On the existence of G-equivariant maps

Let G be a compact Lie group. Let X, Y be free G-spaces. In this paper, by using the numerical index i (X; R), under cohomological conditions on the spaces X and Y, we consider the question of the existence of G-equivariant maps f: X -> Y.

A provisional host-index of the fungi of the United States, by W.G. Farlow and A.B. Seymour.

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Moduli spaces of (G,h)-constellations

Given a reductive group G acting on an affine scheme X over C and a Hilbert function h: Irr G → N_0, we construct the moduli space M_Ө(X) of Ө-stable (G,h)-constellations on X, which is a common generalisation of the invariant Hilbert scheme after Alexeev and Brion and the moduli space of Ө-stable G-constellations for finite groups G introduced by Craw and Ishii. Our construction of a morphism M_Ө(X) → X//G makes this moduli space a candidate for a resolution of singularities of the quotient X//G. Furthermore, we determine the invariant Hilbert scheme of the zero fibre of the moment map of an action of Sl_2 on (C²)⁶ as one of the first examples of invariant Hilbert schemes with multiplicities. While doing this, we present a general procedure for the realisation of such calculations. We also consider questions of smoothness and connectedness and thereby show that our Hilbert scheme gives a resolution of singularities of the symplectic reduction of the action.

Some properties of g- and P-spaces

A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with c.c.c. is given. A P−space with c.c.c. is countable and discrete.

G. bulloides dissolution index of surface sediments

The Atlantic is regarded as a huge carbonate depocenter due to an on average deep calcite lysocline. However, calculations and models that attribute the calcite lysocline to the critical undersaturation depth (hydrographic or chemical lysocline) and not to the depth at which significant calcium carbonate dissolution is observed (sedimentary calcite lysocline) strongly overestimate the preservation potential of calcareous deep-sea sediments. Significant calcium carbonate dissolution is expected to begin firstly below 5000 m in the deep Guinea and Angola Basin and below 4400 m in the Cape Basin. Our study that is based on different calcium carbonate dissolution stages of the planktic foraminifera Globigerina bulloides clearly shows that it starts between 400 and 1600 m shallower depending on the different hydrographic settings of the South Atlantic Ocean. In particular, coastal areas are severely affected by increased supply of organic matter and the resultant production of metabolic CO2 which seems to create microenvironments favorable for dissolution of calcite well above the hydrographic lysocline.

Does health service utilisation vary by remoteness? South Australian population data and the Accessibility and Remoteness Index of Australia

Objective: To compare rates of self-reported use of health services between rural, remote and urban South Australians. Methods: Secondary data analysis from a population-based survey to assess health and well-being, conducted in South Australia in 2000. In all, 2,454 adults were randomly selected and interviewed using the computer-assisted telephone interview (CATI) system. We analysed health service use by Accessibility and Remoteness Index of Australia (ARIA) category. Results: There was no statistically significant difference in the median number of uses of the four types of health services studied across ARIA categories. Significantly fewer residents of highly accessible areas reported never using primary care services (14.4% vs. 22.2% in very remote areas), and significantly more reported high use ( greater than or equal to6 visits, 29.3% vs. 21.5%). Fewer residents of remote areas reported never attending hospital (65.6% vs. 73.8% in highly accessible areas). Frequency of use of mental health services was not statistically significantly different across ARIA categories. Very remote residents were more likely to spend at least one night in a public hospital (15.8%) than were residents of other areas (e.g. 5.9% for highly accessible areas). Conclusion: The self-reported frequency of use of a range of health services in South Australia was broadly similar across ARIA categories. However, use of primary care services was higher among residents of highly accessible areas and public hospital use increased with increasing remoteness. There is no evidence for systematic rural disadvantage in terms of self-reported health service utilisation in this State.

