Positional discriminability in linear orderings

Subjects were taught two eight-term linear orders of the form “A taller than B taller than C ….,” They were then asked to choose the “taller” term in all possible pairwise combinations within each series, and reaction time was measured for each pair. In addition, subjects performed a further task in which they judged whether or not two terms were adjacent in the ordering. In subsequent sessions, subjects were told that the “shortest” term on one list was taller than the “tallest” term on the other, so that the two lists were merged into a single 16-term series. They were then required to choose the “taller” term for both within-groups and between-groups pairs. Subjects did not appear to use the initial groupings in performing this task, even when given training on differential categorical codes (“tall” vs. “short”) for the two sublists. Rather, subjects in all tasks appeared to represent the items as ordered positions along an internal array, so that comparison times depended largely on the differential discriminability of the item positions. In each task decisions were made more quickly if the terms being compared were near the ends of the ordering, rather than near the middle.     

Acquiring complex partial orderings in comparison with acquiring similar-sized linear orderings

The acquisition of a 14-term partial ordering was compared with the acquisition of a 14-term linear ordering. Learning the partial ordering was found to be more difficult because of two factors: (1) Subjects do not appear to have in their knowledge systems a prototype or rule for representing a long list of comparative relations as a partial ordering structure, and (2) the partial ordering must be presented so that some of the adjacently presented premises do not contain a common element. When these two factors were controlled, the partial ordering was as easy to learn as the linear ordering. It was also found that subjects learning the partial ordering showed no evidence of a serial position learning curve, whereas subjects learning the linear ordering showed some tendency to produce a serial position learning curve.     

The role of imagery in the representation of linear orderings

Two experiments were carried out to investigate whether visual imagery was used in representing transitive linear ordering relationships. Subjects were presented with passages describing either a linear ordering or a set inclusion relationship, while being subjected to either visual or verbal interference. Performance was tested by asking subjects to judge the truth or falsity of statements concerning both the information presented in the passages and inferences that could be drawn from this information. In neither experiment was there any evidence for the linear ordering material being selectively disrupted by the visual interference task, as would have been predicted by the imagery theory. Thus it is concluded that linear orderings are probably not represented as visual images.     

The role of memory in the construction of linear orderings

Two experiments examined the construction of linear orderings (e.g., ABCD) from presented pairs of adjacent items (e.g., AB, BC, CD) in an attempt to determine why some orders of presentation are more difficult than others. Experiment 1 found order effects when participants constructed orderings but not when they simply recalled presented pairs, suggesting that order effects reflect processing difficulties encountered during construction. Experiment 2 used several different orders and successive and simultaneous visual presentation of pairs. Results showed that order effects can be attributed to the memory load imposed by certain pairs, the type of processing demanded, the need to reorder previously stored information, and the loss of information with continued rehearsal. Results strongly support the Foos, Smith, Sabol, and Mynatt (1976) model of linear construction.     

Single linear ordering versus multiple discrepant orderings in the cognitive representation of social structures

Previous studies have assumed that people have a predilection for single linear orderings, of which status congruence is a special case. Eighty-two subjects were run in a two-stage experiment to examine preference for linear orderings and whether single or multiple discrepant orderings are preferred when 1 instead of having to learn, subjects freely construct social structures, and 2 the material they are presented is more specified and less simplified than is usually the case in cognitive bias studies. In the first stage Ss were presented with sets of five individual characteristic dimensions, of which three were inherently orderable. Their task was to attribute one characteristic from each dimension to each of five fictitious persons. In the second stage, Ss were asked, for three types of influence (professional, political and cultural), to build an influence structure among the five persons constructed in the first stage. In Stage 1, linear ordering was used for three of the five dimensions. Two of these dimensions used a single ordering, while the third was only weakly related to the first two. In Stage 2, largely transitive but incomplete relations of influence were established, based on a salary-occupational hierarchy. The completeness of the relation depended on the nature of the influence.     

On L-decomposability of random orderings

In the setting of random orderings, we study conditional independence properties related to L-decomposability. We show that if a random ordering satisfies L-decomposability for any labelling of the ranks, then it is quasi-independent, provided the number of alternatives is at least 4, and each ordering has a positive probability.     

