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IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

作者： Ya-Feng Liu Yu-Hong Dai Zhi-Quan Luo State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy and Sciences Beijing China Department of Electronic and Computer Engineering University of Minnesota Minneapolis MN USA

For a general MIMO interference channel, we can determine the feasibility of linear interference alignment via minimizing the leakage interference. This paper gives a complete complexity characterization of the leakage interference minimization problem. It is shown that, when each transmitter (receiver) is equipped with at least three antennas and each receiver (transmitter) is equipped with at least two antennas, the problem of checking whether the interference in the network can be perfectly aligned is strongly NP-hard. Moreover, when each transmit/receive node is equipped with two or more antennas, leakage interference minimization can not be solved (even approximately) in polynomial time, unless P = NP.

关键词： Interference Polynomials Minimization MIMO Complexity theory Receiving antennas

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Elastic property of single double-stranded DNA molecules: Theoretical study and comparison with experiments

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Physical Review E 2000年第1期62卷 1045-1045页

作者： Haijun Zhou Yang Zhang Zhong-can Ou-Yang Institute of Theoretical Physics Academia Sinica P.O. Box 2735 Beijing 100080 China State Key Laboratory of Scientific and Engineering Computing Beijing 100080 China Institute for Advanced Study Tsinghua University Beijing 100084 China

This paper aims at a comprehensive understanding of the novel elastic property of double-stranded DNA (dsDNA) discovered very recently through single-molecule manipulation techniques. A general elastic model for double-stranded biopolymers is proposed, and a structural parameter called the folding angle φ is introduced to characterize their deformations. The mechanical property of long dsDNA molecules is then studied based on this model, where the base-stacking interactions between DNA adjacent nucleotide base pairs, the steric effects of base pairs, and the electrostatic interactions along DNA backbones are taken into account. Quantitative results are obtained by using a path integral method, and excellent agreement between theory and the observations reported by five major experimental groups are attained. The strong intensity of the base stacking interactions ensures the structural stability of DNA, while the short-ranged nature of such interactions makes externally stimulated large structural fluctuations possible. The entropic elasticity, highly extensibility, and supercoiling property of DNA are all closely related to this account. The present work also suggests the possibility that negative torque can induce structural transitions in highly extended DNA from the right-handed B form to left-handed configurations similar to the Z-form configuration. Some formulas concerned with the application of path integral methods to polymeric systems are listed in the Appendixes.

关键词： .base pairs double-stranded Elastic supercoiling backbones Deformations torque Ou-Yang base-stacking folding angle dsDNA molecules

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A fully implicit method for lattice boltzmann equations

A fully implicit method for lattice boltzmann equations

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作者： Huang, Jizu Yang, Chao Cai, Xiao-Chuan Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Institute of Software Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Computer Science Beijing100190 China Department of Computer Science University of Colorado Boulder BoulderCO80309 United States

Existing approaches for solving the lattice Boltzmann equations with finite difference methods are explicit and semi-implicit;both have certain stability constraints on the time step size. In this work, a fully implicit second-order finite difference scheme is developed. We focus on a parallel, highly scalable, Newton-Krylov-RAS algorithm for the solution of a large sparse nonlinear system of equations arising at each time step. Here, RAS is a restricted additive Schwarz preconditioner based on a first-order spatial discretization. We show numerically that by using the fully implicit method the time step size is no longer constrained by the CFL condition, and the Newton-Krylov- RAS algorithm is scalable on a supercomputer with more than ten thousand processors. Moreover, to calculate the steady state solution we investigate an adaptive time stepping strategy. The total compute time required by the implicit method with adaptive time stepping is much smaller than that of an explicit method for several test cases. © 2015 Society for Industrial and Applied Mathematics.

关键词： Finite difference method

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Make regularization effective in training sparse CNN

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Computational Optimization and Applications 2020年第1期77卷 163-182页

作者： He, Juncai Jia, Xiaodong Xu, Jinchao Zhang, Lian Zhao, Liang Department of Mathematics Pennsylvania State University University Park USA Department of Computer Science and Engineering Pennsylvania State University University Park USA State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences and University of Chinese Academy of Sciences Beijing China

Compressed Sensing using $$\ell _1$$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network (CNN)? This paper is aimed to provide an answer to this question and to show how to make it work. Following Xiao (J Mach Learn Res 11(Oct):2543–2596, 2010), We first demonstrate that the commonly used stochastic gradient decent and variants training algorithm is not an appropriate match with $$\ell _1$$ regularization and then replace it with a different training algorithm based on a regularized dual averaging (RDA) method. The RDA method of Xiao (J Mach Learn Res 11(Oct):2543–2596, 2010) was originally designed specifically for convex problem, but with new theoretical insight and algorithmic modifications (using proper initialization and adaptivity), we have made it an effective match with $$\ell _1$$ regularization to achieve a state-of-the-art sparsity for the highly non-convex CNN compared to other weight pruning methods without compromising accuracy (achieving 95% sparsity for ResNet-18 on CIFAR-10, for example).

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Mixed bounce-back boundary scheme of the general propagation lattice Boltzmann method for advection-diffusion equations

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Physical Review E 2019年第6期99卷 063316-063316页

作者： Xiuya Guo Zhenhua Chai Shengyong Pang Yong Zhao Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Material Processing and Die & Mould Technology Huazhong University of Science and Technology Wuhan 430074 China

In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes.

