Related papers: Perspective: network-guided pattern formation of n…

Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…

The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information is through head direction cells and grid cells. Brains use head direction cells…

We consider the problem of learning the dynamics in the topology of time-evolving point clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such as swarms of insects and birds or particles in physics. In…

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and…

Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…

The functional network of the brain continually adapts to changing environmental demands. The environmental changes closely connect with changes of active cognitive processes. In recent years, the network approach has emerged as a promising…

Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…

The majority of real-world networks are dynamic and extremely large (e.g., Internet Traffic, Twitter, Facebook, ...). To understand the structural behavior of nodes in these large dynamic networks, it may be necessary to model the dynamics…

To understand the formation, evolution, and function of complex systems, it is crucial to understand the internal organization of their interaction networks. Partly due to the impossibility of visualizing large complex networks, resolving…

We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

The relationship of network structure and dynamics is one of most extensively investigated problems in the theory of complex systems of the last years. Understanding this relationship is of relevance to a range of disciplines -- from…

One of the most important features observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain…

Models of cooperation grounded on social networks and on the ability of individuals to choose actions and partners aim to describe human social behavior. Extensive computer simulations of these models give important insight in the social…

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve…

We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…

Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the…