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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…

We study the properties and stability of networks with arbitrary Laplacian coupling. Classic approaches to studying networked systems require unrealistic assumptions, including homogeneous node dynamics, one-dimensional and undirected…

The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…

Reliable functioning of supply and transport networks fundamentally support many non-equilibrium dynamical systems, from biological organisms and ecosystems to human-made water, gas, heat, electricity and traffic networks. Strengthening an…

In this paper, we study the factors that contribute to the effect of oversmoothing in deep Graph Neural Networks (GNNs). Specifically, our analysis is based on a new metric (Mean Average Squared Distance - $MASED$) to quantify the extent of…

We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics,…

In this paper, we consider the state controllability of networked systems, where the network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. We investigate how the…

Power law distribution is common in real-world networks including online social networks. Many studies on complex networks focus on the characteristics of vertices, which are always proved to follow the power law. However, few researches…

We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected…

In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with…

In this paper we consider the problem of transmission across a graph and how to effectively control/restrict it with limited resources. Transmission can represent information transfer across a social network, spread of a malicious virus…

Introduction of renewable generation leads to significant reduction of inertia in power system, which deteriorates the quality of frequency control. This paper suggests a new control scheme utilizing controllable load to deal with low…

We show that depending on the disorder, a small noise added to the threshold distribution of the fuse network may or may not completely change the subsequent breakdown process. When the threshold distribution has a lower cutoff at a finite…

Training of deep neural networks heavily depends on the data distribution. In particular, the networks easily suffer from class imbalance. The trained networks would recognize the frequent classes better than the infrequent classes. To…

A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…

In view of the node importance in weighted networks, weighted expected method (WEM), was proposed in this paper, which take an advantages of uncertain graph algorithm. First, a weight processing method is proposed based on the relationship…

We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et. al that quantifies how much a small perturbation to a phase-oscillator's natural…

The operability of a network concerns its ability to remain operational, despite possible failures in its links or equipment. One may model the network through a graph to evaluate and increase this operability. Its vertices and edges…

This paper presents conditions for establishing topological controllability in undirected networks of diffusively coupled agents. Specifically, controllability is considered based on the signs of the edges (negative, positive or zero). Our…

While operating communication networks adaptively may improve utilization and performance, frequent adjustments also introduce an algorithmic challenge: the re-optimization of traffic engineering solutions is time-consuming and may limit…