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arXiv 2019年

作者： Zhou, Yongtao Suzuki, Jorge L. Zhang, Chengjian Zayernouri, Mohsen School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering Michigan State University East LansingMI48824 United States Department of Mechanical Engineering Michigan State University East LansingMI48824 United States School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering Department of Statistics and Probability Michigan State University East LansingMI48824 United States

Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the inverse power-law kernels deteriorates the accuracy and efficiency of many existing numerical methods. We develop two efficient first- and second-order implicit-explicit (IMEX) methods for accurate time-integration of stiff/nonlinear fractional differential equations with fractional order α ∈ (0, 1] and prove their convergence and linear stability properties. The developed methods are based on a linear multi-step fractional Adams-Moulton method (FAMM), followed by the extrapolation of the nonlinear force terms. In order to handle the singularities nearby the initial time, we employ Lubich-like corrections to the resulting fractional operators. The obtained linear stability regions of the developed IMEX methods are larger than existing IMEX methods in the literature. Furthermore, the size of the stability regions increase with the decrease of fractional order values, which is suitable for stiff problems. We also rewrite the resulting IMEX methods in the language of nonlinear Toeplitz systems, where we employ a fast inversion scheme to achieve a computational complexity of O(N log N), where N denotes the number of time-steps. Our computational results demonstrate that the developed schemes can achieve global first- and second-order accuracy for highly-oscillatory stiff/nonlinear problems with singularities. Copyright © 2019, The Authors. All rights reserved.

关键词： Matrix algebra

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Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems

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Communications in Computational Physics 2017年第1期21卷 237-270页

作者： Peng Wang Jialin Hong Dongsheng Xu Institute of Mathematics Jilin UniversityChangchun 130012P.R.China State Key Laboratory of Scientific and Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences100080 BeijingP.R.China University of Chinese Academy of Sciences P.R.China

We study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems(SHS).Three types of systems,SHS with multiplicative noise,special separable Hamiltonians and multiple additive noise,respectively,are considered in this *** Runge-Kutta(SRK)methods for these systems are investigated,and the corresponding conditions for SRK methods to preserve the symplectic property are *** on the weak/strong order and symplectic conditions,some effective schemes are *** particular,using the algebraic computation,we obtained two classes of high weak order symplectic Runge-Kutta methods for SHS with a single multiplicative noise,and two classes of high strong order symplectic Runge-Kutta methods for SHS with multiple multiplicative and additive noise,*** numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

关键词： Stochastic differential equation Stochastic Hamiltonian system symplectic integration Runge-Kutta method order condition

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An additive overlapping domain decomposition method for the helmholtz equation

arXiv

引用

arXiv 2018年

作者： Leng, Wei Ju, Lili State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sci-ences Beijing100190 China Department of Mathematics University of South Carolina ColumbiaSC29208 United States

In this paper, we propose and analyze an additive domain decompo- sition method (DDM) for solving the high-frequency Helmholtz equation with the Sommerfeld radiation condition. In the proposed method, the computational domain is partitioned into structured subdomains along all spatial directions, and each subdomain contains an overlapping region for source transferring. At each iteration all subdomain PML problems are solved completely in parallel, then all horizontal, vertical and corner directional residuals on each subdomain are passed to its corresponding neighbor subdomains as the source for the next iteration. This DDM method is highly scalable in nature and theoretically shown to produce the exact solution for the PML problem defined in 2in the constant medium case. A slightly modified version of the method for bounded truncated domains is also developed for its use in practice and an error estimate is rigorously proved. Various numerical experiments in two and three dimensions are conducted on the supercomputer "Tianhe-2 Cluster" to verify the theoretical results and demonstrate excellent performance of the proposed method as an iterative solver or a preconditioner. Copyright © 2018, The Authors. All rights reserved.

关键词： Domain decomposition methods

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Harmonized-Multinational qEEG norms (HarMNqEEG)

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NEUROIMAGE 2022年 256卷 119190-119190页