Sequences in countable nonstandard models of the natural numbers

Two different equivalence relations on countable nonstandard models of the natural numbers are considered. Properties of a standard sequence A are correlated with topological properties of the equivalence classes of the transfer of A. This provides a method for translating results from analysis into theorems about sequences of natural numbers.Most of the results in this paper appeared in the author's Ph.D. dissertation at the University of Colorado, 1985.     

On the existence of extremal cones and comparative probability orderings

We study the recently discovered phenomenon [Conder, M. D. E., & Slinko, A. M. (2004). A counterexample to Fishburn's conjecture. Journal of Mathematical Psychology, 48(6), 425-431] of existence of comparative probability orderings on finite sets that violate the Fishburn hypothesis [Fishburn, P. C. (1996). Finite linear qualitative probability. Journal of Mathematical Psychology, 40, 64-77; Fishburn, P. C. (1997). Failure of cancellation conditions for additive linear orders. Journal of Combinatorial Designs, 5, 353-365]—we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on a set of n=7 elements and showed that no extremal cones exist on a set of n?6 elements. In this paper we construct an extremal cone on a finite set of prime cardinality p if p satisfies a certain number theoretical condition. This condition has been computationally checked to hold for 1725 of the 1842 primes between 132 and 16,000, hence for all these primes extremal cones exist.     

All roads lead to violations of countable additivity

This paper defends the claim that there is a deep tension between the principle of countable additivity and the one-third solution to the Sleeping Beauty problem. The claim that such a tension exists has recently been challenged by Brian Weatherson, who has attempted to provide a countable additivity-friendly argument for the one-third solution. This attempt is shown to be unsuccessful. And it is argued that the failure of this attempt sheds light on the status of the principle of indifference that underlies the tension between countable additivity and the one-third solution.     

The countable homogeneous universal model of B 2

We give a detailed account of the Algebraically Closed and Existentially Closed members of the second Lee class B ₂ of distributive p-algebras, culminating in an explicit construction of the countable homogeneous universal model of B ₂. The axioms of Schmid [7], [8] for the AC and EC members of B ₂ are reduced to what we prove to be an irredundant set of axioms. The central tools used in this study are the strong duality of Clark and Davey [3] for B ₂ and the method of Clark [2] for constructing AC and EC algebras using a strong duality. Applied to B ₂, this method transfers the entire discussion into an equivalent dual category X ₂ of Boolean spaces which carry a pair of tightly interacting orderings. The doubly ordered spaces of X ₂ prove to be much more readily constructed and analyzed than the corresponding algebras in B ₂.     

A coding procedure for teachers

An observational technique for reliably estimating the per cent of time a student engages in appropriate and inappropriate classroom behavior is described. The regular classroom teacher can utilize the procedure without deviating from regular routine, and the obtained data can serve as a basis for dispensing token reinforcement.     

A thematic coding system for the intimacy motive

A new thematic (TAT) measure of intimacy motivation was developed and cross-validated in four separate arousal studies using three different college populations. A brief sketch of the derived thematic scoring system for intimacy motivation was presented. The goal state of the intimacy motive was defined as experiencing a warm, close, and communicative exchange with another person. In a college sample, subjects scoring high on the intimacy motive were rated by friends and acquaintances as significantly more “warm,” “natural,” “sincere,” “loving,” and “appreciative” and less “dominant,” “outspoken,” and “self-centered” than subjects scoring lower. The results were discussed in terms of the theories of Sullivan on the need for interpersonal intimacy, Maslow on growth motivation and “B-love,” Bakan on communion, and Buber on the I-Thou relation. Differences between the new coding system and the need for Affiliation (n Aff) system for scoring imaginative productions were also suggested.     

