Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with computer algebra systems. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified. The submission also contains an example implementation of the algorithms and formulas of the paper as a package for Maple 10, the technical documentation for this implementation, and a worksheet carrying out the computations for the space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical documentatio

Reconstructing emission from pre-reionization sources with cosmic infrared background fluctuation measurements by the JWST

We present new methodology to use cosmic infrared background (CIB) fluctuations to probe sources at 10<z<30 from a JWST/NIRCam configuration that will isolate known galaxies to 28 AB mag at 0.5--5 micron. At present significant mutually consistent source-subtracted CIB fluctuations have been identified in the Spitzer and Akari data at 2--5 micron, but we demonstrate internal inconsistencies at shorter wavelengths in the recent CIBER data. We evaluate CIB contributions from remaining galaxies and show that the bulk of the high-z sources will be in the confusion noise of the NIRCam beam, requiring CIB studies. The accurate measurement of the angular spectrum of the fluctuations and probing the dependence of its clustering component on the remaining shot noise power would discriminate between the various currently proposed models for their origin and probe the flux distribution of its sources. We show that the contribution to CIB fluctuations from remaining galaxies is large at visible wavelengths for the current instruments precluding probing the putative Lyman-break of the CIB fluctuations. We demonstrate that with the proposed JWST configuration such measurements will enable probing the Lyman break. We develop a Lyman-break tomography method to use the NIRCam wavelength coverage to identify or constrain, via the adjacent two-band subtraction, the history of emissions over 10<z<30 as the Universe comes out of the 'Dark Ages'. We apply the proposed tomography to the current Spitzer/IRAC measurements at 3.6 and 4.5 micron, to find that it already leads to interestingly low upper limit on emissions at z>30.Comment: ApJ, in press. Minor revisions/additions to match the version in proof

Greenhouse gas intensity of an irrigated cropping system in Saskatchewan

Non-Peer ReviewedIn response to increasing global food demands, the proportion of irrigated agricultural land within the Canadian Prairies is likely to increase. However, the implications of this with respect to the agricultural greenhouse gas (GHG) balance are not well understood. This study investigates and compares the greenhouse gas intensity of a typical irrigated and dryland cropping system in Saskatchewan, a semi-arid region of the Canadian Prairies. Compared to their dryland counterpart, irrigated cropping systems have higher GHG emissions which are a result of the energy used for pumping and larger nitrous oxide (N2O) production rates associated with higher N-fertilizer application and moist soil conditions. These emissions may be partially offset by increased carbon sequestration from the greater productivity realized through irrigation. This investigation focuses on the quantification of soil GHG emissions through chamber-based flux measurements. Factors driving these emissions have been determined through in-situ soil temperature, matric potential, and moisture measurements. The emissions associated with pumping and other crop management activities are accounted for using the Intergovernmental Panel on Climate Change (IPCC) literature and methodology. Preliminary results from the first season of study confirm that irrigated cropping systems have greater greenhouse gas intensity. Soil N2O emissions from the irrigated system were four times greater than the dryland and were the greatest source of emissions for the irrigated system. Diesel combustion used to power equipment was comparable between cropping systems. Emissions associated with pumping were notable; however, due to the wet growing season they remained smaller than could be expected most years. The information derived from this study will aid in the development of regional specific soil emission factors, improved management strategies, and will identify new approaches for mitigating emissions

Warped metrics for location-scale models

This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results : i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, ii) the analytic expression of the sectional curvature of this metric, iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms.Comment: preprint of a submission to GSI 2017 conferenc

Effective QCD Partition Function in Sectors with Non-Zero Topological Charge and Itzykson-Zuber Type Integral

It was conjectured by Jackson et.al. that the finite volume effective partition function of QCD with the topological charge $M-N$ coincides with the Itzyskon-Zuber type integral for $M\times N$ rectangular matrices. In the present article we give a proof of this conjecture, in which the original Itzykson-Zuber integral is utilized.Comment: 7pages, LaTeX2

Structure and magnetic properties of the cubic oxide fluoride BaFeO2F

Fluorination of the parent oxide, BaFeO3- δ, with polyvinylidine fluoride gives rise to a cubic compound with a = 4.0603(4) Å at 298K. 57Fe Mössbauer spectra confirmed that all the iron is present as Fe3+. Neutron diffraction data showed complete occupancy of the anion sites indicating a composition BaFeO2F, with a large displacement of the iron off-site. The magnetic ordering temperature was determined as TN = 645±5K. Neutron diffraction data at 4.2K established G-type antiferromagnetism with a magnetic moment per Fe3+ ion of 3.95μB. However, magnetisation measurements indicated the presence of a weak ferromagnetic moment which is assigned to the canting of the antiferromagnetic structure. 57Fe Mössbauer spectra in the temperature range 10 to 300K were fitted with a model of fluoride ion distribution that retains charge neutrality of the perovskite unit cel

Recent insights into the complexity of Tank-binding kinase 1 signaling networks: The emerging role of cellular localization in the activation and substrate specificity of TBK1

AbstractTank-binding kinase 1 (TBK1) serves as an important component of multiple signaling pathways. While the majority of research on TBK1 has focused on its role in innate immunity, critical functions for TBK1 in autophagy and cancer are beginning to emerge. This review highlights recent structural and biochemical studies that provide insights into the molecular mechanism of TBK1 activation and summarizes what is known to date about TBK1 substrate selection. Growing evidence suggests that both processes rely on TBK1 subcellular localization, with a variety of adaptor proteins each directing TBK1 to discrete signaling complexes for different cellular responses. Further study of TBK1-mediated pathways will require careful consideration of TBK1 mechanisms of activation and specificity for proper dissection of these distinct signaling cascades

Multiscale Representations for Manifold-Valued Data

We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere $S^2$, the special orthogonal group $SO(3)$, the positive definite matrices $SPD(n)$, and the Grassmann manifolds $G(n,k)$. The representations are based on the deployment of Deslauriers--Dubuc and average-interpolating pyramids "in the tangent plane" of such manifolds, using the $Exp$ and $Log$ maps of those manifolds. The representations provide "wavelet coefficients" which can be thresholded, quantized, and scaled in much the same way as traditional wavelet coefficients. Tasks such as compression, noise removal, contrast enhancement, and stochastic simulation are facilitated by this representation. The approach applies to general manifolds but is particularly suited to the manifolds we consider, i.e., Riemannian symmetric spaces, such as $S^{n-1}$, $SO(n)$, $G(n,k)$, where the $Exp$ and $Log$ maps are effectively computable. Applications to manifold-valued data sources of a geometric nature (motion, orientation, diffusion) seem particularly immediate. A software toolbox, SymmLab, can reproduce the results discussed in this paper

A few remarks on integral representation for zonal spherical functions on the symmetric space SU(N)/SO(N,R)SU(N)/SO(N,\R)

The integral representation on the orthogonal groups for zonal spherical functions on the symmetric space $SU(N)/SO(N,\R)$ is used to obtain a generating function for such functions. For the case N=3 the three-dimensional integral representation reduces to a one-dimensional one.Comment: Latex file, 10 pages, amssymb.sty require

Quantum Mechanics on SO(3) via Non-commutative Dual Variables

We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the non-commutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the non-trivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semi-classical approximation of the first order path integral and the example of a free particle on SO(3). On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam models.Comment: 29 pages; matches the published version plus footnote 7, a journal reference include