An approach to geometry of visual space with no a priori mapping functions: Multidimensional mapping according to Riemannian metrics

A method of multidimensional mapping is described which constructs a configuration of points {P_i} in a Euclidean map of Riemannian space of constant curvature (hyperbolic, Euclidean, and elliptic) from the dissimilarity matrix (d_ij). The method was applied to the distance matrix in visual space where stimulus points Q_i were either small light points in the dark or small black points in the illuminated field surrounded by white curtains and d_ij represent scaled values of perceptual distances. Configuration of points {Q_i} were at intersections of parallel or distance alleys and horopters for the subject in the horizontal plane of the eye level. In contrast to the theoretical equations for {Q_i} by Luneburg and Blank, no a priori assumption on mapping functions between {Q_i} and {P_i} is necessary in this procedure to fit theoretical curves to {P_i} in the Euclidean map. The data were accounted for better by equations in the hyperbolic plane than by ones in the Euclidean plane. Discussions are made on robustness of Euclidean representation and on how to approach geometry of visual space as a dynamic entity under more natural conditions than the traditional frameless condition for alley and horopter experiments.     

A mathematical analysis of a natural class of partitions of a graph

Any finite graph (nondirected, no loops) can be coupled with its complementary graph producing what we term a completed graph. This paper studies completed graphs in the context of a structural concept called stratification that is motivated by theoretical work in social psychology and sociology. A completed graph is stratified in case its node (vertex) set can be divided into two nonempty subsets with exactly one of the two types of ties holding between every pair of nodes from distinct sets. A completed graph is totally stratified in case every one of its nontrivial completed subgraphs is stratified. The first part of the paper relates the concept of stratification to the familiar graph property of connectedness. In particular, a completed graph is totally stratified if and only if it does not have a four point completed subgraph that is connected in both the original graph relation and its complementary relation. Using the concept of stratification, completed graphs can be decomposed uniquely into taxonomic structures, that is, nested sets of partitions. An algorithm for the decomposition based on the work with the concept of stratification is developed. The relationship between the notion of stratification and the ideas in balance theory is examined, and stratification is viewed as a generalization of Davis' notion of clustering. It turns out that the concepts of clique, status, and structural equivalence used throughout the social networks literature can be defined in an interesting way for completed graphs. Cliques are sets of nodes with similar internal links and statuses are sets of nodes with similar external links. Structurally equivalent sets are both cliques and statuses. The concepts of status and structural equivalence are closely related to the decomposition algorithm. In particular, for any totally stratified completed graph, the set of all statuses and the set of all maximal structurally equivalent sets can be generated by mathematical operations performed on the taxonomic decomposition of the completed graph. Finally some of our resuls are informally related to the blockmodeling approach to analyzing social network data discussed in several previous Journal of Mathematical Psychology articles.     

Passing markers: A theory of contextual influence in language comprehension

Most Artificial Intelligence theories of language either assume a syntactic component which serves as “front end” for the rest of the system, or else reject all attempts at distinguishing modules within the comprehension system. In this paper we will present an alternative which, while keeping modularity, will account for several puzzles for typical “syntax first” theories. The major addition to this theory is a “marker passing” (or “spreading activation”) component, which operates in parallel to the normal syntactic component.     

The effect of repetition on search through active memory

Short lists of digits, some of which contained repeated items, were searched in memory. Repeated items were recognized faster than non-repeated items. Search times for non-repeated items in lists with a repeat were slightly faster than those for lists of the same length in which no items were repeated. A serial position effect was found such that items at either the beginning or end of the memory list were responded to faster than items in the middle of the list. Neither the repeated digit effect nor the serial position effect support serial exhaustive search. An empirical equation was found by which response time is predicted by the log proportion of items in a memory list that match the test stimulus. These results are compatible with the notions of neural pathway activation and trace strength.     

