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The vulnerability of an isolated network to cascades is fundamentally affected by its interactions with other networks. Motivated by failures cascading among electrical grids, we study the Bak-Tang-Wiesenfeld sandpile model on two…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot…
We study the relationship between the modularity of scale-free excitable networks and their ability to support self-sustained oscillation patterns. We find that the probability for a network of given degree-distribution exponent to be able…
Single- and multi-layer complex networks have been proven as a powerful tool to study the dynamics within social, technological,or natural systems. An often observed common goal there is to optimize these systems for specific purposes by…
An elastic membrane that is forced to reside in a container smaller than its natural size will deform and, upon further volume reduction, eventually crumple. The crumpled state is characterized by the localization of energy in a complex…
Components in many real-world complex systems depend on each other for the resources required for survival, and may die of a shortage. These patterns of dependencies often take the form of a complex network whose structure potentially…
Modular networks, such as critical infrastructures, are often built from distinct, densely connected modules (e.g., cities) that are sparsely interconnected. When such networks are gradually and randomly disrupted under a percolation…
The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
A multiplex network of identical dynamical units becomes resilient against parameter perturbation by adding selective linear diffusive cross-coupling links. A parameter drift at any instant in one or multiple network nodes can destroy…
Multilayer networks represent multiple types of connections between the same set of nodes. Clearly, a multilayer description of a system adds value only if the multiplex does not merely consist of independent layers, i.e. if the inter-layer…
We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the…
Generally, the threshold of percolation in complex networks depends on the underlying structural characterization. However, what topological property plays a predominant role is still unknown, despite the speculation of some authors that…
We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, dipolar fluids and…
The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first…
Chimera is a relatively new emerging phenomenon where coexistence of synchronous and asynchronous state is observed in symmetrically coupled dynamical units. We report observation of the chimera state in multiplex networks where individual…
The mathematical framework of multiplex networks has been increasingly realized as a more suitable framework for modelling real-world complex systems. In this work, we investigate the optimization of synchronizability in multiplex networks…
A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures. In this work, we propose a dynamical definition of network's robustness based on Information Theory, that considers…
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…