ROAM: a Radial-basis-function Optimization Approximation Method for diagnosing the three-dimensional coronal magnetic field

The Coronal Multichannel Polarimeter (CoMP) routinely performs coronal polarimetric measurements using the Fe XIII 10747 $\AA$ and 10798 $\AA$ lines, which are sensitive to the coronal magnetic field. However, inverting such polarimetric measurements into magnetic field data is a difficult task because the corona is optically thin at these wavelengths and the observed signal is therefore the integrated emission of all the plasma along the line of sight. To overcome this difficulty, we take on a new approach that combines a parameterized 3D magnetic field model with forward modeling of the polarization signal. For that purpose, we develop a new, fast and efficient, optimization method for model-data fitting: the Radial-basis-functions Optimization Approximation Method (ROAM). Model-data fitting is achieved by optimizing a user-specified log-likelihood function that quantifies the differences between the observed polarization signal and its synthetic/predicted analogue. Speed and efficiency are obtained by combining sparse evaluation of the magnetic model with radial-basis-function (RBF) decomposition of the log-likelihood function. The RBF decomposition provides an analytical expression for the log-likelihood function that is used to inexpensively estimate the set of parameter values optimizing it. We test and validate ROAM on a synthetic test bed of a coronal magnetic flux rope and show that it performs well with a significantly sparse sample of the parameter space. We conclude that our optimization method is well-suited for fast and efficient model-data fitting and can be exploited for converting coronal polarimetric measurements, such as the ones provided by CoMP, into coronal magnetic field data.Comment: 23 pages, 12 figures, accepted in Frontiers in Astronomy and Space Science

Synthesis of Cortistatins A, J, K, and L

The cortistatins are a recently identified class of marine natural products characterized by an unusual steroidal skeleton and have been found to inhibit differentially the proliferation of various mammalian cells in culture by an unknown mechanism. We describe a comprehensive route for the synthesis of cortistatins from a common precursor, which in turn is assembled from two fragments of similar structural complexity. Cortistatins A and J, and for the first time, K and L, have been synthesized in parallel processes from like intermediates prepared from a single compound. With the identification of facile laboratory transformations linking intermediates in the cortistatin L synthetic series with corresponding intermediates to cortistatins A and J, we have been led to speculate that somewhat related paths might occur in nature, offering potential sequencing and chemical detail for cortistatin biosynthetic pathways.Chemistry and Chemical Biolog

Data-Optimized Coronal Field Model: I. Proof of Concept

Deriving the strength and direction of the three-dimensional (3D) magnetic field in the solar atmosphere is fundamental for understanding its dynamics. Volume information on the magnetic field mostly relies on coupling 3D reconstruction methods with photospheric and/or chromospheric surface vector magnetic fields. Infrared coronal polarimetry could provide additional information to better constrain magnetic field reconstructions. However, combining such data with reconstruction methods is challenging, e.g., because of the optical-thinness of the solar corona and the lack and limitations of stereoscopic polarimetry. To address these issues, we introduce the Data-Optimized Coronal Field Model (DOCFM) framework, a model-data fitting approach that combines a parametrized 3D generative model, e.g., a magnetic field extrapolation or a magnetohydrodynamic model, with forward modeling of coronal data. We test it with a parametrized flux rope insertion method and infrared coronal polarimetry where synthetic observations are created from a known "ground truth" physical state. We show that this framework allows us to accurately retrieve the ground truth 3D magnetic field of a set of force-free field solutions from the flux rope insertion method. In observational studies, the DOCFM will provide a means to force the solutions derived with different reconstruction methods to satisfy additional, common, coronal constraints. The DOCFM framework therefore opens new perspectives for the exploitation of coronal polarimetry in magnetic field reconstructions and for developing new techniques to more reliably infer the 3D magnetic fields that trigger solar flares and coronal mass ejections.Comment: 14 pages, 6 figures; Accepted for publication in Ap

A 3-D RBF-FD solver for modeling the atmospheric global electric circuit with topography (GEC-RBFFD v1.0)

A numerical model based on radial basis functiongenerated finite differences (RBF-FD) is developed for simulating the global electric circuit (GEC) within the Earth's atmosphere, represented by a 3-D variable coefficient linearelliptic partial differential equation (PDE) in a sphericallyshaped volume with the lower boundary being the Earth's topography and the upper boundary a sphere at 60 km. To ourknowledge, this is (1) the first numerical model of the GECto combine the Earth's topography with directly approximating the differential operators in 3-D space and, related to this,(2) the first RBF-FD method to use irregular 3-D stencils fordiscretization to handle the topography. It benefits from themesh-free nature of RBF-FD, which is especially suitable formodeling high-dimensional problems with irregular boundaries. The RBF-FD elliptic solver proposed here makes nolimiting assumptions on the spatial variability of the coefficients in the PDE (i.e., the conductivity profile), the righthand side forcing term of the PDE (i.e., distribution of current sources) or the geometry of the lower boundary.This work was supported by NSF awards AGS-1135446 and DMS-094581. The National Center for Atmospheric Research is sponsored by the NSF.Publicad

