We derive a sum rule that constrains the scale based decomposition of the trajectories of finite systems of particles. The sum rule reflects a tradeoff between the finer and larger scale collective degrees of freedom. For short duration trajectories, where acceleration is irrelevant, the sum...

Almost all complex artifacts nowadays, including physical artifacts such as airplanes, as well as informational artifacts such as software, organizational designs, plans and schedules, are created via the interaction of many, sometimes thousands of participants, working on different elements of...

We develop a new approach to the study of the dynamics of link utilization in complex networks using records of communication in a large social network. Counter to the perspective that nodes have particular roles, we find roles change dramatically from day to day. Local hubs have a power law...