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Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…
Recently, new results on percolation of interdependent networks have shown that the percolation transition can be first order. In this paper we show that, when considering antagonistic interactions between interacting networks, the…
Watersheds have been defined both for node and edge weighted graphs. We show that they are identical: for each edge (resp.\ node) weighted graph exists a node (resp. edge) weighted graph with the same minima and catchment basin.
We consider the first-passage percolation problem on effectively one-dimensional graphs with vertex set {1,...,n}\times{0,1} and translation-invariant edge-structure. For three of six non-trivial cases we obtain exact expressions for the…
Traffic modeling of communication networks such as Internet has become a very important field of research. A number of interesting phenomena are found in measurements and traffic simulations. One of them is the propagation of congestion…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
We consider the model of i.i.d. first passage percolation on Z^d, where we associate with the edges of the graph a family of i.i.d. random variables with common distribution G on [0, +$\infty$] (including +$\infty$). Whereas the time…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the…
We prove results for first-passage percolation on the configuration model with i.i.d. degrees having finite mean, infinite variance and i.i.d. weights with strictly positive support of the form Y=a+X, where a is a positive constant. We…
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…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
Climate change exacerbates riverine floods, which occur with higher frequency and intensity than ever. The much-needed forecasting systems typically rely on accurate river discharge predictions. To this end, the SOTA data-driven approaches…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices…
Stream graphs are a very useful mode of representation for temporal network data, whose richness offers a wide range of possible approaches. The various methods aimed at generalising the classical approaches applied to static networks are…
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…