Inferring the physical connectivity of complex networks from their functional dynamics

Model reconstruction from temporal data for coupled oscillator networks

In a complex system, the interactions between individual agents often lead to emergent collective behavior such as spontaneous synchronization, swarming, and pattern formation. Beyond the intrinsic properties of the agents, the topology of the network of interactions can have a dramatic influence over the dynamics. In many studies, researchers start with a specific model for both the intrinsic dynamics of each agent and the interaction network and attempt to learn about the dynamics of the model. Here, we consider the inverse problem: given data from a system, can one learn about the model and the underlying network? We investigate arbitrary networks of coupled phase oscillators that can exhibit both synchronous and asynchronous dynamics. We demonstrate that, given sufficient observational data on the transient evolution of each oscillator, machine learning can reconstruct the interaction network and identify the intrinsic dynamics.

Inference of topology and the nature of synapses, and the flow of information in neuronal networks

The characterization of neuronal connectivity is one of the most important matters in neuroscience. In this work, we show that a recently proposed informational quantity, the causal mutual information, employed with an appropriate methodology, can be used not only to correctly infer the direction of the underlying physical synapses, but also to identify their excitatory or inhibitory nature, considering easy to handle and measure bivariate time series. The success of our approach relies on a surprising property found in neuronal networks by which nonadjacent neurons do "understand" each other (positive mutual information), however, this exchange of information is not capable of causing effect (zero transfer entropy). Remarkably, inhibitory connections, responsible for enhancing synchronization, transfer more information than excitatory connections, known to enhance entropy in the network. We also demonstrate that our methodology can be used to correctly infer directionality of synapses even in the presence of dynamic and observational Gaussian noise, and is also successful in providing the effective directionality of intermodular connectivity, when only mean fields can be measured.

Successful network inference from time-series data using mutual information rate

This work uses an information-based methodology to infer the connectivity of complex systems from observed time-series data. We first derive analytically an expression for the Mutual Information Rate (MIR), namely, the amount of information exchanged per unit of time, that can be used to estimate the MIR between two finite-length low-resolution noisy time-series, and then apply it after a proper normalization for the identification of the connectivity structure of small networks of interacting dynamical systems. In particular, we show that our methodology successfully infers the connectivity for heterogeneous networks, different time-series lengths or coupling strengths, and even in the presence of additive noise. Finally, we show that our methodology based on MIR successfully infers the connectivity of networks composed of nodes with different time-scale dynamics, where inference based on Mutual Information fails.

Mixed outer synchronization of coupled complex networks with time-varying coupling delay

In this paper, the problem of outer synchronization between two complex networks with the same topological structure and time-varying coupling delay is investigated. In particular, we introduce a new type of outer synchronization behavior, i.e., mixed outer synchronization (MOS), in which different state variables of the corresponding nodes can evolve into complete synchronization, antisynchronization, and even amplitude death simultaneously for an appropriate choice of the scaling matrix. A novel nonfragile linear state feedback controller is designed to realize the MOS between two networks and proved analytically by using Lyapunov-Krasovskii stability theory. Finally, numerical simulations are provided to demonstrate the feasibility and efficacy of our proposed control approach.