Classroom applications of stimulus equivalence technology

We review basic concepts and methods of stimulus equivalence research and suggest applications in teaching rudimentary language arts skills in the classroom. We describe methods of establishing equivalence-based networks of matching-to-sample, writing, and naming performances. The methods may be used as a supplement to classroom instruction to assess whether standard curriculum-based approaches establish such integrated networks. Methods derived from equivalence research may be useful for remediation when traditional teaching approaches fail. Recent research suggests that direct focus on spelling performances may be required if entire networks of language arts skills are to be acquired. In addition, the equivalence relations themselves may require concentrated teaching in some children.     

颞叶皮层在灵长类不变性知觉和原型表征中的重要作用

如果要走出人工智能在感知觉领域的困境．就必须认识到人类特有的受生物现实约束的认知特点。综合分析各种证据表明,知觉和客体识别的本质不是分析千差万别的局部特征,而是提取环境中的大范围不变量（早期为拓扑特性检测）,形成并存贮一定原型表征;颞叶皮层在灵长类这种不变性知觉和原型表征中具有重要作用。     

The dynamic programming matching analysis of handwriting movement in delayed vision

Abstract: Dynamic programming matching analysis of the velocity profile of handwriting was used to examine temporally invariant characteristics of handwriting. This was done by comparing the performance of 12 subjects in writing five words under various delayed visual feedback conditions. The rate of temporally invariant handwriting decreased when delay of visual feedback was introduced. That is, the mean number of fluctuations or hesitations increased as a function of the delay time. This indicates that subjects wrote words by segmenting their movements into submovements. The relative positions of the boundaries of submovements was shown using dynamic programming matching analysis by the distribution of fluctuations along a time axis of templates. The results suggest the development of a segmented "move-and-wait" strategy under conditions of delayed vision. It was shown that in the "move" phase, subjects performed appropriate submovements as smoothly as in the no delay condition and waited during the delay until visual feedback caught up. The increased errors were due to inadequate segmentation of movements.     

Concurrent-schedule performance in dairy cows: persistent undermatching.

Performance of dairy cows responding under concurrent variable-interval variable-interval schedules of food delivery was examined, with results analyzed in terms of the generalized matching equation. In Experiment 1, bias measures indicated that crushed barley was preferred over meatmeal when these foods were available under the alternative schedules. For whole-session data, substantial undermatching of response and time-allocation ratios to obtained reinforcement ratios was evident. Postreinforcement pause time ratios approximately matched obtained reinforcement rates. Subtracting these times from total time-allocation values yielded net time-allocation ratios that undermatched obtained reinforcement ratios to a greater degree than did whole-session time-allocation ratios. In Experiment 2, substantial undermatching was evident when the same foods (hay for 2 cows, crushed barley for 2 others) were available under the alternative schedules. Food-related activities and other defined behavior not related to food were quantified by direct observation, and were found to occupy a substantial proportion (roughly 40% to 80%) of experimental sessions. Subtracting the time spent in these activities from the time allocated to each component schedule did not reduce the degree of undermatching obtained. Across all conditions in both experiments, slopes of regression lines relating behavioral outputs to environmental inputs characteristically were below 0.6, which agrees with prior findings and suggests that, contrary to suggestions in the literature, undermatching in dairy cows is not the result of using different foods under alternative schedules or differential pausing under those schedules.     

Relative sensitivity to reinforcer amount and delay in a self-control choice situation.

Rats were exposed to concurrent-chains schedules in which a single variable-interval schedule arranged entry into one of two terminal-link delay periods (fixed-interval schedules). The shorter delay ended with the delivery of a single food pellet; the longer day ended with a larger number of food pellets (two under some conditions and six under others). In Experiment 1, the terminal-link delays were selected so that under all conditions the ratio of delays would exactly equal the ratio of the number of pellets. But the absolute duration of the delays differed across conditions. In one condition, for example, rats chose between one pellet delayed 5 s and six pellets delayed 30 s; in another condition rats chose between one pellet delayed 10 s and six pellets delayed 60 s. The generalized matching law predicts indifference between the two alternatives, assuming that the sensitivity parameters for amount and delay of reinforcement are equal. The rats' choices were, in fact, close to indifference except when the choice was between one pellet delayed 5 s and six pellets delayed 30 s. That deviation from indifference suggests that the sensitivities to amount and delay differ from each other depending on the durations of the delays. In Experiment 2, rats chose between one pellet following a 5-s delay and six pellets following a delay that was systematically increased over sessions to find a point of indifference. Indifference was achieved when the delay to the six pellets was approximately 55 s. These results are consistent with the possibility that the relative sensitivities to amount and delay differ as a function of the delays.     

