Is approximate numerical judgment truly modality-independent? Visual, auditory, and cross-modal comparisons

The numerosity of any set of discrete elements can be depicted by a genuinely abstract number representation, irrespective of whether they are presented in the visual or auditory modality. The accumulator model predicts that no cost should apply for comparing numerosities within and across modalities. However, in behavioral studies, some inconsistencies have been apparent in the performance of number comparisons among different modalities. In this study, we tested whether and how numerical comparisons of visual, auditory, and cross-modal presentations would differ under adequate control of stimulus presentation. We measured the Weber fractions and points of subjective equality of numerical discrimination in visual, auditory, and cross-modal conditions. The results demonstrated differences between the performances in visual and auditory conditions, such that numerical discrimination of an auditory sequence was more precise than that of a visual sequence. The performance of cross-modal trials lay between performance levels in the visual and auditory conditions. Moreover, the number of visual stimuli was overestimated as compared to that of auditory stimuli. Our findings imply that the process of approximate numerical representation is complex and involves multiple stages, including accumulation and decision processes.     

大鼠注意定势转移任务模型的深入研究：种系和检测程序的影响

注意定势转移任务(attentional set-shifting task, AST)可用于特异性检测啮齿类动物前额叶皮层及其皮层下神经通路介导的认知灵活性, 是目前研究认知灵活性及其障碍神经基础的重要模型。本研究系统调查了大鼠种系和检测程序差异对AST结果的影响。通过比较Wistar和Sprague Dawley (SD)两个种系大鼠在七阶段和五阶段两种AST检测程序中的认知表现, 研究发现：(1) SD和Wistar大鼠前额叶认知功能存在差异, 后者的总体认知表现优于前者。尤其是Wistar大鼠在逆反学习阶段的达标训练次数及错误率显著低于SD大鼠, 表明Wistar大鼠具有更高的策略转换灵活性。(2)在AST测试中逆反学习和外维度定势转移是认知灵活性评价的核心指标。这两种认知转换过程分别以前期策略和注意定势建立为基础。结果显示在两种AST检测程序中Wistar和SD大鼠在逆反学习和/或外维度定势转移等复杂学习阶段的达标训练次数和错误率均高于其它简单关联学习阶段, 表明在目前实验条件下大鼠均表现出定势形成和转换困难的反应模式, 不同认知反应间的结构关系具有稳定性。这些结果提示大鼠前额叶皮质介导的认知灵活性存在种系差异, AST各阶段认知反应间的结构效度不受目前使用的大鼠种系和检测程序差异的影响, 扩展了对AST模型的认识。     

Sequential ideal-observer analysis of visual discriminations

Visual stimuli contain a limited amount of information that could potentially be used to perform a given visual task. At successive stages of visual processing, some of this information is lost and some is transmitted to higher stages. This article describes a new analysis, based on the concept of the ideal observer in signal detection theory, that allows one to trace the flow of discrimination information through the initial physiological stages of visual processing, for arbitrary spatio-chromatic stimuli. This ideal-observer analysis provides a rigorous means of measuring the information content of visual stimuli and of assessing the contribution of specific physiological mechanisms to discrimination performance. Here, the analysis is developed for the physiological mechanisms up to the level of the photoreceptor. It is shown that many psychophysical phenomena previously attributed to neural mechanisms may be explained by variations in the information content of the stimuli and by preneural mechanisms.     

Numerical discrimination is mediated by neural coding variation

One foundation of numerical cognition is that discrimination accuracy depends on the proportional difference between compared values, closely following the Weber–Fechner discrimination law. Performance in non-symbolic numerical discrimination is used to calculate individual Weber fraction, a measure of relative acuity of the approximate number system (ANS). Individual Weber fraction is linked to symbolic arithmetic skills and long-term educational and economic outcomes. The present findings suggest that numerical discrimination performance depends on both the proportional difference and absolute value, deviating from the Weber–Fechner law. The effect of absolute value is predicted via computational model based on the neural correlates of numerical perception. Specifically, that the neural coding “noise” varies across corresponding numerosities. A computational model using firing rate variation based on neural data demonstrates a significant interaction between ratio difference and absolute value in predicting numerical discriminability. We find that both behavioral and computational data show an interaction between ratio difference and absolute value on numerical discrimination accuracy. These results further suggest a reexamination of the mechanisms involved in non-symbolic numerical discrimination, how researchers may measure individual performance, and what outcomes performance may predict.     

