A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0

We partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman’s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem Σ12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen’s forcing and Krivine’s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories.

Effects of two different memory training approaches in very preterm-born children

Background: Little research has been conducted to assess the effect of using memory training with school-aged children who were born very preterm. This study aimed to determine whether two types of memory training approaches resulted in an improvement of trained functions and/or a generalization of the training effect to non-trained cognitive domains. Methods: Sixty-eight children born very preterm (7¬-12 years) were randomly allocated to a group undertaking memory strategy training (n=23), working memory training (n=22), or a waiting control group (n=23). Neuropsychological assessment was performed before and immediately after the training or waiting period, and at a six-month follow-up. Results: In both training groups, significant improvement of different memory domains occurred immediately after training (near transfer). Improvement of non-trained arithmetic performance was observed after strategy training (far transfer). At a six-month follow-up assessment, children in both training groups demonstrated better working memory, and their parents rated their memory functions to be better than controls. Performance level before the training was negatively associated with the training gain. Conclusions: These results highlight the importance of cognitive interventions, in particular the teaching of memory strategies, in very preterm-born children at early school age to strengthen cognitive performance and prevent problems at school.

Angiogenesis-related ultrastructural changes to capillaries in human skeletal muscle in response to endurance exercise

The ultrastructure of capillaries in skeletal muscle was morphometrically assessed in vastus lateralis muscle (VL) biopsies taken before and after exercise from 22 participants of two training studies. In study 1 (8 wk of ergometer training), light microscopy revealed capillary-fiber (C/F) ratio (+27%) and capillary density (+16%) to be higher (P ≤ 0.05) in postexercise biopsies than in preexercise biopsies from all 10 participants. In study 2 (6 mo of moderate running), C/F ratio and capillary density were increased (+23% and +20%; respectively, P ≤ 0.05) in VL biopsies from 6 angiogenesis responders (AR) after training, whereas 6 nonangiogenesis responders (NR) showed nonsignificant changes in these structural indicators (-4%/-4%, respectively). Forty capillary profiles per participant were evaluated by point and intersection counting on cross sections after transmission electron microscopy. In study 1, volume density (Vv) and mean arithmetic thickness (T) of endothelial cells (ECs; +19%/+17%, respectively) and pericytes (PCs; +20%/+21%, respectively) were higher (P ≤ 0.05), whereas Vv and T of the pericapillary basement membrane (BM) were -23%/-22% lower (P ≤ 0.05), respectively, in posttraining biopsies. In study 2, exercise-related differences between AR and NR-groups were found for Vv and T of PCs (AR, +26%/+22%, respectively, both P ≤ 0.05; NR, +1%/-3%, respectively, both P > 0.05) and BM (AR, -14%/-13%, respectively, both P ≤ 0.05; NR, -9%/-11%, respectively, P = 0.07/0.10). Vv and T of ECs were higher (AR, +16%/+18%, respectively; NR, +6%/+6%, respectively; all P ≤ 0.05) in both groups. The PC coverage was higher (+13%, P ≤ 0.05) in VL biopsies of individuals in the AR group but nonsignificantly altered (+3%, P > 0.05) in those of the NR group after training. Our study suggests that intensified PC mobilization and BM thinning are related to exercise-induced angiogenesis in human skeletal muscle, whereas training per se induces EC-thickening.

Effects of two different memory training approaches in very pretermborn children

Background: Little research has been conducted to assess the effect of using memory training with school aged children who were born very preterm. This study aimed to determine whether two types of memory training approaches resulted in an improvement of trained functions and/or a generalization of the training effect to non-trained cognitive domains. Methods: Sixty-eight children born very preterm (7-12 years) were randomly allocated to a group undertaking memory strategy training (n=23), working memory training (n=22), or a waiting control group (n=23). Neuropsychological assessment was performed before and immediately after the training or waiting period, and at a six-month follow-up. Results: In both training groups, significant improvement of different memory domains occurred immediately after training (near transfer). Improvement of non-trained arithmetic performance was observed after strategy training (far transfer). At a six-month follow-up assessment, children in both training groups demonstrated better working memory, and their parents rated their memory functions to be better than controls. Performance level before the training was negatively associated with the training gain. Conclusions: These results highlight the importance of cognitive interventions, in particular the teaching of memory strategies, in very preterm-born children at early school age to strengthen cognitive performance and prevent problems at school.

Counting is a spatial process: evidence from eye movements

Spatial-numerical associations (small numbers-left/lower space and large numbers-right/upper space) are regularly found in simple number categorization tasks. These associations were taken as evidence for a spatially oriented mental number line. However, the role of spatial-numerical associations during more complex number processing, such as counting or mental arithmetic is less clear. Here, we investigated whether counting is associated with a movement along the mental number line. Participants counted aloud upward or downward in steps of 3 for 45 s while looking at a blank screen. Gaze position during upward counting shifted rightward and upward, while the pattern for downward counting was less clear. Our results, therefore, confirm the hypothesis of a movement along the mental number line for addition. We conclude that space is not only used to represent number magnitudes but also to actively operate on numbers in more complex tasks such as counting, and that the eyes reflect this spatial mental operation.