  The entanglement of open curves in 3-space appears in many physical systems
and affects their material properties and function. A new framework in knot
theory was introduced recently, that enables to characterize the complexity of
collections of open curves in 3-space using the theory of knotoids and
linkoids, which are equivalence classes of diagrams with open arcs. In this
paper, new invariants of linkoids are introduced via a surjective map between
linkoids and virtual knots. This leads to a new collection of strong invariants
of linkoids that are independent of any given virtual closure. This gives rise
to a collection of novel measures of entanglement of open curves in 3-space,
which are continuous functions of the curve coordinates and tend to their
corresponding classical invariants when the endpoints of the curves tend to
coincide.
