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

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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

Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array

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arXiv 2023年

作者： Reardon, Daniel J. Zic, Andrew Shannon, Ryan M. Hobbs, George B. Bailes, Matthew Di Marco, Valentina Kapur, Agastya Rogers, Axl F. Thrane, Eric Askew, Jacob Ramesh Bhat, N.D. Cameron, Andrew Curylo, Malgorzata Coles, William A. Dai, Shi Goncharov, Boris Kerr, Matthew Kulkarni, Atharva Levin, Yuri Lower, Marcus E. Manchester, Richard N. Mandow, Rami Miles, Matthew T. Nathan, Rowina S. Oslowski, Stefan Russell, Christopher J. Spiewak, Renée Zhang, Songbo Zhu, Xing-Jiang Centre for Astrophysics and Supercomputing Swinburne University of Technology P.O. Box 218 HawthornVIC3122 Australia OzGrav: The Australian Research Council Centre of Excellence for Gravitational Wave Discovery HawthornVIC3122 Australia Australia Telescope National Facility CSIRO Space and Astronomy P.O. Box 76 EppingNSW1710 Australia Department of Physics and Astronomy MQ Research Centre in Astronomy Astrophysics and Astrophotonics Macquarie University NSW2109 Australia School of Physics and Astronomy Monash University VIC3800 Australia OzGrav: The Australian Research Council Centre of Excellence for Gravitational Wave Discovery ClaytonVIC3800 Australia Institute for Radio Astronomy & Space Research Auckland University of Technology Private Bag 92006 Auckland1142 New Zealand International Centre for Radio Astronomy Research Curtin University BentleyWA6102 Australia Astronomical Observatory University of Warsaw Aleje Ujazdowskie 4 Warsaw00-478 Poland Electrical and Computer Engineering University of California La Jolla San DiegoCA United States School of Science Western Sydney University Locked Bag 1797 Penrith South DCNSW2751 Australia L'AquilaI-67100 Italy INFN Laboratori Nazionali del Gran Sasso AssergiI-67100 Italy Space Science Division US Naval Research Laboratory 4555 Overlook Ave SW WashingtonDC20375 United States Physics Department Columbia Astrophysics Laboratory Columbia University 538 West 120th Street New YorkNY10027 United States Center for Computational Astrophysics Flatiron Institute 162 5th Ave NY10011 United States Manly Astrophysics 15/41-42 East Esplanade ManlyNSW2095 Australia CSIRO Scientific Computing Australian Technology Park Locked Bag 9013 AlexandriaNSW1435 Australia Jodrell Bank Centre for Astrophysics Department of Physics and Astronomy University of Manchester ManchesterM13 9PL United Kingdom Purple Mountain Observatory Chinese Academy of Sciences Nanjing210008 China Advanced Instit

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we describe a search for an isotropic stochastic gravitational-wave background (GWB) using observations of 30 millisecond pulsars from the third data release of the Parkes Pulsar Timing Array (PPTA), which spans 18 years. Using current Bayesian inference techniques we recover and characterize a common-spectrum noise process. Represented as a strain spectrum hc = A(f/1yr−1)α, we measure (Equation presented) and α = −0.45 ± 0.20 respectively (median and 68% credible interval). For a spectral index of α = −2/3, corresponding to an isotropic background of GWs radiated by inspiraling supermassive black hole binaries, we recover an amplitude of (Equation presented). However, we demonstrate that the apparent signal strength is time-dependent, as the first half of our data set can be used to place an upper limit on A that is in tension with the inferred common-spectrum amplitude using the complete data set. We search for spatial correlations in the observations by hierarchically analyzing individual pulsar pairs, which also allows for significance validation through randomizing pulsar positions on the sky. For a process with α = −2/3, we measure spatial correlations consistent with a GWB, with an estimated false-alarm probability of p. 0.02 (approx. 2σ). The long timing baselines of the PPTA and the access to southern pulsars will continue to play an important role in the International Pulsar Timing Array. Copyright © 2023, The Authors. All rights reserved.

关键词： Pulsars

A lowest-order mixed finite element method for the elastic transmission eigenvalue problem

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arXiv 2018年

作者： Xi, Yingxia Ji, Xia School of Science Nanjing University of Science and Technology Nanjing210094 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

The goal of this paper is to develop numerical methods computing a few smallest elastic interior transmission eigenvalues, which are of practical importance in inverse elastic scattering theory. The problem is challenging since it is nonlinear, non-self-adjoint, and of fourth order. In this paper, we construct a lowest-order mixed finite element method which is close to the Ciarlet-Raviart mixed finite element method. This scheme is based on Lagrange finite elements and is one of the less expensive methods in terms of the amount of degrees of freedom. Due to the non-self-adjointness, the discretization of elastic transmission eigenvalue problem leads to a non-classical mixed method which does not fit into the framework of classical theoretical analysis. In stead, we obtain the convergence analysis based on the spectral approximation theory of compact operators. Numerical examples are presented to verify the theory. Both real and complex eigenvalues can be *** Codes 65N25, 65N30, 47B07 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Linear Stability of Hyperbolic Moment Models for Boltzmann Equation

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高等学校计算数学学报（英文版） 2017年第2期10卷 255-277页

作者： Yana Di Yuwei Fan Ruo Li Lingchao Zheng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing NCMIS AMSS Chinese Academy of Sciences Beijing 100190China School of Mathematical Sciences Peking University Beijing 100871 China HEDPS & CAPT LMAM & School of Mathematical SciencesPeking University Beijing 100871 China

Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems and thus the regularized models attain local wellposedness for Cauchy *** hyperbolic regularization is only related to the convection term in Boltzmann *** in this paper studied the regularized models with the presentation of collision *** is proved that the regularized models are linearly stable at the local equilibrium and satisfy Yong's first stability condition with commonly used approximate collision terms,and particularly with Boltzmann's binary collision model.

