Synchronized movement of (both unicellular and multicellular) systems can be observed almost everywhere. Understanding of how organisms are regulated to synchronized behavior is one of the challenging issues in the field of collective motion. It is hypothesized that one or a few agents in a group regulate(s) the dynamics of the whole collective, known as leader(s). The identification of the leader (influential) agent(s) is very crucial. This article reviews different mathematical models that represent different types of leadership. We focus on the improvement of the leader-follower classification problem. It was found using a simulation model that the use of interaction domain information significantly improves the leader-follower classification ability using both linear schemes and information-theoretic schemes for quantifying influence. This article also reviews different schemes that can be used to identify the interaction domain using the motion data of agents.

Collective migration of cells is a fundamental behavior in biology. For the quantitative understanding of collective cell migration, live-cell imaging techniques have been used using e.g., phase contrast or fluorescence images. Particle tracking velocimetry (PTV) is a common recipe to quantify cell motility with those image data. However, the precise tracking of cells is not always feasible. Particle image velocimetry (PIV) is an alternative to PTV, corresponding to Eulerian picture of fluid dynamics, which derives the average velocity vector of an aggregate of cells. However, the accuracy of PIV in capturing the underlying cell motility and what values of the parameters should be chosen is not necessarily well characterized, especially for cells that do not adhere to a viscous flow. Here, we investigate the accuracy of PIV by generating images of simulated cells by the Vicsek model using trajectory data of agents at different noise levels. It was found, using an alignment score, that the direction of the PIV vectors coincides with the direction of nearby agents with appropriate choices of PIV parameters. PIV is found to accurately measure the underlying motion of individual agents for a wide range of noise level, and its condition is addressed.

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