Related papers: Percolation on spatial anisotropic networks
Bootstrap percolation models have been extensively studied during the two past decades. In this article, we study the following "anisotropic" bootstrap percolation model: the neighborhood of a point (m,n) is the set…
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…
The study of adversarial robustness has so far largely focused on perturbations bound in p-norms. However, state-of-the-art models turn out to be also vulnerable to other, more natural classes of perturbations such as translations and…
Motivated by the importance of geometric information in real systems, a new model for long-range correlated percolation in link-adding networks is proposed with the connecting probability decaying with a power-law of the distance on the…
The spectrum of the nonbacktracking matrix associated to a network is known to contain fundamental information regarding percolation properties of the network. Indeed, the inverse of its leading eigenvalue is often used as an estimate for…
Bootstrap percolation is a simple but non-trivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single layer (simplex) networks, it has been recently observed that…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…
We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…
The stochastic variations in the structural properties of thin fiber networks govern to a great extent their mechanical performance. To assess the influence of local structural variability on the local strain and mechanical response of the…
We study the elasticity of a two-dimensional random network of rigid rods (``Mikado model''). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…
Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…
The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the…
A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic…
Percolating networks based on interparticle tunneling conduction are shown to yield a logarithmic divergent piezoresistive response close to the critical point as long as the electrical conductivity becomes nonuniversal. At the same time,…
Asymmetries and anisotropies are widespread in biological systems, including in the structure and dynamics of cilia and eukaryotic flagella. These microscopic, hair-like appendages exhibit asymmetric beating patterns that break…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…