Reinforcement probability and ordinal position of response in fixed-interval schedules

Four rats pressed levers and received food pellets under fixed-interval reinforcement schedules of 20, 60, and 180 seconds. The number of responses in each interval was recorded. From these data, the probability of reinforcement was determined as a function of response count. These functions were generally increasing. This finding is consistent with previous suggestions that increasing response rates within fixed intervals may be a function of response count in addition to or instead of elapsed or remaining time.     

Estimation of covariance structure models with parameters subject to functional restraints

This paper demonstrates the feasibility of using the penalty function method to estimate parameters that are subject to a set of functional constraints in covariance structure analysis. Both types of inequality and equality constraints are studied. The approaches of maximum likelihood and generalized least squares estimation are considered. A modified Scoring algorithm and a modified Gauss-Newton algorithm are implemented to produce the appropriate constrained estimates. The methodology is illustrated by its applications to Heywood cases in confirmatory factor analysis, quasi-Weiner simplex model, and multitrait-multimethod matrix analysis.The author is indebted to several anonymous reviewers for creative suggestions for improvement of this paper. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

Avoidance based on shock intensity reduction with no change in shock probability

Rats were trained on a free-operant avoidance procedure in which shock intensity was controlled by interresponse time. Shocks were random at a density of about 10 shocks per minute. Shock probability was response independent. As long as interresponse times remained less than the limit in effect, any shocks received were at the lower of two intensities (0.75 mA). Whenever interresponse times exceeded the limit, any shocks received were at the higher intensity (1.6 mA). The initial limit of 15 seconds was decreased in 3-second steps to either 6 or 3 seconds. All animals lever pressed to avoid higher intensity shock. As the interresponse time limit was reduced, the response rate during the lower intensity shock and the proportion of brief interresponse times increased. Substantial warmup effects were evident, particularly at the shorter interresponse-time limits. Shock intensity reduction without change in shock probability was effective in the acquisition and maintenance of avoidance responding, as well as in differentiation of interresponse times. This research suggests limitations on the generality of a safety signal interpretation of avoidance conditioning.     

Assessing the Predictive Accuracy of hMLH1 and hMSH2 Mutation Probability Models

Hereditary nonpolyposis colorectal cancer (HNPCC) is characterized by a susceptibility to colorectal and extra-colonic cancers. Several guidelines exist for the identification of families suspected of having HNPCC, however these guidelines lack adequate sensitivity and specificity. In an attempt to improve accuracy for the detection of individuals with HNPCC, the Wijnen pre-test probability model (1998) and Myriad Genetics Laboratory prevalence table (2004) were developed. Here we evaluate the Wijnen model and Myriad table at predicting the presence of a mutation in individuals undergoing genetic testing for HNPCC. Forty-nine patients who had undergone genetic testing for germline mutations in hMLH1 and/or hMSH2 were part of our analysis. Our results revealed that the revised Bethesda guidelines performed with the highest sensitivity for germline mutations (94.4%), however the specificity was low (12.9%). Using a 10.0% mutation probability threshold, the Wijnen model and Myriad table had sensitivities of 55.6 and 60.0%, respectively and specificities of 54.8 and 23.8%, respectively. The Wijnen model and Myriad table were poor predictors of mutation prevalence, which is shown by the areas underneath their corresponding receiver operator characteristic curves (0.616 and 0.400, respectively). The results of this study demonsrate that neither the Wijnen model nor the Myriad table are sensitive or specific enough to be used as the only indication when to offer genetic testing for HNPCC.     

Freedom,foreknowledge, and betting

Certain kinds of prediction, foreknowledge, and future-oriented action appear to require settled future truths. But open futurists think that the future is metaphysically unsettled: if it is open whether p is true, then it cannot currently be settled that p is true. So, open futurists—and libertarians who adopt the position—face the objection that their view makes rational action and deliberation impossible. I defuse the epistemic concern: open futurism does not entail obviously counterintuitive epistemic consequences or prevent rational action.     

