Related papers: Percolation in living neural networks
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and…
We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for…
Complex networks are the representative graphs of interactions in many complex systems. Usually, these interactions are abstractions of the communication/diffusion channels between the units of the system. Real complex networks, e.g.…
In clinical neuroscience, epileptic seizures have been associated with the sudden emergence of coupled activity across the brain. The resulting functional networks - in which edges indicate strong enough coupling between brain regions - are…
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…
The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between…
Boolean networks, widely used to model gene regulation, exhibit a phase transition between regimes in which small perturbations either die out or grow exponentially. We show and numerically verify that this phase transition in the dynamics…
Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted…
In two dimensions, the average electrical conductance from a point in a percolating network to the network boundary should be related by a conformal transformation to the conductance from one point to another in an unbounded network. We…
Suspensions of hard core spherical particles of diameter $D$ with inter-core connectivity range $\delta$ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two…
Using computer simulations, we have studied the percolation and the electrical conductance of two-dimensional, random percolating networks of curved, zero-width metallic nanowires. We mimicked the curved nanowires using circular arcs. The…
We investigate the dynamics of two models of biological networks with purely suppressive interactions between the units; species interacting via niche competition and neurons via inhibitory synaptic coupling. In both of these cases,…
\emph{Full-bond percolation} with parameter $p$ is the process in which, given a graph, for every edge independently, we delete the edge with probability $1-p$. Bond percolation is motivated by problems in mathematical physics and it is…
Our recent study on the Bethe lattice reported that a discontinuous percolation transition emerges as the number of occupied links increases and each node rewires its links to locally suppress the growth of neighboring clusters. However,…
Much work has been devoted to studying percolation of networks and interdependent networks under varying levels of failures. Researchers have considered many different realistic network structures, but thus far no study has incorporated the…
The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed…