We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which represents a generalization of degree-ordered percolation, we derive a scaling solution on uncorrelated complex network...
A general phase-plot is proposed for discrete particle shells that allows for thermal fluctuations of the shell geometry and of the inter-particle connectivities. The phase plot contains a first-order melting transition, a buckling transition and a collapse transition and is used to interpret the thermodynamics of microbiological shells.
Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an oversimplification, for instance, in social interactions that occur frequently within groups. To overcome this li...
This paper is dedicated to the study of the interaction between dynamical systems and percolation models, with views towards the study of viral infections whose virus mutate with time. Recall that r-bootstrap percolation describes a deterministic process where vertices of a graph are infected once r neighbors of it are infected. We generalize this ...
Published in Physical review letters
Global transport and communication networks enable information, ideas, and infectious diseases to now spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like processes, there is a need to predict the speed of a particular contagion in a particular network, and to distinguis...
We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heterogeneity. Our analytical solution is able to predict the shift in the critical properties induced by...
Published in Physical Review. E
Recent progress on multiplex networks has provided a powerful way to abstract the diverse interaction of a network system with multiple layers. In this paper, we show that a multiplex structure can greatly affect the spread of an epidemic driven by traffic dynamics. One of the interesting findings is that the multiplex structure could suppress the ...
Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes and links appear and disappear. We focus on the effects of "accessibility", whether there is a temporally con...
Published in Physical Review. E
In contemporary society, understanding how information, such as trends and viruses, spreads in various social networks is an important topic in many areas. However, it is difficult to mathematically measure how widespread the information is, especially for a general network structure. There have been studies on opinion spreading, but many studies a...
The two-species symbiotic contact process (2SCP) is a stochastic process where each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules ot...
