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King et al. introduced square and triangle shaped matrices in which the cells report the knot types of the subchains of a linear chain2,24. This type of matrix, however, does not adequately reflect the circular periodicity found in a closed chain and, thus, is not well suited to report the knot types of subchains for closed, circular chains. To overcome this problem, we introduce a disk matrix (see Fig. 1) that reports the knot type of every subchain in a fixed embedding of a circular polygonal chain. It is helpful to think of the disk matrix as being composed of cells delimited by longitude lines radiating from the center of the disk and concentric latitude circles with increasing radius. The matrix cells close to the center of the disk represent Vans Black Shoes For Men

The longitudinal position of a cell indicates the position of the midpoint of the associated subchain and the latitude indicates the length, in number of segments, of the associated subchain. positive x axis) corresponds to subchains whose center point is the first vertex of the polygonal chain. The numbering of longitude lines goes in a counter clockwise direction in our matrix. the knot type most frequently resulting from a uniform closure procedure of the open chain Vans Era White Gum Sole

Fig. 1 shows the disk matrix reporting the two knot types occurring in subchains of the symmetric trefoil knot configuration shown in the center of this disk matrix. The polygonal trefoil knot, 31, consists of the center lines of 47 cylindrical segments. This trefoil configuration has a three fold rotational symmetry that one also can see in the symmetry of the disk matrix. Near the center of the matrix, we have entr.

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the knot type of every subchain in a closed chainTaylor and later Vans For Men Red

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very short subchains (starting from one segment), whereas cells Vans Game Over Shoes bordering the rim of the disk represent long subchains (missing just one segment).

(see Refs. 3, 25,26,27,28 and the Materials and Methods section). The intensity of a given color reflects how frequently this dominant knot type occurs among the tested closures3,28.

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