Some uniqueness results for PARAFAC2

Whereas the unique axes properties of PARAFAC1 have been examined extensively, little is known about uniqueness properties for the PARAFAC2 model for covariance matrices. This paper is concerned with uniqueness in the rank two case of PARAFAC2. For this case, Harshman and Lundy have recently shown, subject to mild assumptions, that PARAFAC2 is unique when five (covariance) matrices are analyzed. In the present paper, this result is sharpened. PARAFAC2 is shown to be usually unique with four matrices. With three matrices it is not unique unless a certain additional assumption is introduced. If, for instance, the diagonal matrices of weights are constrained to be non-negative, three matrices are enough to have uniqueness in the rank two case of PARAFAC2. The authors are obliged to Richard Harshman for stimulating this research, and to the Associate Editor and reviewers for suggesting major improvements in the presentation.     

Spatial compatibility of signal-response position in pointing

Two experiments are reported in which, by means of a pointing task, we studied the stimulus-position effect, i.e. the inverted U-shape form of the reaction-time function in relation to stimulus position in tasks in which stimuli and/or responses are arranged in a horizontal array. The response consisted of aiming the index finger from a central starting point at a target area on a screen. Reaction time was the main dependent variable. The spatial relation between the position of the imperative signal and the position of the response was manipulated by varying the spatial S-R compatibility and physical distance that separated the positions of stimulus and response. The stimulus-position effect was shown to depend on the compatibility of the S-R relation (Exp. 1). In Exp. 2 it was found that the modulation of the stimulus-position effect by spatial compatibility disappeared completely when the distance between the positions of stimulus and response was reduced. None of the experiments revealed that the stimulus position effect depended on signal discriminability, which renders an interpretation of this effect in terms of perceptual processes unlikely. We argue that the attentional model of spatial coding provides the most reasonable explanation of the obtained reaction-time patterns.     

Boundary regulation in family and personal systems: Perceptions of late adolescents

Examination of boundary regulation can provide family therapists with a framework to describe both the functioning of family systems and personal systems (i.e., the intrapsychic functioning of individual family members). In the present study, late adolescents' perceptions of boundary regulation within their family systems (i.e., ratings of family health, communication, leadership, expressiveness, cohesion, and family conflict) were related to regulation of their personal boundaries (i.e., self-reported personal competence, distress, and patterns of defense mechanism use). In addition, personal system variables reliably discriminated between adolescents who described their families as psychologically healthy versus psychologically unhealthy.     

An injection olfactometer for humans and a new method for the measurement of the shape of the olfactory pulse

An injection olfactometer for human psychophysical experiments is described. The olfactometer is capable of presenting, either mono- or birhinally, single odorants and binary mixtures. The pulse form of the olfactory stimulus at the exit of the olfactometer approaches a rectangular form, which makes the olfactometer well suited for olfactory reaction time measurements. Since stimulation periods are independent of the subject’s inhalation, time-intensity measurements over prolonged periods of time are possible as well. In the second part of this paper, a new technique is described for the measurement of the stimulus pulse form at the exit of the olfactometer.     

Cartesian or condillacian linguistics?

This paper intends to deal with Condillacian Linguistics. Although the Condillacian philosophy of mind and analysis of language were the most important in the late eighteenth century, none of them is mentioned in Chomsky's work (1966, Cartesian Linguistics). It would be useful for the history of Western thought if Chomsky's monumental error were generally recognized and if Condillacian Linguistics were at last to find the place it rightly deserves. The main thesis of Condillac's linguistic ideas (language is the first step in the analysis of thought) is briefly presented with reference to its context and consequences.     

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.     

Dilthey''s narrative model of human development: Necessary reconsiderations after the philosophical hermeneutics of Heidegger and Gadamer

Paper delivered at theEighth International Human Science Research Conference at Aarhus University (Denmark), 18–22 August 1989.