Related papers: Spectral dimension reduction of complex dynamical …

Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…

Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…

A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…

Various disasters stem from minor perturbations, such as the spread of infectious diseases, cascading failure in power grids, etc. Analyzing perturbations is crucial for both theoretical and application fields. Previous researchers have…

Fixed point networks are dynamic networks that encode stimuli via distinct output patterns. Although such networks are omnipresent in neural systems, their structures are typically unknown or poorly characterized. It is therefore valuable…

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical…

This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…

Networked systems are systems of interconnected components, in which the dynamics of each component are influenced by the behavior of neighboring components. Examples of networked systems include biological networks, critical…

Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…

We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent space is challenging…

Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…

We introduce a method that can be used to evolve the topology of a network in a way that preserves both the network's spectral as well as local structure. This method is quite versatile in the sense that it can be used to evolve a network's…

The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security. In this paper, statistical techniques for link prediction based on the…

To understand the structural dynamics of a large-scale social, biological or technological network, it may be useful to discover behavioral roles representing the main connectivity patterns present over time. In this paper, we propose a…

This paper introduces a novel direct approach to system identification of dynamic networks with missing data based on maximum likelihood estimation. Dynamic networks generally present a singular probability density function, which poses a…

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh--Nagumo oscillators. For a large range of within- and between-network couplings, the…

Effectively preserving both the structural and dynamical properties during the reduction of complex networks remains a significant research topic. Existing network reduction methods based on renormalization group or sampling often face…

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…