A monotonically convergent algorithm for orthogonal congruence rotation

Brokken has proposed a method for orthogonal rotation of one matrix such that its columns have a maximal sum of congruences with the columns of a target matrix. This method employs an algorithm for which convergence from every starting point is not guaranteed. In the present paper, an iterative majorization algorithm is proposed which is guaranteed to converge from every starting point. Specifically, it is proven that the function value converges monotonically, and that the difference between subsequent iterates converges to zero. In addition to the better convergence properties, another advantage of the present algorithm over Brokken's one is that it is easier to program. The algorithms are compared on 80 simulated data sets, and it turned out that the new algorithm performed well in all cases, whereas Brokken's algorithm failed in almost half the cases. The derivation of the algorithm is given in full detail because it involves a series of inequalities that can be of use to derive similar algorithms in different contexts.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to Willem J. Heiser and Jos M. F. ten Berge for useful comments on an earlier version of this paper.     

Concurrent choice: Effects of overall reinforcer rate and the temporal distribution of reinforcers

Six pigeons responded on a series of concurrent exponential variable-interval schedules, offering a within-subject comparison with previously published data from concurrent arithmetic variable-interval schedules. Both relative and overall reinforcer rates were varied between conditions. The generalized matching law described the data well, with undermatching much more frequent than strict matching. Time-allocation sensitivity consistently exceeded response-allocation sensitivity for both schedule types, and exponential-schedule sensitivity exceeded arithmetic-schedule sensitivity for both measures of choice. A further set of conditions using variable-interval schedules whose shortest interval was correlated with the mean interval, like arithmetic schedules, but that provided a constant conditional probability of reinforcement, like exponential schedules, produced sensitivities between those produced by conventional arithmetic and exponential schedules. Unlike previous arithmetic-schedule results, exponential sensitivity changed nonmonotonically with changes in overall reinforcer rate. The results clarify our knowledge of the effects of arithmetic and exponential schedules but confuse our understanding of the effects of overall reinforcer rate on concurrent choice.     

Molecular contingencies: reinforcement probability

Pigeons obtained food by responding in a discrete-trials two-choice probability-learning experiment involving temporal stimuli. A given response alternative, a left- or right-key peck, had 11 associated reinforcement probabilities within each session. Reinforcement probability for a choice was an increasing or a decreasing function of the time interval immediately preceding the choice. The 11 equiprobable temporal stimuli ranged from 1 to 11 sec in 1-sec classes. Preference tended to deviate from probability matching in the direction of maximizing; i.e., the percentage of choices of the preferred response alternative tended to exceed the probability of reinforcement for that alternative. This result was qualitatively consistent with probability-learning experiments using visual stimuli. The result is consistent with a molecular analysis of operant behavior and poses a difficulty for molar theories holding that local variations in reinforcement probability may safely be disregarded in the analysis of behavior maintained by operant paradigms.     

Response bias and the discrimination of stimulus duration

Pigeons discriminated stimulus duration in a psychophysical choice situation. Following presentation of any duration from a set of short duration (11 to 15 sec), responses on a red key were reinforced intermittently. Following presentation of any duration from a set of long durations (16 to 22 sec), responses on a green key were reinforced intermittently. Relative reinforcement rates were manipulated for choice responses across conditions. As relative reinforcement rates were varied, psychometric functions showed shifts in green-key responses at all durations. A signal-detection analysis showed that sensitivity remained roughly constant across conditions while response bias changed as a function of changes in relative reinforcement rate. Relative error rates tended to match relative reinforcement rates.     

A solution to the weighted procrustes problem in which the transformation is in agreement with the loss function

This paper provides a generalization of the Procrustes problem in which the errors are weighted from the right, or the left, or both. The solution is achieved by having the orthogonality constraint on the transformation be in agreement with the norm of the least squares criterion. This general principle is discussed and illustrated by the mathematics of the weighted orthogonal Procrustes problem.