A dual-task investigation of automaticity in visual word processing

An analysis of activation models of visual word processing suggests that frequency-sensitive forms of lexical processing should proceed normally while unattended. This hypothesis was tested by having participants perform a speeded pitch discrimination task followed by lexical decisions or word naming. As the stimulus onset asynchrony between the tasks was reduced, lexical-decision and naming latencies increased dramatically. Word-frequency effects were additive with the increase, indicating that frequency-sensitive processing was subject to postponement while attention was devoted to the other task. Either (a) the same neural hardware shares responsibility for lexical processing and central stages of choice reaction time task processing and cannot perform both computations simultaneously, or (b) lexical processing is blocked in order to optimize performance on the pitch discrimination task. Either way, word processing is not as automatic as activation models suggest.     

Values in Adolescent Males and Father-Son Relations

The role of the father in the transmission of values to adolescent sons has often been either misrepresented or neglected in the various media. Four special factors for fathers in value development are discussed: the model of masculine behavior, the communicator (listening to different views and offering a problem-solving methodology), the moral model (striving to live somewhere between the absolutist and the complete relativist), and the fallible reinforcing agent.     

Representing approximate ordering and equivalence relations

The central question considered is: given appropriate precisations of the ideas of an empirical system's approximately satisfying laws of measurement with error at most ? (for some ? ≥ 0), and of a real-valued function over its domain providing an approximate representation of its basic operations and relations with error at most δ, can it be shown that satisfaction of the laws with ‘sufficiently small’ error insures numerical representability with arbitrarily small error? Positive answers are given in the cases of ordinal and nominal measurement, together with some indications of the sizes of the errors involved. Problems of extending the theory to more complex types of measurement are discussed, some open problems and conjectures are formulated, and a relation between the ‘approximate representation’ and ‘stochastic choice model’ approaches to measurement with fallible data is established.     

流动儿童歧视知觉与心理健康关系的元分析

本研究基于心理健康双因素模型,通过运用元分析技术探讨流动儿童歧视知觉与各项心理健康指标的关系,以及调节变量对二者关系的影响,以期为提升流动儿童心理健康提供有效借鉴。经过文献检索和筛选,共纳入原始文献3篇,含49个独立样本,被试总数达到40351名。根据同质性检验结果,选择随机效应模型分析发现,流动儿童歧视知觉与积极心理健康指标存在中等程度的负相关(r=-0.323,95%CI为[-0.378,-0.266]),与消极心理健康指标存在中等程度的正相关(r = 0.41, 95%CI为[0.36,0.458])。流动儿童歧视知觉测量工具、学龄段对流动儿童歧视知觉与积极心理健康的关系存在显著的调节效应,而对流动儿童歧视知觉与消极心理健康的关系不存在显著的调节效应。同时,元回归分析结果发现,性别对二者的关系不存在显著的调节效应。后续研究应该进一步探索流动儿童歧视知觉与心理健康间的调节变量,结合中国流动儿童心理发展特点, 探索提升流动儿童心理健康水平的新路径。     

Analysis of a guided-response procedure in visual discriminations by rats.

A guided-response procedure was used to train a visual pattern discrimination by rats in a modified Sutherland box. The method consisted of guiding the animal to the correct choice by means of a retractable bridge that led to reinforcers, followed by gradually removing this prompt. This method was compared to a stimulus-fading procedure, in which the initial differences between discriminative stimuli were gradually faded until they differed only with respect to the critical dimension for discrimination, and to a trial-and-error procedure. Both gradual procedures resulted in fewer errors compared to the trial-and-error procedure. The higher efficiency of the fading procedures was attributed to less aversiveness derived from performance with few errors and to the use of step-by-step requirements relative to the criterion performance.     

When does measurement error in covariates impact causal effect estimates? Analytic derivations of different scenarios and an empirical illustration

The average causal treatment effect (ATE) can be estimated from observational data based on covariate adjustment. Even if all confounding covariates are observed, they might not necessarily be reliably measured and may fail to obtain an unbiased ATE estimate. Instead of fallible covariates, the respective latent covariates can be used for covariate adjustment. But is it always necessary to use latent covariates? How well do analysis of covariance (ANCOVA) or propensity score (PS) methods estimate the ATE when latent covariates are used? We first analytically delineate the conditions under which latent instead of fallible covariates are necessary to obtain the ATE. Then we empirically examine the difference between ATE estimates when adjusting for fallible or latent covariates in an applied example. We discuss the issue of fallible covariates within a stochastic theory of causal effects and analyse data of a within-study comparison with recently developed ANCOVA and PS procedures that allow for latent covariates. We show that fallible covariates do not necessarily bias ATE estimates, but point out different scenarios in which adjusting for latent covariates is required. In our empirical application, we demonstrate how latent covariates can be incorporated for ATE estimation in ANCOVA and in PS analysis.     

