Inferring domain of interactions among particles from ensemble of trajectories.

An information-theoretic scheme is proposed to estimate the underlying domain of interactions and the timescale of the interactions for many-particle systems. The crux is the application of transfer entropy which measures the amount of information transferred from one variable to another, and the introduction of a "cutoff distance variable" which specifies the distance within which pairs of particles are taken into account in the estimation of transfer entropy. The Vicsek model often studied as a metaphor of collectively moving animals is employed with introducing asymmetric interactions and an interaction timescale. Based on ensemble data of trajectories of the model system, it is shown that using the interaction domain significantly improves the performance of classification of leaders and followers compared to the approach without utilizing knowledge of the domain. Given an interaction timescale estimated from an ensemble of trajectories, the first derivative of transfer entropy averaged over the ensemble with respect to the cutoff distance is presented to serve as an indicator to infer the interaction domain. It is shown that transfer entropy is superior for inferring the interaction radius compared to cross correlation, hence resulting in a higher performance for inferring the leader-follower relationship. The effects of noise size exerted from environment and the ratio of the numbers of leader and follower on the classification performance are also discussed.

[1]  Jing Han,et al.  How does the interaction radius affect the performance of intervention on collective behavior? , 2018, PloS one.

[2]  E. Grasland-Mongrain,et al.  Orientation and polarity in collectively migrating cell structures: statics and dynamics. , 2011, Biophysical journal.

[3]  Wei Li,et al.  Singularities and symmetry breaking in swarms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[5]  Lucas Barberis,et al.  Large-Scale Patterns in a Minimal Cognitive Flocking Model: Incidental Leaders, Nematic Patterns, and Aggregates. , 2016, Physical review letters.

[6]  Xinghuo Yu,et al.  Second-order tracking control for leader-follower multi-agent flocking in directed graphs with switching topology , 2011, Syst. Control. Lett..

[7]  Ajay Gopinathan,et al.  Self-organized sorting limits behavioral variability in swarms , 2016, Scientific Reports.

[8]  H Delanoë-Ayari,et al.  4D traction force microscopy reveals asymmetric cortical forces in migrating Dictyostelium cells. , 2010, Physical review letters.

[9]  Erik M. Bollt,et al.  Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings , 2014, 1504.03769.

[10]  Feng Hu,et al.  Information Dynamics in the Interaction between a Prey and a Predator Fish , 2015, Entropy.

[11]  Mihir Durve,et al.  First-order phase transition in a model of self-propelled particles with variable angular range of interaction. , 2016, Physical review. E.

[12]  T. Nagai,et al.  Red fluorescent cAMP indicator with increased affinity and expanded dynamic range , 2018, Scientific Reports.

[13]  Takeomi Mizutani,et al.  Leader cells regulate collective cell migration via Rac activation in the downstream signaling of integrin β1 and PI3K , 2015, Scientific Reports.

[14]  David Cai,et al.  Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information. , 2018, Physical review. E.

[15]  T. Vicsek,et al.  Collective Motion , 1999, physics/9902023.

[16]  Sachit Butail,et al.  Model-free information-theoretic approach to infer leadership in pairs of zebrafish. , 2016, Physical review. E.

[17]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[18]  Ajinkya Kulkarni,et al.  Sparse Game Changers Restore Collective Motion in Panicked Human Crowds. , 2017, Physical review letters.

[19]  Tu,et al.  Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together. , 1995, Physical review letters.

[20]  Charlotte K. Hemelrijk,et al.  Leadership in fish shoals , 2000 .

[21]  R. Golestanian,et al.  Active Phase Separation in Mixtures of Chemically Interacting Particles. , 2019, Physical review letters.

[22]  Sachit Butail,et al.  Analysis of Pairwise Interactions in a Maximum Likelihood Sense to Identify Leaders in a Group , 2017, Front. Robot. AI.

[23]  Jie Sun,et al.  Anatomy of leadership in collective behaviour. , 2018, Chaos.