Run length, visit duration, and reinforcers per visit in concurrent performance

The contingencies in each alternative of concurrent procedures consist of reinforcement for staying and reinforcement for switching. For the stay contingency, behavior directed at one alternative earns and obtains reinforcers. For the switch contingency, behavior directed at one alternative earns reinforcers but behavior directed at the other alternative obtains them. In Experiment 1, responses on the main lever, in S1, incremented stay and switch schedules and obtained a stay reinforcer when it became available. Responses on the switch lever changed S1 to S2 and obtained switch reinforcers when available. In S2, neither responses on the main lever nor on the switch lever were reinforced, but a switch response changed S2 to S1. Run lengths and visit durations were a function of the ratio of the scheduled probabilities of reinforcement (staying/switching). From run lengths and visit durations, traditional concurrent performance was synthesized, and that synthesized performance was consistent with the generalized matching law. Experiment 2 replicated and extended this analysis to concurrent variable-interval schedules. The synthesized results challenge any theory of matching that requires a comparison among the alternatives.     

Human symbolic matching-to-sample performance: Effects of reinforcer and sample-stimulus probabilities

Four experiments, each with 6 human subjects, varied the distribution of reinforcers for correct responses and the probability of sample-stimulus presentation in symbolic matching-to-sample procedures. Experiment 1 held the sample-stimulus probability constant and varied the ratio of reinforcers obtained for correct responses on the two alternatives across conditions. There was a positive relation between measures of response bias and the ratio of reinforcers. Experiment 2 held the ratio of reinforcers constant and varied the sample-stimulus probability across conditions. Unlike previous studies that used pigeons as subjects, there was a negative relation between bias and the ratio of sample-stimulus presentations. In Experiment 3, the sample-stimulus probability and the reinforcer ratio covaried across conditions. Response bias did not vary systematically across conditions. In Experiments 1 to 3, correct responses were reinforced intermittently. Experiment 4 used the same procedure as Experiment 3, but all correct responses now produced some scheduled consequence. There was a positive relation between response bias and the ratio of reinforcers. The results suggest that human performance in these tasks was controlled by both the relative frequency of reinforced responses and the relative frequency of nonreinforced responses.     

QUANTUM PHYSICS, PHILOSOPHY, AND THE IMAGE OF GOD: INSIGHTS FROM WOLFGANG PAULI

Abstract. Nobel Laureate in physics Wolfgang Pauli studied philosophy and the history of ideas intensively, especially in his later years, to form an accurate ontology vis-à-vis quantum theory. Pauli's close contacts with the Swiss psychiatrist C.G. Jung gave him special qualifications for also understanding the basic problems of empirical knowledge. After Pauli's sudden death in 1958, this work was maintained mainly in his posthumously published correspondence, which so far extends only to 1939. Because Pauli's view differs essentially from the direction physics research took after the deaths of the founding fathers of quantum theory, this article attempts to describe the main features in Pauli's revolutionary thought, which is based on nature's "epistemological lesson" as revealed by Pauli's atomic research. Pauli's conclusions have important implications for various issues in Western culture, not least with the limits of science and the relation of science to religion.     

Molar versus local reinforcement probability as determinants of stimulus value.

During one component of a multiple schedule, pigeons were trained on a discrete-trial concurrent variable-interval variable-interval schedule in which one alternative had a high scheduled rate of reinforcement and the other a low scheduled rate of reinforcement. When the choice proportion between the alternatives matched their respective relative reinforcement frequencies, the obtained probabilities of reinforcement (reinforcer per peck) were approximately equal. In alternate components of the multiple schedule, a single response alternative was presented with an intermediate scheduled rate of reinforcement. During probe trials, each alternative of the concurrent schedule was paired with the constant alternative. The stimulus correlated with the high reinforcement rate was preferred over that with the intermediate rate, whereas the stimulus correlated with the intermediate rate of reinforcement was preferred over that correlated with the low rate of reinforcement. Preference on probe tests was thus determined by the scheduled rate of reinforcement. Other subjects were presented all three alternatives individually, but with a distribution of trial frequency and reinforcement probability similar to that produced by the choice patterns of the original subjects. Here, preferences on probe tests were determined by the obtained probabilities of reinforcement. Comparison of the two sets of results indicates that the availability of a choice alternative, even when not responded to, affects the preference for that alternative. The results imply that models of choice that invoke only obtained probability of reinforcement as the controlling variable (e.g., melioration) are inadequate.