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Warping degree and ascending number are two closely related knotinvariants defined by A. Kawauchi and M. Ozawa. Warping degree iscomputed for knots up to n=9 crossings by A. Shimizu, and we extend this computation to all knots up to n=12 crossings. Ascending numbers are computed by different authors for knots withat most n=8 crossings, and we determine exact ascending numbersfor 64 knots with at most n=10 crossings. By using the general formulae for the signature of knots, for 13 families of knots general formulae are obtained for their ascending numbers. The concepts of warping degree and ascending number we extend to pseudo knots and virtual knots.

warping degree, ascending number, pseudo knots, virtual knots