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In addition, Observe that the function being obtained as a fixed point for contraction mappings, it depends continuously on the parameter τ.
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Proof Let V be a clade of the subtree S. Vertices mapped in S coincide in both mappings, as their clades belong to V ; the image of such vertices coincides in both mappings, as it depends only on S. By definition of the duplication, the set of duplications in S coincides in both mappings.
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It depends on us".
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