From individual to group impressions: Availability heuristics in stereotype formation

When subjects are presented with information about the attributes of individuals and are then asked to make judgments about the characteristics of the group composed of those individuals, the group impression may depend on the way in which data on individuals are organized in memory. Experiment 1 demonstrated that under conditions of low memory load (16 instances of person-trait pairings), subjects organize their perceptions of a group around the characteristics of its individual members, whereas under high memory load (64 instances of person-trait pairings), subjects organize trait information in an undifferentiated way around the group as a whole. Under low memory load, subjects distinguish between repeated occurrences of a trait in the same individual and comparable repeated occurrences of that trait in different individuals; under high memory load, subjects do not make such a differentiation. Subjects' judgments about the frequency of categories of traits were related to the ease of recall of category instances, as predicted by an availability heuristic. Experiments 2 and 3 demonstrated that group members who are most available in memory will be disproportionately represented in the group impression. Specifically, the proportion of extreme individuals in a group was retro-spectively overestimated; this was true for both physical stimuli (height) and social stimuli (criminal acts).     

An attempt to understand students' understanding of basic algebra

This paper reports the results obtained with a group of 24 14-year-old students when presented with a set of algebra tasks by the Leeds Modelling System, LMS. These same students were given a comparable paper-and-pencil test and detailed interviews some four months later. The latter studies uncovered several kinds of student misunderstandings that LMS had not detected. Some students had profound misunderstandings of algebraic notation: Others used strategies such as substituting numbers for variables until the equation balanced. Additionally, it appears that the student errors fall into several distinct classes: namely, manipulative, parsing, clerical, and “random.” LMS and its rule database have been enhanced as the result of this experiment, and LMS is now able to diagnose the majority of the errors encountered in this experiment. Finally, the paper gives a process-oriented explanation for student errors, and re-examines related work in cognitive modelling in the light of the types of student errors reported in this experiment. Misgeneralization is a mechanism suggested to explain some of the mal-rules noted in this study.     

Why John married Mary: Understanding stories involving recurring goals

A story understander needs a great deal of knowledge about people's goals. This knowledge is needed to infer explanations for the behavior of the characters in a story. Sometimes a character's behavior cannot be explained in terms of a particular goal, but only in relation to a set of recurring goals that a character anticipates having. The concept of goal subsumption is introduced to deal with these situations. Goal subsumption is a way of planning for many goals at the same time. It occurs in three different types of story situations, each of which has its own rules for recognition and understanding.     

Attention to eye contact opportunity and facial motion by three-month-old infants

Thirty-two 3-month-old infants participated in two experiments showing color videotapes of facial stimuli in a paired comparison format. In Experiment 1, the experimenter, serving as the stimulus, looked either directly at the infant or averted his gaze to the side; the face was presented either still or in motion. Eye contact opportunity had no effect while motion of the head was an effective attractor of visual fixation. In Experiment 2, the amount of available eye contact opportunity was parametrically varied by occluding the eyes with different patterns of blinking, each at the same rate. The no-motion 100% eye contact available condition received less attention than the three blinking stimuli, which were all equally attended to, though they varied with respect to the amount of eye contact opportunity they afforded. The contrast in effect of eye contact availability and rather subtle stimulus motion would imply that 3-month-old infants are comparatively insensitive to being the object of another's visual regard.     

Research note: The accuracy of group majorities for disjunctive and conjunctive decision tasks

For complex group decision tasks which can be described in terms of establishing the truth value of conjunctive (and) or disjunctive (or) composite propositions, the advantage for group judgmental accuracy of disaggregating the decision task into separate individual evaluations of the truth value of each component atomic proposition in the composite is investigated. For true propositions it is shown that disaggregation is preferable for conjunctive tasks, but not for disjunctive tasks; while the reverse is true for false propositions.     

A critique of top-down independent levels models of speech production: Evidence from non-plan-internal speech errors

A number of speech errors are examined which are difficult to account for by top-down serial processing models of speech production which hove independent levels of processing. In particular, most of these errors are characterized by the presence of an interfering element which is external to the utterance under current construction. This paper has two main aims: to classify these errors, and to examine the constraints upon them. It is found that phonological similarity between the target and intrusion is a major determinant of error occurrence. The consequences for models of speech production are discussed in a framework consisting of the architecture and control structure of those models. A particular model to account for these data is proposed, consisting of a spreading activation lexical network.     

