For more than a century, rigid-body displacements have been viewed as affine transformations described as homogeneous transformation matrices wherein the linear part is a rotation matrix. In group-theoretic terms, this classical description makes rigid-body motions a semi-direct product. The distinction between a rigid-body displacement of Euclidean space and a change in pose from one reference...

Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qual­ itative property called product synergy. The current definition of product synergy is insuf­ ficient for intercausal reasoning where there are additional uninstantiated causes of the common effect. We propose a new defi...

There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on top. The in shuffle I leaves the original top card second from the top. Applications to the design of computer networks and card tricks are reviewed. The main result is the determination of the group (I, 0) generated by the two ...