König's Infinity Lemma and Beth's Tree Theorem

König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected (undirected) graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite (undirected) tree with a root has a infinite branch. This tree lemma can be traced to [Beth, E. W. 1955. ‘Semantic entailment and formal derivability’, Mededelingen der Kon. Ned. Akad. v. Wet., new series 18, 13, 309–42]. It is argued that Beth independently discovered the tree lemma in the early 1950s and that it was later recognized among logicians that Beth's result was a consequence of the infinity lemma. The equivalence of these lemmas is an easy consequence of a well known result in graph theory: every connected, locally finite graph has among its partial subgraphs a spanning tree.     

A structural equation modeling of executive functions,IQ and mathematical skills in primary students: Differential effects on number production,mental calculus and arithmetical problems

Though the relationship between executive functions (EFs) and mathematical skills has been well documented, little is known about how both EFs and IQ differentially support diverse math domains in primary students. Inconsistency of results may be due to the statistical techniques employed, specifically, if the analysis is conducted with observed variables, i.e., regression analysis, or at the latent level, i.e., structural equation modeling (SEM). The current study explores the contribution of both EFs and IQ in mathematics through an SEM approach. A total of 118 8- to 12-year-olds were administered measures of EFs, crystallized (Gc) and fluid (Gf) intelligence, and math abilities (i.e., number production, mental calculus and arithmetical problem-solving). Confirmatory factor analysis (CFA) offered support for the three-factor solution of EFs: (1) working memory (WM), (2) shifting, and (3) inhibition. Regarding the relationship among EFs, IQ and math abilities, the results of the SEM analysis showed that (i) WM and age predict number production and mental calculus, and (ii) shifting and sex predict arithmetical problem-solving. In all of the SEM models, EFs partially or totally mediated the relationship between IQ, age and math achievement. These results suggest that EFs differentially supports math abilities in primary-school children and is a more significant predictor of math achievement than IQ level.     

The effect of spatial frequency information and visual similarity in threat detection

In the current research, we sought to examine the role of spatial frequency on the detection of threat using a speeded visual search paradigm. Participants searched for threat-relevant (snakes or spiders) or non-threat-relevant (frogs or cockroaches) targets in an array of neutral (flowers or mushrooms) distracters, and we measured search performance with images filtered to contain different levels (high and low) of spatial frequency information. The results replicate previous work demonstrating more rapid detection of threatening versus non-threatening stimuli [e.g. LoBue, V. & DeLoache, J. S. (2008). Detecting the snake in the grass: Attention to fear-relevant stimuli by adults and young children. Psychological Science, 19, 284–289. doi:10.1111/j.1467-9280.2008.02081.x]. Most importantly, the results suggest that low spatial frequency or relatively coarse levels of visual information is sufficient for the rapid and accurate detection of threatening stimuli. Furthermore, the results also suggest that visual similarity between the stimuli used in the search tasks plays a significant role in speeded detection. The results are discussed in terms of the theoretical implications for the rapid detection of threat and methodological implications for properly accounting for similarity between the stimuli in visual search studies.     

A Comparative Analysis of the Psychological Literature on Collaboration Between Clergy and Mental-Health Professionals—Perspectives from Secular and Religious Journals: 1970–1999

A search of the psychological literature was conducted to obtain a better understanding of the issues surrounding collaboration between clergy and psychologists. An electronic search of PsycINFO for 1970–1999 ultimately yielded 52 articles in secular journals and 37 articles in religiously oriented journals that discussed collaboration. Whereas interest in collaboration peaked in religious journals during the 1980's, the number of articles on collaboration appearing in secular journals increased significantly from 1970 to 1999. Content analysis confirmed six major themes about collaboration found by A. J. Weaver, K. J. Flannelly, L. T. Flannelly, and J. E. Oppenheimer (2003). One of the most common themes was the clergy's role as frontline mental-health workers, which was mentioned significantly more often in secular than religious journals. The need for greater education and knowledge was also mentioned significantly more often in secular than religious journals. Insufficient knowledge or education was frequently seen as an obstacle to collaboration. Other factors affecting collaboration are discussed.     

