This research is a continuation of a project whose goal is to combine the mathematical expertise available at the International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, with the evolving physics research in this country on complexity. The Moscow group is a world leader in statistical studies of seismicity. The PI is a leader in the discovery of new approaches to complex physical systems; especially self-organized criticality as applied to regional seismicity. Some of the results thus far include 1) a systematic test of the intermediate-term earthquake prediction algorithms previously developed by the group with notable successes, 2) development of an earthquake mechanism-seismicity model that exhibits useful properties that can be tested with seismic data, and 3) development of a uniform seismic hazard methodology model. Future work will continue the seismicity-earthquake dynamics modeling, extend the intermediate-term earthquake prediction algorithms, and develop new short-term prediction algorithms within the intermediate-term prediction alarms. The goals are to advance our understanding of earthquake mechanics, improve earthquake hazard assessment, and advance earthquake prediction techniques. This research is a component of the National Earthquake Hazard Reduction Program.