Language loss in bilingual Chicano children

The results of two studies on language loss in bilingual Chicano children are reported. In Study I, focusing on normal language acquisition in balanced bilinguals, 41 children in kindergarten through fourth grade were administered the Bilingual Language Acquisition Scale (BLAS), an instrument testing comprehension and production of the following features: number, gender, word order, relatives, conditionals, and Spanish subjunctive and its English equivalents. Most development occurred between kindergarten and the upper grades in the English Comprehension and Production subscales. In the production of Spanish, significant differences appeared between kindergarten and the upper grades to grade three. Unexpectedly, in the fourth grade, performance dropped sharply, with children performing almost at the kindergarten level. There were no significant differences by grade in Spanish comprehension. Most significant differences among grades were produced in the more complex categories (conditionals, Spanish subjunctive/English equivalents, and relatives) in the production subscales in English and Spanish. By fourth grade, in Spanish (and sometimes by third grade), children were performing with significantly lower accuracy than the younger children, particularly in the more complex structures (subjunctive and conditionals, for example). In Study II, 32 of the original subjects were retested two years later using the same instruments and procedures. While performance in English continued to improve for the sample as a whole, performance in Spanish production deteriorated to a significant degree. In Spanish, significant differences in performance between the two administrations were found, both for the scale as a whole and for the following categories: past tense, relatives, and the subjunctive. The influence of personal history and language use patterns was tested. The most severe incidence of loss occurred among children who tended to use both English and Spanish with the same speaker.     

Male alcoholics,secondary psychopathy and Eysenck's theory of personality

The scores of several samples of male alcoholics and others on the MAC Scale (an MMPI-derived scale for the differentiation of male alcohol abusers from non-substance-abusing male psychiatric outpatients) are summarized, and the responses of the false negatives and false positives from the scale's standardization samples are analyzed. The following 7conclusions were reached: (1) There are two broad classes of male alcoholics—those who fall into the E + N + quadrant of secondary psychopathy and those who fall into the E - N + quadrant of neurotic introversion; (2) Unselected runs of male alcoholics populate these two quadrants in a quite stable ratio of 17 to 3, respectively; (3) Pari passu, Eysenck's placement of alcoholics in the E + N + quadrant will be upheld in approximately 85% of the cases while those who hold that alcoholics are ‘dysthymics who also drink too much’ will find themselves in error in approximately similar degree.     

Some deterministic models of concept identification

It is shown that deterministic models can compete effectively with stochastic models in summarizing concept identification behavior. Three groups of deterministic models are examined. Examination of individual learners' trial by trial behavior in a concept experiment shows: (1) One person exhibited behavior consistent with a Hypothesis Permutation (HP) model despite being a nonlearner who showed no evidence of improvement over a period of 24 trials. However, when all 50 persons studied in each of two treatment groups were examined, only 22 members of one group and 10 of the other showed no inconsistencies with deterministic local consistency assumptions. (2) Certain deterministic computer programs could find at least one satisfactory order for predicting all responses by 18 of the 22 consistent solvers and 6 of the 10 consistent solvers, respectively, in the two groups just mentioned. For these 24 persons, then, a less restrictive deterministic model is adequate than for the others. (3) Those 38 original members of the first treatment group who met a stringent learning criterion were compared with respect to predictions generated by stochastic and mathematized deterministic models. One deterministic model (RSS-U 9-state) is in some respects the best of the models examined, but this success is a partial reflection of estimating eight parameters from the data.     

Workers' central life interests and personality characteristics

Industrial workers who perceive work as their central life interest (CLI) also describe themselves as having a higher level of decisiveness, initiative, and supervisory ability than workers with other CLI orientations. Workers with CLI orientations in nonwork institutions have the lowest scores on decisiveness, need for occupational achievement, and initiative, and the highest need for job security, of the groups studied. Workers with no anchored CLI had the highest need for self-actualization and need for occupational achievement, of all groups. These personality characteristics are seen as consistent with the CLI orientations of individual workers, suggesting that the personality does “fit” some institutional setting, but not necessarily all those in which the individual functions.     

Caregiver behavior in center and family day care

In an effort to examine relationships between variations within day care settings and adult caregiving behaviors the social experiences of 40 toddlers and their caregivers in family and center care were systematically observed. Caregivers were interviewed and conditions of caregiving recorded. Caregivers in both settings with fewer children in their care, who worked shorter hours, with less housework responsibilities engaged in more facilitative social stimulation, expressed more positive affect, were more responsive, and less restrictive and negative. Family day care caregivers who worked in spaces specifically designed to be safe and appropriate for children were less restrictive of toddler activity. Adult-child ratio and caregiver training appeared to be the best indicators of quality care in center day care, while a safe and appropriate caregiving environment and small groups appeared as quality indicators in family day care.