US-France (INRIA) Cooperative Research: Symbolic and Numerical Methods for Geometric Modeling

0421771戈德曼这三年的美国-法国合作研究项目致力于解决多项式方程系统和应用问题的几何建模和分子生物学。 莱斯大学的罗纳德戈德曼和法国国家信息学和应用数学研究所（INRIA）的GALAAD小组将开发代数计算技术。 GALAAD团队将专注于多项式方程及其在计算生物学中的应用。 这是补充莱斯大学的重点多项式方程及其应用程序的计算几何modeling.Intellectual优点：几何建模和计算生物学的许多应用程序需要快速强大的方法来解决系统的多项式方程。 研究人员提出了两种解决多项式方程组的方法：创新的合成技术和基于Bezier细分的数值方法。 他们还将在C++库SYNAPS中实现他们的算法。更广泛的影响：所提出的方法将应用于几何建模和计算生物学中的问题。 为了帮助几何建模，他们将研究一些计算机表示形状的方法，并将他们的技术应用于更有效地解决代表理性曲线和曲面的标准问题。 在计算生物学中，他们将试图从核磁共振实验产生的部分信息中恢复分子的三维结构。 这一结果对药物设计、蛋白质折叠和细胞特性研究具有重要意义。 该项目还通过与INRIA集团的研究沉浸在国际环境中为美国研究生提供培训，并为未来的国际合作提供了发展联系的机会。

0421771GoldmanThis three-year U.S.-France cooperative research project addresses solutions for polynomial equations systems and applications to problems in geometric modeling and molecular biology. Ronald Goldman of Rice University and the GALAAD group at the French National Institute for Research in Informatics and Applied Mathematics (INRIA), led by Bernard Mourrain, will develop techniques in algebraic computation. The GALAAD team will concentrate on polynomial equations and applications to computational biology. This is complemented by Rice University's focus on polynomial equations and their applications to computational geometric modeling.Intellectual Merit: Many applications in geometric modeling and computational biology require fast robust methods for solving systems of polynomial equations. The investigators propose two approaches to solving systems of polynomial equations: innovative resultant techniques and numerical methods based on Bezier subdivision. They will also implement their algorithms in the C++ library SYNAPS.Broader Impact: The proposed methods will be applied to problems in geometric modeling and computational biology. To aid in geometric modeling, they will investigate some approaches to computer representations of shape and apply their techniques to more efficient solutions to standard problems representing rational curves and surfaces. In computational biology they will try to recover the three-dimensional structure of a molecule from partial information generated by NMR experiments. The results may be useful for automated drug design, protein folding and studies of cell properties. The project also gives a U.S. graduate student training in an international environment via research immersion with the INRIA group and provides an opportunity to develop connections for future international collaboration.