三角形瓦片的离散differential geometry与闭轨线代数
Discrete differential geometry of triangle tiles and algebra of closed trajectories
摘要：
本文提出了一种新的数学框架，可应用于生物学问题，如蛋白质和蛋白质复合物的结构分析。特别是，它给出了一个新的方法编码的三维结构的蛋白质到一个二进制序列，其中蛋白质近似的折叠四面体序列。它也为描述分子复合物及其相互作用提供了一个新的代数框架。为了简单起见，我们将在二维物体的情况下解释框架。然后，得到了平面曲线的二进制码作为曲线的"二阶导数“，并用代数方法描述了闭合轨迹的”融合与分裂“。
英文摘要：
This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional structure of a protein into a binary sequence, where proteins are approximated by a folded tetrahedron sequence. It also gives a new algebraic framework for describing molecular complexes and their interactions. For simplicity, we shall explain the framework in the case of two-dimensional objects. Then, the binary code of a plane curve is obtained as the ``second derivative'' of the curve and ``fusion and fission'' of closed trajectories is described algebraically.
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