The reasons why using the arms can increase standing vertical jump height are investigated by computer simulations. The human models consist of four/five segments connected by frictionless joints. The head-trunk-arms act as a fourth segment in the first model while the arms become a fifth segment in the second model. Planar model movement is actuated by joint torque generators. Each joint torqu...

Let P be a set of n points in d-dimensional Euclidean space. A (k,eps)-kernel is a subset of P that, for every direction, epsilon-approximates the directional width of P, when k “outliers’’ can be ignored in that direction. We prove that small (k,eps)-kernels exist and describe efficient algorithms for computing them. Such kernels are instrumental in solving shape-fitting problems with k outlie...