133,777 research outputs found
Deterministic hierarchical networks
It has been shown that many networks associated with complex systems are
small-world (they have both a large local clustering coefficient and a small
diameter) and also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances
the probabilistic and simulation techniques and, therefore, it provides a better understanding of the modeled systems. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems.Peer ReviewedPostprint (author's final draft
From homogeneous to fractal normal and tumorous microvascular networks in the brain
We studied normal and tumorous three-dimensional (3D) microvascular networks in primate and rat
brain. Tissues were prepared following a new preparation technique intended for high-resolution
synchrotron tomography of microvascular networks. The resulting 3D images with a spatial
resolution of less than the minimum capillary diameter permit a complete description of the entire
vascular network for volumes as large as tens of cubic millimeters. The structural properties of the
vascular networks were investigated by several multiscale methods such as fractal and power-
spectrum analysis. These investigations gave a new coherent picture of normal and pathological
complex vascular structures. They showed that normal cortical vascular networks have scale-
invariant fractal properties on a small scale from 1.4 lm up to 40 to 65 lm. Above this threshold,
vascular networks can be considered as homogeneous. Tumor vascular networks show similar
characteristics, but the validity range of the fractal regime extend to much larger spatial dimensions.
These 3D results shed new light on previous two dimensional analyses giving for the first time a
direct measurement of vascular modules associated with vessel-tissue surface exchange
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