A simplification of a result by zellini on the maximal rank of symmetric three-way arrays

Zellini (1979, Theorem 3.1) has shown how to decompose an arbitrary symmetric matrix of ordern ×n as a linear combination of 1/2n(n+1) fixed rank one matrices, thus constructing an explicit tensor basis for the set of symmetricn ×n matrices. Zellini's decomposition is based on properties of persymmetric matrices. In the present paper, a simplified tensor basis is given, by showing that a symmetric matrix can also be decomposed in terms of 1/2n(n+1) fixed binary matrices of rank one. The decomposition implies that ann ×n ×p array consisting ofp symmetricn ×n slabs has maximal rank 1/2n(n+1). Likewise, an unconstrained INDSCAL (symmetric CANDECOMP/PARAFAC) decomposition of such an array will yield a perfect fit in 1/2n(n+1) dimensions. When the fitting only pertains to the off-diagonal elements of the symmetric matrices, as is the case in a version of PARAFAC where communalities are involved, the maximal number of dimensions can be further reduced to 1/2n(n–1). However, when the saliences in INDSCAL are constrained to be nonnegative, the tensor basis result does not apply. In fact, it is shown that in this case the number of dimensions needed can be as large asp, the number of matrices analyzed.     

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.     

Attention switching is not a fatigable process: methodological comments on Axelrod and Guzy (1972)

Guzy and Axelrod investigated auditory attention switching by means of the click-counting paradigm and concluded that attention switching is a fatigable process. In the present comment it is shown that this conclusion is based on a faulty analysis of the data: The scores subjected to the analysis of variance were transformed such that they were no longer linear combinations of the factorial effects. Reanalyzing the data in the correct way renders perfectly linear conting functions that deviate from theoretical fatigue functions. It is concluded that the attention-switching mechanism is not fatigable.     

Manifestations, acquisition and diagnostic categories of dental fear in a self-referred population

This study aimed to clarify how manifestations and acquisition relate to diagnostic categories of dental fear in a population of self-referred dental fear patients, since diagnostic criteria specifically related to dental fear have not been validated. DSM III-R diagnostic criteria for phobias were used to compare with four existing dental fear diagnostic categories, referred to as the Seattle system. Subjects were 208 persons with dental fear who were telephone interviewed, of whom a subsample of 155 responded to a mailed Dental Anxiety Scale (DAS), State-Trait Anxiety Inventory and a modified FSS-II Geer Fear Scale (GFS). Personal interviews and a Dental Beliefs Scale of perceived trust and social interaction with dentists were also used to evaluate a subsample of 80 patients selected by sex and high dental fear. Results showed that the majority of the 80 patients (66%), suffered from social embarrassment about their dental fear problem and their inability to do something about it. The largest cause of their fear (84%) was reported to be traumatic dental experiences, especially in childhood (70%). A minority of patients (16%) could not isolate traumatic experiences and had a history of general fearfulness or anxiety. Analysis of GFS data for the 155 subjects showed that fear of snakes and injuries were highest among women; heights and injections among men. Fear of blood was rarely reported. Spearman correlations between GFS individual items and DAS scores indicated functional independence between dental fear and common fears such as blood, injections and enclosures in most cases. Only in specific types of dental fear did these results support Rachman and Lopatka's contention that fears are thought to summate.(ABSTRACT TRUNCATED AT 250 WORDS)     

Some clarifications of the CANDECOMP algorithm applied to INDSCAL

Carroll and Chang have claimed that CANDECOMP applied to symmetric matrices yields equivalent coordinate matrices, as needed for INDSCAL. Although this claim has appeared to be valid for all practical purposes, it has gone without a rigorous mathematical footing. The purpose of the present paper is to clarify CANDECOMP in this respect. It is shown that equivalent coordinate matrices are not granted at global minima when the symmetric matrices are not Gramian, or when these matrices are Gramian but the solution not globally optimal.Part of this research has been supported by The Netherlands Organization for Scientific Research (NWO), PSYCHON-grant (560-267-011).     

Effect on numerosity judgment of grouping of tones by auditory channels

Previous research suggests that numerosity judgments for sequences of tones improve when the sequence is structured such that equal and small groups of tones alternate between the ears. The present. study systematically investigates the effects of the structure of tone sequences on number judgment. Tone frequency is chosen as the grouping principle instead of spatial location. In the first experiment, sequences with equal groups of 2, 3, 4, 5, 6, or 7 tones (groups alternating between 800 and 1, 250 Hz) were compared with monotonous sequences. At a slow repetition rate of the tones (280 msec onset to onset), grouping the sequence deteriorated the numerosity judgment. At II fast repetition rate of the tones (100 msec onset to onset) grouping improved numerosity judgment, but only if the group size did not exceed 4 to 5 tones. In the second experiment, the equality of group size in the sequence as a necessary condition for the improvement was investigated. It was found that tone sequences comprised of equal groups were judged more accurately in number than sequences comprised of unequal groups. These results seem to give support for the existence of an auditory subitizing process. The results of this study are also compared with the results of studies in which sequences of tones, alternating one by om! between locations or frequencies, had to be judged in number.     

Breastfeeding and offspring’s compassion and empathy in adulthood: A study with an over 30-year follow-up

This study investigated whether breastfeeding predicts offspring’s dispositional compassion and empathy from early adulthood to middle age. The parents of the participants (N = 1,394) of the Young Finns study answered questions about breastfeeding in 1983, and the participants’ compassion and empathy were evaluated in 1997‒2012 (participants were aged 20‒50 years). Breastfeeding did not predict the course of compassion or empathy in adulthood at the age of 20‒50 years. The associations remained non-significant, when adjusted for age, gender, socioeconomic factors, and a wide range of characteristics of the family environment (including mother’s gestational age; premature birth; birth weight; number of other children at home; parental mental disorder; parental relationship status; parental postnatal smoking; parental postnatal alcohol use; parenting behavior; and child’s externalizing behavior). In conclusion, breastfeeding seems not to predict offspring’s compassion or empathy in adulthood. The findings may present a hopeful perspective for children growing up with non-breastfeeding caregivers.     

Memory for multidimensional source information

Source memory may comprise recollection of multiple features of the encoding episode. To analyze the simultaneous representation and retrieval of those multiple features, a multinomial memory model is presented that measures memory for crossed dimensions of source information. The first experiment investigated the validity of the new model. The model showed an excellent statistical fit to empirical data, and the parameters of multidimensional source memory were sensitive to manipulations of source similarity on distinct dimensions. The second experiment used the model to test the hypothesis that source memory for individual context attributes is stochastically related in the case of conscious recollection but independent in the case of familiarity-based recognition judgments. The prediction was supported by the introduction of a "remember"-"know" distinction in a multidimensional source memory test.