The jigsaw percolation process on graphs was introduced by Brummitt et al. (2015) as a model of collaborative solutions of puzzles in social networks. Percolation in this process may be viewed as the joint connectedness of two graphs on a common vertex set. Our aim is to extend a result of Bollobás et al. (2017) concerning this process to hypergraphs for a variety of possible definitions of connectedness. In particular, we determine the asymptotic order of the critical threshold probability for percolation when both hypergraphs are chosen binomially at random.

Discrete kinematic synthesis of discretely actuated hyper-redundant manipulators is a new practical problem in robotics. The problem concerns with determining the type of each manipulator module from among several specific types, so that the manipulator could reach several specified target frames with the lowest error. This paper suggests using a breadth-first search method and a workspace mean frame to solve this problem. To reduce errors, two heuristic ideas are proposed: two-by-two searching method and iteration. The effectiveness of the proposed method is verified through several numerical problems.