A comparison of natural-image-based models of simple-cell coding

Models such as that of Olshausen and Field (O&F, 1997 Vision Research 37 3311-3325) and principal components analysis (PCA) have been used to model simple-cell receptive fields, and to try to elucidate the statistical principles underlying visual coding in area V1. They connect the statistical structure of natural images with the statistical structure of the coding used in V1. The O&F model has created particular interest because the basis functions it produces resemble the receptive fields of simple cells. We evaluate these models in terms of their sparseness and dispersal, both of which have been suggested as desirable for efficient visual coding. However, both attributes have been defined ambiguously in the literature, and we have been obliged to formulate specific definitions in order to allow any comparison between models at all. We find that both attributes are strongly affected by any preprocessing (e.g. spectral pseudo-whitening or a logarithmic transformation) which is often applied to images before they are analysed by PCA or the O&F model. We also find that measures of sparseness are affected by the size of the filters--PCA filters with small receptive fields appear sparser than PCA filters with larger spatial extent. Finally, normalisation of the means and variances of filters influences measures of dispersal. It is necessary to control for all of these factors before making any comparisons between different models. Having taken these factors into account, we find that the code produced by the O&F model is somewhat sparser than the code produced by PCA. However, the difference is rather smaller than might have been expected, and a measure of dispersal is required to distinguish clearly between the two models.     

A test of the minimum principle requires a perceptual coding system

The minimum principle states that a perceiver will see the simplest possible interpretation of a pattern. Some theorists of human perception take this principle as a core explanatory concept. Others, especially Rock and Hochberg, hold the view that a perceptual minimum principle is untenable. Rock presents a great number of demonstrations which, in his opinion, rule out the minimum principle. Hochberg states that 'impossible' figures especially present a difficulty for this principle. It is argued here that, in order to test the minimum principle, a method is needed to describe interpretations of patterns in such a way that they can be ordered according to simplicity. To achieve this, Leeuwenberg's coding system was used. The analyses reported here of the patterns which Rock produces as evidence against the principle show that, contrary to Rock's claim, the way these patterns are preferentially perceived provides strong support for the minimum principle. Next, it is demonstrated that interpreting certain patterns as 'impossible' figures is not incompatible with the principle. Finally, it is argued that a test of the minimum principle is necessarily conflated with two other hypotheses, one concerning the metric of simplicity and one concerning the task conception of the experimental subjects.     

A predictive coding model of gaze shifts and the underlying neurophysiology

A comprehensive model of gaze control must account for a number of empirical observations at both the behavioural and neurophysiological levels. The computational model presented in this article can simulate the coordinated movements of the eye, head, and body required to perform horizontal gaze shifts. In doing so it reproduces the predictable relationships between the movements performed by these different degrees of freedom (DOFs) in the primate. The model also accounts for the saccadic undershoot that accompanies large gaze shifts in the biological visual system. It can also account for our perception of a stable external world despite frequent gaze shifts and the ability to perform accurate memory-guided and double-step saccades. The proposed model also simulates peri-saccadic compression: the mis-localization of a briefly presented visual stimulus towards the location that is the target for a saccade. At the neurophysiological level, the proposed model is consistent with the existence of cortical neurons tuned to the retinal, head-centred, body-centred, and world-centred locations of visual stimuli and cortical neurons that have gain-modulated responses to visual stimuli. Finally, the model also successfully accounts for peri-saccadic receptive field (RF) remapping which results in reduced responses to stimuli in the current RF location and an increased sensitivity to stimuli appearing at the location that will be occupied by the RF after the saccade. The proposed model thus offers a unified explanation for this seemingly diverse range of phenomena. Furthermore, as the proposed model is an implementation of the predictive coding theory, it offers a single computational explanation for these phenomena and relates gaze shifts to a wider framework for understanding cortical function.     

A comparison of MMPI-2 high-point coding strategies

High-point coding refers to the popular practice of classifying Minnesota Multiphasic Personality Inventory (Hathaway & McKinley, 1983) profiles based on which clinical scales are the most elevated. A previous review of high-point code studies (McGrath & Ingersoll, 1999a) noted marked discrepancies across studies in the rules used to define high-point codes. This study was conducted to evaluate the costs and benefits of different strategies for high-point coding. The impact of 4 rules for high-point coding on effect sizes and group sizes was evaluated. The 4 rules included requiring a minimum elevation, excluding potentially invalid protocols, restricting coding to well-defined codes, and replacing the lower scale in infrequently occurring codes with the next most elevated scale. The evidence supported the clinical utility of requiring a minimum elevation for code scales. The results were more equivocal concerning the value of well-defined coding and for not replacing the lower scale in infrequent codes. Results were surprisingly negative concerning the utility of excluding potentially invalid protocols, suggesting that guidelines developed in situations in which there is a clear motivation to distort results may not generalize to other settings.