A generalization of Kristof's theorem on the trace of certain matrix products

Kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form \(X_1 \hat \Gamma _1 X_2 \hat \Gamma _2 \cdots X_n \hat \Gamma _n\) where the matrices \(\hat \Gamma _i\) are diagonal and fixed and theX _i vary unrestrictedly and independently over the set of orthonormal matrices. The theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints. The present paper contains a generalization of Kristof's theorem to the case where theX _i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank. The generalized theorem contains the Schwarz inequality as a special case. Various examples from the psychometric literature, illustrating the practical use of the generalized theorem, are discussed.     

Categorization reaction time,category structure,and category size in semantic memory using artificial categories

This study examined the effects of category structure and category size on categorization reaction time, artificial categories being used to obtain greater experimental control than is usually found in semantic memory research. Four artificial categories varying in structure (hierarchical and nonhierarchical) and size (8 or 16 instances) were introduced to 20 adolescent subjects over a 12-week period by means of stories, exercises, and discussions. Significantly longer categorization reaction times were required for instances from the hierarchical categories, but no set size effect was found. The application of clustering and multidimensional scaling procedures to subjects’ free recall data revealed that subjects had acquired the hierarchical structures but imposed their own structures on the other categories. These findings were interpreted within a spreading activation framework.     

Social networks,information-seeking,and the utilization of services

Voluntary participation by low-income and/ar high-risk populations in prevention-oriented human service programs is minimal and dropout rates are high. Examination of social networks as they relate to information-seeking and utilization behavior may provide a source of understanding. Two investigations are reported. The results of Study 1 indicate that high-risk referred women with denser networks attended fewer parent group sessions than did those whose networks were less dense and that the more contact a woman had with her kin, the fewer parent group sessions she attended. The results of Study 2 indicate that in a sample of low-income women participating in a supplementary food program, those women whose networks were characterized by lower density and less frequent kin contact were more likely to pursue professional child-rearing information and advice than women in denser, more kin-involved networks. In addition, a significant interaction between one's sense of competence as a parent and the structure of one's network was found to determine the overall frequency of information seeking.     

The generalization of the effects of a cognitive-behavioral treatment program for aggressive children

A cognitive-behavioral treatment program for aggressive children was assessed using 12 outcome measures classified into five categories which reflected a continuum of generalization of treatment effects. From a summer daycamp 41 children, ages 7 through 12, were selected based on aggressive behavior displayed during the first week of camp. They were randomly assigned to either a treatment group or a nontreatment control group. Treatment consisted of four weeks of coping-skills training using behavioral rehearsal and self-instruction training. Considering all 12 measures, treatment was found effective (F=2.90, p < .01). The most meaningful results included improved interpersonal problem-solving skills and a decrease in being disciplined for fighting. No changes were found, however, in physical or verbal aggression and in peer rating of aggression. Modest support for the effectiveness of these treatment procedures was identified, although caution is needed in considering their clinical utility. Further research and application appear justified.     

Variables influencing the learnability of individual signs and sign lexicons: A review of the literature

The last decade has seen an increase in investigations of the psycholinguistic and production attributes of sign and the features of sign which influence learning and memory. However, these investigations usually have not adequately delineated between the learning of individual signs as opposed to the learning of sign lexicons or sign strings and have not discussed features which might differentially influence the learning and recall of single signs and sign lexicons. The current paper reviews existing literature in the area of sign learning and identifies psycholinguistic, psychological, and production features which may influence learning and recall of individual signs as well as sign lexicons. Included in the discussion of features which are hypothesized to influence the learning of individual signs are sign translucency (rather than sign iconicity) and referential concreteness of the sign gloss. Varibles hypothesized to influence sign lexicon learning are cheremic similarity, acoustical confusion, and their relationship to proactive and retroactive interference. Implications of the effects of these variables on the learning of individual signs and on the learning of sign lexicons are discussed.     

Deep dysphasia: An analog of deep dyslexia in the auditory modality

A right-handed patient, with two left hemisphere lesions, a small one in the prefrontal lobe and a larger one in the temporal, presents an unusual syndrome: a massive deficit for oral language (expression and comprehension) contrasting with a fairly good preservation of written language (expression and comprehension). The processing of isolated words and sentences has been extensively tested with repetition and dictation tasks. The patient performs rather well with nouns, verbs, and adjectives, poorly with adverbs and function words, and completely fails with nonsense words. A remarkable feature of his repetition is the frequency of semantic paraphasias. Thus, this patient exhibits a behavior rather similar to deep dyslexia, hence the possible label "deep dysphasia." The paper presents a "preunderstanding" hypothesis to account for such behaviors.     

Lesions of the basal ganglia, thalamus, and deep white matter: Differential effects on language functions

Forty-five patients with unilateral demarcated vascular lesions in the basal ganglia, the thalamus and the deep white matter were investigated with an "aphasia battery." Patients with basal ganglia lesions performed worse than both other groups in tests of articulation, syntax, and lexical functions. The deficit of patients with basal ganglia lesions on all expressive language modalities was lateralized to the left hemisphere. Patients with left thalamic lesions showed impairments of speech fluency and in the Token Test. Patients with white matter lesions alone showed no effect of laterality in tests of language functions. The results are discussed on the basis of a recent theory of the participation of the deep nuclei in language processing.     

Attentional biases and the right-ear effect in dichotic listening

Most dichotic listening experiments permit subjects to deploy attention in any way they choose. We argue that this adds uncontrolled variance to the observed right-ear advantage. In the first experiment, more robust laterality effects were obtained in an identification task with focused than with divided attention. Such differences were not found in the second experiment, when a detection procedure was used. Virtually all the laterality effect observed in the second study could be attributed to subjects who were biased attenders, in the sense that they exhibited more intrusions from the right ear to the left than vice versa. However, rather than indicating that laterality effects are simply attentional bias, this effect can be attributed to an asymmetry of perceptual discrimination.     

Inferential processing of context: Studies of cognitively impaired subjects

Language comprehension tasks involving pronoun coreference were administered to a group of demented patients, a group of patients with cardiac disease, and groups of normal elderly persons and young adults. Pronoun coreference was constrained by either lexical, syntactic, or contextual cues. No differences were found between old and young subjects for any task. While the demented patients were impaired on all tasks, the cardiac patients were specifically impaired in the inferential processing of context.     

Acquisition of probabilities in anticipatory appraisals of stress

Processes involved in predicting stressor events were examined from the perspective of ‘associative memory models’. Subjects were exposed to alphabetic letters which supposedly represented electrical resistors used in audio equipment, in the guise of marketing research. Each letter presentation was followed either by a burst of aversive white noise, signifying ‘resistor failure’ during a brief surge of current, or by a green light, signifying ‘resistor effectiveness’. After a programmed series of presentations, subjects were asked to make several judgments about each resistor; analyses of these judgments focused on the comparative influence exerted by the alternate stimulus events. Regardless of the type of judgment (e.g. probability of future noise, frequency of earlier silent outcomes, and so on), the determining stimulus property was the cumulative frequency of earlier aversive outcomes. Moreover, the dominance of this property was not altered by manipulations designed to elevate the salience of equally relevant benign outcomes. Results were discussed with reference to models of categorical memory and predictive confidence. Circumstances under which stress predictions may be especially inaccurate were considered, as were implications of the present findings for studies of differences in categorical-frequency memory processes associated with ‘depresed mood’.