Angular homeostasis: IV. Polygonal orbits

Some properties are discussed of regular polygons that may result from angular homeostatic processes in stable orbit. To characterize these homeostatic polygons we need to discuss the winding number, the sidedness (integer, fractional and irrational), multiplicity, envelopes, and density. A regular (i.e., equilateral, equiangular) polygon may be closed in one revolution about its unique center, in multiple revolutions, or not at all. A homeostatic polygon can be generated only if all vertices are included in a single polygon, which occurs if and only if the number of vertices and the number of revolutions required to complete the polygon are relatively prime. For the homeostatic polygon to have a finite number of sides (without repeating itself) the angle subtended by any two successive vertices at the center must be a rational multiple of 2. Biological implications of these properties are illustrated.     

Learning to argue with parents and peers

The infant's first natural response when faced with opposition or when he opposes others' actions is to cry. As this kind of behavior becomes ineffective, the responses of the individuals with which he interacts force him to adopt more conventional — especially verbal — patterns of arguing, leading him to rational argumentation. The purpose of the present paper is to observe progressions in children's earliest verbal arguments and to see how and when they learn to adjust their strategies for different kinds of opponents (peers; parents; other adults). In order to examine the emergence of such persuasive strategies, and their distribution according to the different categories of opponents, systematic audiotape recordings of two Spanish-speaking girls between 2 and 3 years were analyzed. The data suggest that, although there were some differences in how the girls argued with parents versus peers, they were only beginning to adjust their speech to make it appropriate for one or the other type of listener. In general, they resorted to one dominant strategy for all listeners (insist, repeat, cry, scream, ...). Each girl, however, developed a small number of less frequently used strategies that she reserved for a subcategory of opponents. For example, one of them, Nancy, only threatened and insulted peers, while the other, Marisa, only used please and a temporizing strategy with parents. The girls used less adaptive, more agressive strategies (e.g. threats and insults) with their peers. With one exception, all of the girls' moves were self-centered. In fact, the girls had not yet reached the stage of rational argumentation.     

Utility maximization and melioration: Internalities in individual choice

How do people go about choosing between alternatives in relatively simple settings? This study explores some of the variables that past work suggests may be relevant. Volunteer subjects worked for money in six procedures in which the probability of a payment from either of two alternatives was 1.0, but the rate of pay (i.e. the speed with which a payment was delivered or the size of the payment) interacted with the subjects recent allocation of choices, which we define as the ‘internalities’. Because of the internalities, choosing the currently more profitable alternative did not maximize total earnings. Subjects were more likely to fail to maximize when the interaction between present pay and past choices was spread over longer sequences of choices, or when the reward variable was the speed, rather than the value, of each payment. Subjects often disregarded the internalities and were instead guided by the current yields of the two alternatives, which is a frequently observed tendency, called ‘melioration’, in experiments on choices by animals. The tendency toward melioration was only partially counteracted by explicit instructions on how to maximize earnings. We discuss a theoretical framework for melioration that postulates both motivational and cognitive sources.     

Choice and multiple reinforcers

Pigeons chose between equivalent two-component mixed and multiple terminal-link schedules of reinforcement in the concurrent-chains procedure. The pigeons preferred the multiple schedule over the mixed when the components of the compound schedules were differentiated in terms of density of reinforcement, but the pigeons were indifferent when the components were differentiated in terms of number of reinforcers per cycle. Taken together, these results indicate that a local variable, the interval to the first reinforcer, but not a molar variable, the number of reinforcers, was sufficient to differentiate the components and thereby evoke preference.     

Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study

In order to make the parallel analysis criterion for determining the number of factors easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. The correlation matrices were derived from distributions of normally distributed random numbers. The independent variables are log (N–1) and log {[n(n–1)/2]–[(i–1)n]}, whereN is the number of observations;n, the number of variables; andi, the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.This research was supported by the Office of Naval Research under Contract N00014-67-A-0305-0012, Lloyd G. Humphreys, principal investigator, and by the Department of Computer Science of which Richard G. Montanelli, Jr., is a member.     

Dimensional stimulus control following brief wavelength training

Pigeons with extensive training pecking a key illuminated by a white line then had brief training with the key illuminated by 555 nanometers. This was immediately followed by a wavelength generalization test in extinction. Dimensional stimulus control about the training wavelength increased with the duration and number of reinforcements given on variable-interval 30-sec and variable-interval 10-sec schedules in Experiment I. In Experiment II, dimensional stimulus control was obtained after only 4 min of wavelength training from birds with prior and independent discrimination training. Experiment III provided groups equated in number of reinforcers with groups in Experiment I and two 8-min duration groups. Analyses, which included results from both Experiments I and III, showed that dimensional stimulus control increased: (a) more rapidly as a function of the duration of variable-interval 10-sec than variable-interval 30-sec reinforcement; (b) at the same rate across variable-interval reinforcement schedules, as a function of the number of reinforcers available during brief wavelength training.     

友伴人际品格对儿童人际品格的影响:友伴数量的调节作用及儿童群体差异

友伴是儿童发展的重要影响源。本研究从儿童积极发展的视角探讨友伴人际品格（仁慈和公正）对儿童人际品格的影响及友伴数量在其中的调节作用,并检验了儿童的群体（学段、性别、是否独生）差异状况。研究采用班级同伴提名法及儿童品格调查问卷对1555名4~9年级儿童及其互提名友伴展开调查。结果发现：（1）友伴仁慈和公正显著预测所有儿童群体的仁慈和公正;（2）儿童的友伴数量更多时,友伴公正对其公正的预测作用更显著;该调节效应仅体现在初中生和男生群体上。研究结果表明,儿童与具有积极品格特征的友伴交往对其积极品格的发展至关重要,且对于特定群体（如初中生、男生）,与越多具有积极品质的友伴交往,其受到的积极影响越大。     

数学焦虑个体近似数量加工的神经机制:一项EEG研究

近似数量加工是对大数目物体数量在不依赖逐个数数前提下的估计。行为学研究提示高数学焦虑人群近似数量加工能力下降, 但神经机制未明。本研究探讨高数学焦虑个体近似数量加工的神经机制, 比较高低数学焦虑脑电活动的差异:(1)行为上无显著组间差异; (2)高数学焦虑组的P2p成分波幅增加; (3) δ频段ERS及β频段ERD无显著数量比例效应, 而低数学焦虑组在上述指标的数量比例效应显著。本研究为高数学焦虑人群近似数量加工能力下降提供了电生理学的证据。