Related papers: Eigenvalue Spectra of Modular Networks
Recent studies have been using graph theoretical approaches to model complex networks (such as social, infrastructural or biological networks), and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how…
We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external signal inputs. Particular emphasis is…
Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general…
We study high-density traffic of information packets on sparse modular networks with scale-free subgraphs. With different statistical measures we distinguish between the free flow and congested regime and point out the role of modules in…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
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,…
Dynamic multilayer networks frequently represent the structure of multiple co-evolving relations; however, statistical models are not well-developed for this prevalent network type. Here, we propose a new latent space model for dynamic…
Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem…
A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
Frequency modulation by perturbation is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of identical limit cycle oscillators whose frequencies are modulated sensitively by the…
The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and…
Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted…
Many observables of brain dynamics appear to be optimized for computation. Which connectivity structures underlie this fine-tuning? We propose that many of these structures are naturally encoded in the space that more directly relates to…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…
The dynamics of complex networks, being a current hot topic of many scientific fields, is often coded through the corresponding Laplacian matrix. The spectrum of this matrix carries the main features of the networks' dynamics. Here we…
This paper is concerned with the spectral properties of matrices associated with linear filters for the estimation of the underlying trend of a time series. The interest lies in the fact that the eigenvectors can be interpreted as the…
We present a new and simple method for the identification of a single transfer function that is embedded in a dynamical network. In existing methods the consistent identification of the desired transfer function relies on the positive…
Given the large size and complexity of most biochemical regulation and signaling networks, there is a non-trivial relationship between the micro-level logic of component interactions and the observed macro-dynamics. Here we address this…