Operating on Functions with Variable Domains

The sum, difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propositions and conditional events as three-valued indicator functions that are undefined when their condition is false. Extended operations of and, or, not and conditioning are then defined on these conditional events with variable conditions. The probabilities of the disjunction (or) and of the conjunction (and) of two conditionals are expressed in terms of the conditional probabilities of the component conditionals. In a special case, these are shown to be weighted averages of the component conditional probabilities where the weights are the relative probabilities of the various conditions. Next, conditional random variables are defined to be random variables X whose domain has been restricted by a condition on a second random variable Y. The extended sum, difference, product and conditioning operations on functions are then applied to these conditional random variables. The expectation of a random variable and the conditional expectation of a conditional random variable are recounted. Theorem 1 generalizes the standard result that the conditional expectation of the sum of two conditional random variables with disjoint and exhaustive conditions is a weighted sum of the conditional expectations of the component conditional random variables. Because of the extended operations, the theorem is true for arbitrary conditions. Theorem 2 gives a formula for the expectation of the product of two conditional random variables. After the definition of independence of two random variables is extended to accommodate the extended operations, it is applied to the formula of Theorem 2 to simplify the expectation of a product of conditional random variables. Two examples end the paper. The first concerns a work force of n workers of different output levels and work shifts. The second example involves two radars with overlapping surveillance regions and different detection error rates. One radar's error rate is assumed to be sensitive to fog and the other radar's error rate is assumed to be sensitive to air traffic density. The combined error rate over the combined surveillance region given heavy fog and moderate air traffic is computed.     

A review of processing and analysing visual metaphors in psychology

IntroductionA visual metaphor is an image depicting an incongruity in the spatial distribution of visual elements, which is not consistent with reality. In this paper, we present an overview of theoretical and empirical studies on visual metaphor processing.ObjectiveFirstly, attention is given to the spatial distribution of visual elements, which defines the type of visual metaphors as well as the meaning operations required to understand the communicative message. The paper then reviews several empirical studies that collect behavioural measures for assessing visual metaphor processing using questionnaires and exploring the role played by cognitive abilities. In line with the contemporary literature, we then present three semiotic dimensions for visual metaphor processing, namely the expression, conceptualisation, and communication. We then present a pilot study that focusses on these three dimensions. Few research studies have collected behavioural data for visual metaphors processing. This may be due to the lack of theoretical framework in the corresponding field of research. These three semiotic dimensions highlight the value of pursuing research on visual metaphors in the scope of psychology. The presented pilot study could be a starting point for the investigation of visual metaphors in the framework of psychology.ConclusionWe propose future avenues of research that consider the visual structure of metaphors and meaning operations while assessing the influence of cognitive abilities in visual metaphor processing.     

认知操作和认知方式与生态文化因素的关系

采用认识测试、查阅人类学资料、现场调查和谈话等多种方法探讨了我国不同生产方式、不同地区和不同民族４６０名成人的分析综合的认知操作和认知方式及其与生态文化因素的关系．认知测试分数的８×２×３的ＡＮＯＶＡ协方差分析表明,在分析操作水平上存在着显著的组间差异、性别差异、年龄差异和协变量（现代化影响）的效应;在综合操作上,存在着显著的组间差异、年龄差异和协变量效应;在认知方式上,存在着显著的组间差异和协变量效应．Ｓｔｅ－ｐｗｉｓｅ方法的多重回归分析表明,生态环境艰难程度、生产方式所决定的食物贮存程度、社会结构的紧密性、社会化的倾向性和现代化影响是预测被试认知操作和认知方式的有效因素．研究结果与“中国人认知操作和认知方式与生态文化关系”的理论模式所提出的预测基本一致,即研究结果支持了该理论模式．     

FUNCTIONAL ANALYSIS OF EPISODIC SELF-INJURY CORRELATED WITH RECURRENT OTITIS MEDIA

A functional analysis examined the consequences that maintained episodic self-injury and the relationship between those consequences and otitis media for a child with moderate developmental disabilities. Results indicated that self-injury occurred only during periods of otitis media. Otitis media may have served as an establishing operation related to escape from ambient noise.     

THE EFFECTS OF MEAL SCHEDULE AND QUANTITY ON PROBLEMATIC BEHAVIOR

We present 2 case examples that illustrate the effects of meal schedule and quantity on displays of problematic behavior. In the first example, self-injury displayed by a toddler with severe developmental delays was maintained by parent attention, but only when he was satiated for food. When he was food deprived, self-injury decreased but did not appear to be differentiated across low or high social conditions. In the second example, crying and self-injury displayed by an elementary-aged girl with severe disabilities were correlated: Both behaviors were associated with food quantity, and neither behavior was responsive to social stimuli. These results replicate and extend previous findings demonstrating that meal schedule or food quantity can affect problematic behavior. In the present studies, brief functional analyses of aberrant behavior provided useful information for interpreting distinct patterns of behavior displayed by each child. We discuss these results in terms of the concept of establishing operations.     

