Related papers: Explosive Percolation: Novel critical and supercri…
We introduce the simplest model which relates the emergence of collective social/economic phenomena to the existence of a (possibly self-organized) percolation transition. We suggest a series of extensions to financial, economic, political…
Connectivity - or the lack thereof - is crucial for the function of many man-made systems, from financial and economic networks over epidemic spreading in social networks to technical infrastructure. Often, connections are deliberately…
Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In…
We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate…
Critical phenomena of a second-order percolation transition are known to be independent of cluster merging or pruning process. However, those of a hybrid percolation transition (HPT), mixed properties of both first-order and second-order…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
We report the critical point for site percolation for the "explosive" type for 2D square lattices using Monte Carlo simulations and compare it to the classical well known percolation. We use similar algorithms as have been recently reported…
We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap…
A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
We identify a new universality class of phase transitions that emerges in non-normal systems, extending the classical framework beyond eigenvalue instabilities. Unlike traditional critical phenomena, where transitions occur when eigenvalues…
In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this…
The phenomenon of explosive synchronization, which originates from hypersensitivity to small perturbation caused by some form of frustration prevailed in various physical and biological systems, has been shown to lead events of cascading…
Percolation, describing critical behaviors of phase transition in a geometrical context, prompts wide investigations in natural and social networks as a fundamental model. The introduction of quantum-intrinsic interference and tunneling…
In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…
The emergence of collective motion, also known as flocking or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that is manifested at multiple spatial…