Understanding Fallible Warrant and Fallible Knowledge: Three Proposals

One of contemporary epistemology's more important conceptual challenges is that of understanding the nature of fallibility. Part of why this matters is that it would contribute to our understanding the natures of fallible warrant and fallible knowledge. This article evaluates two candidates – and describes a shared form of failing. Each is concealedly infallibilist. This failing is all‐too‐representative of the difficulty of doing justice to the notion of fallibility within the notions of fallible warrant and fallible knowledge. The article ends with a proposal for an improved (even if schematic) form of conception of fallible warrant and fallible knowledge.     

Two types of behavioral contrast in discrimination learning

Two groups of pigeons received daily discrimination training at two values on a line-tilt continuum. S+ (VI 1) and S- (EXT) intervals alternated, and a 30-sec criterion of no responding to S- was required before S+ returned. Rates of responding to S+ showed two separate contrast effects: at an intermediate stage of training a high peak rate appeared which declined, later in training, to a stable level still in excess of the VI baseline rate. The peak rate was correlated with the total number of responses to S-, while the final rate was not; suggesting that the peak rate and final rate may not be functions of the same variable. These results were compared with performance on a red-green discrimination where the two stages were not so clear. A line-tilt discrimination was repeated with fixed length S- intervals terminated by TO, and showed the same contrast magnitude in the final rate without any peak. The peak rate was interpreted as an effect of the ;punishment' contingency where responding to S- prolongs S- for 30 sec, while the final rate was taken to be analogous to previous demonstrations of contrast.     

Counting Stages

This paper defends stage theory against the argument from diachronic counting. It argues that stage theorists can appeal to quantifier domain restriction in order to accommodate intuitions about diachronic counting sentences. Two approaches involving domain restriction are discussed. According to the first, domains of counting are usually restricted to stages at the time of utterance. This approach explains intuitions in many cases, but is theoretically costly and delivers wrong counts if diachronic counting is combined with fission or fusion. On the second approach, domains of counting are usually restricted in an indeterminate way, so as to include at most one member of any maximal class of counterpart-interrelated stages (with respect to a certain utterance). This view can accommodate all the relevant intuitions about counting sentences, and it fits well with a new stage-theoretic view of reference that allows speakers to refer to both present and past stages.     

Temporal information processing and pitch discrimination as predictors of general intelligence.

In the present study, the relationship between performance on temporal and pitch discrimination and psychometric intelligence was investigated in a sample of 164 participants by means of an experimental dissociation paradigm. Performance on both temporal and pitch discrimination was substantially related to psychometric intelligence (r=.43 and r =.39). Regression analysis and structural equation modeling suggested that both psychophysical domains can be considered as valid predictors of psychometric intelligence. Both predictor variables contributed substantial portions of both shared and unique variance to the prediction of individual differences in psychometric intelligence. Thus, the present study yielded further evidence for a functional relationship between psychometric intelligence and temporal as well as pitch discrimination acuity. Eventually, findings are consistent with the notion that temporal discrimination - in addition to general aspects of sensory discrimination shared with pitch discrimination reflects specific intelligence-related aspects of neural information processing.     

Group motives in threatening contexts: When a loyalty conflict paradoxically reduces the influence of an anti‐discrimination ingroup norm

The influence of pro‐ versus anti‐discrimination ingroup norms on Swiss nationals' attitudes towards foreigners was investigated as a function of national identification and perceived material ingroup threat. As predicted, results revealed a significant interaction between identification and threat: High identifiers showed a more negative attitude than low identifiers mainly when perceived threat was high. In other words, high identifiers conformed to the pro‐discrimination norm, but showed a counter‐conformity effect for the anti‐discrimination norm. Additional results revealed that high identifiers actually disagreed with the anti‐discrimination norm when perceived threat was high, but that they were more attached to the ingroup. These findings suggest that when the ingroup norm is not an appropriate response to an ingroup threat (i.e. anti‐discrimination norm), high identifiers find themselves in a loyalty conflict: they are unable to simultaneously conform to the group norm and protect the group. This conflict was resolved through a compensatory mechanism: High identifiers distanced themselves from the ingroup norm in order to protect the group (i.e. by increasing negative attitudes towards foreigners) but reinforced other ingroup ties (i.e. by increasing attachment to the ingroup values). Copyright © 2008 John Wiley & Sons, Ltd.     

