. It is proposed as an extension of the Equiluz
and Zimmermann's (EZ) model for crowding and information transmission in
financial markets. Still, we must emphasize that in EZ model the PLD without
exponential correction is obtained only for a particular parameter, while our
pattern will give it within a wide range. The Zipf exponent depends on the
parameters in a nontrivial way and is exactly calculated in this paper.Comment: 5 pages and 4 figure
Some diophantine problems.
The starting point of this thesis is a generalization of polygonal numbers to an arbitrary dimension. Three kinds of numbers are obtained: figurate numbers, powers of numbers, and a third kind, believed to be new, hyperoctahedral numbers. [...
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