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Uplink-downlink duality between multiple-access and broadcast channels with compressing relays

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arXiv 2020年

作者： Liu, Liang Liu, Ya-Feng Patil, Pratik Yu, Wei the Department of Electronic and Information Engineering The Hong Kong Polytechnic University 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 Edward S. Rogers Sr. Department of Electrical and Computer Engineering the University of Toronto the Department of Statistics and Data Science and the Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 10 King’s College Road TorontoONM5S3G4 Canada

—Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers;the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink. Copyright © 2020, The Authors. All rights reserved.

关键词： Linear programming

An orthogonalization-free parallelizable framework for all-electron calculations in density functional theory

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arXiv 2020年

作者： Bin, G.A.O. Guanghui, H.U. Kuang, Yang Xin, L.I.U. ICTEAM Institute UCLouvain Louvain-la-Neuve Belgium Department of Mathematics University of Macau Macao SAR China Zhuhai UM Science & Technology Research Institute Guangdong Province China Department of Mathematics National University of Singapore Singapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the model formulations, both nonlinear eigenvalue problem and total energy minimization problem pursue orthogonal solutions. Most existing algorithms for solving these two models invoke orthogonalization process either explicitly or implicitly in each iteration. Their efficiency suffers from this process in view of its cubic complexity and low parallel scalability in terms of the number of electrons for large scale systems. To break through this bottleneck, we propose an orthogonalization-free algorithm framework based on the total energy minimization problem. It is shown that the desired orthogonality can be gradually achieved without invoking orthogonalization in each iteration. Moreover, this framework fully consists of Basic Linear Algebra Subprograms (BLAS) operations and thus can be naturally parallelized. The global convergence of the proposed algorithm is established. We also present a precondition technique which can dramatically accelerate the convergence of the algorithm. The numerical experiments on all-electron calculations show the efficiency and high scalability of the proposed algorithm. Copyright © 2020, The Authors. All rights reserved.

关键词： Density functional theory

Joint switch upgrade and controller deployment in hybrid software-defined networks

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arXiv 2019年

作者： Guo, Zehua Chen, Weikun Liu, Ya-Feng Xu, Yang Zhang, Zhi-Li Department of Computer Science and Engineering University of Minnesota Twin Cities MinneapolisMN55455 United States 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 School Of Computer Science Fudan University Shanghai200433 China

To improve traffic management ability, Internet Service Providers (ISPs) are gradually upgrading legacy network devices to programmable devices that support Software-Defined Networking (SDN). The coexistence of legacy and SDN devices gives rise to a hybrid SDN. Existing hybrid SDNs do not consider the potential performance issues introduced by a centralized SDN controller: flow requests processed by a highly loaded controller may experience long tail processing delay;inappropriate multi-controller deployment could increase the propagation delay of flow requests. In this paper, we propose to jointly consider the deployment of SDN switches and their controllers for hybrid SDNs. We formulate the joint problem as an optimization problem that maximizes the number of flows that can be controlled and managed by the SDN and minimizes the propagation delay of flow requests between SDN controllers and switches under a given upgrade budget constraint. We show this problem is NP-hard. To efficiently solve the problem, we propose some techniques (e.g., strengthening the constraints and adding additional valid inequalities) to accelerate the global optimization solver for solving the problem for small networks and an efficient heuristic algorithm for solving it for large networks. The simulation results from real network topologies illustrate the effectiveness of the proposed techniques and show that our proposed heuristic algorithm uses a small number of controllers to manage a high amount of flows with good performance. Copyright © 2019, The Authors. All rights reserved.

