Binary Refinement Implies Discrete Exponentiation

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary re.nement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary re.nement implies that the class of detachable subsets of a set form a set. Binary re.nement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was su.cient to prove that the Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. Presented by Victor Marek     

Relationship between annual household income and suicidal ideation: a cross-sectional study

Previous studies have shown that high income was associated with low risk of death by suicide; however, the extent to which household income reduces suicidal ideation remains unclear. We performed a survey to examine the relationship between annual household income and suicidal ideation and determine the level of annual household income at which suicidal ideation no longer decreased as income increased. In total, 94,131 members of Internet survey panels were recruited as participants by a major Japanese Internet survey company in 2016. The participants completed a self-administered questionnaire consisting of items pertaining to demographics, annual household income, and suicidal ideation. We performed logistic regression analysis with suicidal ideation as the dependent variable and income level as the independent variable. The results showed that odds ratios for suicidal ideation decreased as annual household incomes increased, with sex, age, educational level, marital status, and parenthood adjusted for; however, once annual household incomes exceeded 8 million JPY (approximately 77,700 USD), the risk of suicidal ideation no longer decreased. We conclude that suicidal ideation was negatively associated with annual household income and 8 million JPY (approximately 77,700 USD) is a threshold beyond which further increases in income no longer reduce individuals’ suicidal ideation.     

Segregation accuracy in item‐method directed forgetting across multiple tests

Two experiments examined recall across tests following item‐method directed‐forgetting instructions and the varying of presentation duration of items at study. For both immediate testing (Experiment 1) and delayed testing (Experiment 2), accurate recall of remember instruction items (R‐items) exceeded the accurate recall of forget instruction items (F‐items). However, some F‐items from study were inaccurately recalled as R‐items and R‐items from study as F‐items. Inaccurate recall persisted across tests for both immediate and delayed recall and increased across tests for immediate recall. We view the R‐item advantage in accurate recall as consistent with the account they receive more rehearsal at study than do F‐items. We view inaccurate recall as reflecting the bias to report items retrieved on an immediate test lacking instructional tags as F‐items. On delayed tests, items retrieved lacking instructional tags are first assessed against a criterion point on a memory‐strength continuum and those with strength above the criterion reported as R‐items and those below the criterion as F‐items.     

Cognitively active externalization for situated reflection

This paper offers an explanation of how collaboration leads to abstract and flexible problem solving. We asked the individual and paired subjects to indicate 3/4 of 2/3 of the area of a square sheet of paper and found that (1) they primarily folded or partitioned the paper rather than algorithmically calculating the answer, (2) they strongly tendened to backtrack and confirm their proto‐plans on externalized traces such as creases on the paper, and (3) only the paired subjects shifted to the mathematical strategy in their second trials. Based on these results, we propose that two factors, individuals' activeness in choosing and confirming the initial strategies and the frequent role exchange between task‐doing and monitoring in collaborative situations, interact in collaboration to generate various solutions differing in the degree of abstraction, which are then reflected upon by the participants to lead them to abstraction.     

Hypermnesia: The role of multiple retrieval cues

We demonstrate that encoding multiple cues enhances hypermnesia. College students were presented with 36 (Experiment 1) or 60 (Experiments 2 and 3) sets of words and were asked to encode the sets under single- or multiple-cue conditions. In the single-cue conditions, each set consisted of a cue and a target. In the multiple-cue conditions, each set consisted of three cues and a target. Following the presentation of the word sets, the participants received either three cued recall tests (Experiments 1 and 2) or three free recall tests (Experiment 3). With this manipulation, we observed greater hypermnesia in the multiple-cue conditions than in the single-cue conditions. Furthermore, the greater hypermnesic recall resulted from increased reminiscence rather than reduced intertest forgetting. The present findings support the hypothesis that the availability of multiple retrieval cues plays an important role in hypermnesia.     

The influence of instructional intervention on children's understanding of fractions

An experimental instructional program based mainly on an equal-whole schema in fractions was given to two fourth-grade classes of a Japanese elementary school. As a control, conventional teaching based on a traditional Japanese textbook was given to another fourth-grade class. The study tested the hypothesis that students given the experimental program would understand order and magnitude as central characteristics of fractions better than those who were instructed using the traditional textbook. Students in the experimental group showed better understanding of both the order of fractions and the representation of the sizes of fractions than did the textbook group. However, there were no differences between the experimental and textbook groups in the performance of assessment tasks which were less related to the equal-whole schema. These results are discussed in view of the important instructional aim of having students understand fractions.     

Complexity and goodness of dot patterns varying in symmetry

Summary Two experiments were performed to specify stimulus determinants of pattern complexity and pattern goodness. Dot patterns distributed in 3×3 and 4×4 matrices with a rectilinear frame were used in Experiment 1, and dot patterns in hexagonal frameworks with a circular frame were used in Experiment 2. The patterns were invariant for transformations of rotation or reflection, and formed symmetry groups of different orders, i.e., cyclic and dihedral groups. The complexity and goodness of the patterns depended upon such stimulus variables as follows: (1) complexity decreased with the order of symmetry groups with equal weights for cyclic and dihedral groups, whereas goodness increased with the order of both symmetry groups with different weights; (2) the simplicity and goodness of patterns with a vertical axis were greater than those with a horizontal axis and those with an oblique one; (3) the complexity of the patterns that had collinear elements with equal length was rated the simplest; (4) pattern goodness increased as a function of the number of dots and the concentrations of dot to rotation/reflection axis in 3×3 and 4 × 4 matrices. Thus, complexity and goodness of pattern differed with respect to these stimulus variables.     

Abnormal articulatory dynamics in a patient with apraxia of speech: X-ray microbeam observation

The temporal organization of articulatory movements in a patient diagnosed as having apraxia of speech was explored by means of pellet tracking techniques using an X-ray microbeam system. The results indicated that the temporal organization among different articulators of the patient was sometimes disturbed in his production of a meaningful Japanese word /deenee/. It was also observed that the pattern and velocity of the articulatory movements of the patient in repetitions of monosyllables were different from those of typical dysarthric patients.     

Prevalence of suicidal ideation in patients with atopic dermatitis

The prevalence of suicidal ideation in patients with mild, moderate, and severe atopic dermatitis between the age of 15 to 49 years were 0.21%, 6%, and 19.6%, respectively. In addition, the prevalence of homicide-suicidal ideation in mothers or fathers of patients (aged 0-14 years) with mild, moderate, and severe atopic dermatitis were 0.11%, 0.35%, and 3.28%, respectively. These results indicate that patients with atopic dermatitis or even parents of patients with atopic dermatitis have high prevalence of suicidal ideation.