Finite-Type Invariants of order one for long virtual knots
  We extend to the long virtual knot case the constructions first presented by A. Henrich and later generalized by the author to the framed virtual knot case. These consist of three Vassiliev invariants of order one, including a universal one, as well as the notions of a based matrix and a singular based matrix and their relation to long flat virtual knots. 
Nicolas Petit
math.GT