Related papers: Scaling of spin avalanches in growing networks
We introduce the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche…
The classical drift diffusion (DD) model of spin transport treats spin relaxation via an empirical parameter known as the ``spin diffusion length''. According to this model, the ensemble averaged spin of electrons drifting and diffusing in…
It has been found that the networks with scale-free distribution are very resilient to random failures. The purpose of this work is to determine the network design guideline which maximize the network robustness to random failures with the…
We study diffusion (random walks) on recursive scale-free graphs, and contrast the results to similar studies in other analytically soluble media. This allows us to identify ways in which diffusion in scale-free graphs is special. Most…
The scaling relation derived by Dorogovtsev, Goltsev, Mendes and Samukhin [Phys. Rev. E, 68 (2003) 046109] states that the exponents of the power-law connectivity distribution, gamma, and the power-law eigenvalue distribution of the…
We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
Simulations with more than $10^{12}$ spins are used to study the motion of a domain wall driven through a three-dimensional random-field Ising magnet (RFIM) by an external field $H$. The interface advances in a series of avalanches whose…
Real-world complex systems always interact with each other, which causes these systems to collapse in an avalanche or cascading manner in the case of random failures or malicious attacks. The robustness of multilayer networks has attracted…
We analyse by numerical simulations and scaling arguments the avalanche statistics of 1-dimensional elastic interfaces in random media driven at a single point. Both global and local avalanche sizes are power-law distributed, with universal…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…
We consider the zero-temperature single-spin-flip dynamics of the random-field Ising model on a Bethe lattice in the presence of an external field h. We derive the exact self-consistent equations to determine the distribution Prob(s) of…
We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social…
Uniform spherical beads were used to explore the behavior of a granular system near its critical angle of repose on a conical bead pile. We found two tuning parameters that could take the system to a critical point where a simple power-law…
A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…
We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for…
In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…
Understanding deep neural networks (DNNs) is a key challenge in the theory of machine learning, with potential applications to the many fields where DNNs have been successfully used. This article presents a scaling limit for a DNN being…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
We consider a fiber bundle model with a equal load sharing and uniformly distributed breakdown thresholds. A unified probability-theoretic approach was used to describe bundle under continuous and discrete load increase. It was shown that…