Concentration in flux-function limits of solutions to a deposition model

This paper is concerned with a singular flux-function limit of the Riemann solutions to a deposition model. As a result, it is shown that the Riemann solutions to the deposition model just converge to the corresponding Riemann solutions to the limit system, which is one of typical models admitting delta-shocks. Especially, the phenomenon of concentration and the formation of delta-shocks in the limit are analyzed in detail, and the process of concentration is numerically simulated.Comment: 18 page

Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations

The sign problem is a major obstacle in quantum Monte Carlo simulations for many-body fermion systems. We examine this problem with a new perspective based on the Majorana reflection positivity and Majorana Kramers positivity. Two sufficient conditions are proven for the absence of the fermion sign problem. Our proof provides a unified description for all the interacting lattice fermion models previously known to be free of the sign problem based on the auxiliary field quantum Monte Carlo method. It also allows us to identify a number of new sign-problem-free interacting fermion models including, but not limited to, lattice fermion models with repulsive interactions but without particle-hole symmetry and interacting topological insulators with spin-flip terms.Comment: small corrections to Supplementary Material/Appendix

Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem

The celebrated Seq2Seq technique and its numerous variants achieve excellent performance on many tasks such as neural machine translation, semantic parsing, and math word problem solving. However, these models either only consider input objects as sequences while ignoring the important structural information for encoding, or they simply treat output objects as sequence outputs instead of structural objects for decoding. In this paper, we present a novel Graph-to-Tree Neural Networks, namely Graph2Tree consisting of a graph encoder and a hierarchical tree decoder, that encodes an augmented graph-structured input and decodes a tree-structured output. In particular, we investigated our model for solving two problems, neural semantic parsing and math word problem. Our extensive experiments demonstrate that our Graph2Tree model outperforms or matches the performance of other state-of-the-art models on these tasks.Comment: Long Paper in EMNLP 2020. 12 pages including reference

Properties on n-dimensional convolution for image deconvolution

Convolution system is linear and time invariant, and can describe the optical imaging process. Based on convolution system, many deconvolution techniques have been developed for optical image analysis, such as boosting the space resolution of optical images, image denoising, image enhancement and so on. Here, we gave properties on N-dimensional convolution. By using these properties, we proposed image deconvolution method. This method uses a series of convolution operations to deconvolute image. We demonstrated that the method has the similar deconvolution results to the state-of-art method. The core calculation of the proposed method is image convolution, and thus our method can easily be integrated into GPU mode for large-scale image deconvolution

Recurrent MVSNet for High-resolution Multi-view Stereo Depth Inference

Deep learning has recently demonstrated its excellent performance for multi-view stereo (MVS). However, one major limitation of current learned MVS approaches is the scalability: the memory-consuming cost volume regularization makes the learned MVS hard to be applied to high-resolution scenes. In this paper, we introduce a scalable multi-view stereo framework based on the recurrent neural network. Instead of regularizing the entire 3D cost volume in one go, the proposed Recurrent Multi-view Stereo Network (R-MVSNet) sequentially regularizes the 2D cost maps along the depth direction via the gated recurrent unit (GRU). This reduces dramatically the memory consumption and makes high-resolution reconstruction feasible. We first show the state-of-the-art performance achieved by the proposed R-MVSNet on the recent MVS benchmarks. Then, we further demonstrate the scalability of the proposed method on several large-scale scenarios, where previous learned approaches often fail due to the memory constraint. Code is available at https://github.com/YoYo000/MVSNet.Comment: Accepted by CVPR201

Metallic rugate structures for perfect absorbers in visible and near-infrared regions

Metallic rugate structures are theoretically investigated for achieving perfect absorption in the visible and near-infrared regions. Our model builds on nanoporous metal films whose porosity (volume fraction of voids) follows a sine-wave along the film thickness. By setting the initial phase of porosity at the top surface as 0, perfect absorption is obtained. The impacts of various structural parameters on the characteristic absorption behaviors are studied. Furthermore, multiple peaks or bands with high-absorption can be achieved by integrating several periodicities in one structure. The rugate absorbers show perfect or near-perfect absorption for TE and TM polarizations and large incident angles

