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Sparse linear regression is one of the classical and extensively studied problems in high-dimensional statistics and compressed sensing. Despite the substantial body of literature dedicated to this problem, the precise determination of its minimax risk remains elusive. This paper aims to fill this gap by deriving asymptotically constant-sharp characterization for the minimax risk of sparse linear regression. More specifically, the paper focuses on scenarios where the sparsity level, denoted as k, satisfies the condition $(k \log p)/n {\to} 0$, with p and n representing the number of features and observations respectively. We establish that the minimax risk under isotropic Gaussian random design is asymptotically equal to $2{\sigma}^2k/n log(p/k)$, where ${\sigma}$ denotes the standard deviation of the noise. In addition to this result, we will summarize the existing results in the literature, and mention some of the fundamental problems that have still remained open.

Prominence bubbles, the dark arch-shaped "voids" below quiescent prominences, are generally believed to be caused by the interaction between the prominences and the slowly-emerging or quasi-stable underlying magnetic loops. However, this scenario could not explain some short-lived bubbles with extremely dynamic properties of evolution. Based on high-resolution H$\alpha$ observations, here we propose that bubbles should be classified into two categories according to their dynamic properties: quasi-steady (Type-I) bubbles and transient (Type-II) bubbles. Type-I bubbles could remain relatively stable and last for several hours, indicating the existence of a quasi-stable magnetic topology, while Type-II bubbles grow and collapse quickly within one hour without stability duration, which are usually associated with erupting mini-filaments. Analysis of several typical Type-II bubbles from different views, especially including an on-disk event, reveals that Type-II bubbles quickly appear and expand at a velocity of $\thicksim$5--25 km s$^{-1}$ accompanied by an erupting mini-filament below. The mini-filament's rising velocity is slightly larger than that of the Type-II bubbles' boundary, which will lead to the collision with each other in a short time, subsequent collapse of Type-II bubbles, and formation of a large plume into the above prominence. We also speculate that only if the angle between the axis of the erupting mini-filament and the line-of-sight is large enough, the interaction between the erupting mini-filament and the overlying prominence could trigger a Type-II bubble with a typical arch-shaped but quickly-expanding bright boundary., Comment: 10 pages, 4 images, 2 tables

The present paper introduces a hybrid explicit-implicit topology optimization method for shell-infill composite structure design. The proposed approach effectively combines the advantages of the explicit Moving Morphable Component (MMC) method, which describes structural topology only using a set of geometric parameters, and the implicit Solid Isotropic Material with Penalization (SIMP) method, which offers greater design freedom for characterizing the structural features. Compared to the existing methods for shell-infill structure design, the proposed approach can obtain optimized shell-infill structures with complex infill topology without resorting to complex filtering/projection operations. Numerical examples demonstrate the effectiveness of the proposed approach.

Partial eruptions of solar filaments are the typical representative of solar eruptive behavior diversity. Here we investigate a typical filament partial eruption event and present integrated evidence for configuration of the pre-eruption filament and its formation. The CHASE H$\alpha$ observations reveal structured Doppler velocity distribution within the pre-eruption filament, where distinct redshift only appeared in the east narrow part of the south filament region and then disappeared after the partial eruption while the north part dominated by blueshift remained. Combining the SDO, ASO-S observations, and NLFFF modeling results, we verify that there were two independent material flow systems within the pre-flare filament, whose magnetic topology is a special double-decker configuration consisting of two magnetic flux ropes (MFRs) with opposite magnetic twist. During the formation of this filament system, continuous magnetic flux cancellation and footpoint motion were observed around its north end. Therefore, we propose a new double-decker formation scenario that the two MFRs composing such double-decker configuration originated from two magnetic systems with different initial connections and opposite magnetic twist. Subsequent magnetic reconnection with surrounding newly-emerging fields resulted in the motion of footpoint of the upper MFR to the region around footpoint of the lower MFR, thus leading to eventual formation of the double-decker configuration consisting of two MFRs with similar footpoints but opposite signs of magnetic twist. These results provide a potential way to determine unambiguously the progenitor configuration of a partial-eruptive filament and reveal a special type of double-decker MFR configuration and a new double-decker formation scenario., Comment: 16 pages, 8 figures, 1 table, accepted for publication in ApJ as part of the Focus Issue "Early results from the Chinese Ha Solar Explorer (CHASE)"

Since its development, the minimax framework has been one of the corner stones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional problems. In this paper, we will first show through the example of sparse Gaussian sequence model, that the theoretical results under the classical minimax framework are insufficient for explaining empirical observations. In particular, both hard and soft thresholding estimators are (asymptotically) minimax, however, in practice they often exhibit sub-optimal performances at various signal-to-noise ratio (SNR) levels. The first contribution of this paper is to demonstrate that this issue can be resolved if the signal-to-noise ratio is taken into account in the construction of the parameter space. We call the resulting minimax framework the signal-to-noise ratio aware minimaxity. The second contribution of this paper is to showcase how one can use higher-order asymptotics to obtain accurate approximations of the SNR-aware minimax risk and discover minimax estimators. The theoretical findings obtained from this refined minimax framework provide new insights and practical guidance for the estimation of sparse signals.

