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There continues to be a lot of research done, papers delivered, and talks about adaptive systems using a variety of methods and approaches. While some interesting and even useful results have been produced, a coherent body of knowledge still seems to be eluding us. Is there, or could there even in theory, be an underlying mathematics of emergent properties yet to be discovered that would allow us to understand all manner of natural and build synthetic systems with the robustness seen in nature? This talk will present some recent results in understanding complex behavior and discuss application to agent-based systems.