Knots cascade detected by a monotonically decreasing sequence of values.
Knots cascade detected by a monotonically decreasing sequence of values.
复制标题
通过单调递减的值序列检测到的结级联
DOI：
10.1038/srep24118
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发表时间：
2016-04-07
影响因子：
4.6
通讯作者：
Ricca RL
中科院分区：
文献类型：
--
作者：
Liu X;Ricca RL
由于相邻链的重新连接或重组，超流涡旋纽结以及DNA质粒环面纽结和链环被发现经历几乎相同的级联过程，该过程往往通过逐步解开链环来降低拓扑复杂性。在此，通过使用最近为流体纽结引入的HOMFLYPT多项式，我们证明在拓扑复杂性通过逐步解开链环而降低的假设下，这个级联过程遵循由一个独特的、数值单调递减的序列所检测到的路径。这一结果对于任何标准嵌入的环面纽结T(2, 2n + 1)和环面链环T(2, 2n)的序列都成立。通过这个结果，我们表明这种经过调整的HOMFLYPT多项式的计算为测量各种物理系统的拓扑复杂性提供了一个强大的工具。
Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems.