We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the...

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the...

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that it is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent ζ = 3. Because of data limitations, previous studies in...

We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of...

We introduce a model of proportional growth to explain the distribution P(g) of business firm growth rates. The model predicts that P(g) is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent ζ = 3. Because of data limitations, previous studies...

We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent φ = 2+b/(1−b) which...

We study the structure of business firm networks in the Life Sciences (LS) and the Information and Communication Technology (ICT) sectors. We analyze business firm networks and scale-free models with degree distribution P(q) proportional to (q + c)^-λ using the method of k-shell decomposition....

The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior σ(S) similar to S^-β(S) where S is the firm size and β(S) almost equal to 0.2 is an exponent weakly dependent on S. Here we show how a model of proportional growth...

We refer to the framework developed by Ijiri and Simon (1977) and to the notion of independent submarkets (Sutton 1998) to provide a simple candidate explanation for the shape of the firm growth distribution based on a model of proportional growth at the level of both the introduction of new...

We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of...