Topics on global analysis of manifolds and representation theory of reductive groups

Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect representation theoretic properties on function spaces, with focus on multiplicities and spectrum.Comment: 14 page

Different proteolipid protein mutants exhibit unique metabolic defects

PMD (Pelizaeus–Merzbacher disease), a CNS (central nervous system) disease characterized by shortened lifespan and severe neural dysfunction, is caused by mutations of the PLP1 (X-linked myelin proteolipid protein) gene. The majority of human PLP1 mutations are caused by duplications; almost all others are caused by missense mutations. The cellular events leading to the phenotype are unknown. The same mutations in non-humans make them ideal models to study the mechanisms that cause neurological sequelae. In the present study we show that mice with Plp1 duplications (Plp1tg) have major mitochondrial deficits with a 50% reduction in ATP, a drastically reduced mitochondrial membrane potential and increased numbers of mitochondria. In contrast, the jp (jimpy) mouse with a Plp1 missense mutation exhibits normal mitochondrial function. We show that PLP in the Plp1tg mice and in Plp1-transfected cells is targeted to mitochondria. PLP has motifs permissive for insertion into mitochondria and deletions near its N-terminus prevent its co-localization to mitochondria. These novel data show that Plp1 missense mutations and duplications of the native Plp1 gene initiate uniquely different cellular responses

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

Reconstructing grassland fire history using sedimentary charcoal: Considering count, size and shape

Citation: Leys, B. A., Commerford, J. L., & McLauchlan, K. K. (2017). Reconstructing grassland fire history using sedimentary charcoal: Considering count, size and shape. Plos One, 12(4), 15. doi:10.1371/journal.pone.0176445Fire is a key Earth system process, with 80% of annual fire activity taking place in grassland areas. However, past fire regimes in grassland systems have been difficult to quantify due to challenges in interpreting the charcoal signal in depositional environments. To improve reconstructions of grassland fire regimes, it is essential to assess two key traits: (1) charcoal count, and (2) charcoal shape. In this study, we quantified the number of charcoal pieces in 51 sediment samples of ponds in the Great Plains and tested its relevance as a proxy for the fire regime by examining 13 potential factors influencing charcoal count, including various fire regime components (e.g. the fire frequency, the area burned, and the fire season), vegetation cover and pollen assemblages, and climate variables. We also quantified the width to length (W: L) ratio of charcoal particles, to assess its utility as a proxy of fuel types in grassland environments by direct comparison with vegetation cover and pollen assemblages. Our first conclusion is that charcoal particles produced by grassland fires are smaller than those produced by forest fires. Thus, a mesh size of 120 mu m as used in forested environments is too large for grassland ecosystems. We recommend counting all charcoal particles over 60 mu m in grasslands and mixed grass-forest environments to increase the number of samples with useful data. Second, a W: L ratio of 0.5 or smaller appears to be an indicator for fuel types, when vegetation surrounding the site is before composed of at least 40% grassland vegetation. Third, the area burned within 1060m of the depositional environments explained both the count and the area of charcoal particles. Therefore, changes in charcoal count or charcoal area through time indicate a change in area burned. The fire regimes of grassland systems, including both human and climatic influences on fire behavior, can be characterized by long-term charcoal records

Extragalactic Results from the Infrared Space Observatory

More than a decade ago the IRAS satellite opened the realm of external galaxies for studies in the 10 to 100 micron band and discovered emission from tens of thousands of normal and active galaxies. With the 1995-1998 mission of the Infrared Space Observatory the next major steps in extragalactic infrared astronomy became possible: detailed imaging, spectroscopy and spectro-photometry of many galaxies detected by IRAS, as well as deep surveys in the mid- and far- IR. The spectroscopic data reveal a wealth of detail about the nature of the energy source(s) and about the physical conditions in galaxies. ISO's surveys for the first time explore the infrared emission of distant, high-redshift galaxies. ISO's main theme in extragalactic astronomy is the role of star formation in the activity and evolution of galaxies.Comment: 106 pages, including 17 figures. Ann.Rev.Astron.Astrophys. (in press), a gzip'd pdf file (667kB) is also available at http://www.mpe.mpg.de/www_ir/preprint/annrev2000.pdf.g

The multiple roles of myelin protein genes during the development of the oligodendrocyte

It has become clear that the products of several of the earliest identified myelin protein genes perform functions that extend beyond the myelin sheath. Interestingly, these myelin proteins, which comprise proteolipid protein, 2′,3′-cyclic nucleotide 3′-phosphodiesterase and the classic and golli MBPs (myelin basic proteins), play important roles during different stages of oligodendroglial development. These non-myelin-related functions are varied and include roles in the regulation of process outgrowth, migration, RNA transport, oligodendrocyte survival and ion channel modulation. However, despite the wide variety of cellular functions performed by the different myelin genes, the route by which they achieve these many functions seems to converge upon a common mechanism involving Ca2+ regulation, cytoskeletal rearrangements and signal transduction. In the present review, the newly emerging functions of these myelin proteins will be described, and these will then be discussed in the context of their contribution to oligodendroglial development

Psychometric properties of the Chinese quality of life instrument (HK version) in Chinese and Western medicine primary care settings

Background: The Chinese Quality of Life Measure (ChQOL) had only been validated on a small number of selected subjects in Hong Kong and had never been tested in the Western medicine (WM) primary care setting. Aims: and objectives To test the psychometrics properties of ChQOL(HK version) in both TCM and WM general outpatient clinics. Methods: Three samples of Chinese adult patients [(1) 569 consulting TCM clinics for episodic illnesses; (2) 524 consulting WM clinics for episodic illnesses; (3) 205 consulting WM clinics for chronic disease follow-up] in Hong Kong were invited to complete the ChQOL(HK version) and the SF-36 Health Survey during their consultations and 2 weeks after consultations. The scaling assumptions, factor structure, convergent construct validity, reliability, responsiveness, and discriminatory power of the ChQOL were evaluated. Results: Majority of items satisfied the scaling assumptions. A two instead of 3-factor structure was found with physical form and emotion facets loading on one factor. Convergent construct validity was confirmed with moderate correlations with SF-36 scores. Internal consistency and test-retest reliability were satisfactory. The ChQOL(HK version) was able to detect significant improvements 2 weeks after consultations, and it was able to discriminate between groups with different illness severity, age, and sex. Conclusion The ChQOL(HK version) was shown to have satisfactory validity, reliability, discriminatory power, and responsiveness in both TCM and Western medicine primary care settings. The validity of the 3-domain scaling structure needs further evaluation. © The Author(s) 2011.published_or_final_versionSpringer Open Choice, 21 Feb 201

Ten Simple Rules for Effective Computational Research

<p>Ten Simple Rules for Effective Computational Research</p

Anisotropy studies around the galactic centre at EeV energies with the Auger Observatory

Data from the Pierre Auger Observatory are analyzed to search for anisotropies near the direction of the Galactic Centre at EeV energies. The exposure of the surface array in this part of the sky is already significantly larger than that of the fore-runner experiments. Our results do not support previous findings of localized excesses in the AGASA and SUGAR data. We set an upper bound on a point-like flux of cosmic rays arriving from the Galactic Centre which excludes several scenarios predicting sources of EeV neutrons from Sagittarius $A$. Also the events detected simultaneously by the surface and fluorescence detectors (the `hybrid' data set), which have better pointing accuracy but are less numerous than those of the surface array alone, do not show any significant localized excess from this direction.Comment: Matches published versio