In postmenopausal women with osteoporosis, denosumab significantly improved trabecular bone score (TBS), an index of trabecular microarchitecture

Background/Purpose: The trabecular bone score (TBS), a novel graylevel texture index determined from lumbar spine DXA scans, correlates with 3D parameters of trabecular bone microarchitecture known to predict fracture. TBS may enhance the identification of patients at increased risk for vertebral fracture independently of bone mineral density (BMD) (Boutroy JBMR 2010; Hans JBMR 2011). Denosumab treatment for 36 months decreased bone turnover, increased BMD, and reduced new vertebral fractures in postmenopausal women with osteoporosis (Cummings NEJM 2009). We explored the effect of denosumab on TBS over 36 months and evaluated the association between TBS and lumbar spine BMD in women who had DXA scans obtained from eligible scanners for TBS evaluation in FREEDOM. Methods: FREEDOM was a 3-year, randomized, double-blind trial that enrolled postmenopausal women with a lumbar spine or total hip DXA T-score __2.5, but not __4.0 at both sites. Women received placebo or 60 mg denosumab every 6 months. A subset of women in FREEDOM participated in a DXA substudy where lumbar spine DXA scans were obtained at baseline and months 1, 6, 12, 24, and 36. We retrospectively applied, in a blinded-to-treatment manner, a novel software program (TBS iNsightR v1.9, Med-Imaps, Pessac, France) to the standard lumbar spine DXA scans obtained in these women to determine their TBS indices at baseline and months 12, 24, and 36. From previous studies, a TBS _1.35 is considered as normal microarchitecture, a TBS between 1.35 and _1.20 as partially deteriorated, and 1.20 reflects degraded microarchitecture. Results: There were 285 women (128 placebo, 157 denosumab) with a TBS value at baseline and _1 post-baseline visit. Their mean age was 73, their mean lumbar spine BMD T-score was _2.79, and their mean lumbar spine TBS was 1.20. In addition to the robust gains in DXA lumbar spine BMD observed with denosumab (9.8% at month 36), there were consistent, progressive, and significant increases in TBS compared with placebo and baseline (Table & Figure). BMD explained a very small fraction of the variance in TBS at baseline (r2_0.07). In addition, the variance in the TBS change was largely unrelated to BMD change, whether expressed in absolute or percentage changes, regardless of treatment, throughout the study (all r2_0.06); indicating that TBS provides distinct information, independently of BMD. Conclusion: In postmenopausal women with osteoporosis, denosumab significantly improved TBS, an index of lumbar spine trabecular microarchitecture, independently of BMD.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Another (better) index of adiposity.

Comment on: Bergman RN, Stefanovski D, Buchanan TA, Sumner AE, Reynolds JC, Sebring NG, Xiang AH, Watanabe RM. A better index of body adiposity. Obesity (Silver Spring). 2011 May; 19(5):1083-9. PMID: 21372804.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Metabolic connectivity as index of verbal working memory.

Positron emission tomography (PET) data are commonly analyzed in terms of regional intensity, while covariant information is not taken into account. Here, we searched for network correlates of healthy cognitive function in resting state PET data. PET with [(18)F]-fluorodeoxyglucose and a test of verbal working memory (WM) were administered to 35 young healthy adults. Metabolic connectivity was modeled at a group level using sparse inverse covariance estimation. Among 13 WM-relevant Brodmann areas (BAs), 6 appeared to be robustly connected. Connectivity within this network was significantly stronger in subjects with above-median WM performance. In respect to regional intensity, i.e., metabolism, no difference between groups was found. The results encourage examination of covariant patterns in FDG-PET data from non-neurodegenerative populations.

Random number generation as an index of controlled processing

Random number generation (RNG) is a functionally complex process that is highly controlled and therefore dependent on Baddeley's central executive. This study addresses this issue by investigating whether key predictions from this framework are compatible with empirical data. In Experiment 1, the effect of increasing task demands by increasing the rate of the paced generation was comprehensively examined. As expected, faster rates affected performance negatively because central resources were increasingly depleted. Next, the effects of participants' exposure were manipulated in Experiment 2 by providing increasing amounts of practice on the task. There was no improvement over 10 practice trials, suggesting that the high level of strategic control required by the task was constant and not amenable to any automatization gain with repeated exposure. Together, the results demonstrate that RNG performance is a highly controlled and demanding process sensitive to additional demands on central resources (Experiment 1) and is unaffected by repeated performance or practice (Experiment 2). These features render the easily administered RNG task an ideal and robust index of executive function that is highly suitable for repeated clinical use.