A tour on Hermitian symmetric manifolds

Hermitian symmetric manifolds are Hermitian manifolds which are homogeneous and such that every point has a symmetry preserving the Hermitian structure. The aim of these notes is to present an introduction to this important class of manifolds, trying to survey the several different perspectives from which Hermitian symmetric manifolds can be studied.Comment: 56 pages, expanded version. Written for the Proceedings of the CIME-CIRM summer course "Combinatorial Algebraic Geometry". Comments are still welcome

Electronic transport through ballistic chaotic cavities: reflection symmetry, direct processes, and symmetry breaking

We extend previous studies on transport through ballistic chaotic cavities with spatial left-right (LR) reflection symmetry to include the presence of direct processes. We first analyze fully LR-symmetric systems in the presence of direct processes and compare the distribution w(T) of the transmission coefficient T with that for an asymmetric cavity with the same "optical" S matrix. We then study the problem of "external mixing" of the symmetry caused by an asymmetric coupling of the cavity to the outside. We first consider the case where symmetry breaking arises because two symmetrically positioned waveguides are coupled to the cavity by means of asymmetric tunnel barriers. Although this system is asymmetric with respect to the LR operation, it has a striking memory of the symmetry of the cavity it was constructed from. Secondly, we break LR symmetry in the absence of direct proceses by asymmetrically positioning the two waveguides and compare the results with those for the completely asymmetric case.Comment: 15 pages, 8 Postscript figures, submitted to Phys. Rev.

Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem

We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by their local density leads to universality of their local fluctuations for large M. A relation between the partial time delays and diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal coupling. This helped us in deriving the joint probability distribution of partial time delays and the distribution of the Wigner time delay.Comment: 4 pages, revtex, no figures; published versio

Q-dependence of the inelastic neutron scattering cross section for molecular spin clusters with high molecular symmetry

For powder samples of polynuclear metal complexes the dependence of the inelastic neutron scattering intensity on the momentum transfer Q is known to be described by a combination of so called interference terms. They reflect the interplay between the geometrical structure of the compound and the spatial properties of the wave functions involved in the transition. In this work, it is shown that the Q-dependence is strongly interrelated with the molecular symmetry of molecular nanomagnets, and, if the molecular symmetry is high enough, is actually completely determined by it. A general formalism connecting spatial symmetry and interference terms is developed. The arguments are detailed for cyclic spin clusters, as experimentally realized by e.g. the octanuclear molecular wheel Cr8, and the star like tetranuclear cluster Fe4.Comment: 8 pages, 1 figures, REVTEX

Theoretical study of the absorption spectra of the sodium dimer

Absorption of radiation from the sodium dimer molecular states correlating to Na(3s)-Na(3s) is investigated theoretically. Vibrational bound and continuum transitions from the singlet X Sigma-g+ state to the first excited singlet A Sigma-u+ and singlet B Pi-u states and from the triplet a Sigma-u+ state to the first excited triplet b Sigma-g+ and triplet c Pi-g states are studied quantum-mechanically. Theoretical and experimental data are used to characterize the molecular properties taking advantage of knowledge recently obtained from ab initio calculations, spectroscopy, and ultra-cold atom collision studies. The quantum-mechanical calculations are carried out for temperatures in the range from 500 to 3000 K and are compared with previous calculations and measurements where available.Comment: 19 pages, 8 figures, revtex, eps

Towards an international understanding of the power of celebrity persuasions: a review and a research agenda

Research into advertising using celebrity has been undertaken for nearly 40 years. It has principally used surveys and experiments to explore how consumers respond to celebrity advertisements. A recent meta-study of 32 papers has demonstrated that different populations respond in different ways to celebrity endorsements. Specifically, both US subjects and college students are more likely to respond in a significant way to the presence of celebrity than subjects who are not from the US, or who are not studying at college. Given that the nationality and student status of subjects matter, this article explores the make up of the samples that have been used to examine celebrity advertising. The article finds that these samples are not representative of US populations (because so many are students), nor of populations outside the US (because so few live beyond it). Furthermore, the history of dominance of US-based student samples, and the citation practices which keep them circulating in academia, suggests that theories of celebrity advertising have for a long time been excessively influenced by ideas tested on this unrepresentative group. This fact will limit the applicability of research into celebrity advertising to the wider world. I explore whether this matters, and how deficiencies might be addressed in further research

Maternal Diet Quality During Pregnancy and Offspring Hepatic Fat in Early Childhood: The Healthy Start Study

