Dynamical systems on/of networks

I am interested in studying dynamical processes of and on top of networks. My recent works are on large deviation theory applied to random walks on graphs and methodologies to define chaotic evoution of temporal networks.

Lyapunov exponents for temporal networks

We’ve reimagined temporal networks as trajectories within a latent system, introducing a concept called dynamical instability. We’ve developed a measure for this using the network maximum Lyapunov exponent (nMLE). Using extended time-series analysis methods, we quantify initial condition sensitivities and estimate nMLE from a single trajectory. Our method is validated across various network models and has diverse applications.

Maximal dispersion of adaptive random walks

We’ve developed an Adaptive Random Walk (ARW) method that optimizes information spread in networks without requiring global structure knowledge. Unlike traditional Maximum Entropy Random Walks (MERWs) that rely on complete network insights, our ARW method utilizes local data as it navigates the network. This makes it a practical and efficient approach for real-world applications, and we’ve successfully tested its performance across diverse networks.