Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general $H-$matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper

Who are the Devils Wearing Prada in New York City?

Fashion is a perpetual topic in human social life, and the mass has the penchant to emulate what large city residents and celebrities wear. Undeniably, New York City is such a bellwether large city with all kinds of fashion leadership. Consequently, to study what the fashion trends are during this year, it is very helpful to learn the fashion trends of New York City. Discovering fashion trends in New York City could boost many applications such as clothing recommendation and advertising. Does the fashion trend in the New York Fashion Show actually influence the clothing styles on the public? To answer this question, we design a novel system that consists of three major components: (1) constructing a large dataset from the New York Fashion Shows and New York street chic in order to understand the likely clothing fashion trends in New York, (2) utilizing a learning-based approach to discover fashion attributes as the representative characteristics of fashion trends, and (3) comparing the analysis results from the New York Fashion Shows and street-chic images to verify whether the fashion shows have actual influence on the people in New York City. Through the preliminary experiments over a large clothing dataset, we demonstrate the effectiveness of our proposed system, and obtain useful insights on fashion trends and fashion influence

Study on the Dual Asymmetric Effect of Monetary Policy Shocks: Empirical Test Based on China’s Stock and Bond Market

The research on dual asymmetric effects of monetary policy shock has important practical significance for laying down capital market regulation monetary policy. This paper uses two-step OLS method to empirically test the dual asymmetric effects of monetary policy shock on stock and bond markets. The test results show that the expansionary and tight monetary policy shocks on the stock and bond markets have dual asymmetric effects; the expansionary and tight monetary policy shocks have dual asymmetric effects during the rise and fall periods. Therefore, when laying down capital market regulation and control policies, government needs to consider the dual asymmetric effects of monetary policy shock, and adopts appropriate monetary policies. Key words: Monetary policy shocks; Dual asymmetric effects; Two-step OLS method; Empirical tes

Stacking sequence determines Raman intensities of observed interlayer shear modes in 2D layered materials - A general bond polarizability model

2D layered materials have recently attracted tremendous interest due to their fascinating properties and potential applications. The interlayer interactions are much weaker than the intralayer bonds, allowing the as-synthesized materials to exhibit different stacking sequences (e.g. ABAB, ABCABC), leading to different physical properties. Here, we show that regardless of the space group of the 2D material, the Raman frequencies of the interlayer shear modes observed under the typical configuration blue shift for AB stacked materials, and red shift for ABC stacked materials, as the number of layers increases. Our predictions are made using an intuitive bond polarizability model which shows that stacking sequence plays a key role in determining which interlayer shear modes lead to the largest change in polarizability (Raman intensity); the modes with the largest Raman intensity determining the frequency trends. We present direct evidence for these conclusions by studying the Raman modes in few layer graphene, MoS2, MoSe2, WSe2 and Bi2Se3, using both first principles calculations and Raman spectroscopy. This study sheds light on the influence of stacking sequence on the Raman intensities of intrinsic interlayer modes in 2D layered materials in general, and leads to a practical way of identifying the stacking sequence in these materials.Comment: 30 pages, 8 figure

Molecular geometric deep learning

Geometric deep learning (GDL) has demonstrated huge power and enormous potential in molecular data analysis. However, a great challenge still remains for highly efficient molecular representations. Currently, covalent-bond-based molecular graphs are the de facto standard for representing molecular topology at the atomic level. Here we demonstrate, for the first time, that molecular graphs constructed only from non-covalent bonds can achieve similar or even better results than covalent-bond-based models in molecular property prediction. This demonstrates the great potential of novel molecular representations beyond the de facto standard of covalent-bond-based molecular graphs. Based on the finding, we propose molecular geometric deep learning (Mol-GDL). The essential idea is to incorporate a more general molecular representation into GDL models. In our Mol-GDL, molecular topology is modeled as a series of molecular graphs, each focusing on a different scale of atomic interactions. In this way, both covalent interactions and non-covalent interactions are incorporated into the molecular representation on an equal footing. We systematically test Mol-GDL on fourteen commonly-used benchmark datasets. The results show that our Mol-GDL can achieve a better performance than state-of-the-art (SOTA) methods. Source code and data are available at https://github.com/CS-BIO/Mol-GDL