相关论文: Laplacian Dynamics on Cographs: Controllability An…

Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such…

In this article, a new notion of modal strong structural controllability is introduced and examined for a family of LTI networks. These networks include structured LTI subsystems, whose system matrices have the same zero/nonzero/arbitrary…

The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…

In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the convergence of graph Laplacians obtained from…

We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian.…

We show that the degree distributions of graphs do not suffice to characterize the synchronization of systems evolving on them. We prove that, for any given degree sequence satisfying certain conditions, there exists a connected graph…

A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network…

The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…

A common approach for analyzing hypergraphs is to consider the projected adjacency or Laplacian matrices for each order of interactions (e.g., dyadic, triadic, etc.). However, this method can lose information about the hypergraph structure…

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…

This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…

Coalescing involves gluing one or more rooted graphs onto another graph. Under specific conditions, it is possible to start with cospectral graphs that are coalesced in similar ways that will result in new cospectral graphs. We present a…

We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…

Renormalization of complex networks requires principled criteria for assessing whether a coarse-graining preserves dynamical content. We prove that discrete harmonic morphisms -- surjective maps preserving harmonic functions -- provide the…

In this paper we study the controllability of networked systems with static network topologies using tools from algebraic graph theory. Each agent in the network acts in a decentralized fashion by updating its state in accordance with a…

Turing's model has been widely used to explain how simple, uniform structures can give rise to complex, patterned structures during the development of organisms. However, it is very hard to establish rigorous theoretical results for the…

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…

Laplace operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. Assuming rational independence of edge lengths, necessary and sufficient…

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…

In a paper by Nishikawa and Motter, a quantity called the normalized spread of the Laplacian eigenvalues is used to measure the synchronizability of certain network dynamics. Through simulations, and without theoretical validation, it is…