作者： Li, Min Wang, Ying Lopez-Naranjo, Carlos Hu, Shiang Reyes, Ronaldo Cesar Garcia Paz-Linares, Deirel Areces-Gonzalez, Ariosky Hamid, Aini Ismafairus Abd Evans, Alan C. Savostyanov, Alexander N. Calzada-Reyes, Ana Villringer, Arno Tobon-Quintero, Carlos A. Garcia-Agustin, Daysi Yao, Dezhong Dong, Li Aubert-Vazquez, Eduardo Reza, Faruque Razzaq, Fuleah Abdul Omar, Hazim Abdullah, Jafri Malin Galler, Janina R. Ochoa-Gomez, John F. Prichep, Leslie S. Galan-Garcia, Lidice Morales-Chacon, Lilia Valdes-Sosa, Mitchell J. Trondle, Marius Zulkifly, Mohd Faizal Mohd Rahman, Muhammad Riddha Bin Abdul Milakhina, Natalya S. Langer, Nicolas Rudych, Pavel Koenig, Thomas Virues-Alba, Trinidad A. Lei, Xu Bringas-Vega, Maria L. Bosch-Bayard, Jorge F. Valdes-Sosa, Pedro Antonio [a]The Clinical Hospital of Chengdu Brain Science Institute MOE Key Lab for Neuroinformation School of Life Science and Technology University of Electronic Science and Technology of China Chengdu China [b]Cuban Center for Neurocience La Habana Cuba [c]McGill Centre for Integrative Neuroscience Ludmer Centre for Neuroinformatics and Mental Health Montreal Neurological Institute Canada [d]Department of Neurosciences School of Medical Sciences Universiti Sains Malaysia Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [e]Brain and Behaviour Cluster School of Medical Sciences Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [f]Hospital Universiti Sains Malaysia Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [g]Humanitarian Institute Novosibirsk State University Novosibirsk 630090 Russia [h]Laboratory of Psychophysiology of Individual Differences Federal State Budgetary Scientific Institution Scientific Research Institute of Neurosciences and Medicine Novosibirsk 630117 Russia [i]Laboratory of Psychological Genetics at the Institute of Cytology and Genetics Siberian Branch of the Russian Academy of Sciences Novosibirsk 630090 Russia [j]University of Pinar del Río “Hermanos Saiz Montes de Oca” Pinar del Río Cuba [k]Department of Neurology Max Planck Institute for Human Cognitive and Brain Sciences Leipzig Germany [l]Department of Cognitive Neurology University Hospital Leipzig Leipzig Germany [m]Center for Stroke Research Charité-Universitätsmedizin Berlin Berlin Germany [n]Grupo Neuropsicología y Conducta - GRUNECO Faculty of Medicine Universidad de Antioquia Colombia [o]Research Department Institución Prestadora de Servicios de Salud IPS Universitaria Colombia [p]The Cuban center aging longevity and health Havana Cuba [q]Research Unit of NeuroInformation Chinese Academy of Medical Sciences Chengdu 2019RU035 China [r]School of Electrical Engineering Zhengzhou University Zhengzhou 4500

This paper extends frequency domain quantitative electroencephalography (qEEG) methods pursuing higher sensitivity to detect Brain Developmental Disorders. Prior qEEG work lacked integration of cross-spectral information omitting important functional connectivity descriptors. Lack of geographical diversity precluded accounting for site-specific variance, increasing qEEG nuisance variance. We ameliorate these weaknesses. (i) Create lifespan Riemannian multinational qEEG norms for cross-spectral tensors. These norms result from the HarMNqEEG project fostered by the Global Brain Consortium. We calculate the norms with data from 9 countries, 12 devices, and 14 studies, including 1564 subjects. Instead of raw data, only anonymized metadata and EEG cross spectral tensors were shared. After visual and automatic quality control, developmental equations for the mean and standard deviation of qEEG traditional and Riemannian DPs were calculated using additive mixed-effects models. We demonstrate qEEG "batch effects " and provide methods to calculate harmonized z-scores. (ii) We also show that harmonized Riemannian norms produce z-scores with increased diagnostic accuracy predicting brain dysfunction produced by malnutrition in the first year of life and detecting COVID induced brain dysfunction. (iii) We offer open code and data to calculate different individual z-scores from the HarMNqEEG dataset. These results contribute to developing bias-free, low-cost neuroimaging technologies applicable in various health settings.

关键词： Quantitative EEG EEG cross-spectrum Riemannian geometry Batch effects Z-score Harmonization Malnutrition Covid induced brain dysfunction Developmental Brain Chart

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On the relationship between the diffuse reflection and bounce-back boundary condition in the continuum limit

arXiv

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arXiv 2018年

作者： Meng, Jianping Gu, Xiao-Jun Emerson, David R. Peng, Yong Zhang, Jianmin Scientific Computing Department STFC Daresbury Laboratory WarringtonWA4 4AD United Kingdom State Key Laboratory of Hydraulics and Mountain River Engineering Sichuan University Chengdu610065 China

In this work, we show that the widely used bounce-back boundary condition is an incomplete form of the diffuse reflection boundary condition at the continuum limit for lattice Boltzmann simulations. By utilizing this fact, we can force the diffuse reflection scheme to work at its continuum limit so that the no-slip boundary condition can be implemented without any nonphysical slip velocity error being induced by the standard bounce-back scheme. The revised boundary formulation is validated numerically by solving a pressure-driven channel flow, a lid-driven cavity flow and channel flow around a square cylinder. Copyright © 2018, The Authors. All rights reserved.

