Related papers: Structure, Scaling and Phase Transition in the Opt…
How local cracks can contribute to the global cracks landscape is a goal of several scientific topics, for example, how bottlenecks can impact the robustness of traffic into a city? In one direction, cracks from cascading failures into…
There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques…
It has recently been shown that the average energy required to control a subset of nodes in a complex network scales exponentially with the cardinality of the subset. While the mean scales exponentially, the variance of the control energy…
We analyze the Optimal Channel Network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the…
The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…
We consider decay of supercurrent via phase slips in a discrete one-dimensional superconductor (a chain of nodes connected by superconducting links), aiming to explain the experimentally observed power-3/2 scaling of the activation barrier…
Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a…
We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for…
Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…
We investigate how the underlying graph of a network supports a flow between a source node and a destination node and propose to compute the expected number of nodes and links that contribute to transferring items in random graphs. Since…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
The theory of current transport in a narrow superconducting channel accounting for thermal fluctuations is developed. These fluctuations result in the appearance of small but finite dissipation in the sample. The value of corresponding…
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…
The dramatic increase of network infrastructure comes at the cost of rapidly increasing energy consumption, which makes optimization of energy efficiency (EE) an important topic. Since EE is often modeled as the ratio of rate to power, we…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the…
Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e. models that generate uncorrelated scale-free networks. Most models to date however show structural negative…
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…