Hearing Delzant Polytopes From the Equivariant Spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.

Hearing in the mind's ear: A PET investigation of musical imagery and perception

Neuropsychological studies have suggested that imagery processes may be mediated by neuronal mechanisms similar to those used in perception. To test this hypothesis, and to explore the neural basis for song imagery, 12 normal subjects were scanned using the water bolus method to measure cerebral blood flow (CBF) during the performance of three tasks. In the control condition subjects saw pairs of words on each trial and judged which word was longer. In the perceptual condition subjects also viewed pairs of words, this time drawn from a familiar song; simultaneously they heard the corresponding song, and their task was to judge the change in pitch of the two cued words within the song. In the imagery condition, subjects performed precisely the same judgment as in the perceptual condition, but with no auditory input. Thus, to perform the imagery task correctly an internal auditory representation must be accessed. Paired-image subtraction of the resulting pattern of CBF, together with matched MRI for anatomical localization, revealed that both perceptual and imagery. tasks produced similar patterns of CBF changes, as compared to the control condition, in keeping with the hypothesis. More specifically, both perceiving and imagining songs are associated with bilateral neuronal activity in the secondary auditory cortices, suggesting that processes within these regions underlie the phenomenological impression of imagined sounds. Other CBF foci elicited in both tasks include areas in the left and right frontal lobes and in the left parietal lobe, as well as the supplementary motor area. This latter region implicates covert vocalization as one component of musical imagery. Direct comparison of imagery and perceptual tasks revealed CBF increases in the inferior frontal polar cortex and right thalamus. We speculate that this network of regions may be specifically associated with retrieval and/or generation of auditory information from memory.

Examining the Role of Vocational Rehabilitation on Access to Care and Public Health Outcomes for People Living with HIV/AIDS

The purpose of this study is to examine the role of vocational rehabilitation services in contributing to the goals of the National HIV/AIDS strategy. Three key research questions are addressed: (a) What is the relationship among factors associated with the use of vocational rehabilitation services for people living with HIV/AIDS? (b) Are the factors associated with use of vocational rehabilitation also associated with access to health care, supplemental employment services and reduced risk of HIV transmission? And (c) What unique role does use of vocational rehabilitation services play in access to health care and HIV prevention? Survey research methods were used to collect data from a broad sample of volunteer respondents who represented diverse racial (37% Black, 37% White, 18% Latino, 7% other), gender (65% male, 34% female, 1% transgender) and sexual orientation (48% heterosexual, 44% gay, 8% bisexual) backgrounds. The fit of the final structural equation model was good (root mean square error of approximation = .055, Comparative Fit Index=.953, Tucker Lewis Index=.945). Standardized effects with bootstrap confidence intervals are reported. Overall, the findings support the hypothesis that vocational rehabilitation services can play an important role in health and prevention strategies outlined in the National HIV/AIDS strategy.