An observational revisit of band-split solar type-II radio bursts

Band split of solar type II radio bursts, discovered several decades ago, is a fascinating phenomenon with the type-II lanes exhibiting two almost-parallel sub-bands with similar morphology. The underlying split mechanism remains elusive. One popular interpretation is that the splitting bands are emitted from the shock upstream and downstream, respectively, with their frequency ratio ({\gamma}) determined by the shock compression ratio. This interpretation has been taken as the physical basis for many published references. Here we report an observational analysis of type II events with nice split selected from the ground-based RSTN data from 2001 to 2014, in the metric-decametric wavelength. We investigate the temporal variation and distribution of {\gamma}, and conduct correlation analyses on the deduced spectral values. It is found that {\gamma} varies in a very narrow range with >80% of {\gamma} (one-minute averaged data) being between 1.15 to 1.25. For some well-observed and long-lasting events, {\gamma} does not show a systematic variation trend within observational uncertainties, from the onset to the termination of the splits. In addition, the parameters representing the propagation speed of the radio source (presumably the coronal shock) show a very weak or basically no correlation with {\gamma}. We suggest that these results do not favor the upstreamdownstream scenario of band splits

A solar type II radio burst from CME-coronal ray interaction: simultaneous radio and EUV imaging

Simultaneous radio and extreme ultraviolet (EUV)/white-light imaging data are examined for a solar type II radio burst occurring on 2010 March 18 to deduce its source location. Using a bow-shock model, we reconstruct the 3-dimensional EUV wave front (presumably the type-II emitting shock) based on the imaging data of the two STEREO spacecraft. It is then combined with the Nan\c{c}ay radio imaging data to infer the 3-dimensional position of the type II source. It is found that the type II source coincides with the interface between the CME EUV wave front and a nearby coronal ray structure, providing evidence that the type II emission is physically related to the CME-ray interaction. This result, consistent with those of previous studies, is based on simultaneous radio and EUV imaging data for the first time.Comment: 5 figure

Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks

Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov Chain Monte Carlo (MCMC) tend to be computationally intensive and inefficient for such high dimensional problems. To address this issue, several methods based on surrogate models have been proposed to speed up the inference process. More specifically, the calibration-emulation-sampling (CES) scheme has been proven to be successful in large dimensional UQ problems. In this work, we propose a novel CES approach for Bayesian inference based on deep neural network (DNN) models for the emulation phase. The resulting algorithm is not only computationally more efficient, but also less sensitive to the training set. Further, by using an Autoencoder (AE) for dimension reduction, we have been able to speed up our Bayesian inference method up to three orders of magnitude. Overall, our method, henceforth called \emph{Dimension-Reduced Emulative Autoencoder Monte Carlo (DREAM)} algorithm, is able to scale Bayesian UQ up to thousands of dimensions in physics-constrained inverse problems. Using two low-dimensional (linear and nonlinear) inverse problems we illustrate the validity this approach. Next, we apply our method to two high-dimensional numerical examples (elliptic and advection-diffussion) to demonstrate its computational advantage over existing algorithms.Comment: 40 pages, 20 figure

EUV and Magnetic Activities Associated with Type-I Solar Radio Bursts

Type-I bursts (i.e. noise storms) are the earliest-known type of solar radio emission at the metre wavelength. They are believed to be excited by non-thermal energetic electrons accelerated in the corona. The underlying dynamic process and exact emission mechanism still remain unresolved. Here, with a combined analysis of extreme ultraviolet (EUV), radio and photospheric magnetic field data of unprecedented quality recorded during a type-I storm on 30 July 2011, we identify a good correlation between the radio bursts and the co-spatial EUV and magnetic activities. The EUV activities manifest themselves as three major brightening stripes above a region adjacent to a compact sunspot, while the magnetic field there presents multiple moving magnetic features (MMFs) with persistent coalescence or cancelation and a morphologically similar three-part distribution. We find that the type-I intensities are correlated with those of the EUV emissions at various wavelengths with a correlation coefficient of 0.7-0.8. In addition, in the region between the brightening EUV stripes and the radio sources there appear consistent dynamic motions with a series of bi-directional flows, suggesting ongoing small-scale reconnection there. Mainly based on the induced connection between the magnetic motion at the photosphere and the EUV and radio activities in the corona, we suggest that the observed type-I noise storms and the EUV brightening activities are the consequence of small-scale magnetic reconnection driven by MMFs. This is in support of the original proposal made by Bentely et al. (Solar Phys. 193, 227, 2000)