关键词： Software defined networking

Impacts of prior parameter distributions on Bayesian evaluation of groundwater model complexity

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Water Science and engineering 2018年第2期11卷 89-100页

作者： Saeideh Samani Ming Ye Fan Zhang Yong-zhen Pei Guo-ping Tang Ahmed Elshall Asghar A.Moghaddam Department of Earth Sciences University of Tabriz Department of Scientific Computing Florida State University School of Computer Science and Software Engineering Tianjin Polytechnic University Department of Earth Ocean and Atmospheric Science Florida State University Key Laboratory of Tibetan Environment Changes and Land Surface Processes Institute of Tibetan Plateau Research Chinese Academy of Sciences Environmental Sciences Division Oak Ridge National Laboratory

This study used the marginal likelihood and Bayesian posterior model probability for evaluation of model complexity in order to avoid using over-complex models for numerical simulations. It focused on investigation of the impacts of prior parameter distributions(involved in calculating the marginal likelihood) on the evaluation of model complexity. We argue that prior parameter distributions should define the parameter space in which numerical simulations are made. New perspectives on the prior parameter distribution and posterior model probability were demonstrated in an example of groundwater solute transport modeling with four models, each simulating four column experiments. The models had different levels of complexity in terms of their model structures and numbers of calibrated parameters. The posterior model probability was evaluated for four cases with different prior parameter distributions. While the distributions substantially impacted model ranking, the model ranking in each case was reasonable for the specific circumstances in which numerical simulations were made. For evaluation of model complexity, it is thus necessary to determine the parameter spaces for modeling, which can be done by conducting numerical simulation and usineg engineering judgment based on understanding of the system being studied.

关键词： Marginal likelihood Posterior model probability Advection-dispersion equation Mobile-immobile model Groundwater model

Photocatalytic Hydrogen Production on a sp2-Carbon-Linked Covalent Organic Framework

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Angewandte Chemie 2022年第42期134卷

作者： Si Ma Prof. Dr. Tianqi Deng Dr. Ziping Li Zhenwei Zhang Ji Jia Qizhen Li Prof. Dr. Gang Wu Prof. Dr. Hong Xia Prof. Dr. Shuo-Wang Yang Prof. Dr. Xiaoming Liu College of Chemistry Jilin University Changchun 130012 P.R. China Institute of Advanced Semiconductors & Zhejiang Provincial Key Laboratory of Power Semiconductor Materials and Devices ZJU-Hangzhou Global Scientific and Technological Innovation Center Hangzhou 311200 P.R. China State Key Laboratory of Silicon Materials & School of Materials Science and Engineering Zhejiang University Hangzhou 310027 P.R. China Department of Biomedical Engineering Southern University of Science and Technology Shenzhen 518055 P.R. China Institute of High Performance Computing Agency for Science Technology and Research 1 Fusionopolis Way #16-16 Connexis Singapore 138632 Singapore State Key Laboratory on Integrated Optoelectronics College of Electronic Science and Technology Jilin University Changchun 130012 P.R. China

Two-dimensional covalent organic frameworks (2D-COFs) have emerged as attractive platforms for solar-to-chemical energy conversion. In this study, we have implemented a gradient heating strategy to synthesize a sp 2 -carbon-linked triazine-based COF, COF-JLU100, exhibiting high crystallinity, large surface area, good durability and carrier mobility for solar-driven photocatalytic hydrogen evolution. The Pt-doped COF-JLU100 demonstrated a high hydrogen evolution rate of over 100 000 μmol g −1 h −1 for water splitting under visible-light illumination (λ>420 nm). Experimental and theoretical studies corroborate that the cyano-vinylene segments in COF-JLU100 extend the π-delocalization and enable fast charge transfer and separation rates as well as good dispersion in water. Moreover, COF-JLU100 can be prepared by low-cost and easily available monomers and has excellent stability, which is desirable for practical solar-driven hydrogen production.

