Related papers: Taylor's power law for the $N$-stars network evolu…
Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can…
There has been some confusion concerning the animal group-size: an exponential distribution was deduced by maximizing the entropy; lognormal distributions were practically used; a power-law decay with exponent {3/2} was proposed in physical…
The present Letter, deals with the statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002) and Phys. Rev E {\bf 72}, 036108 (2005)], which predicts the probability distribution $p(E) \propto \exp_{\kappa} (-I)$, where, $I \propto \beta E…
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
Zipf's power law is a general empirical regularity found in many natural and social systems. A recently developed theory predicts that Zipf's law corresponds to systems that are growing according to a maximally sustainable path in the…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
We study a novel model for evolution of complex networks. We introduce information filtering for reduction of the number of available nodes to a randomly chosen sample, as stochastic component of evolution. New nodes are attached to the…
Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that…
The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these…
This article describes a complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown both analytically and experimentally that the strength…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…
We show a statistical version of Taylor's theorem and apply this result to non-parametric density estimation from truncated samples, which is a classical challenge in Statistics \cite{woodroofe1985estimating, stute1993almost}. The…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer''…
Taylor's law (TL), a power-law relationship between the mean and variance of a quantity, has been observed across diverse scientific disciplines. Despite its ubiquity, the underlying mechanisms responsible for TL are not yet fully…
The present paper is devoted to the relativistic statistical theory, introduced in Phys. Rev. E {\bf 66} (2002) 056125 and Phys. Rev. E {\bf 72} (2005) 036108, predicting the particle distribution function $p(E)= \exp_{\kappa}…
Both theoretical and applied economics have a great deal to say about many aspects of the firm, but the literature on the extinctions, or demises, of firms is very sparse. We use a publicly available data base covering some 6 million firms…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…