Collaborative Research: A Formal Theory of Robust Numerical Computation Geometry and Its Validation on Configuration Space Construction

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3D shape matching, massive dataset visualization, and protein structure prediction.The theoretical issues involve combinatorial geometry, algorithm designand basic complexity theory. This effort is aimed at deriving newcomputational methods for solving problems of a geometric or biological naturethat have resisted past investigations because of one two reasons: either the inputdata is too massive to be processed directly and it can only be "sampled" cleverly orthe number of variables is itself so high that standard methods suffer from an exponential blowupin the time it takes to run them. New dimension reduction techniques are needed to resolve this bottleneck.