Related papers: Scaling in critical random Boolean networks
We introduce a simple one-parameter network growth algorithm which is able to reproduce a wide variety of realistic network structures but without having to invoke any global information about node degrees such as preferential-attachment…
Supply networks are essential for modern production, yet their critical properties remain understudied. We present a stochastic model with random production capacities to analyze material flow to a root node, focusing on topology and buffer…
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.…
The growth in number and nature of dynamical attractors in Kauffman NK network models are still not well understood properties of these important random boolean networks. Structural circuits in the underpinning graph give insights into the…
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges.…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to…
Consider a critical random multigraph $\mathcal{G}_n$ with $n$ vertices constructed by the configuration model such that its vertex degrees are independent random variables with the same distribution $\nu$ (criticality means that the second…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
The Kauffman model of genetic computation highlights the importance of criticality at the border of order and chaos. The model with connectivity one is of special interest because it is exactly solvable. But our understanding of its…
We show that in a broad class of processes that show a $1/f^{\alpha}$ spectrum, the power also explicitly depends on the characteristic time scale. Despite an enormous amount of work, this generic behavior remains so far overlooked and…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…
Let $S$ be the random walk obtained from "coin turning" with some sequence $\{p_n\}_{n\ge 1}$, as introduced in [6]. In this paper we investigate the scaling limits of $S$ in the spirit of the classical Donsker invariance principle, both…
We present a stochastic dynamics model of coupled evolution for the binary states of nodes and links in a complex network. In the context of opinion formation node states represent two possible opinions and link states a positive or…
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
Probabilistic networks display a wide range of high average clustering coefficients independent of the number of nodes in the network. In particular, the local clustering coefficient decreases with the degree of the subtending node in a…