Related papers: Static Pairwise Annihilation in Complex Networks
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
We consider random sequential adsorption processes where the initially empty sites of a graph are irreversibly occupied, in random order, either by monomers which block neighboring sites, or by dimers. We also consider a process where…
We analyze fading interference relay networks where M single-antenna source-destination terminal pairs communicate concurrently and in the same frequency band through a set of K single-antenna relays using half-duplex two-hop relaying.…
Partitioning large networks into stable clusters of synchronized nodes is a challenging task. Recent approaches based on spectral analysis can provide exact results on specific dynamics but remain unfeasible for very large networks.…
The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of…
We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…
We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on random networks. By studying temporal evolution and…
Across scientific disciplines, thresholded pairwise measures of statistical dependence between time series are taken as proxies for the interactions between the dynamical units of a network. Yet such correlation measures often fail to…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and…
We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is given by mutual annihilation A+B->0. The initial condition…
The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and "Pseudo-Darwinian" strategy. At each evolution step and regarding the selected strategy, one removes either a…
We consider a system of q diffusing particle species A_1,A_2,...,A_q that are all equivalent under a symmetry operation. Pairs of particles may annihilate according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the symmetry, and…
Threshold rules of spreading in binary-state networks lead to cascades. We study persistent cascade-recovery dynamics on quasi-robust networks, i.e., networks which are robust against small trigger but may collapse for larger one. It is…
We introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact…
One of the most common approaches to the analysis of dynamic networks is through time-window aggregation. The resulting representation is a sequence of static networks, i.e. the snapshot graph. Despite this representation being widely used…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
We study diffusion-limited pair annihilation $A+A\to 0$ on one-dimensional lattices with inhomogeneous nearest neighbour hopping in the limit of infinite reaction rate. We obtain a simple exact expression for the particle concentration…
Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior -- quantifying how contact…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…