关键词： Covalent Organic Frameworks Gradient Heating Hydrogen Evolution Photocatalysis sp2 Carbon Linkage

On the complexity of an augmented lagrangian method for nonconvex optimization

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arXiv 2019年

作者： Grapiglia, Geovani N. Yuan, Ya-Xiang Departamento de Matemática Universidade Federal do Paraná Centro Politécnico Cx. postal 19.081 Paraná Curitiba81531-980 Brazil State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China

In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of O(| log(ǫ)|) outer iterations for the referred algorithm to generate an ǫ-approximate KKT point, for ǫ ∈ (0, 1). When the penalty parameters are unbounded, we prove an outer iteration complexity bound of O (ǫ−2/(α−1)), where α > 1 controls the rate of increase of the penalty parameters. For linearly constrained problems, these bounds yield to evaluation complexity bounds of O(| log(ǫ)|2ǫ−2) and O ( ǫ− ( 2(2+ α−1 α) +2 )), respectively, when appropriate first-order methods (p = 1) are used to approximately solve the unconstrained subproblems at each iteration. In the case of problems having only linear equality constraints, the latter bounds are improved to O(| log(ǫ)|2ǫ−(p+1)/p) and O ( ǫ− ( α−4 1 + p+1 p )), respectively, when appropriate p-order methods (p ≥ 2) are used as inner solvers. Copyright © 2019, The Authors. All rights reserved.

关键词： Nonlinear programming

Low-rank matrix optimization using polynomial-filtered subspace extraction

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arXiv 2019年

作者： LI, YONGFENG LIU, HAOYANG WEN, ZAIWEN YUAN, YAXIANG Beijing International Center for Mathematical Research Peking University China Beijing International Center for Mathematical Research Peking University State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScinceChinese Academy of Sciences China

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at each iteration which takes most of the computation time. In order to reduce the cost, we propose an inexact algorithm framework based on a polynomial subspace extraction. The idea is to use an additional polynomial-filtered iteration to extract an approximated eigenspace, and project the iteration matrix on this subspace, followed by an optimization update. The accuracy of the extracted subspace can be controlled by the degree of the polynomial filters. This kind of subspace extraction also enjoys the warm start property: The subspace of the current iteration is refined from the previous one. Then this framework is instantiated into two algorithms: The polynomial-filtered proximal gradient method and the polynomial-filtered alternating direction method of multipliers. We give a theoretical guarantee to the two algorithms that the polynomial degree is not necessarily very large. They share the same convergence speed as the corresponding original methods if the polynomial degree grows with an order (log k) at the k-th iteration. If the warm-start property is considered, the degree can be reduced to a constant, independent of the iteration k. Preliminary numerical experiments on several low-rank matrix optimization problems show that the polynomial filtered algorithms usually provide multi-fold speedups. Copyright © 2019, The Authors. All rights reserved.

关键词： Extraction

Analysis of the neighborhood pattern similarity measure for the role extraction problem

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arXiv 2020年

作者： Marchand, Melissa Gallivan, Kyle Huang, Wen van Dooren, Paul Department of Mathematics Florida State University 208 Love Building 1017 Academic Way TallahasseeFL32306-4510 United States Department of Mathematics Florida State University 208 Love Building 1017 Academic Way TallahasseeFL32306-4510 United States School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University XiamenFujian China Department of Mathematical Engineering Université catholique de Louvain Louvain-La-Neuve Belgium

In this paper we analyze an indirect approach, called the Neighborhood Pattern Similarity approach, to solve the so-called role extraction problem of a large-scale graph. The method is based on the preliminary construction of a node similarity matrix which allows in a second stage to group together, with an appropriate clustering technique, the nodes that are assigned to have the same role. The analysis builds on the notion of ideal graphs where all nodes with the same role, are also structurally equivalent. Copyright © 2020, The Authors. All rights reserved.

关键词： Extraction

Potential numerical techniques and challenges for atmospheric modeling

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Potential numerical techniques and challenges for atmospheri...

作者： Li, J. Steppeler, J. Fang, F. Pain, C.C. Zhu, J. Peng, X. Dong, L. Li, Y. Tao, L. Leng, W. Wang, Y. Zheng, J. International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Hamburg Germany Applied Modelling and Computation Group Department of Earth Science and Engineering Imperial College London London United Kingdom International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Department of Atmospheric Sciences University of Chinese Academy of Sciences Beijing China State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences Beijing China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China School of Mathematics and Statistics Henan University Kaifeng China Center for Excellence in Regional Atmospheric Environment Institute of Urban Environment Chinese Academy of Sciences Xiamen China