The Sigma Profile: A Formal Tool to Study Organization and its Evolution at Multiple Scales

TL;DR

The paper introduces the sigma profile as a formal tool to analyze and understand the multi-scale organization and evolution of systems, including their complexity and cooperation dynamics.

Contribution

It proposes a novel formal framework using the sigma profile to study system organization across scales and its evolution over time.

Findings

Sigma profile effectively captures system organization at multiple scales.

The model predicts natural tendencies in complexity and cooperation evolution.

Experiments demonstrate the utility of the sigma profile in virtual ecosystems.

Abstract

The $\sigma$ 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 $\sigma \in [0,1]$ ("satisfaction") as the degree to which the goals of each agent at each scale have been met. $\sigma$ reflects the organization degree at that scale. The $\sigma$ 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. A general tendency on the evolution of complexity and cooperation naturally follows from the $\sigma$ profile. Experiments on a virtual ecosystem are used as illustration.