A Uniform Approach for Characterizing the Provably Total Number-Theoretic Functions of KPM and (Some of) its Subsystems

In this article we show how to extract with the use of the Buchholz-Cichon-Weiermann approach to subrecursive hierarchies from Rathjen's 1991 ordinal analysis of KPM a characterization of the provably total number-theoretic functions of KPM and some of its (most prominent) subsystems in a uniform and direct way.     

Only correlated sequences that are actively processed contribute to implicit sequence learning

The purpose of the study was to investigate how implicit sequence learning is affected by the presence of secondary information that is correlated with the primary sequence but not necessarily relevant to performance. In a previous work, we have shown that correlation plays an important role but other prerequisites may also be involved. In Experiments 1 and 2, using a task sequence learning paradigm, we found that primary sequence learning was not affected by secondary information that was sequenced but irrelevant to performance, even though the two streams of information were correlated. In contrast, in Experiment 3, we found that sensitivity to the main sequence was greater with the provision of extra sequenced information that was relevant to performance in addition to being correlated. This suggests that sequence learning was enhanced through the integration of information. We conclude that information in secondary as well as primary sequences must be actively processed if it is to have a beneficial impact. By actively processed we mean information that is selectively attended and necessary for carrying out the tasks.     

What matters in implicit task sequence learning: perceptual stimulus features, task sets, or correlated streams of information?

Implicit task sequence learning may be attributed to learning the order of perceptual stimulus features associated with the task sequence, learning a series of automatic task set activations, or learning an integrated sequence that derives from 2 correlated streams of information. In the present study, our purpose was to distinguish among these 3 possibilities. In 4 separate experiments, we replicated and extended a previous study by Heuer, Schmidtke, and Kleinsorge (2001). The presence or absence of a sequence of tasks, as well as that of a sequence of different task-to-response mappings, was manipulated independently within experiments. Evidence of implicit sequence learning was found only when correlated sequences of tasks and mappings were present. No sequence learning effects were found when only a single task sequence or a single mapping sequence was present, even when the structure of the single sequence was identical to the structure of the integrated sequence of task-mapping combinations. These results suggest that implicit task sequence learning is not dependent on either perceptual learning of stimulus features or automatic task-set activation per se. Rather, it appears to be driven by correlated streams of information.     

Slow Versus Fast Growing

We survey a selection of results about majorization hierarchies. The main focus is on classical and recent results about the comparison between the slow and fast growing hierarchies.     

Incidental sequence learning across the lifespan

The purpose of the present study was to investigate incidental sequence learning across the lifespan. We tested 50 children (aged 7-16), 50 young adults (aged 20-30), and 50 older adults (aged >65) with a sequence learning paradigm that involved both a task and a response sequence. After several blocks of practice, all age groups slowed down when the training sequences were removed, providing indirect evidence for sequence learning. This performance slowing was comparable between groups, indicating no age-related differences. However, when explicit sequence knowledge was considered, age effects were found. For both children and older adults with no or only little explicit knowledge, incidental sequence learning was largely reduced and statistically not significant. In contrast, young adults showed sequence learning irrespective of the amount of explicit knowledge. These results indicate that different learning processes are involved in incidental sequence learning depending on age.