Using the Cayley-Hamilton theorem with N-partitioned matrices

A definition is given for the characteristic equation of anN-partitioned matrix. It is then proved that this matrix satisfies its own characteristic equation. This can then be regarded as a version of the Cayley-Hamilton theorem, of use withN-dimensional systems.

A brief index of affective job satisfaction

This article responds to criticisms that affective job satisfaction research suffers serious measurement problems: Noncomparable measures; studies conceptualizing job satisfaction affectively but measuring it cognitively; and ad hoc measures lacking systematic development and validation, especially across populations by nationality, job level, and job type. We address these problems through a series of qualitative (total N = 28) and quantitative (total N = 901) studies to systematically develop and validate a short affective job satisfaction measure ultimately deriving from Brayfield and Rothe’s (1951) job satisfaction index. Unlike any previous job satisfaction measure, the resulting four-item Brief Index of Affective Job Satisfaction is overtly affective, minimally cognitive, and optimally brief. The new measure also differs from any previous job satisfaction measure in being comprehensively validated not just for internal consistency reliability, temporal stability, convergent and criterion-related validities, but also for cross-population invariance by nationality, job level, and job type.

Cognitive influences on the affective representation of touch and the sight of touch in the human brain

We show that the affective experience of touch and the sight of touch can be modulated by cognition, and investigate in an fMRI study where top-down cognitive modulations of bottom-up somatosensory and visual processing of touch and its affective value occur in the human brain. The cognitive modulation was produced by word labels, 'Rich moisturizing cream' or 'Basic cream', while cream was being applied to the forearm, or was seen being applied to a forearm. The subjective pleasantness and richness were modulated by the word labels, as were the fMRI activations to touch in parietal cortex area 7, the insula and ventral striatum. The cognitive labels influenced the activations to the sight of touch and also the correlations with pleasantness in the pregenual cingulate/orbitofrontal cortex and ventral striatum. Further evidence of how the orbitofrontal cortex is involved in affective aspects of touch was that touch to the forearm [which has C fiber Touch (CT) afferents sensitive to light touch] compared with touch to the glabrous skin of the hand (which does not) revealed activation in the mid-orbitofrontal cortex. This is of interest as previous studies have suggested that the CT system is important in affiliative caress-like touch between individuals.

Enhanced affective brain representations of chocolate in cravers vs. non-cravers

To examine the neural circuitry involved in food craving, in making food particularly appetitive and thus in driving wanting and eating, we used fMRI to measure the response to the flavour of chocolate, the sight of chocolate and their combination in cravers vs. non-cravers. Statistical parametric mapping (SPM) analyses showed that the sight of chocolate produced more activation in chocolate cravers than non-cravers in the medial orbitofrontal cortex and ventral striatum. For cravers vs. non-cravers, a combination of a picture of chocolate with chocolate in the mouth produced a greater effect than the sum of the components (i.e. supralinearity) in the medial orbitofrontal cortex and pregenual cingulate cortex. Furthermore, the pleasantness ratings of the chocolate and chocolate-related stimuli had higher positive correlations with the fMRI blood oxygenation level-dependent signals in the pregenual cingulate cortex and medial orbitofrontal cortex in the cravers than in the non-cravers. To our knowledge, this is the first study to show that there are differences between cravers and non-cravers in their responses to the sensory components of a craved food in the orbitofrontal cortex, ventral striatum and pregenual cingulate cortex, and that in some of these regions the differences are related to the subjective pleasantness of the craved foods. Understanding individual differences in brain responses to very pleasant foods helps in the understanding of the mechanisms that drive the liking for specific foods and thus intake of those foods.