Related papers: Criticality in spreading processes without time-sc…
We study a model that generalizes the CP with diffusion. An additional transition is included in the model so that at a particular point of its phase diagram a crossover from the directed percolation to the compact directed percolation…
We investigate the sensitivity of epidemic behavior to a bounded susceptibility constraint -- susceptible nodes are infected by their neighbors via the regular SI/SIS dynamics, but subject to a cap on the infection rate. Such a constraint…
We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events…
The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point of all past studies is, however, that there is only one peak of infected density in each single…
Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point…
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…
We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value…
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…
The field of epidemiology has presented fascinating and relevant questions for mathematicians, primarily concerning the spread of viruses in a community. The importance of this research has greatly increased over time as its applications…
Neural synchronisation plays a critical role in information processing, storage and transmission. Characterising the pattern of synchronisation is therefore of great interest. It has recently been suggested that the brain displays broadband…
Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network,…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
Cortical neurons exhibit a hierarchy of timescales across brain regions in response to input stimuli, which is thought to be crucial for information processing of different temporal scales. Modeling studies suggest that both intra-regional…
We introduce a new percolation model to describe and analyze the spread of an epidemic on a general directed and locally finite graph. We assign a two-dimensional random weight vector to each vertex of the graph in such a way that the…
$k$-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network under random damage, an extension of this model is introduced,…
We present a detailed analytical and numerical study for the spreading of infections in complex population networks with acquired immunity. We show that the large connectivity fluctuations usually found in these networks strengthen…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
Understanding the resilience of infrastructures such as transportation network has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with…
In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical…
As shown recently (arXiv:0801.3056), several types of neuronal complex networks involving non-linear integration-and-fire dynamics exhibit an abrupt activation along their transient regime. Interestingly, such an avalanche of activation has…