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1. Investigating Transport and Dissipation in the Subauroral E Region With Ionospheric Modification Experiments and Very High Frequency Radar Backscatter

   https://doi.org/10.1029/2018RS006749  

   Hysell, D. L.; Munk, J.; McCarrick, M. (March 2019, Radio Science)

   Abstract Ionospheric modification experiments have been performed at the High‐Frequency Active Auroral Research Program (HAARP) facility in Gakona, Alaska, using a Very High Frequency (VHF) coherent scatter radar in Homer, Alaska, for experimental diagnostics. The experiments were intended to determine the threshold pump electric field required to initiate thermal parametric instability in theEregion. The pump power level was ramped systematically to determine the threshold, and the experiment was repeated at four closely spaced pump frequencies. This provided threshold estimates at fourEregion altitudes. The theory for thermal parametric instability based on the work of Dysthe et al. (1983,https://doi.org/10.1063/1.863993) has been modified for application in theEregion. The theory considers magneto‐ionic effects on the pump mode, linear mode conversion theory for upper hybrid wave generation, wave heating, and the effects of transport and dissipation based on fluid theory. The theory amounts to an eigenvalue problem where the eigenvalue is the threshold pump electric field for instability. The theory shows how the threshold depends on ionospheric transport coefficients and on the fractional cooling rate for inelastic electron‐neutral collisions. The theoretical predictions for threshold are roughly consistent with experimental values although the latter are probably affected by excess ionospheric absorption. 

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2. An $$\ell_{\infty}$$ eigenvector perturbation bound and its application to robust covariance estimation

   Fan, J.; Wang, W.; Zhong, Y. (October 2018, Journal of machine learning research)

   In statistics and machine learning, we are interested in the eigenvectors (or singular vectors) of certain matrices (e.g.\ covariance matrices, data matrices, etc). However, those matrices are usually perturbed by noises or statistical errors, either from random sampling or structural patterns. The Davis-Kahan $$\sin \theta$$ theorem is often used to bound the difference between the eigenvectors of a matrix $$A$$ and those of a perturbed matrix $$\widetilde{A} = A + E$$, in terms of $$\ell_2$$ norm. In this paper, we prove that when $$A$$ is a low-rank and incoherent matrix, the $$\ell_{\infty}$$ norm perturbation bound of singular vectors (or eigenvectors in the symmetric case) is smaller by a factor of $$\sqrt{d_1}$$ or $$\sqrt{d_2}$$ for left and right vectors, where $$d_1$$ and $$d_2$$ are the matrix dimensions. The power of this new perturbation result is shown in robust covariance estimation, particularly when random variables have heavy tails. There, we propose new robust covariance estimators and establish their asymptotic properties using the newly developed perturbation bound. Our theoretical results are verified through extensive numerical experiments. 

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3. 3-D Ionospheric Electron Density Variations during the 2017 Great American Solar Eclipse: A Revisit

   https://doi.org/10.3390/atmos14091379  

   Aa, Ercha; Zhang, Shun-Rong; Erickson, Philip J.; Wang, Wenbin; Coster, Anthea J. (September 2023, Atmosphere)

   This paper studies the three-dimensional (3-D) ionospheric electron density variation over the continental US and adjacent regions during the August 2017 Great American Solar Eclipse event, using Millstone Hill incoherent scatter radar observations, ionosonde data, the Swarm satellite measurements, and a new TEC-based ionospheric data assimilation system (TIDAS). The TIDAS data assimilation system can reconstruct a 3-D electron density distribution over continental US and adjacent regions, with a spatial–temporal resolution of 1∘× 1∘ in latitude and longitude, 20 km in altitude, and 5 min in universal time. The combination of multi-instrumental observations and the high-resolution TIDAS data assimilation products can well represent the dynamic 3-D ionospheric electron density response to the solar eclipse, providing important altitude information and fine-scale details. Results show that the eclipse-induced ionospheric electron density depletion can exceed 50% around the F2-layer peak height between 200 and 300 km. The recovery of electron density following the maximum depletion exhibits an altitude-dependent feature, with lower altitudes exhibiting a faster recovery than the F2 peak region and above. The recovery feature was also characterized by a post-eclipse electron density enhancement of 15–30%, which is particularly prominent in the topside ionosphere at altitudes above 300 km. 

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4. Virtual Height Characteristics of Ionospheric and Ground Scatter Observed by Mid‐Latitude SuperDARN HF Radars

   https://doi.org/10.1029/2022RS007429  

   Thomas, E. G.; Shepherd, S. G. (June 2022, Radio Science)

   Abstract Propagation of high‐frequency (HF) radio signals is strongly dependent on the ionospheric electron density structure along a communications link. The ground‐based, HF space weather radars of the Super Dual Auroral Radar Network (SuperDARN) utilize the ionospheric refraction of transmitted signals to monitor the global circulation ofE‐ andF‐region plasma irregularities. Previous studies have assessed the propagation characteristics of backscatter echoes from ionospheric irregularities in the auroral and polar regions of the Earth's ionosphere. By default, the geographic location of these echoes are found using empirical models which estimate the virtual backscattering height from the measured range along the radar signal path. However, the performance of these virtual height models has not yet been evaluated for mid‐latitude SuperDARN radar observations or for ground scatter (GS) propagation modes. In this study, we derive a virtual height model suitable for mid‐latitude SuperDARN observations using 5 years of data from the Christmas Valley East and West radars. This empirical model can be applied to both ionospheric and GS observations and provides an improved estimate of the ground range to the backscatter location compared to existing high‐latitude virtual height models. We also identify a region of overlapping half‐hopF‐region ionospheric scatter and one‐hopE‐region GS where the measured radar parameters (e.g., velocity, spectral width, elevation angle) are insufficient to discriminate between the two scatter types. Further studies are required to determine whether these backscatter echoes of ambiguous origin are observed by other mid‐latitude SuperDARN radars and their potential impact on scatter classification schemes. 

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5. The geometric median and applications to robust mean estimation

   Minsker, Stanislav; Strawn, Nate (May 2024, SIAM Journal on Mathematics of Data Science (SIMODS))

   This paper is devoted to the statistical properties of the geometric median, a robust measure of centrality for multivariate data, as well as its applications to the problem of mean estimation via the median of means principle. Our main theoretical results include (a) the upper bound for the distance between the mean and the median for general absolutely continuous distributions in $$\mathbb R^d$$, and examples of specific classes of distributions for which these bounds do not depend on the ambient dimension $$d$$; (b) exponential deviation inequalities for the distance between the sample and the population versions of the geometric median, which again depend only on the trace-type quantities and not on the ambient dimension. As a corollary, we deduce the improved bounds for the multivariate median of means estimator that hold for large classes of heavy-tailed distributions. 

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