相关论文: Potential energy of complex networks: a novel pers…

Real-world complex systems exhibit intricate interconnections and dependencies, especially social networks, technological infrastructures, and communication networks. These networks are prone to disconnection due to random failures or…

Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…

With an increasing emphasis on network security, much more attention has been attracted to the vulnerability of complex networks. The multi-scale evaluation of vulnerability is widely used since it makes use of combined powers of the links'…

Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and…

We prove Strichartz estimates for the Schr\"odinger equation with scaling-critical electromagnetic potentials in dimensions $n\geq3$. The decay assumption on the magnetic potentials is critical, including the case of the Coulomb potential.…

We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…

A nonnegative function on the vertices of an infinite graph G which vanishes at a distinguished vertex o, has Laplacian 1 at o, and is harmonic at all other vertices is called a potential. We survey basic properties of potentials in…

This paper explores the estimation of a panel data model with cross-sectional interaction that is flexible both in its approach to specifying the network of connections between cross-sectional units, and in controlling for unobserved…

This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem (i) we propose a metric…

Network synchronization is an emerging phenomenon in complex networks. The spectrum of Laplacian matrix will be immensely helpful for getting the network dynamics information. Especially, network synchronizability is characterized by the…

Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of discrete optimization problems, and subsequently, machine learning and control theory problems. On the one hand, SCCs are…

Quantifying the relations (e.g., similarity) between complex networks paves the way for studying the latent information shared across networks. However, fundamental relation metrics are not well-defined between networks. As a compromise,…

We perform an analytical analysis of the long-range degree correlation of the giant component in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the…

As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a…

This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach…

It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…

Densifying the network and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, due to the complicated distributions of random signal and interference channel gains,…

A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…