Background: Overnutrition in utero may increase offspring risk of nonalcoholic fatty liver disease (NAFLD), but the specific contribution of maternal diet quality during pregnancy to this association remains understudied in humans. Objectives: This study aimed to examine the associations of maternal diet quality during pregnancy with offspring hepatic fat in early childhood (median: 5 y old, range: 4–8 y old). Methods: Data were from 278 mother–child pairs in the longitudinal, Colorado-based Healthy Start Study. Multiple 24-h recalls were collected from mothers during pregnancy on a monthly basis (median: 3 recalls, range: 1–8 recalls starting after enrollment), and used to estimate maternal usual nutrient intakes and dietary pattern scores [Healthy Eating Index-2010 (HEI-2010), Dietary Inflammatory Index (DII), and Relative Mediterranean Diet Score (rMED)]. Offspring hepatic fat was measured in early childhood by MRI. Associations of maternal dietary predictors during pregnancy with offspring log-transformed hepatic fat were assessed using linear regression models adjusted for offspring demographics, maternal/perinatal confounders, and maternal total energy intake. Results: Higher maternal fiber intake and rMED scores during pregnancy were associated with lower offspring hepatic fat in early childhood in fully adjusted models [Back-transformed β (95% CI): 0.82 (0.72, 0.94) per 5 g/1000 kcal fiber; 0.93 (0.88, 0.99) per 1 SD for rMED]. In contrast, higher maternal total sugar and added sugar intakes, and DII scores were associated with higher offspring hepatic fat [Back-transformed β (95% CI): 1.18 (1.05, 1.32) per 5% kcal/d added sugar; 1.08 (0.99, 1.18) per 1 SD for DII]. Analyses of dietary pattern subcomponents also revealed that lower maternal intakes of green vegetables and legumes and higher intake of “empty calories” were associated with higher offspring hepatic fat in early childhood. Conclusions: Poorer maternal diet quality during pregnancy was associated with greater offspring susceptibility to hepatic fat in early childhood. Our findings provide insights into potential perinatal targets for the primordial prevention of pediatric NAFLD

Distribution of glutamate and preproenkephalin messenger RNAs following transient focal cerebral ischemia

Middle cerebral artery occlusion may result in increased activation of N-methyl- d-aspartate- or α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA)-type receptors by glutamate and lead to neuronal cell death. To characterize molecular events that precede cell death following transient focal ischemia, in situ hybridization histochemistry was used to measure levels of glutamate receptor subunit 1 (GluR1), GluR2, GluR3, N-methyl- d-aspartate receptor subunit 1 (NR1) and preproenkephalin messenger RNAs in adult rats at various recirculation times (1.5, 3 and 24 h) following a 90-min period of middle cerebral artery occlusion. At 1.5 and 3 h recirculation, autoradiography showed pronounced but differential decreases in AMPA, NR1 and preproenkephalin messenger RNA expression throughout the infarcted ipsilateral striatum. Non-uniform patterns of in situ hybridization grains emerged such that many striatal neurons were depleted of AMPA and preproenkephalin messenger RNAs, while others retained control levels. In cortical regions destined to undergo infarction, GluR2 and NR1 messenger RNAs were preferentially reduced relative to the contralateral side (to 75±8.5% and 66±4.5%, respectively); GluR1, GluR3 and preproenkephalin messenger RNAs were unaltered. At 24 h recirculation, depletion of striatal and cortical messenger RNAs became less selective. GluR3 and preproenkephalin messenger RNAs were up-regulated in ipsilateral spared regions of the striatum, and GluR1 and GluR2 messenger RNAs increased bilaterally in the cingulate cortex and in selective nuclei of the amygdala. Histological cell death or neurodegeneration was not detected in areas of reduced glutamate and preproenkephalin messenger RNA expression in either the ipsilateral striatum or cortex before 24 h. These findings suggest that complex and long-lasting decreases in messenger RNA expression occur prior to significant cell loss in regions destined to undergo infarction. Increased formation of Ca 2+-permeable AMPA receptor assemblies may occur in “unspared” and “spared” regions via different mechanisms and contribute to alterations in post-ischemic synaptic activity. The possibility arises that there may be altered relationships between glutamatergic and enkephalin synapses, since the dorsolateral striatum, where preproenkephalin messenger RNA expression is acutely reduced, receives innervation by the affected ipsilateral cortical region