  Quandle cocycle invariants form a powerful and well developed tool in knot
theory. This paper treats their variations - namely, positive and twisted
quandle cocycle invariants, and shadow invariants. We interpret the former as
particular cases of the latter. As an application, several constructions from
the shadow world are extended to the positive and twisted cases. Another
application is a sharpening of twisted quandle cocycle invariants for
multi-component links.
