Robust globally divergence-free weak Galerkin finite element methods for natural convection problems

This paper proposes and analyzes a class of weak Galerkin (WG) finite element methods for stationary natural convection problems in two and three dimensions. We use piecewise polynomials of degrees k, k-1, and k(k>=1) for the velocity, pressure, and temperature approximations in the interior of elements, respectively, and piecewise polynomials of degrees l, k, l(l = k-1,k) for the numerical traces of velocity, pressure and temperature on the interfaces of elements. The methods yield globally divergence-free velocity solutions. Well-posedness of the discrete scheme is established, optimal a priori error estimates are derived, and an unconditionally convergent iteration algorithm is presented. Numerical experiments confirm the theoretical results and show the robustness of the methods with respect to Rayleigh number.Comment: 32 pages, 13 figure

animation : An R Package for Creating Animations and Demonstrating Statistical Methods

Animated graphs that demonstrate statistical ideas and methods can both attract interest and assist understanding. In this paper we first discuss how animations can be related to some statistical topics such as iterative algorithms, random simulations, (re)sampling methods and dynamic trends, then we describe the approaches that may be used to create animations, and give an overview to the R package animation, including its design, usage and the statistical topics in the package. With the animation package, we can export the animations produced by R into a variety of formats, such as a web page, a GIF animation, a Flash movie, a PDF document, or an MP4/AVI video, so that users can publish the animations fairly easily. The design of this package is flexible enough to be readily incorporated into web applications, e.g., we can generate animations online with Rweb, which means we do not even need R to be installed locally to create animations. We will show examples of the use of animations in teaching statistics and in the presentation of statistical reports using Sweave or knitr. In fact, this paper itself was written with the knitr and animation package, and the animations are embedded in the PDF document, so that readers can watch the animations in real time when they read the paper (the Adobe Reader is required).Animations can add insight and interest to traditional static approaches to teaching statistics and reporting, making statistics a more interesting and appealing subject

Dynamic Graphics and Reporting for Statistics

Statistics as a scientific discipline has a dynamic nature, which can be observed in many statistical algorithms and theories as well as in data analysis. For example, asymptotic theories in statistics are inherently dynamic: they describe how a statistic or an estimator behaves as the sample size increases. Data analysis is almost never a static process. Instead, it is an iterative process involving cleaning, describing, modeling, and re-cleaning the data. Reports may end up being re-written due to changes in the data and analysis. This thesis consists of three parts, addressing the dynamic aspects of statistics and data analysis. In the first part, we show how to explain the ideas behind some statistical methods using animations, followed by an introduction to the design and functionality of the animation package. In the second part, we discuss the design of an interactive statistical graphics system, with an emphasis on the reactive programming paradigm and its connection with the data infrastructure in R, as utilized in the cranvas package. In the third part, we provide a solution to statistical reporting, which is implemented in the knitr package, making use of literate programming. It frees us from the traditional approach of cut-and-paste, and provides a seamless integration of computing and reporting that enhances reproducible research. Demos and examples were given along with the discussion

Uformer: A Unet based dilated complex & real dual-path conformer network for simultaneous speech enhancement and dereverberation

Complex spectrum and magnitude are considered as two major features of speech enhancement and dereverberation. Traditional approaches always treat these two features separately, ignoring their underlying relationship. In this paper, we propose Uformer, a Unet based dilated complex & real dual-path conformer network in both complex and magnitude domain for simultaneous speech enhancement and dereverberation. We exploit time attention (TA) and dilated convolution (DC) to leverage local and global contextual information and frequency attention (FA) to model dimensional information. These three sub-modules contained in the proposed dilated complex & real dual-path conformer module effectively improve the speech enhancement and dereverberation performance. Furthermore, hybrid encoder and decoder are adopted to simultaneously model the complex spectrum and magnitude and promote the information interaction between two domains. Encoder decoder attention is also applied to enhance the interaction between encoder and decoder. Our experimental results outperform all SOTA time and complex domain models objectively and subjectively. Specifically, Uformer reaches 3.6032 DNSMOS on the blind test set of Interspeech 2021 DNS Challenge, which outperforms all top-performed models. We also carry out ablation experiments to tease apart all proposed sub-modules that are most important.Comment: Accepted by ICASSP 202

VE-KWS: Visual Modality Enhanced End-to-End Keyword Spotting

The performance of the keyword spotting (KWS) system based on audio modality, commonly measured in false alarms and false rejects, degrades significantly under the far field and noisy conditions. Therefore, audio-visual keyword spotting, which leverages complementary relationships over multiple modalities, has recently gained much attention. However, current studies mainly focus on combining the exclusively learned representations of different modalities, instead of exploring the modal relationships during each respective modeling. In this paper, we propose a novel visual modality enhanced end-to-end KWS framework (VE-KWS), which fuses audio and visual modalities from two aspects. The first one is utilizing the speaker location information obtained from the lip region in videos to assist the training of multi-channel audio beamformer. By involving the beamformer as an audio enhancement module, the acoustic distortions, caused by the far field or noisy environments, could be significantly suppressed. The other one is conducting cross-attention between different modalities to capture the inter-modal relationships and help the representation learning of each modality. Experiments on the MSIP challenge corpus show that our proposed model achieves 2.79% false rejection rate and 2.95% false alarm rate on the Eval set, resulting in a new SOTA performance compared with the top-ranking systems in the ICASSP2022 MISP challenge.Comment: 5 pages. Accepted at ICASSP202