The application of the first order system transfer function for fitting the 3-arm radial maze learning curve

The application of the first order system transfer function for fitting The California Verbal Learning Test Learning Curve

“…The mathematical background of the application of the transfer function of the fi rst order linear system in response to a stepwise input action for assessment of the learning curve was provided elsewhere (Stepanov & Abramson, 2008 ). During a free recall memory test (such as the CVLT-II), presentation of a list of words acts as a stepwise input signal that begins to act upon a participant under testing for the fi rst time on the fi rst trial.…”

“…Learning itself begins when the list of words is presented repeatedly, Trial 2 being the fi rst repetition. The solution of the background differential equation shows that B2 = 1/ τ (Stepanov & Abramson, 2008 ). The time constant reveals how much time (after trial 1) is necessary for achievement of 63% of the difference between the initial and asymptotic System transfer function for The California Verbal Learning Test Learning Curve 445 levels of the output signal (Grodins, 1963 ;Milsum, 1966 ).…”

“…We have shown that the learning curve could be more or less equally well approximated with the hyperbola, the arc cotangent, the logarithmic or exponential transfer function, but the proposed transfer function model is preferable to others because it coincides with the popular Rescorla-Wagner model of classical conditioning, and the model's coeffi cients allow psychophysiological interpretation (Stepanov & Abramson, 2008 ). The model was found to provide excellent fi ts for both group data and for individual animals under acquisition and reacquisition and was able to detect strain differences among Wistar and albino rats.…”

Assessment of the learning curve from the California Verbal Learning Test—Children's Version with the first-order system transfer function

“…The time constant reveals how much time (after Trial 1) is necessary for achievement of 63% of the difference between the initial and asymptotic levels of the output signal (Grodins, 1963;Milsum, 1966). The solution of the background differential equation shows that B2 = 1/τ (Stepanov & Abramson, 2008). Thus, regarding learning of target words 1/B2 is the number of trials after Trial 1 needed to reach 63% from the difference between the initial (B3) and asymptotic (B4) values of correctly recalled words.…”

“…The model was found to provide excellent fits for both group data and for individual animals under acquisition and reacquisition and was able to detect strain differences among Wistar and albino rats. The authors showed that the learning curve could be more or less equally well approximated with the hyperbola, the arc cotangent, the logarithmic or exponential transfer function, but the proposed transfer function model is preferable to others because it coincides with the popular Rescorla-Wagner model of classical conditioning, and the model's coefficients allow psychophysiological interpretation (Stepanov & Abramson, 2008).…”