Organizing Components into Combinations: How Stage Transition Works

This paper investigates the nature of transition between stages. The Model of Hierarchical Complexity of tasks leads to a quantal notion of stage, and therefore delineates the nature of stage transition. Piaget's dialectical model of stage change was extended and precisely specified. Transition behavior was shown to consist of alternations in previous-stage behavior. As transition proceeded, the alternations increased in rate until the previous stage behaviors were “smashed” together. Once the smashed-together pieces became coordinated, new-stage behavior could be said to have formed. Because stage transition is quantal, individuals can only change performance by whole stage. We reviewed theories of the specific means by which new-stage behavior may be acquired and the emotions and personalities associated with steps in transition. Contemporary challenges in the society increasingly call for transition to postformal and postconventional responses on the part of both individuals and institutions as the examples illustrate.     

Two-stage model of visual backward masking: sensory transmission and accrual of effective information as a function of target intensity and similarity.

A functional model is used to describe the effect of target intensity and target-set similarity on backward visual masking. The model consists of two distinct stages of visual information processing. The first stage is related to sensory transduction and transmission and is assumed to require a finite and measurable amount of time during which performance remains at chance. The second stage, associated with central processing, is characterized by a negatively accelerated growth function reflecting the accrual of effective information. Results show that the duration of the transmission stage is inversely related to target intensity. Surprisingly, the rate of information accrual is an interactive function of both target intensity and target-set similarity. The pattern of results is consistent with the interpretation that both intensity and similarity mediate their effect through a common mechanism--the accrual of effective information.     

Effect of small cue-response separation on pattern discrimination in macaques (Macaca fuscata and M. mulatta)

In order to elucidate the nature of the effect of small cue-response separations on pattern discriminations by monkeys, three studies were performed. When training on a pattern discrimination with a cue-response separation was discontinued during performance at the chance level, there was no saving on the rate of learning a second task (with identical cues but a different cue-response separation) relative to the performance of naive control animals. By contrast, when training was discontinued at a performance level a little better than chance, there was significant saving on learning a second task. After learning the second task, a third task with new pattern cues was learned, with marked saving on the duration of performance at the chance level. The results indicate that during the initial stage of performance at the chance level, monkeys do not attend to cues if there is even a small separation between the cue and the response site.     

Consonant recognition with two levels of decision complexity

The perceptual tuning hypothesis can be expressed as a prediction that discrimination of a particular stimulus dimension will be enhanced if it is the only dimension requiring discrimination and not one of a set of dimensions in a multidimensional discrimination task. In previous tests of the tuning hypothesis, using speech material, the size of a message set has been manipulated as an indirect means of controlling the number of dimensions an observer is required to discriminate. In the present experiments the particular items appearing in a message set have been selected in order to control precisely the number of dimensions relevant to the discrimination task, and performance is estimated in terms of the discrimination of each relevant dimension. No evidence is found for a perceptual tuning effect even though it is argued that the conditions of the present experiment represent those most favourable for its elicitation.     

The contribution of an added counter to a fixed-ratio schedule

Although previous research showed that a visual counter increased the rate of responding on a large fixed-ratio schedule, a theoretical analysis of the factors responsible for fixed-ratio performance suggests that the primary control by number of responses since reinforcement is to weaken the performance. The present experiment employed a multiple schedule in which the same fixed-ratio value alternated with and without an added counter. It tested the hypothesis that the differential reinforcement of high-rate responding masked the attenuation of the fixed-ratio performance from the unoptimal discriminative control produced by the fixed relation between number of responses and reinforcement. In the present experiment the postreinforcement pause was consistently longer in the components with the added counter, while running rates remained comparable between the components of the multiple schedule. Both components of the multiple schedule involved differential reinforcement of high-rate responding while only the components with the added counter amplified the discriminative control by number of pecks since reinforcement.