This is the first in a series of papers studying w-knots, and more generally, w-knotted objects (w-braids, w-tangles, etc). These are classes of knotted objects which are wider, but weaker than their "usual" counterparts.
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Bar-Natan et al. (2016) studied this question.
Synapse has enriched 2 closely related papers on similar clinical questions. Consider them for comparative context: