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The social sciences can play important roles in assisting military planners and decision-makers who are trying to understand complex human social behaviors and systems, potentially facilitating a wide range of missions including humanitarian, stability, and counter-insurgency operations. Current social science approaches to studying behavior rely on a variety of modeling methods—both qualitative and quantitative—which seek to make inferences about the causes of social phenomena on the basis of observations in the real-world. Yet little is known about how accurate these methods and models really are, let alone whether the connections they observe and predict are truly matters of cause and effect or mere correlations.
The Lagrange program seeks to develop new mathematical approaches to optimization problems in uncertain, dynamic, multiscale, and high-dimensional settings. By bridging methodologies developed for both discrete and continuous optimizations, Lagrange aims to enable solutions for complex, realistic problems that involve dynamic environments, rapidly changing requirements, and increasing or decreasing amounts of information.
The goal of the Mathematics of Sensing, Exploitation and Execution (MSEE) program is to explore and develop high-impact methods for scalable autonomous systems capable of understanding scenes and events for learning, planning, and execution of complex tasks. The program is exploring powerful mathematical frameworks for unified knowledge representation for shared perception, learning, reasoning, and action. One of the central concepts in MSEE is to exploit methods based on minimalist generative grammar, similar to human language, to represent and process visual scenes and actions.
Complex, nonlinear, multiscale dynamical systems are ubiquitous. Examples include weather, fluids, materials, biological systems, communication networks, and social systems. These systems often evolve to a critical state built up from a series of irreversible and unexpected events, which severely limits development and implementation of mathematical models to accurately predict formation and evolution of patterns in such systems.
The explosive growth of global digital connectivity has opened new possibilities for designing and conducting social science research. Once limited by practical constraints to experiments involving just a few dozen participants-often university students or other easily available groups-or to correlational studies of large datasets without any opportunity for determining causation, scientists can now engage thousands of diverse volunteers online and explore an expanded range of important topics and questions.