The Variability and Flexibility of Gender-Typed Toy Play: A Close Look at Children's Behavioral Responses to Counterstereotypic Models

Gender differences in play behavior are well documented. However, little work has examined the issue of variability of gender-typed behaviors within individuals or within genders. We investigated whether children's gender-typed toy play behavior is (a) variable across time within individuals, and (b) variable in response to exposure to counterstereotypic models. Extensive observations (N=203) were made of 8 highly gender-typed preschool children over 4 months. Variability was assessed by examining changes in the percentage of masculine and feminine toy play across successive days in which (a) gender neutral stories were read (within-individual variability) and (b) gender counterstereotypic stories were introduced (environmental variability). Variability of gender-typed play within individuals and in response to environmental stimuli was found among girls, but not among boys.     

The influence of levels of processing on recall from working memory and delayed recall tasks

Recent research in working memory has highlighted the similarities involved in retrieval from complex span tasks and episodic memory tasks, suggesting that these tasks are influenced by similar memory processes. In the present article, the authors manipulated the level of processing engaged when studying to-be-remembered words during a reading span task (Experiment 1) and an operation span task (Experiment 2) in order to assess the role of retrieval from secondary memory during complex span tasks. Immediate recall from both span tasks was greater for items studied under deep processing instructions compared with items studied under shallow processing instructions regardless of trial length. Recall was better for deep than for shallow levels of processing on delayed recall tests as well. These data are consistent with the primary-secondary memory framework, which suggests that to-be-remembered items are displaced from primary memory (i.e., the focus of attention) during the processing phases of complex span tasks and therefore must be retrieved from secondary memory.     

The effect of message framing on self-management of chronic pain: a new perspective on intervention?

This study examines framed messages as a novel approach to promote self-management of chronic pain. Primary care patients reporting chronic pain (pain rated ≥?4 on 0-10 NRS-I for ≥3 months) were randomly assigned to receive a gain- or loss-framed message promoting self-management of pain. Impact of the framed message on behavioural self-management (including communicating with providers, relaxation, activity pacing, pleasant activities and healthy lifestyle) was assessed. Post-message, individuals in the loss-frame condition reported significantly greater interest in and more knowledge gained from the information presented in the message (p≤0.03). Loss-frame participants were significantly more likely to express confidence that they would practice relaxation (p≤0.03). Pain readiness to change, pain self-efficacy and message frame independently influenced motivation to engage in relaxation as a self-management strategy. Across all behaviours assessed, there were no observed interactions between message frame and either pain self-efficacy or pain readiness to change (p>0.05). Framing may be useful to promote pain self-management; larger trials are needed to fully evaluate its potential and to further assess the applicability of framed communication to impact a broader range of chronic conditions.     

Stronger neural dynamics capture changes in infants' visual working memory capacity over development

Visual working memory (VWM) capacity has been studied extensively in adults, and methodological advances have enabled researchers to probe capacity limits in infancy using a preferential looking paradigm. Evidence suggests that capacity increases rapidly between 6 and 10 months of age. To understand how the VWM system develops, we must understand the relationship between the looking behavior used to study VWM and underlying cognitive processes. We present a dynamic neural field model that captures both real-time and developmental processes underlying performance. Three simulation experiments show how looking is linked to VWM processes during infancy and how developmental changes in performance could arise through increasing neural connectivity. These results provide insight into the sources of capacity limits and VWM development more generally.     

Social problem solving and strategy use in young children

In the present study, the authors investigated what prosocial-assertive, passive, and coercive strategies 6-year-olds (N=257) would propose in response to stories about 2 socially challenging situations: displacing another child in a game and obtaining a toy from another child. The scenarios also varied the gender composition of the characters. Participants' verbalizations while acting out their responses using toy props fell into 13 categories of strategies. Teachers reported antisocial behavior and social competence of the participants. Girls and boys responded similarly in their general suggestions of prosocial or assertive strategies, but girls were more likely to offer prosocial strategies with other girls than with boys. Teacher-rated competence and antisocial behavior interacted in predicting coercive responses by girls but not by boys. The results demonstrate that prosocial and antisocial behaviors need to be considered in interaction to fully understand the nature of social competence.