Related papers: Asymptotic Network Robustness
This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all…
By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. We observe the largest damage in networks with connectivity close to the isostatic point…
The capability of nodes to broadcast their message to the entire wireless network when nodes employ cooperation is considered. We employ an asymptotic analysis using an extended random network setting and show that the broadcast performance…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
The control of dynamical, networked systems continues to receive much attention across the engineering and scientific research fields. Of particular interest is the proper way to determine which nodes of the network should receive external…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
Network structures in a wide array of systems such as social networks, transportation, power and water distribution infrastructures, and biological and ecological systems can exhibit critical thresholds or tipping points beyond which there…
Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial for understanding the function, performance and evolution of complex systems. In the last few…
In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks…
Metros (heavy rail transit systems) are integral parts of urban transportation systems. Failures in their operations can have serious impacts on urban mobility, and measuring their robustness is therefore critical. Moreover, as physical…
This paper focuses on network resilience to perturbation of edge weight. Other than connectivity, many network applications nowadays rely upon some measure of network distance between a pair of connected nodes. In these systems, a metric…
We investigate the performance of linear consensus algorithms subject to a scaling of the underlying network size. Specifically, we model networked systems with $n^{\text{th}}$ order integrator dynamics over families of undirected, weighted…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
In contrast to conventional artificial neural networks, which are structurally static, we present two approaches for evolving small networks into larger ones during training. The first method employs an auxiliary weight that directly…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
We study the relative importance of "top-speed" (long-term growth rate) and "acceleration" (how quickly the long-term growth rate can be reached) in the evolutionary race to increase population size. We observe that fitness alone does not…
We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, a measure of how much deviation from the assumed linear…