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Network slicing for service-oriented networks under resource constraints

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arXiv 2017年

作者： Zhang, Nan Liu, Ya-Feng Farmanbar, Hamid Chang, Tsung-Hui Hong, Mingyi Luo, Zhi-Quan School of Mathematical Sciences Peking University 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 Beijing China Huawei Canada Research Center Ottawa Canada Department of Electrical and Computer Engineering University of Minnesota United States Shenzhen Research Institute of Big Data Chinese University of Hong Kong Shenzhen China

To support multiple on-demand services over fixed communication networks, network operators must allow flexible customization and fast provision of their network resources. One effective approach to this end is network virtualization, whereby each service is mapped to a virtual subnetwork providing dedicated on-demand support to network users. In practice, each service consists of a prespecified sequence of functions, called a service function chain (SFC), while each service function in a SFC can only be provided by some given network nodes. Thus, to support a given service, we must select network function nodes according to the SFC and determine the routing strategy through the function nodes in a specified order. A crucial network slicing problem that needs to be addressed is how to optimally localize the service functions in a physical network as specified by the SFCs, subject to link and node capacity constraints. In this paper, we formulate the network slicing problem as a mixed binary linear program and establish its strong NP-hardness. Furthermore, we propose efficient penalty successive upper bound minimization (PSUM) and PSUM-R(ounding) algorithms, and two heuristic algorithms to solve the problem. Simulation results are shown to demonstrate the effectiveness of the proposed algorithms. Copyright © 2017, The Authors. All rights reserved.

关键词： Network function virtualization

A semi-smooth newton method for solving semidefinite programs in electronic structure calculations

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arXiv 2017年

作者： Li, Yongfeng Wen, Zaiwen Yang, Chao Yuan, Yaxiang Beijing International Center for Mathematical Research Peking University China Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States State Key Laboratory of Scientific and Engineering Computing Academy OfMathematics and Systems Science Chinese Academy of Sciences China

The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron wavefunctions. This problem can be formulated as a semidefinite programming problem. Due the large size of the problem, the well-known interior point method can only be used to tackle problems with a few atoms. First-order methods such as the the alternating direction method ofmultipliers (ADMM) have much lower computational cost per iteration. However, their convergence can be slow, especially for obtaining highly accurate approximations. In this paper, we present a practical and efficient second-order semi-smooth Newton type method for solving the SDP formulation of the energy minimization problem. We discuss a number of techniques that can be used to improve the computational efficiency of the method and achieve global convergence. Extensive numerical experiments show that our approach is competitive to the state-of-the-art methods in terms of both accuracy and speed. Copyright © 2017, The Authors. All rights reserved.

关键词： Computational efficiency

The effect of numerical noises on statistics of a chaotic dynamical system

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Journal of Physics: Conference Series 2018年第1期1039卷

作者： Xiaoming Li Xiaochen Li Shijun Liao School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai 200240 China School of Civil Engineering and Transportation South China University of Technology Guangzhou 510641 China MoE Key Laboratory in Scientific and Engineering Computing Shanghai 200240 China

It is well known that chaotic dynamical systems have the sensitive dependence on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error) always exist in practice. Thus, due to the SDIC, long-term accurate prediction of chaotic dynamical systems is practically impossible. In this paper, using the so-called 'clean numerical simulation' (CNS) whose numerical noises might be much smaller even than micro-level physical uncertainty and thus are negligible, we gain accurate prediction of a chaotic dynamical system in a long enough interval of time. Then, based on these reliable simulations, the influence of numerical noises on statistic computations is investigated. It is found that the influence of numerical noises is negligible when statistic results are time-independent. Unfortunately, when the statistics of a chaotic dynamical system are time-dependent, numerical noises have a great influence even on statistic computations.

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Jacobi polynomials on the Bernstein ellipse

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arXiv 2017年

作者： Wang, Haiyong Zhang, Lun 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 School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathe-matics Fudan University Shanghai200433

In this paper, we are concerned with Jacobi polynomials P(α,β)n(x) on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral interpolation. An explicit representation of P(α,β)n(x) is derived in the variable of parametrization. This formula further allows us to show that the maximum value of |P(α,β)n(z)| over the Bernstein ellipse is attained at one of the endpoints of the major axis if α+β ≥ -1. For the minimum value, we are able to show that for a large class of Gegenbauer polynomials (i.e., α = β), it is attained at two endpoints of the minor axis. These results particularly extend those previously known only for some special cases. Moreover, we obtain a more refined asymptotic estimate for Jacobi polynomials on the Bernstein ellipse.65N35, 65D05, 41A05, 41A25 Copyright © 2017, The Authors. All rights reserved.

