APDEs Seminar

Consider an ensemble of agents interacting with each other non-locally. One of the main defining factors of such interactions is the communication protocol, which describes the magnitude of interactions between every pair of the agents. For example in the widely studied Cucker-Smale model, each agent interacts with every other agent with magnitude inversely proportional to the distance between them. The talk is dedicated to the presentation of a density induced communication protocol best described by: ”Each agent is affected only by sufficiently dense nearby crowd”. Such a protocol reflects an individual’s tendency to conform with groupthink. It leads to nonsymmetric, short-range interactions and interesting behaviour of the agents. I will present how 1st order collective dynamics with the presented communication protocol applies to data segmentation. At the end of the talk I will present a quick overview of possible directions of future research including kinetic and hydrodynamic limits of the model.