Generalized eigenvalue problems with positive semi-definite matrices

In a recent paper in this journal McDonald, Torii, and Nishisato show that generalized eigenvalue problems in which both matrices are singular can sometimes be solved by reducing them to similar problems of smaller order. In this paper a more extensive analysis of such problems is used to sharpen and clarify the results of McDonald, Torii, and Nishisato. Possible extensions are also indicated. The relevant mathematical literature is reviewed briefly.     

Scene perception: Detecting and judging objects undergoing relational violations

Five classes of relations between an object and its setting can characterize the organization of objects into real-world scenes. The relations are (1) Interposition (objects interrupt their background), (2) Support (objects tend to rest on surfaces), (3) Probability (objects tend to be found in some scenes but not others), (4) Position (given an object is probable in a scene, it often is found in some positions and not others), and (5) familiar Size (objects have a limited set of size relations with other objects). In two experiments subjects viewed brief (150 msec) presentations of slides of scenes in which an object in a cued location in the scene was either in a normal relation to its background or violated from one to three of the relations. Such objects appear to (1) have the background pass through them, (2) float in air, (3) be unlikely in that particular scene, (4) be in an inappropriate position, and (5) be too large or too small relative to the other objects in the scene. In Experiment I, subjects attempted to determine whether the cued object corresponded to a target object which had been specified in advance by name. With the exception of the Interposition violation, violation costs were incurred in that the detection of objects undergoing violations was less accurate and slower than when those same objects were in normal relations to their setting. However, the detection of objects in normal relations to their setting (innocent bystanders) was unaffected by the presence of another object undergoing a violation in that same setting. This indicates that the violation costs were incurred not because of an unsuccessful elicitation of a frame or schema for the scene but because properly formed frames interfered with (or did not facilitate) the perceptibility of objects undergoing violations. As the number of violations increased, target detectability generally decreased. Thus, the relations were accessed from the results of a single fixation and were available sufficiently early during the time course of scene perception to affect the perception of the objects in the scene. Contrary to expectations from a bottom-up account of scene perception, violations of the pervasive physical relations of Support and Interposition were not more disruptive on object detection than the semantic violations of Probability, Position and Size. These are termed semantic because they require access to the referential meaning of the object. In Experiment II, subjects attempted to detect the presence of the violations themselves. Violations of the semantic relations were detected more accurately than violations of Interposition and at least as accurately as violations of Support. As the number of violations increased, the detectability of the incongruities between an object and its setting increased. These results provide converging evidence that semantic relations can be accessed from the results of a single fixation. In both experiments information about Position was accessed at least as quickly as information on Probability. Thus in Experiment I, the interference that resulted from placing a fire hydrant in a kitchen was not greater than the interference from placing it on top of a mail ? in a street scene. Similarly, violations of Probability in Experiment II were not more detectable than violations of Position. Thus, the semantic relations which were accessed included information about the detailed interactions among the objects—information which is more specific than what can be inferred from the general setting. Access to the semantic relations among the entities in a scene is not deferred until the completion of spatial and depth processing and object identification. Instead, an object's semantic relations are accessed simultaneously with its physical relations as well as with its own identification.     

Perception of autonomic reactions and actual heart rate in phobic patients

The relationship between perceived physiological arousal and actual heart-rate reactions was studied in two behavioral test situations. The subjects were 70 phobic patients (34 social phobics and 36 claustrophobics) who were given the general form of the Autonomic Perception Questionnaire about 1 month before the respective behavioral test and the specific form immediately after the test. The results showed significant correlations between APQ and actual heart rate for the social phobics, while the picture was more complicated for the claustrophobics. The implications of these results are discussed.This research was supported by Grant 05452 from the Swedish Medical Research Council.     

The influence of relative frequencies of pure and mixed stimuli on mixture suppression in taste

In experiments on saltiness suppression in NaCL-sucrose mixtures, the amount of suppression depends not only on the suppressing sucrose component in the mixture, but also on the relative frequencies of pure NaCL stimuli and mixed stimuli in the series. The observed variation of mixture suppression as a function of these frequencies can be explained by Helson’s adaptation level theory.     

Behavior analysis of cigarette smoking

Patterns of cigarette smoking, treated as series of discrete events in time, were investigated with a variety of quantitative techniques designed to characterize individual subject smoking series and to illuminate the relationship between cigarette smoking and environmental events. Data were collected from a total of 35 subjects who were either participants in residential laboratory studies or in a smoking cessation program. Cigarette smoking events were found to be fairly irregularly distributed with respect to time within individual subject series. However, strong dependencies were found between the occurrence in time of individual acts of cigarette smoking and coffee drinking. In addition, the distribution and frequency of smoking events throughout one-hour activity sequences were found to be dependent upon the nature of the activity, and the temporal scheduling of activities was found to affect several quantitative indices of smoking patterns.     

A constructivist analysis of the Rotter I-E scale1

A conception of locus of control attribution was advanced as an alternative to the generalized expectancy view presented by Rotter. That alternative stems from regarding the individual as actively constructing a pattern of specific choice consequence relations out of his/her ongoing experience. An integration of structural and factor approaches was used to analyze the Rotter I-E scale. The structural analysis categorized items on four dimensions (focus, area, self-attribution and world attribution) and indicated that the I-E scale unevenly represents the domain it encompasses. Nevertheless, specification of that structural matrix helps to provide a more comprehensive framework for interpreting I-E response patterns of 216 high school juniors and seniors. For example, male responses cohered around asserting active control over tasks hut attributing control to external sources with regard both to personal issues and to more abstract systems-related issues. Females organized their senses of self-efficacy with a central theme being that of a passive agent stance, plus an expectation that circumstances would provide equality of opportunities to which they could respond. Thus the present approach has demonstrated its utility in interpreting I-E findings and its conceptual advantage for personality research on locus of control and on similiar attributional characteristics.     

Concurrent schedule assessment of food preference in cows

Six dairy cows (Bos taurus) were trained on several pairs of concurrent variable-interval schedules with different types of food available on each alternative. The required response was a plate press made by the animal's muzzle. Performance generally replicated that found with other species. The generalized matching law accounted for the preference data, showing that food preference could be quantitatively analyzed as a special case of response bias. The preference functions showed that the response- and time-allocation ratios were not as extreme as obtained reinforcement rate ratios (undermatching).     

A study of orientation errors in response to Kohs-type figures(1)

In order to elucidate the nature of the orientation errors encountered when subjects are required to reproduce Kohs-type figures, subjects drawn from a culture where such errors are reported to be relatively common were required to reproduce orientation of simple figures. It was found that the responses made in the case of square figures showed a definite drift towards a “stable” orientation; the drift observed in the case of circular stimuli was too weak to permit an unambiguous interpretation. The relevance of these data to previous data on cross-cultural differences in responses to Kohs-type stimuli is briefly examined.