Fitting model-based psychometric functions to simultaneity and temporal-order judgment data: MATLAB and R routines

Research on temporal-order perception uses temporal-order judgment (TOJ) tasks or synchrony judgment (SJ) tasks in their binary SJ2 or ternary SJ3 variants. In all cases, two stimuli are presented with some temporal delay, and observers judge the order of presentation. Arbitrary psychometric functions are typically fitted to obtain performance measures such as sensitivity or the point of subjective simultaneity, but the parameters of these functions are uninterpretable. We describe routines in MATLAB and R that fit model-based functions whose parameters are interpretable in terms of the processes underlying temporal-order and simultaneity judgments and responses. These functions arise from an independent-channels model assuming arrival latencies with exponential distributions and a trichotomous decision space. Different routines fit data separately for SJ2, SJ3, and TOJ tasks, jointly for any two tasks, or also jointly for the three tasks (for common cases in which two or even the three tasks were used with the same stimuli and participants). Additional routines provide bootstrap p-values and confidence intervals for estimated parameters. A further routine is included that obtains performance measures from the fitted functions. An R package for Windows and source code of the MATLAB and R routines are available as Supplementary Files.

Converging evidence that common timing processes underlie temporal-order and simultaneity judgments: a model-based analysis

Perception of simultaneity and temporal order is studied with simultaneity judgment (SJ) and temporal-order judgment (TOJ) tasks. In the former, observers report whether presentation of two stimuli was subjectively simultaneous; in the latter, they report which stimulus was subjectively presented first. SJ and TOJ tasks typically give discrepant results, which has prompted the view that performance is mediated by different processes in each task. We looked at these discrepancies from a model that yields psychometric functions whose parameters characterize the timing, decisional, and response processes involved in SJ and TOJ tasks. We analyzed 12 data sets from published studies in which both tasks had been used in within-subjects designs, all of which had reported differences in performance across tasks. Fitting the model jointly to data from both tasks, we tested the hypothesis that common timing processes sustain simultaneity and temporal order judgments, with differences in performance arising from task-dependent decisional and response processes. The results supported this hypothesis, also showing that model psychometric functions account for aspects of SJ and TOJ data that classical analyses overlook. Implications for research on perception of simultaneity and temporal order are discussed.

On the well-posedness of a mathematical model for lithium-ion batteries.

We discuss the well-posedness of a mathematical model that is used in the literature for the simulation of lithium-ion batteries. First, a mathematical model based on a macrohomogeneous approach is presented, following previous work. Then it is shown, from a physical and a mathematical point of view, that a boundary condition widely used in the literature is not correct. Although the errors could be just sign typos (which can be explained as carelessness in the use of d/dx versus d/dn, with n the outward unit vector) and authors using this model probably use the correct boundary condition when they solve it in order to do simulations, readers should be aware of the right choice. Therefore, the deduction of the correct boundary condition is done here, and a mathematical study of the well-posedness of the corresponding problem is presented.