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For a chain with n contacts, the topology can be described by an n by n matrix in which each element illustrates the relation between a pair of contacts and may take one of the three states, P, S and X. Multivalent contacts can also be categorised in full or via decomposition into several binary contacts. Similarly, circuit topology allows for the classification of the pairwise arrangements of chain crossings and tangles, thus providing a complete 3D description of folded chains. Furthermore, one can apply circuit topology operations to soft

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