The perching response and the laws of animal timing

peer reviewedHoming pigeons were trained under differential-reinforcement-of-low-rate (DRL) or differential-reinforcement-of-response-duration (DRRD) schedules using a perching response. Schedule values ranged from 10 s to 70 s for DRL and from 12 s to 40 s for DRRD. In general, mean interresponse times or response durations were very close to the schedule requirement at all schedule values. A linear relation between mean response measure and schedule value described the data well, but power functions fared even better. The data also conformed well to the generalized Weber law; standard deviations of response measures varied as a linear function of the mean. Overall, the perching response produced data that conformed much more accurately to the schedule requirement-particularly at the longer schedule values-than did data from previous studies with both rats and pigeons. The results conformed well to the linear-type timing consistent with scalar timing theory

Complementary group resolution of the SU(n) outer multiplicity problem. I. The Littlewood rules and a complementary U(2n−2) group structure

A complementary group to SU(n) is found that realizes all features of the Littlewood rule for Kronecker products of SU(n) representations. This is accomplished by considering a state of SU(n) to be a special Gel'fand state of the complementary group {\cal U}(2n-2). The labels of {\cal U}(2n-2) can be used as the outer multiplicity labels needed to distinguish multiple occurrences of irreducible representations (irreps) in the SU(n)\times SU(n)\downarrow SU(n) decomposition that is obtained from the Littlewood rule. Furthermore, this realization can be used to determine SU(n)\supset SU(n-1)\times U(1) Reduced Wigner Coefficients (RWCs) and Clebsch-Gordan Coefficients (CGCs) of SU(n), using algebraic or numeric methods, in either the canonical or a noncanonical basis. The method is recursive in that it uses simpler RWCs or CGCs with one symmetric irrep in conjunction with standard recoupling procedures. New explicit formulae for the multiplicity for SU(3) and SU(4) are used to illustrate the theory.Comment: 15 pages, LaTe