关键词： Lattice-Boltzmann methods

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A software platform for continuum modeling of ion channels based on unstructured mesh

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Computational Science and Discovery 2014年第1期7卷

作者： Tu, B. Bai, S.Y. Chen, M.X. Xie, Y. Zhang, L.B. Lu, B.Z. State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Center for System Biology Department of Mathematics Soochow University Suzhou215006 China

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson-Nernst-Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels. © 2014 IOP Publishing Ltd.

关键词： Finite element method

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Adaptive regularized newton method for riemannian optimization

arXiv

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arXiv 2017年

作者： Hu, Jiang Milzarek, Andre Wen, Zaiwen Yuan, Yaxiang Beijing International Center for Mathematical Research Peking University China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive regularized Newton method which approximates the original objective function by the second-order Taylor expansion in Euclidean space but keeps the Riemannian manifold constraints. The regularization term in the objective function of the subproblem enables us to establish a Cauchy-point like condition as the standard trust-region method for proving global convergence. The subproblem can be solved inexactly either by first-order methods or a modified Riemannian Newton method. In the later case, it can further take advantage of negative curvature directions. Both global convergence and superlinear local convergence are guaranteed under mild conditions. Extensive computational experiments and comparisons with other state-of-the-art methods indicate that the proposed algorithm is very promising. Copyright © 2017, The Authors. All rights reserved.

关键词： Newton-Raphson method

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Covariance-Based Joint Device Activity and Delay Detection in Asynchronous mMTC

arXiv

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arXiv 2021年

作者： Wang, Zhaorui Liu, Ya-Feng Liu, Liang The Department of Information Engineering The Chinese University of Hong Kong Hong Kong The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong

In this letter, we study the joint device activity and delay detection problem in asynchronous massive machine-type communications (mMTC), where all active devices asynchronously transmit their preassigned preamble sequences to the base station (BS) for device identification and delay detection. We first formulate this joint detection problem as a maximum likelihood estimation problem, which depends on the received signal only through its sample covariance, and then propose efficient coordinate descent type of algorithms to solve the formulated problem. Our proposed covariance-based approach is sharply different from the existing compressed sensing (CS) approach for the same problem. Numerical results show that our proposed covariance-based approach significantly outperforms the CS approach in terms of the detection performance since our proposed approach can make better use of the BS antennas than the CS approach. © 2021, CC BY.

关键词： Compressed sensing

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Role of gas density in the stability of single-bubble sonoluminescence

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Physical Review E 2001年第1期64卷 016317-016317页

作者： L. Yuan C. Y. Ho M.-C. Chu P. T. Leung State Key Laboratory of Scientific and Engineering Computing and Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of Physics The Chinese University of Hong Kong Shatin New Territories Hong Kong China

Recent full hydrodynamic simulations of a sonoluminescing bubble interior have shown that the bubble content is compressed to a very dense state during the violent collapse. In this paper, we numerically studied the shape stability of a radially oscillating gas bubble by using Hilgenfeldt et al. theoretical model with corrections taking into account the gas density effect. Our results show that gas density variations not only significantly suppress the Rayleigh-Taylor instability, but also enhance the threshold of the parametric instability under sonoluminescence conditions.

关键词： Sonoluminescence

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Incorporating Born solvation energy into the three-dimensional Poisson-Nernst-Planck model to study ion selectivity in KcsA K+ channels

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Physical Review E 2017年第6期96卷 062416-062416页

作者： Xuejiao Liu Benzhuo Lu State Key Laboratory of Scientific and Engineering Computing National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China and School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China

Potassium channels are much more permeable to potassium than sodium ions, although potassium ions are larger and both carry the same positive charge. This puzzle cannot be solved based on the traditional Poisson-Nernst-Planck (PNP) theory of electrodiffusion because the PNP model treats all ions as point charges, does not incorporate ion size information, and therefore cannot discriminate potassium from sodium ions. The PNP model can qualitatively capture some macroscopic properties of certain channel systems such as current-voltage characteristics, conductance rectification, and inverse membrane potential. However, the traditional PNP model is a continuum mean-field model and has no or underestimates the discrete ion effects, in particular the ion solvation or self-energy (which can be described by Born model). It is known that the dehydration effect (closely related to ion size) is crucial to selective permeation in potassium channels. Therefore, we incorporated Born solvation energy into the PNP model to account for ion hydration and dehydration effects when passing through inhomogeneous dielectric channel environments. A variational approach was adopted to derive a Born-energy-modified PNP (BPNP) model. The model was applied to study a cylindrical nanopore and a realistic KcsA channel, and three-dimensional finite element simulations were performed. The BPNP model can distinguish different ion species by ion radius and predict selectivity for K+ over Na+ in KcsA channels. Furthermore, ion current rectification in the KcsA channel was observed by both the PNP and BPNP models. The I−V curve of the BPNP model for the KcsA channel indicated an inward rectifier effect for K+ (rectification ratio of ∼3/2) but indicated an outward rectifier effect for Na+ (rectification ratio of ∼1/6).

关键词： Electrostatic interactions Biomolecules Finite-element method

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