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

三维形状匹配，海量数据可视化，蛋白质结构预测。理论问题涉及组合几何、算法设计和基本复杂性理论。这项工作的目的是推导出新的计算方法来解决几何或生物性质的问题，这些问题在过去的研究中一直受到一两个原因的阻碍：要么是输入数据太大，无法直接处理，只能巧妙地“采样”，要么是变量的数量本身太高，以至于标准方法在运行它们所花费的时间上呈指数级增长。需要新的降维技术来解决这一瓶颈。

3D shape matching, massive dataset visualization, and protein structure prediction. The theoretical issues involve combinatorial geometry, algorithm design and basic complexity theory. This effort is aimed at deriving new computational methods for solving problems of a geometric or biological nature that have resisted past investigations because of one two reasons: either the input data is too massive to be processed directly and it can only be "sampled" cleverly or the 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.