On the Sensitivity of 3-D Thermal Convection Codes to Numerical Discretization: A Model Intercomparison

Fully 3-D numerical simulations of thermal convection in a spherical shell have become a standard for studying the dynamics of pattern formation and its stability under perturbations to various parameter values. The question arises as to how does the discretization of the governing equations affect the outcome and thus any physical interpretation. This work demonstrates the impact of numerical discretization on the observed patterns, the value at which symmetry is broken, and how stability and stationary behavior is dependent upon it. Motivated by numerical simulations of convection in the Earth\u27s mantle, we consider isoviscous Rayleigh-Bénard convection at infinite Prandtl number, where the aspect ratio between the inner and outer shell is 0.55. We show that the subtleties involved in development mantle convection models are considerably more delicate than has been previously appreciated, due to the rich dynamical behavior of the system. Two codes with different numerical discretization schemes: an established, community-developed, and benchmarked finite element code (CitcomS) and a novel spectral method that combines Chebyshev polynomials with radial basis functions (RBF) are compared. A full numerical study is investigated for the following three cases. The first case is based on the cubic (or octahedral) initial condition (spherical harmonics of degree ℓ =4). How variations in the behavior of the cubic pattern to perturbations in the initial condition and Rayleigh number between the two numerical discrezations is studied. The second case investigates the stability of the dodecahedral (or icosahedral) initial condition (spherical harmonics of degree ℓ = 6). Although both methods converge first to the same pattern, this structure is ultimately unstable and systematically degenerates to cubic or tetrahedral symmetries, depending on the code used. Lastly, a new steady state pattern is presented as a combination of order 3 and 4 spherical harmonics leading to a five cell or a hexahedral pattern and stable up to 70 times the critical Rayleigh number. This pattern can provide the basis for a new accuracy benchmark for 3-D spherical mantle convection codes

FGF receptor genes and breast cancer susceptibility: results from the Breast Cancer Association Consortium

Background:Breast cancer is one of the most common malignancies in women. Genome-wide association studies have identified FGFR2 as a breast cancer susceptibility gene. Common variation in other fibroblast growth factor (FGF) receptors might also modify risk. We tested this hypothesis by studying genotyped single-nucleotide polymorphisms (SNPs) and imputed SNPs in FGFR1, FGFR3, FGFR4 and FGFRL1 in the Breast Cancer Association Consortium. Methods:Data were combined from 49 studies, including 53 835 cases and 50 156 controls, of which 89 050 (46 450 cases and 42 600 controls) were of European ancestry, 12 893 (6269 cases and 6624 controls) of Asian and 2048 (1116 cases and 932 controls) of African ancestry. Associations with risk of breast cancer, overall and by disease sub-type, were assessed using unconditional logistic regression. Results:Little evidence of association with breast cancer risk was observed for SNPs in the FGF receptor genes. The strongest evidence in European women was for rs743682 in FGFR3; the estimated per-allele odds ratio was 1.05 (95 confidence interval=1.02-1.09, P=0.0020), which is substantially lower than that observed for SNPs in FGFR2. Conclusion:Our results suggest that common variants in the other FGF receptors are not associated with risk of breast cancer to the degree observed for FGFR2. © 2014 Cancer Research UK

Exact polynomial reproduction for oscillatory radial basis functions on infinite lattices

AbstractUntil now, only nonoscillatory radial basis functions (RBFs) have been considered in the literature. It has recently been shown that a certain family of oscillatory RBFs based on J-Bessel functions gives rise to nonsingular interpolation problems and seems to be the only class of functions not to diverge in the limit of flat basis functions for any node layout. This paper proves another interesting feature of these functions: exact polynomial reproduction of arbitrary order on an infinite lattice in ℝn. First, a closed form expression is derived for calculating the expansion coefficients for any order polynomial in any dimension. Then, a proof is given showing that the resulting interpolant, using this class of oscillatory RBFs, will give exact polynomial reproduction. Examples in one and two dimensions are presented. It is specifically noted that such closed form expressions cannot be derived for other classes of RBFs due to the fact that J-Bessel RBFS reproduce polynomials via a different mechanism

A Hybrid Radial Basis Function - Pseudospectral Method for Thermal Convection in a 3-D Spherical Shell

A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral (PS) methods in a “2+1” approach is presented for numerically simulating thermal convection in a 3-D spherical shell. This is the first study to apply RBFs to a full 3D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be “scattered” over the surface of a sphere. In the radial direction, Chebyshev polynomials are used, which are also spectrally accurate and provide the necessary clustering near the boundaries to resolve boundary layers. Applications of this new hybrid methodology are given to the problem of convection in the Earth’s mantle,which is modeled by a Boussinesq fluid at infinite Prandtl number. To see whether this numerical technique warrants further investigation, the study limits itself to an isoviscous mantle.Benchmark comparisons are presented with other currently used mantle convection codes for Rayleigh number 7 · 103 and 105. The algorithmic simplicity of the code (mostly due to RBFs)allows it to be written in less than 400 lines of Matlab and run on a single workstation. We find that our method is very competitive with those currently used in the literature