Data on wealth distributions in trading markets show a power law behavior x(-)(1+alpha) at the high end, where, in general, alpha is greater than 1 (Pareto's law). Models based on kinetic theory, where a set of interacting agents trade money, yield power law tails if agents are assigned a saving propensity. In this paper we are solving the inverse problem, that is, in finding the saving propens...

Several studies on real complex networks from different fields as biology, economy , or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like P (k) ≈ k −γ , where P (k) denotes the frequency of the nodes that are connected to k other nodes. Here we have carried out a study on scale-free networks, where a line grap...

We consider the defect size distributions at different stages of damage evolution, from the initial stage of defect nucleation and accumulation, through the intermediate stage of defect propagation and into the final stage leading to the appearance of the major crack. Critical events considered in this context are related to (a) the formation of microcracks exceeding the structural threshold as...

Empirical studies of real world networks revealed that degree distribution often follows a heavytailed distribution, a power law. At that time, there were two kinds of network models: the Erdos-Renyi random graph Gn,p and the Small World graphs of Watts and Strogatz. In both models the degrees were very close to the mean degree and there was little variation. Thus, there was the question of fin...

Empirical studies of real world networks revealed that degree distribution often follows a heavytailed distribution, a power law. At that time, there were two kinds of network models: the Erdos-Renyi random graph Gn,p and the Small World graphs of Watts and Strogatz. In both models the degrees were very close to the mean degree and there was little variation. Thus, there was the question of fin...

Numerical simulations are used to investigate the multiaffine exponent alpha(q) and multigrowth exponent beta(q) of ballistic deposition growth for noise obeying a power-law distribution. The simulated values of beta(q) are compared with the asymptotic function beta(q)=1/q that is approximated from the power-law behavior of the distribution of height differences over time. They are in good agre...

Recently Osorio et al [1] reported that probability distribution of epileptic seizure energies and inter-seizure intervals follow a power law with exponents 1.67 and 1.5 respectively. Earlier Beggs and Plenz [2] had observed spontaneous neuronal avalanches in neocortical tissues. The distribution of sizes of these avalanches, computed by summing local field potentials, followed a power law with...

We consider a model for complex networks that was introduced by Krioukov et al. [14], where the intrinsic hierarchies of a network are mapped into the hyperbolic plane. Krioukov et al. show that this model exhibits clustering and the distribution of its degrees has a power law tail. We show that asymptotically this model locally behaves like the well-known Chung-Lu model in which two nodes are ...

A system with a self-similar property is scale-independent and statistically exhibits that property at all levels of observation. In addition, a power law describes the distribution of a scale-independent property. Many investigators have observed social activities and structures, particularly in the science system, that are best described by a power-law distribution. However, unlike classical ...

Several experimental studies on different fields as molecular biology, economy, or sociology have shown that real complex networks are following a power-law distribution like P (k) ≈ k −γ. However, many real networks hold two kind of nodes, being able to be projected as two embedded networks, e.g. movie-actor collaboration network (actors network and movies network), metabolic pathways (substra...