关键词： Polynomials

Sample Approximation-Based Deflation Approaches for Chance SINR-Constrained Joint Power and Admission Control

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Sample Approximation-Based Deflation Approaches for Chance S...

作者： Liu, Ya-Feng Hong, Mingyi Song, Enbin State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing100190 China Iowa State University AmesIA50011 United States Department of Mathematics Sichuan University Chengdu610064 China

Consider the joint power and admission control (JPAC) problem for a multiuser single-input single-output (SISO) interference channel. Most existing works on JPAC assume the perfect instantaneous channel state information (CSI). In this paper, we consider the JPAC problem with the imperfect CSI, i.e., we assume that only the channel distribution information (CDI) is available. We formulate the JPAC problem into a chance (probabilistic)-constrained program, where each link's SINR outage probability is enforced to be less than or equal to a specified tolerance. To circumvent the computational difficulty of the chance SINR constraints, we propose to use the sample (scenario) approximation scheme to convert them into finitely many simple linear constraints. Furthermore, we reformulate the sample approximation of the chance SINR-constrained JPAC problem as a composite group sparse minimization problem and then approximate it by a second-order cone program (SOCP). The solution of the SOCP approximation can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure (the deflation approach). We exploit the special structure of the SOCP approximation and custom-design an efficient algorithm for solving it. Finally, we illustrate the effectiveness and efficiency of the proposed sample approximation-based deflation approaches by simulations. © 2016 IEEE.

关键词： Channel state information

Lattice boltzmann modeling of wall-bounded ternary fluid flows

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arXiv 2017年

作者： Liang, Hong Xu, Jiangrong Chen, Jiangxing Chai, Zhenhua Shi, Baochang Department of Physics Hangzhou Dianzi University Hangzhou310018 China 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

In this paper, a wetting boundary scheme used to describe the interactions among ternary fluids and solid is proposed in the framework of the lattice Boltzmann method. This scheme for three-phase fluids can preserve the reduction consistency property with the diphasic situation such that it could give physically relevant results. Combining this wetting boundary scheme and the lattice Boltzmann (LB) ternary fluid model based on the multicomponent phase-field theory, we simulated several ternary fluid flow problems involving solid substrate, including the spreading of binary drops on the substrate, the spreading of a compound drop on the substrate, and the shear of a compound liquid drop on the substrate. The numerical results are found to be good agreement with the analytical solutions or some available results. Finally, as an application, we use the LB model coupled with the present wetting boundary scheme to numerically investigate the impact of a compound drop on a solid circular cylinder. It is found that the dynamics of a compound drop can be remarkably influenced by the wettability of the solid surface and the dimensionless Weber number. Copyright © 2017, The Authors. All rights reserved.

关键词： Circular cylinders

Adaptive Gaussian process approximation for Bayesian inference with expensive likelihood functions

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arXiv 2017年

作者： Wang, Hongqiao Li, Jinglai Institute of Natural Sciences School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences School of Mathematical Sciences MOE Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data, built upon a recent work [10]. In particular, we write the joint density approximately as a product of an approximate posterior density and an exponentiated GP surrogate. We then provide an adaptive algorithm to construct such an approximation, where an active learning method is used to choose the design points. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for Bayesian computation. Copyright © 2017, The Authors. All rights reserved.

关键词： Inverse problems

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

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arXiv 2017年

作者： Liang, Hong Xu, Jiangrong Chen, Jiangxing Wang, Huili Chai, Zhenhua Shi, Baochang Department of Physics Hangzhou Dianzi University Hangzhou310018 China 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

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A novel forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and Spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. At last, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature. Copyright © 2017, The Authors. All rights reserved.

关键词： Navier Stokes equations

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

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arXiv 2017年

作者： Wu, Chen Shu, Chang Shi, Baochang Chen, Zhen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore119260 Singapore 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

An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing 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 LBE 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 time splitting scheme as in the conventional high-order Runge-Kutta (RK) based kinetic methods, the present method solves the original BE, 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. Copyright © 2017, The Authors. All rights reserved.

关键词： Boltzmann equation