Light bridges (LBs) are among the most striking sub-structures in sunspots, where various activities have been revealed by recent high-resolution observations from the Interface Region Imaging Spectrograph (IRIS). According to the variety of physical properties, we classified these activities into four distinct categories: transient brightening (TB), intermittent jet (IJ), type-I light wall (LW-I), and type-II light wall (LW-II). In IRIS 1400/1330 {\AA} observations, TBs are characterized by abrupt emission enhancements, and IJs appear as collimated plasma ejections with a width of 1-2 Mm at some LB sites. Most observed TBs are associated with IJs and show superpositions of some chromosphere absorption lines on enhanced and broadened wings of C II and Si IV lines, which could be driven by intermittent magnetic reconnection in the lower atmosphere. LW-I and LW-II are wall-shaped structures with bright fronts above the whole LB. An LW-I has a continuous oscillating front with a typical height of several Mm and an almost stationary period of 4-5 minutes. On the contrary, an LW-II has a indented front with a height of over 10 Mm, which has no stable period and is accompanied by recurrent TBs in the entire LB. These results support that LW-IIs are driven by frequent reconnection occurring along the whole LB due to large-scale magnetic flux emergence or intrusion, rather than the leakage of waves producing LW-Is. Our observations reveal a highly dynamical scenario of activities above LBs driven by different basic physical processes, including magneto-convection, magnetic reconnection, and wave leakage., Comment: 23 pages, 11 figures, 2 tables, accepted for publication in ApJ

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different tasks, and do not consider the additional task-specific observable side information. In this work, we model the meta-parameter through an order-$3$ tensor, which can adapt to the observed task features of the task. We propose two methods to estimate the underlying tensor. The first method solves a tensor regression problem and works under natural assumptions on the data generating process. The second method uses the method of moments under additional distributional assumptions and has an improved sample complexity in terms of the number of tasks. We also focus on the meta-test phase, and consider estimating task-specific parameters on a new task. Substituting the estimated tensor from the first step allows us estimating the task-specific parameters with very few samples of the new task, thereby showing the benefits of learning tensor representations for meta-learning. Finally, through simulation and several real-world datasets, we evaluate our methods and show that it improves over previous linear models of shared representations for meta-learning., Comment: Forthcoming at AISTATS-2022

Explicit topology optimization methods have received ever-increasing interest in recent years. In particular, a 188-line Matlab code of the two-dimensional (2D) Moving Morphable Component (MMC)-based topology optimization method was released by Zhang et al. (Struct Multidiscip Optim 53(6):1243-1260, 2016). The present work aims to propose an efficient and easy-to-extend 256-line Matlab code of the MMC method for three-dimensional (3D) topology optimization implementing some new numerical techniques. To be specific, by virtue of the function aggregation technique, accurate sensitivity analysis, which is also easy-to-extend to other problems, is achieved. Besides, based on an efficient identification algorithm for load transmission path, the degrees of freedoms (DOFs) not belonging to the load transmission path are removed in finite element analysis (FEA), which significantly accelerates the optimization process. As a result, compared to the corresponding 188-line 2D code, the performance of the optimization results, the computational efficiency of FEA, and the convergence rate and the robustness of optimization process are greatly improved. For the sake of completeness, a refined 218-line Matlab code implementing the 2D-MMC method is also provided., Comment: Accepted by Structural and Multidisciplinary Optimization on 3-26-2022

Bubbles, the semi-circular voids below quiescent prominences (filaments), have been extensively investigated in the past decade. However, hitherto the magnetic nature of bubbles cannot be verified due to the lack of on-disk photospheric magnetic field observations. Here for the first time, we find and investigate an on-disk prominence bubble around a filament barb on 2019 March 18 based on stereoscopic observations from NVST, SDO, and STEREO-A. In high-resolution NVST H$\alpha$ images, this bubble has a sharp arch-like boundary and a projected width of $\thicksim$26 Mm. Combining SDO and STEREO-A images, we further reconstruct 3D structure of the bubble boundary, whose maximum height is $\thicksim$15.6 Mm. The squashing factor Q map deduced from extrapolated 3D magnetic fields around the bubble depicts a distinct arch-shaped interface with a height of $\thicksim$11 Mm, which agrees well with the reconstructed 3D structure of the observed bubble boundary. Under the interface lies a set of magnetic loops, which is rooted on a surrounding photospheric magnetic patch. To be more persuasive, another on-disk bubble on 2019 June 10 is presented as a supplement. According to these results obtained from on-disk bubble observations, we suggest that the bubble boundary corresponds to the interface between the prominence dips (barb) and the underlying magnetic loops rooted nearby. It is thus reasonable to speculate that the bubble can form around a filament barb below which there is a photospheric magnetic patch., Comment: 10 pages, 5 figures, 2 movies, accepted for publication in ApJL