关键词： Channel flow

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One-Bit precoding and constellation range design for massive MIMO with QAM Signaling

arXiv

引用

arXiv 2018年

作者： Sohrabi, Foad Liu, Ya-Feng Yu, Wei Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S3G4 Canada State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing100190 China

The use of low-resolution digital-to-analog converters (DACs) for transmit precoding provides crucial energy efficiency advantage for massive multiple-input multiple-output (MIMO) implementation. This paper formulates a quadrature amplitude modulation (QAM) constellation range and one-bit symbol-level precoding design problem for minimizing the average symbol error rate (SER) in downlink massive MIMO transmission. A tight upper-bound for SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of one-bit precoding can be interpreted as a decrease in the effective minimum distance of the QAM constellation. Using the obtained SER expression, we propose a QAM constellation range design for the singleuser case. It is shown that in the massive MIMO limit, a reasonable choice for constellation range with one-bit precoding is that of the infinite-resolution precoding with per-symbol power constraint, but reduced by a factor of p 2/π or about 0:8. The corresponding minimum distance reduction translates to about 2dB gap between the performance of one-bit precoding and infinite-resolution precoding. This paper further proposes a low-complexity heuristic algorithm for one-bit precoder design. Finally, the proposed QAM constellation range and precoder design are generalized to the multi-user downlink. We propose to scale the constellation range for infinite-resolution zero-forcing (ZF) precoding with per-symbol power constraint by the same factor of p 2/π for one-bit precoding. The proposed one-bit precoding scheme is shown to be within 2dB of infinite-resolution ZF. In term of number of antennas, one-bit precoding requires about 50% more antennas to achieve the same performance as infinite-resolution precoding. Copyright © 2018, The Authors. All rights reserved.

关键词： Quadrature amplitude modulation

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Third-order discrete unified gas kinetic scheme for continuum and rarefied flows: Low-speed isothermal case

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Physical Review E 2018年第2期97卷 023306-023306页

作者： Chen Wu Baochang Shi Chang Shu Zhen Chen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan 430074 China 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 Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore 119260 Singapore

An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation-based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second order (or lower order) of accuracy in the time-splitting scheme as in the conventional high-order Runge-Kutta-based kinetic methods, the present method solves the original Boltzmann equation, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows.

关键词： Boltzmann theory

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Lattice Boltzmann model for high-order nonlinear partial differential equations

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Physical Review E 2018年第1期97卷 013304-013304页

作者： Zhenhua Chai Nanzhong He Zhaoli Guo 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 Coal Combustion Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Computer Wuhan Textile University Wuhan 430200 China

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ+∑k=1mαk∂xkΠk(ϕ)=0 (1≤k≤m≤6), αk are constant coefficients, Πk(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009); H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)] for high-order nonlinear partial differential equations.

关键词： Lattice-Boltzmann methods

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Optimized base-station cache allocation for cloud radio access network with multicast backhaul

arXiv

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arXiv 2018年

作者： Dai, Binbin Liu, Ya-Feng Yu, Wei Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada 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 performance of cloud radio access network (C-RAN) is limited by the finite capacities of the backhaul links connecting the centralized processor (CP) with the base-stations (BSs), especially when the backhaul is implemented in a wireless medium. This paper proposes the use of wireless multicast together with BS caching, where the BSs pre-store contents of popular files, to augment the backhaul of C-RAN. For a downlink C-RAN consisting of a single cluster of BSs and wireless backhaul, this paper studies the optimal cache size allocation strategy among the BSs and the optimal multicast beamforming transmission strategy at the CP such that the user’s requested messages are delivered from the CP to the BSs in the most efficient way. We first state a multicast backhaul rate expression based on a joint cache-channel coding scheme, which implies that larger cache sizes should be allocated to the BSs with weaker channels. We then formulate a two-timescale joint cache size allocation and beamforming design problem, where the cache is optimized offline based on the long-term channel statistical information, while the beamformer is designed during the file delivery phase based on the instantaneous channel state information. By leveraging the sample approximation method and the alternating direction method of multipliers (ADMM), we develop efficient algorithms for optimizing cache size allocation among the BSs, and quantify how much more cache should be allocated to the weaker BSs. We further consider the case with multiple files having different popularities and show that it is in general not optimal to entirely cache the most popular files first. Numerical results show considerable performance improvement of the optimized cache size allocation scheme over the uniform allocation and other heuristic schemes. Copyright © 2018, The Authors. All rights reserved.

关键词： Base stations

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Capacity optimality of AMP in coded systems

arXiv

引用

arXiv 2019年

作者： Liu, Lei Liang, Chulong Ma, Junjie Ping, Li Hong Kong SAR China Nomi 923-1292 Japan Department of Electrical Engineering City University of Hong Kong Hong Kong SAR China Algorithm Department ZTE Corporation Shenzhen 518057 China State Key Laboratory of Mobile Network Mobile Multimedia Technology ZTE Corporation Shenzhen 518057 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Science Beijing China Department of Electronic Engineering City University of Hong Kong Hong Kong SAR China

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed. © 2019, CC BY-NC-SA.

关键词： Message passing

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