Related papers: Percolation and epidemics in a two-dimensional sma…
We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution…
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…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network,…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
The systematic study of large-scale networks has unveiled the ubiquitous presence of connectivity patterns characterized by large scale heterogeneities and unbounded statistical fluctuations. These features affect dramatically the behavior…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…
The contact model for the spread of disease may be viewed as a directed percolation model on $\ZZ \times \RR$ in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly…
The concentration and distribution of quantum entanglement is an essential ingredient in emerging quantum information technologies. Much theoretical and experimental effort has been expended in understanding how to distribute entanglement…
We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed…
We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an…
Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop…
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…
The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations…
Percolation phenomena are pervasive in nature, ranging from capillary flow, crack propagation, ionic transport, fluid permeation, etc. Modeling percolation in highly-branched media requires the use of numerical solutions, as problems can…
This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a…
Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…
We propose a percolation based M2M networking architecture and its data transmission method. The proposed network architecture can be server-free and router-free, which allows us to operate routing efficiently with percolations based on six…