Convexity theorems for semisimple symmetric spaces

We prove a remarkable generalization of a convexity theorem for semisimple symmetric spaces G/H established earlier in 1986 by the second named author. The latter result generalized Kostant's non-linear convexity theorem for the Iwasawa decomposition of a real semisimple Lie group. The present generalization involves Iwasawa decompositions related to minimal parabolic subgroups of G of arbitrary type instead of the particular type relative to H considered in 1986.Comment: LaTeX, 52 pages, v2 contains minor corrections and modification

Normalizations of Eisenstein integrals for reductive symmetric spaces

We construct minimal Eisenstein integrals for a reductive symmetric space G/H as matrix coefficients of the minimal principal series of G. The Eisenstein integrals thus obtained include those from the \sigma-minimal principal series. In addition, we obtain related Eisenstein integrals, but with different normalizations. Specialized to the case of the group, this wider class includes Harish-Chandra's minimal Eisenstein integrals.Comment: 66 pages. Minor revisions. To be published in Journal of Functional Analysi

KK-invariant cusp forms for reductive symmetric spaces of split rank one

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms coincides with the closure of the $K$-finite generalized matrix coefficients of discrete series representations if and only if there exist no $K$-spherical discrete series representations. Moreover, we prove that every $K$-spherical discrete series representation occurs with multiplicity $1$ in the Plancherel decomposition of $G/H$.Comment: 12 page

Symplectic geometry of semisimple orbits

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold. Moreover, we generalize this result to hyperbolic orbits in a real semisimple Lie algebra.Comment: 25 page

Fast and non-destructive pore structure analysis using terahertz time-domain spectroscopy.

Pharmaceutical tablets are typically manufactured by the uni-axial compaction of powder that is confined radially by a rigid die. The directional nature of the compaction process yields not only anisotropic mechanical properties (e.g. tensile strength) but also directional properties of the pore structure in the porous compact. This study derives a new quantitative parameter, Sa, to describe the anisotropy in pore structure of pharmaceutical tablets based on terahertz time-domain spectroscopy measurements. The Sa parameter analysis was applied to three different data sets including tablets with only one excipient (functionalised calcium carbonate), samples with one excipient (microcrystalline cellulose) and one drug (indomethacin), and a complex formulation (granulated product comprising several excipients and one drug). The overall porosity, tablet thickness, initial particle size distribution as well as the granule density were all found to affect the significant structural anisotropies that were observed in all investigated tablets. The Sa parameter provides new insights into the microstructure of a tablet and its potential was particularly demonstrated for the analysis of formulations comprising several components. The results clearly indicate that material attributes, such as particle size and granule density, cause a change of the pore structure, which, therefore, directly impacts the liquid imbibition that is part of the disintegration process. We show, for the first time, how the granule density impacts the pore structure, which will also affect the performance of the tablet. It is thus of great importance to gain a better understanding of the relationship of the physical properties of material attributes (e.g. intragranular porosity, particle shape), the compaction process and the microstructure of the finished product

Vasoactive intestinal polypeptide mediates circadian rhythmicity and synchrony in mammalian clock neurons

The mammalian suprachiasmatic nucleus (SCN) is a master circadian pacemaker. It is not known which SCN neurons are autonomous pacemakers or how they synchronize their daily firing rhythms to coordinate circadian behavior. Vasoactive intestinal polypeptide (VIP) and the VIP receptor VPAC(2) (encoded by the gene Vipr2) may mediate rhythms in individual SCN neurons, synchrony between neurons, or both. We found that Vip(−/−) and Vipr2(−/−) mice showed two daily bouts of activity in a skeleton photoperiod and multiple circadian periods in constant darkness. Loss of VIP or VPAC(2) also abolished circadian firing rhythms in approximately half of all SCN neurons and disrupted synchrony between rhythmic neurons. Critically, daily application of a VPAC(2) agonist restored rhythmicity and synchrony to VIP(−/−) SCN neurons, but not to Vipr2(−/−) neurons. We conclude that VIP coordinates daily rhythms in the SCN and behavior by synchronizing a small population of pacemaking neurons and maintaining rhythmicity in a larger subset of neurons

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe