Title: A von Neumann operator for exact analytical calculus of hybrid functions in complex systems
Complex systems, which include self-reproducing automata, exhibit hybrid functions consisting of both continuous and discrete variables - i.e., so-called "concrete" multivariate functions in the sense of D. Knuth. Gradient-based operators from classical multivariate differential calculus and sensitivity analysis are not applicable to a broad class of such systems due to the presence of discrete variables. This problem was known to von Neumann, who envisioned but apparently did not propose a solution, perhaps due to his premature death. The "nabladot" operator for hybrid functions of continuous and discrete variables is defined and illustrated with examples from complex systems. Results show new features of complex systems previously unavailable through traditional approaches based on approximations.
Dr. Cioffi-Revilla is University Professor of Computational Social Science, founding and former Chair of the Department of Computational Social Science, and founding and current Director of the Mason Center for Social Complexity at George Mason University. He holds two doctoral degrees in Political Science and International Relations and has conducted extensive scientific research on conflict and disasters, international relations, computational social science modeling, and social complexity with funding from DARPA, NSF, ONR, NATO, and European research agencies. He has authored six books, the most recent being Introduction to Computational Social Science (Springer 2014), the first comprehensive textbook in CSS, and over 90 papers in peer-reviewed journals and publications. He has served in various senior science advisory capacities in the US and other NATO governments, including as Jefferson Science Fellow of the National Academy of Sciences, and is an Associate Research Scientist at the Smithsonian National Museum of Natural History in Washington DC.