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

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

Don't bleach chaotic data

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.Comment: 12 dense pages (82K) of ordinary LaTeX; uses macro psfig.tex for inclusion of figures in text; figures are uufile'd into a single file of size 306K; the final dvips'd postscript file is about 1.3mb Replaced 9/30/93 to incorporate final changes in the proofs and to make the LaTeX more portable; the paper will appear in CHAOS 4 (Dec, 1993

Noise and Nonlinearity in Measles Epidemics: Combining Mechanistic and Statistical Approaches to Population Modeling

We present and evaluate an approach to analyzing population dynamics data using semimechanistic models. These models incorporate reliable information on population structure and underlying dynamic mechanisms but use nonparametric surface-fitting methods to avoid unsupported assumptions about the precise form of rate equations. Using historical data on measles epidemics as a case study, we show how this approach can lead to better forecasts, better characterizations of the dynamics, and better understanding of the factors causing complex population dynamics relative to either mechanistic models or purely descriptive statistical time-series models. The semimechanistic models are found to have better forecasting accuracy than either of the model types used in previous analyses when tested on data not used to fit the models. The dynamics are characterized as being both nonlinear and noisy, and the global dynamics are clustered very tightly near the border of stability (dominant Lyapunov exponent λ < 0). However, locally in state space the dynamics oscillate between strong short-term stability and strong short-term chaos (i.e., between negative and positive local Lyapunov exponents). There is statistically significant evidence for short-term chaos in all data sets examined. Thus the nonlinearity in these systems is characterized by the variance over state space in local measures of chaos versus stability rather than a single summary measure of the overall dynamics as either chaotic or nonchaotic

Consequences of marine barriers for genetic diversity of the coral-specialist yellowbar angelfish from the Northwestern Indian Ocean

© 2019 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd. Ocean circulation, geological history, geographic distance, and seascape heterogeneity play an important role in phylogeography of coral-dependent fishes. Here, we investigate potential genetic population structure within the yellowbar angelfish (Pomacanthus maculosus) across the Northwestern Indian Ocean (NIO). We then discuss our results with respect to the above abiotic features in order to understand the contemporary distribution of genetic diversity of the species. To do so, restriction site-associated DNA sequencing (RAD-seq) was utilized to carry out population genetic analyses on P. maculosus sampled throughout the species’ distributional range. First, genetic data were correlated to geographic and environmental distances, and tested for isolation-by-distance and isolation-by-environment, respectively, by applying the Mantel test. Secondly, we used distance-based and model-based methods for clustering genetic data. Our results suggest the presence of two putative barriers to dispersal; one off the southern coast of the Arabian Peninsula and the other off northern Somalia, which together create three genetic subdivisions of P. maculosus within the NIO. Around the Arabian Peninsula, one genetic cluster was associated with the Red Sea and the adjacent Gulf of Aden in the west, and another cluster was associated with the Arabian Gulf and the Sea of Oman in the east. Individuals sampled in Kenya represented a third genetic cluster. The geographic locations of genetic discontinuities observed between genetic subdivisions coincide with the presence of substantial upwelling systems, as well as habitat discontinuity. Our findings shed light on the origin and maintenance of genetic patterns in a common coral reef fish inhabiting the NIO, and reinforce the hypothesis that the evolution of marine fish species in this region has likely been shaped by multiple vicariance events

Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the ob-served data. However, the assumption that the spatial dependence is constant through-out the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage fordealing with non-stationarity in geodetic data. We then compared stationary and non-stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC

Resolution of two-dimensional Currents in Superconductors from a two-dimensional magnetic field measurement by the method of regularization

The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization. Regularization directly addresses the inherent instability of this inversion problem for non-exact (noisy) data. Performance of the technique is evaluated for different current distributions and for data with varying amounts of added noise. Comparisons are made to other methods, and the present method is demonstrated to achieve a better regularizing (noise filtering) effect while also employing the generalized-cross validation (GCV) method to choose the optimal regularization parameter from the data, without detailed knowledge of the true (and generally unknown) solution. It is also shown that clean, noiseless data is an ineffective test of an inversion algorithm.Comment: To appear in the Physical Review B. Some text/figure additions and modification