The sectional curvature remains positive when taking quotients by certain nonfree actions

We study some cases when the sectional curvature remains positive under the taking of quotients by certain nonfree isometric actions of Lie groups. We consider the actions of the groups $S^1$ and $S^3$ such that the quotient space can be endowed with a smooth structure using the fibrations $S^3/S^1{\simeq}S^2$ and $S^7/S^3\simeq S^4$. We prove that the quotient space carries a metric of positive sectional curvature, provided that the original metric has positive sectional curvature on all 2-planes orthogonal to the orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam

The trace of the heat kernel on a compact hyperbolic 3-orbifold

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold H^3/\Ga are evaluated in the case in which the discrete group \Ga contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are briefly discussed in the examples.Comment: 11 page

Homogenisation of carnivorous mammal ensembles caused by global range reductions of large-bodied hypercarnivores during the late Quaternary

Carnivorous mammals play crucial roles in ecosystems by influencing prey densities and behaviour, and recycling carrion. Yet, the influence of carnivores on global ecosystems has been affected by extinctions and range contractions throughout the Late Pleistocene and Holocene (~130 000 years ago to the current). Large-bodied mammals were particularly affected, but how dietary strategies influenced species’ susceptibility to geographic range reductions remains unknown. We investigated 1) the importance of dietary strategies in explaining range reductions of carnivorous mammals (≥5% vertebrate meat consumption), and 2) differences in functional diversity of continental carnivore ensembles by comparing current, known ranges to current, expected ranges under a present-natural counterfactual scenario. The present-natural counterfactual estimates current mammal ranges had modern humans not expanded out of Africa during the Late Pleistocene and were not a main driver of extinctions and range contractions, alongside changing climates. Ranges of large-bodied hypercarnivorous mammals are currently smaller than expected, compared to smaller-bodied carnivorous mammals that consume less vertebrate meat. This resulted in consistent differences in continental functional diversity, whereby current ensembles of carnivorous mammals have undergone homogenisation through structural shifts towards smaller-bodied insectivorous and herbivorous species. The magnitude of ensemble structural shift varied among continents, with Australia experiencing the greatest difference. Weighting functional diversity by species’ geographic range sizes caused a three-fold greater shift in ensemble centroids than when using presence-absence alone. Conservation efforts should acknowledge current reductions in the potential geographic ranges of large-bodied hypercarnivores and aim to restore functional roles in carnivore ensembles, where possible, across continents

Transfer of K-types on local theta lifts of characters and unitary lowest weight modules

In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer of K-types on these representations of O(n,m), and we study their effects on the dual pair correspondences. These results provide examples that the theta lifting is compatible with the transfer of K-types. Finally we will use these results to study subquotients of some cohomologically induced modules

The Intracellular Localization of Hormonal Activity in Transplantable Thyrotropin-Secreting Pituitary Tumors in Mice

Mouse pituitary tumors secreting almost exclusively thyroid stimulating hormone have been characterized electron microscopically. Tumors of known thyrotropin content were separated into nuclear, mitochondrial, microsomal, and soluble fractions by differential centrifugation. The hormonal activity of these fractions was correlated with that of the total homogenates and with their nitrogen and phosphorus content. Essentially all the thyrotropin of the homogenate was recovered in a particulate fraction sedimenting between 20,000 and 40,000 g. This fraction contained the RNA granules and membranous components typical of microsomal pellets, but also showed the presence of small dense bodies surrounded by smooth membranes. These bodies were also visible within the endoplasmic reticulum of intact cells, and it is postulated that these bodies may represent the sites of intracellular elaboration and/or storage of TSH. Thyrotropin is tightly associated with microsomal particles but can be brought into solution by treatment with alkaline media, deoxycholate, and certain organic solvents

Uniqueness of Bessel models: the archimedean case

In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.Comment: 22 page

The resource theory of quantum reference frames: manipulations and monotones

Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of superselection rule, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focussing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically nonincreasing under various classes of operations that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio

Dirac cohomology, elliptic representations and endoscopy

The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 7-12) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for further investigations.Comment: This paper will appear in `Representations of Reductive Groups, in Honor of 60th Birthday of David Vogan', edited by M. Nervins and P. Trapa, published by Springe

Climatic versus biotic constraints on carbon and water fluxes in seasonally drought-affected ponderosa pine ecosystems

We investigated the relative importance of climatic versus biotic controls on gross primary production (GPP) and water vapor fluxes in seasonally drought-affected ponderosa pine forests. The study was conducted in young (YS), mature (MS), and old stands (OS) over 4 years at the AmeriFlux Metolius sites. Model simulations showed that interannual variation of GPP did not follow the same trends as precipitation, and effects of climatic variation were smallest at the OS (50%), and intermediate at the YS (<20%). In the young, developing stand, interannual variation in leaf area has larger effects on fluxes than climate, although leaf area is a function of climate in that climate can interact with age-related shifts in carbon allocation and affect whole-tree hydraulic conductance. Older forests, with well-established root systems, appear to be better buffered from effects of seasonal drought and interannual climatic variation. Interannual variation of net ecosystem exchange (NEE) was also lowest at the OS, where NEE is controlled more by interannual variation of ecosystem respiration, 70% of which is from soil, than by the variation of GPP, whereas variation in GPP is the primary reason for interannual changes in NEE at the YS and MS. Across spatially heterogeneous landscapes with high frequency of younger stands resulting from natural and anthropogenic disturbances, interannual climatic variation and change in leaf area are likely to result in large interannual variation in GPP and NEE