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...

In recent years, understanding the structure and function of complex networks has become the foundation for explaining many different real-world complex biological, technological, and informal social phenomena. Techniques from statistical physics have been successfully applied to the analysis of...

Advancing peace and conflict studies into a quantitative science requires advanced mathematical methods and concepts. Lim, Metzler and Bar-Yam (2007, “LMBâ€) provide a wavelet based method for predicting the location of violence in a country based upon the hypothesis that well mixed or...