Neural superstatistics for Bayesian estimation of dynamic cognitive models

Dynamics of task preparation processes revealed by effect course analysis on response times and error rates

Cuing or executing a task impacts processing pathways for task-relevant information. While there is ample evidence that processing associated with task execution changes with practice, such evidence regarding cue-induced task preparation is scarce. Here we explored practice-related changes of processing pathways by task cuing in order to assess the plasticity of task preparation. We first developed and validated a new method for the study of practice-related changes, the effect course analysis. The effect course analysis is a model-free, non-parametric method designed to reveal effect changes within an experimental session on a continuous time scale. Then we applied this method to a new study in which cued task sets were supposed to remain activated during assessment of task-relevant pathways, as potential task execution was postponed at the end of the trial. The results showed that, with little practice, task cuing amplified task-relevant pathways, whereas this effect vanished with practice, suggesting that practice prompts fundamental changes of how task cues are used for task preparation. Hence, if one cannot be certain that cognitive processing is stationary, investigating the time course of experimental effects appears to be crucial to determine how cognitive processing is influenced by practice.

Superstatistics from a dynamical perspective: Entropy and relaxation

Distributions that deviate from equilibrium predictions are commonly observed across a broad spectrum of systems, ranging from laboratory experiments to astronomical phenomena. These distributions are generally regarded as a manifestation of a quasiequilibrium state and can very often be represented as a superposition of statistics, i.e., superstatistics. The underlying idea in this methodology is that the nonequilibrium system consists of a collection of smaller subsystems that remain infinitely close to equilibrium. This procedure has been effectively implemented in a kinetic setting, but thus far, only in the collisionless regime, limiting its scope of application. In this paper, we address the effect of collisions on the relaxation process and time evolution of superstatistical systems. After confronting the superstatistical distributions with experimental and simulation data, relevant to our analysis, we first study the effect of superstatistics on entropy. We explicitly show that, in the absence of long-range interactions, the extensivity of entropy is preserved, albeit influenced by the specific class of temperature fluctuations. Then, we examine how collisions drive the system towards a global equilibrium state, characterized by a maximum entropy, by employing the relaxation time approximation. This allows us to define a dynamical version of superstatistics, characterized by a singular time-varying parameter q(t), which undergoes a continuous evolution towards equilibrium. We show how this approach enables the determination of the evolution of the underlying temperature distribution under the influence of collisions, which act as stochastic forces, gradually narrowing the temperature distribution over time.