Evaluating the effects of functional communication training in the presence and absence of establishing operations

We conducted functional analyses of aberrant behavior with 4 children with developmental disabilities. We then implemented functional communication training (FCT) by using different mands across two contexts, one in which the establishing operation (EO) that was relevant to the function of aberrant behavior was present and one in which the EO that was relevant to the function of aberrant behavior was absent. The mand used in the EO-present context served the same function as aberrant behavior, and the mand used in the EO-absent context served a different function than the one identified via the functional analysis. In addition, a free-play (control) condition was conducted for all children. Increases in relevant manding were observed in the EO-present context for 3 of the 4 participants. Decreases in aberrant behavior were achieved by the end of the treatment analysis for all 4 participants. Irrelevant mands were rarely observed in the EO-absent context for 3 of the 4 participants. Evaluating the effectiveness of FCT across different contexts allowed a further analysis of manding when the establishing operations were present or absent. The contributions of this study to the understanding of functional equivalence are also discussed.     

Inducing Vocal Verbal Behavior in Children with Severe Language Delays Through Rapid Motor Imitation Responding

We conducted two experiments demonstrating the use of a rapid motor imitation sequence to evoke echoic and independent mands in three preschoolers with no vocal verbal behavior, who were unresponsive to alternative procedures. We further tested the procedure in the induction of echoics and independent tacts. The dependent variables for both experiments were echoics, mands, and tacts. In Experiment 1, we used a within subject multiple baseline design, across two mand and two tact forms, which were introduced in a counterbalanced order. In Experiment 2 we used a multiple baseline across subjects design with a tandem tact and mand training schedule, during which opportunities for echoic and independent mand training were contingent upon correct echoic and independent tact responses. Results showed that the rapid motor imitation antecedent was successful in inducing echoic and independent mands and tacts. Tacts required fewer opportunities than mands for mastery during the first experiment.     

Multiple-attribute decision making based on single-valued neutrosophic Schweizer-Sklar prioritized aggregation operator

Single-valued neutrosophic (SVN) sets can successfully describe the uncertainty problems, and Schweizer-Sklar (SS) t-norm (TN) and t-conorm (TCN) can build the information aggregation process more flexible by a parameter. To fully consider the advantages of SVNS and SS operations, in this article, we extend the SS TN and TCN to single-valued neutrosophic numbers (SVNN) and propose the SS operational laws for SVNNs. Then, we merge the prioritized aggregation (PRA) operator with SS operations, and develop the single-valued neutrosophic Schweizer-Sklar prioritized weighted averaging (SVNSSPRWA) operator, single-valued neutrosophic Schweizer-Sklar prioritized ordered weighted averaging (SVNSSPROWA) operator, single-valued neutrosophic Schweizer-Sklar prioritized weighted geometric (SVNSSPRWG) operator, and single-valued neutrosophic Schweizer-Sklar prioritized ordered weighted geometric (SVNSSPROWG) operator. Moreover, we study some useful characteristics of these proposed aggregation operators (AOs) and propose two decision making models to deal with multiple-attribute decision making (MADM) problems under SVN information based on the SVNSSPRWA and SVNSSPRWG operators. Lastly, an illustrative example about talent introduction is given to testify the effectiveness of the developed methods.     

An evaluation of the high-probability instruction sequence with and without programmed reinforcement for compliance with high-probability instructions

We assessed the effects of reinforcement and no reinforcement for compliance to high-probability (high-p) instructions on compliance to low-probability (low-p) instructions using a reversal design. For both participants, compliance with the low-p instruction increased only when compliance with high-p instructions was followed by reinforcement. These results suggest that providing reinforcement for high-p instructions may result in increased compliance to low-p instructions.     

ENHANCING THE EFFECTIVENESS OF A PLAY INTERVENTION BY ABOLISHING THE REINFORCING VALUE OF STEREOTYPY: A PILOT STUDY

An alternating treatments design compared one condition in which a child with autism was allowed to engage in stereotypy freely prior to the intervention (abolishing operation component) to a second condition without the free‐access period. Levels of stereotypy and problem behavior were lower and levels of functional play were higher in the condition with the abolishing operation component. These data provide preliminary support for the use of abolishing operations in interventions to increase the play skills of children with autism.