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The distance between an entangled node i and one of the points on the entangled segment between nodes j and j+1 from another chain is zero. In the rare case where more than a single pair can be assigned to an entanglement, only one of them is specified via the last two columns in Z...
Generally, the concept of geodesics is related to the definition of distance between two points of a manifold, and to the notion of the length of a curve. A length-minimizer geodesic is a curve connecting two elements in the manifold whose length is minimal. Roughly speaking, the idea of c...
and we observe\frac{ \partial G_i}{\partial Y'_j} = \frac{ \partial F'_i }{ \partial Y'_j}whenj\le k. We now study the relationship betweenX'and the ideal{\mathsf J}= \langle {\mathcal G}\rangleinkvariables, where{\mathcal G}= \{ G_1,\ldots , G_n \}. Proposition...