Orthogonal rotation algorithms

The quartimax and varimax algorithms for orthogonal rotation attempt to maximize particular simplicity criteria by a sequence of two-factor rotations. Derivations of these algorithms have been fairly complex. A simple general theory for obtaining two factor at a time algorithms for any polynomial simplicity criteria satisfying a natural symmetry condition is presented. It is shown that the degree of any symmetric criterion must be a multiple of four. A basic fourth degree algorithm, which is applicable to all symmetric fourth degree criteria, is derived and applied using a variety of criteria. When used with the quartimax and varimax criteria the algorithm is mathematically identical to the standard algorithms for these criteria. A basic eighth degree algorithm is also obtained and applied using a variety of eighth degree criteria. In general the problem of writing a basic algorithm for all symmetric criteria of any specified degree reduces to the problem of maximizing a trigonometric polynomial of degree one-fourth that of the criteria.This research was supported by the Bell Telephone Laboratories, Murray Hill, New Jersey and NIH Grant FR-3.     

Modification of severe disruptive and aggressive behavior using brief timeout and reinforcement procedures

Brief timeout for disruptive and aggressive behaviors and reinforcement for appropriate behaviors were used with two retarded patients in a state hospital ward setting. The procedures reduced loud vocal behavior in one patient and aggressive behavior in another to near-zero levels when first applied. The behaviors returned to previous levels when the procedures were removed and were again greatly reduced when timeout and reinforcement were reapplied. The results were significant because the behavior problems were severe and long-standing and the procedures were instituted without greatly disturbing normal ward routine.