Hierarchical Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations

In this paper, we apply the hierarchical modeling technique and study some numerical linear algebra problems arising from the Brownian dynamics simulations of biomolecular systems where molecules are modeled as ensembles of rigid bodies. Given a rigid body $p$ consisting of $n$ beads, the $6 \times 3n$ transformation matrix $Z$ that maps the force on each bead to $p$'s translational and rotational forces (a $6\times 1$ vector), and $V$ the row space of $Z$, we show how to explicitly construct the $(3n-6) \times 3n$ matrix $\tilde{Q}$ consisting of $(3n-6)$ orthonormal basis vectors of $V^{\perp}$ (orthogonal complement of $V$) using only $\mathcal{O}(n \log n)$ operations and storage. For applications where only the matrix-vector multiplications $\tilde{Q}{\bf v}$ and $\tilde{Q}^T {\bf v}$ are needed, we introduce asymptotically optimal $\mathcal{O}(n)$ hierarchical algorithms without explicitly forming $\tilde{Q}$. Preliminary numerical results are presented to demonstrate the performance and accuracy of the numerical algorithms

ReCO: A Large Scale Chinese Reading Comprehension Dataset on Opinion

This paper presents the ReCO, a human-curated ChineseReading Comprehension dataset on Opinion. The questions in ReCO are opinion based queries issued to the commercial search engine. The passages are provided by the crowdworkers who extract the support snippet from the retrieved documents. Finally, an abstractive yes/no/uncertain answer was given by the crowdworkers. The release of ReCO consists of 300k questions that to our knowledge is the largest in Chinese reading comprehension. A prominent characteristic of ReCO is that in addition to the original context paragraph, we also provided the support evidence that could be directly used to answer the question. Quality analysis demonstrates the challenge of ReCO that requires various types of reasoning skills, such as causal inference, logical reasoning, etc. Current QA models that perform very well on many question answering problems, such as BERT, only achieve 77% accuracy on this dataset, a large margin behind humans nearly 92% performance, indicating ReCO presents a good challenge for machine reading comprehension. The codes, datasets are freely available at https://github.com/benywon/ReCO.Comment: AAAI-2020 camera read

Evolution mechanism of principal modes in climate dynamics

Eigen analysis has been a powerful tool to distinguish multiple processes into different simple principal modes in complex systems. For a non-equilibrium system, the principal modes corresponding to the non-equilibrium processes are usually evolving with time. Here, we apply the eigen analysis into the complex climate systems. In particular, based on the daily surface air temperature in the tropics (30? S–30? N, 0? E–360? E) between 1979-01-01 and 2016-12-31, we uncover that the strength of two dominated intra-annual principal modes represented by the eigenvalues significantly changes with the El Niño/southern oscillation from year to year. Specifically, according to the ‘regional correlation’ introduced for the first intra-annual principal mode, we find that a sharp positive peak of the correlation between the El Niño region and the northern (southern) hemisphere usually signals the beginning (end) of the El Niño. We discuss the underlying physical mechanism and suppose that the evolution of the first intra-annual principal mode is related to the meridional circulations; the evolution of the second intra-annual principal mode responds positively to the Walker circulation. Our framework presented here not only facilitates the understanding of climate systems but also can potentially be used to study the dynamical evolution of other natural or engineering complex systems. © 2020 The Author(s)

Correlation and scaling behaviors of fine particulate matter (PM2.5) concentration in China

Air pollution has become a major issue and caused widespread environmental and health problems. Aerosols or particulate matters are an important component of the atmosphere and can transport under complex meteorological conditions. Based on the data of PM2.5 observations, we develop a network approach to study and quantify their spreading and diffusion patterns. We calculate cross-correlation functions of the time lag between sites within different seasons. The probability distribution of correlation changes with season. It is found that the probability distributions in four seasons can be scaled into one scaling function with averages and standard deviations of correlation. This seasonal scaling behavior indicates that there is the same mechanism behind correlations of PM2.5 concentration in different seasons. Further, the weighted degrees reveal the strongest correlations of PM2.5 concentration in winter and in the North China Plain for the positive correlation pattern that is mainly caused by the transport of PM2.5. These directional degrees show net influences of PM2.5 along Gobi and inner Mongolia, the North China Plain, Central China, and Yangtze River Delta. The negative correlation pattern could be related to the large-scale atmospheric waves. Copyright (C) EPLA, 2018Peer reviewe