Geometric construction of spinors in orthogonal modular categories

A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations. Quantum dimensions and twist coefficients for 1-graded simple objects (spinors) are calculated. We show that our even orthogonal modular categories admit cohomological refinements and the odd orthogonal ones lead to spin refinements. The relation with the quantum group approach is discussed.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-32.abs.htm

Suboptimal Choice Behaviour across Different Reinforcement Probabilities

Six adult roosters’ choice behaviour was investigated across a series of five experimental conditions and a series of replication of the same five experimental conditions. Stagner and Zentall (2010) found that pigeons prefer to choose an alternative with highly reliable discriminative stimuli but with less food reward over an alternative with non-discriminative stimuli but with more food reward. The current research systematically changed the probability of reinforcement associated with the discriminative stimulus through a series of experimental conditions. Experimental sessions were completed with six adult roosters. The experimental procedure was based on Stagner and Zentall’s (2010) experiment in which the suboptimal alternative with discriminative stimuli was associated with 100% reinforcement on 20% of the trials, and non-reinforcement on 80% of the trials; the optimal alternative with non-discriminative stimuli was associated with both 50% reinforcement on all trials. This research modified the probabilities of reinforcement associated with the discriminative alternative. In the first experimental condition, the probability of getting access to reinforcement was the same (50%) for each discriminative stimulus, thus, what was seen for the first time was that both alternatives were associated with non-discriminative stimuli. To insure reliability, a replication of the conditions was done after the first five experimental conditions were completed. The results showed that four of the roosters had suboptimal choice behaviour in the first five experimental conditions; however, only two of them maintained such suboptimal behaviour in the replication conditions. This result does not support the idea that the suboptimal choice behaviour with strong discriminative stimuli is a robust effect