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We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate…
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…
A method of `network filtering' has been proposed recently to detect the effects of certain external perturbations on the interacting members in a network. However, with large networks, the goal of detection seems a priori difficult to…
During the last decades macroecology has identified broad-scale patterns of abundances and diversity of microbial communities and put forward some potential explanations for them. However, these advances are not paralleled by a full…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
We propose a resource distribution strategy to reduce the average travel time in a transportation network given a fixed generation rate. Suppose that there are essential resources to avoid congestion in the network as well as some extra…
Link prediction is an open problem in the complex network, which attracts much research interest currently. However, little attention has been paid to the relation between network structure and the performance of prediction methods. In…
Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a…
Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…
The work presented in this thesis concerns different aspects of dynamical processes on networks. The first subject considered is the theoretical modeling of exploration processes of complex networks, such as the ``traceroute'' process used…
Interdependencies are ubiquitous throughout the world. Every real-world system interacts with and is dependent on other systems, and this interdependency affects their performance. In particular, interdependencies among networks make them…
Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional…
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and…
We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the…
In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…
For large-scale power networks, the failure of particular transmission lines can offload power to other lines and cause self-protection trips to activate, instigating a cascade of line failures. In extreme cases, this can bring down the…
In this work, we propose an interdependent, multilayer network model and percolation process that matches infrastructures better than previous models by allowing some nodes to survive when their interdependent neighbors fail. We consider a…
We consider biochemical reaction chains and investigate how random external fluctuations, as characterized by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of…