@article {Gershenson:2010a, title = {The Sigma Profile: A Formal Tool to Study Organization and its Evolution at Multiple Scales}, journal = {Complexity}, volume = {16}, number = {5}, year = {2011}, pages = {37-44}, abstract = {The σ profile is presented as a tool to analyze the organization of systems at different scales, and how this organization changes in time. Describing structures at different scales as goal-oriented agents, one can define σ ∈ [0,1] (satisfaction) as the degree to which the goals of each agent at each scale have been met. σ reflects the organization degree at that scale. The σ profile of a system shows the satisfaction at different scales, with the possibility to study their dependencies and evolution. It can also be used to extend game theoretic models. The description of a general tendency on the evolution of complexity and cooperation naturally follows from the σ profile. Experiments on a virtual ecosystem are used as illustration.}, doi = {10.1002/cplx.20350}, url = {http://arxiv.org/abs/0809.0504}, author = {Carlos Gershenson} }