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Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai. The model describes the pressure field thanks to Darcy's type…
We report numerical simulations of a strongly biased diffusion process on a one-dimensional substrate with directed shortcuts between randomly chosen sites, i.e. with a small-world-like structure. We find that, unlike many other dynamical…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
We analyze information diffusion using empirical data that tracks online communication around two instances of mass political mobilization, including the year that lapsed in-between the protests. We compare the global properties of the…
The dynamics of swollen fractal networks (Rouse model) has been studied through computer simulations. The fluctuation-relaxation theorem was used instead of the usual Langevin approach to Brownian dynamics. We measured the equivalent of the…
We study the effect of a single excluded site on the diffusion of a particle undergoing random walk in a d-dimensional lattice. The determination of the characteristic function allows to find explicitly the asymptotical behaviour of…
Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
Understanding the influence of structure of dispersal network on the species persistence and modeling a much realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the…
We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various…
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
A point process on the topological space S is at most countable subset without a random accumulation point in S. In studies of the point processes, there is a problem of seeing the properties of rigidity and tolerance, and this problem is…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
A lattice-based model for continuum percolation is applied to the case of randomly located, partially aligned sticks with unequal lengths in 2D which are allowed to cross each other. Results are obtained for the critical number of sticks…
We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect…
A notion of disturbance propagation stability is defined for dynamical network processes, in terms of decrescence of an input-output energy metric along cutsets away from the disturbance source. A characterization of the disturbance…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…