Related papers: New exponential law for real networks
A new complex network model is proposed which is founded on growth with new connections being established proportionally to the current dynamical activity of each node, which can be understood as a generalization of the Barabasi-Albert…
A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…
The explosive growth of Web 2.0, which was characterized by the creation of online social networks, has reignited the study of factors that could help us understand the growth and dynamism of these networks. Various generative network…
The aim of this paper, is to define a bivariate exponentiated generalized linear exponential distribution based on Marshall-Olkin shock model. Statistical and reliability properties of this distribution are discussed. This includes…
Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical…
Random key graphs were introduced to study various properties of the Eschenauer-Gligor key predistribution scheme for wireless sensor networks (WSNs). Recently this class of random graphs has received much attention in contexts as diverse…
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…
In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the…
What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…
Based on the concept and techniques of first-passage probability in Markov chain theory, this letter provides a rigorous proof for the existence of the steady-state degree distribution of the scale-free network generated by the…
The Watts-Strogatz algorithm transferring a regular lattice to the small world network is modified by introducing preferential rewiring constrained by connectivity demand. The probability to link to/ unlink form a node is dependent on a…
We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wavefunction amplitudes in a real-space basis. For single-particle 'quantum billiards', these real-space amplitudes are known to have Gaussian…
In practical quantum networks, a variety of multi-qubit stabilized states emitted from independent sources are distributed among the agents, and the correlations across the entire network can be derived from each agent's local measurements…
An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions…
Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…
We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabasi-Albert model of network evolution is extended by…
We consider the voter model dynamics in random networks with an arbitrary distribution of the degree of the nodes. We find that for the usual node-update dynamics the average magnetization is not conserved, while an average magnetization…
We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical example is the high temperature Ising model. This distribution is shown to converge…
Consider a family of distributions $\{\pi_{\beta}\}$ where $X\sim\pi_{\beta}$ means that $\mathbb{P}(X=x)=\exp(-\beta H(x))/Z(\beta)$. Here $Z(\beta)$ is the proper normalizing constant, equal to $\sum_x\exp(-\beta H(x))$. Then…
We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…