MURI researchers at Caltech have made dramatic progress in creating a fundamental theory of uncertainty management in complex, multiscale systems with a variety of applications from shear flow turbulence to networking protocols to global optimization. Military and commercial technological visions emphasize ubiquitous control, communications, and computing, with both biology and nanotechnology creating additional novel multi-scale challenges. A rigorous, practical, and unified theoretical framework will be essential for this vision, but until now it has proven stubbornly elusive. This research offers not only a theoretical research direction of unprecedented promise, but one that has already proven remarkably useful in a wide variety of practical applications. The results of this research will not only provide a rigorous basis for designing future networks of networks involving ubiquitous control, communications, and computing, but also will resolve many persistent mysteries at the foundation of physics. The major objective of this research is to develop an understanding of uncertainty management in complex systems. In addition to fundamental theory, the authors' objective is to provide tools for modeling, tractable simulation, and control of complex systems, with an emphasis on uncertainty and robustness. The increase in robustness, productivity, and throughput created by the enormous internal complexity of the power grid, the Internet, and other complex systems is accompanied by new hypersensitivities to perturbations the system was not designed to handle. This phenomenon is at the heart of power law statistics observed in failure events, with mostly small events but a "heavy tail" of large events. This "robust-yet-fragile" feature is characteristic of complex systems throughout engineering and biology. Appendixes discuss highly optimized transitions to turbulence and laminar-turbulent transition forced by free-stream turbulence. (95 refs.).