Related papers: Percolation Theory on Interdependent Networks Base…
Nowadays, the diffusion of information through social networks is a powerful phenomenon. One common way to model diffusions in social networks is the Independent Cascade (IC) model. Given a set of infected nodes according to the IC model, a…
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size…
Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases the theory predicts a geometrical…
Previous work has shown that for contagion processes on extended star networks (trees with exactly one node of degree > 2), there is a simple, closed-form expression for a highly accurate approximation to the maximum likelihood infection…
We propose a generative model and an inference scheme for epidemic processes on dynamic, adaptive contact networks. Network evolution is formulated as a link-Markovian process, which is then coupled to an individual-level stochastic SIR…
The emergence of large-scale connectivity underlies the proper functioning of many networked systems, ranging from social networks and technological infrastructure to global trade networks. Percolation theory characterizes network formation…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
A fundamental problem in network science is to predict how certain individuals are able to initiate new networks to spring up "new ideas". Frequently, these changes in trends are triggered by a few innovators who rapidly impose their ideas…
In the real world, many complex systems interact with other systems. In addition, the intra- or inter-systems for the spread of information about infectious diseases and the transmission of infectious diseases are often not random, but with…
It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and hence system-wide disasters. A recent model shows how pairs of interdependent networks can exhibit an…
Large-scale power blackouts caused by cascading failure are inflicting enormous socioeconomic costs. We study the problem of cascading link failures in power networks modelled by random geometric graphs from a percolation-based viewpoint.…
We study the problems of estimating the past and future evolutions of two diffusion processes that spread concurrently on a network. Specifically, given a known network $G=(V, \overrightarrow{E})$ and a (possibly noisy) snapshot…
We investigate how the properties of epidemic networks change depending on the availability of different types of data on a disease outbreak. This is achieved by introducing mathematical and computational methods that estimate the…
We prove a nonuniqueness theorem for Bernoulli site percolation on properly embedded planar graphs, and we obtain a general connectivity principle beyond planarity. Let $G$ be an infinite connected graph properly embedded in $\RR^2$ with…
This paper is dedicated to the memory of Dietrich Stauffer, who was a pioneer in percolation theory and applications of it to problems of society, such as epidemiology. An epidemic is a percolation process gone out of control, that is,…
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…
Many physical, biological, and social phenomena can be described by cascades taking place on a network. Often, the activity can be empirically observed, but not the underlying network of interactions. In this paper we offer three…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using…
Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however…