Data-driven discovery of stochastic dynamical equations of collective motion.

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, the size of many real flocks falls within 'mesoscopic' scales (10 to 100 individuals), where stochasticity arising from the finite flock sizes is important. Previous studies on mesoscopic models have typically focused on non-spatial models.

Disentangling intrinsic motion from neighborhood effects in heterogeneous collective motion.

Most real-world collectives, including animal groups, pedestrian crowds, active particles, and living cells, are heterogeneous. The differences among individuals in their intrinsic properties have emergent effects at the group level. It is often of interest to infer how the intrinsic properties differ among the individuals based on their observed movement patterns.

Mapping distinct timescales of functional interactions among brain networks.

Brain processes occur at various timescales, ranging from milliseconds (neurons) to minutes and hours (behavior). Characterizing functional coupling among brain regions at these diverse timescales is key to understanding how the brain produces behavior. Here, we apply instantaneous and lag-based measures of conditional linear dependence, based on Granger-Geweke causality (GC), to infer network connections at distinct timescales from functional magnetic resonance imaging (fMRI) data.