关键词： Boltzmann equation Grad's moment method hyperbolic moment equation linear stability

A Compact Scheme for Coupled Stochastic Nonlinear Schrodinger Equations

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Communications in computational Physics 2017年第1期21卷 93-125页

作者： Chuchu Chen Jialin Hong Lihai Ji Linghua Kong Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Institute of Applied Physics and ComputationalMathematics Beijing 100094China School of Mathematics and Information Science Jiangxi Normal UniversityNanchangJiangxi 330022China

In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger *** prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law,discrete charge conservation law and discrete energy evolution law almost *** experiments confirm well the theoretical analysis ***,we present a detailed numerical investigation of the optical phenomena based on the compact *** numerical experiments for various amplitudes of noise,we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to *** particular,if the noise is relatively strong,the soliton will be totally ***,we observe that the phase shift is sensibly modified by the ***,the numerical results present inelastic interaction which is different from the deterministic case.

关键词： Coupled stochastic nonlinear Schrodinger equations compact scheme stochastic multi-symplectic conservation law energy evolution law charge conservation law soliton evolution soliton interaction

On the perturbation of an L2-orthogonal projection

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arXiv 2018年

作者： Xu, Xuefeng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

The L2-orthogonal projection is an important mathematical tool in scientific computing and numerical analysis, which has been widely applied in many fields such as linear least squares problems, eigenvalue problems, ill-posed problems, and randomized algorithms. In some numerical applications, the entries of a matrix will seldom be known exactly, so it is necessary to develop some bounds to characterize the effects of the uncertainties caused by matrix perturbation. In this paper, we establish new perturbation bounds for the L2orthogonal projection onto the column space of a matrix, which involve upper (lower) bounds and combined upper (lower) bounds. The new results contain some sharper counterparts of the existing bounds. Numerical examples are also given to illustrate our theoretical results.15A09, 15A18, 47A55, 65F35 Copyright © 2018, The Authors. All rights reserved.

关键词： Singular value decomposition

On the perturbation of the Moore–Penrose inverse of a matrix

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arXiv 2018年

Over the past decades, the Moore–Penrose inverse has been extensively investigated and widely applied in many fields. One reason for this interest is that the Moore–Penrose inverse can succinctly express some important geometric constructions in finite-dimensional spaces, such as the orthogonal projection onto a subspace and the linear least squares problem. However, the entries of a matrix will seldom be known exactly in numerical applications, so it is necessary to develop some bounds to characterize the effects of matrix perturbation. In this paper, we establish new perturbation bounds for the Moore–Penrose inverse of a matrix, which include some sharper counterparts of the existing upper bounds. Numerical examples are also provided to illustrate our theoretical results. Copyright © 2018, The Authors. All rights reserved.

关键词： Inverse problems

A nano-carbon route to rare earth free permanent magnetism

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arXiv 2019年

作者： Moorsom, Timothy Alghamdi, Shoug Stansill, Sean Teobaldi, Gilberto Beg, Marijan Fangohr, Hans Rogers, Matt Aslam, Zabeada Ali, Mannan .J.Hickey, B Cespedes, Oscar University of Leeds Leeds United Kingdom Taibah University Medina Saudi Arabia Scientific Computing Department STFC Rutherford Appleton Laboratory Beijing Computational Science Research Center Beijing China Stephenson Institute for Renewable Energy Department of Chemistry University of Liverpool School of Chemistry University of Southhampton Southampton United Kingdom Faculty of Engineering and Physical Sciences University of Southampton Southampton United Kingdom European XFEL GmbH Holzkoppel 4 Schenefeld22869 Germany

The mechanism by which paramagnetic or diamagnetic molecules are able to alter the anisotropy of transition metals remains elusive. Here, we present a molecule-metal bilayer whose low temper- ature coercivity of up to 1.6 T and energy product of over 350 kJ/m3rival those of rare earth per- manent magnets at low temperatures. Since this result is obtained using a non-magnetic molecule, C60, such large coercivities cannot be explained by conventional exchange bias models. Instead, we propose a new form of surface anisotropy, dubbed -anisotropy, based on the spin-dependent π-d hybridisation at metallo-molecular interfaces and the resultant spin-dependent interfacial dipole. We give evidence that this effect is currently limited to low temperatures only because of the rotational degree of freedom of the C60molecule and anticipate that further research may reveal metal-molecule composites which could exhibit this behaviour at higher temperatures. Copyright © 2019, The Authors. All rights reserved.

关键词： Coercive force

Capacity optimality of AMP in coded systems

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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