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Fractal and multifractal analyses of bipartite networks

Scientific reports 2017年第1期7卷 45588页

作者： Jin-Long Liu Jian Wang Zu-Guo Yu Xian-Hua Xie Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia.

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

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OPTIMAL L∞(L2) AND L1(L2) A POSTERIORI ERROR ESTIMATES FOR THE FULLY DISCRETE APPROXIMATIONS OF TIME FRACTIONAL PARABOLIC DIFFERENTIAL EQUATIONS

arXiv

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arXiv 2023年

作者： Cao, Jiliang Wang, Wansheng Xiao, Aiguo Department of Mathematics Shanghai Normal University Shanghai200234 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China

We derive optimal order a posteriori error estimates in the L∞(L2) and L1(L2)-norms for the fully discrete approximations of time fractional parabolic differential equations. For the discretization in time, we use the L1 methods, while for the spatial discretization, we use standard conforming finite element methods. The linear and quadratic space-time reconstructions are introduced, which are generalizations of the elliptic space reconstruction. Then the related a posteriori error estimates for the linear and quadratic space-time reconstructions play key roles in deriving global and pointwise final error estimates. Numerical experiments verify and complement our theoretical results. Copyright © 2023, The Authors. All rights reserved.

关键词： Finite element method

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Error Analysis of Virtual Element Method for the Poisson-Boltzmann Equation

arXiv

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arXiv 2023年

作者： Huang, Linghan Shu, Shi Yang, Ying Guangxi Guilin541004 China School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Xiangtan411105 China Guangxi541004 China

The Poisson-Boltzmann equation is a nonlinear elliptic equation with Dirac distribution sources, which has been widely applied to the prediction of electrostatics potential of biological biomolecular systems in solution. In this paper, we discuss and analysis the virtual element method for the Poisson-Boltzmann equation on general polyhedral meshes. Under the low regularity of the solution of the whole domain, nearly optimal error estimates in both L2-norm and H1-norm for the virtual element approximation are obtained. The numerical experiment on different polyhedral meshes shows the efficiency of the virtual element method and verifies the proposed theoretical prediction. Copyright © 2023, The Authors. All rights reserved.

关键词： Poisson equation

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Two-relaxation-time regularized lattice Boltzmann model for convection-diffusion equation with variable coefficients

arXiv

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arXiv 2023年

作者： Yu, Yuan Qin, Zuojian Yuan, Haizhuan Shu, Shi School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

In this paper, a new two-relaxation-time regularized (TRT-R) lattice Boltzmann (LB) model for convection-diffusion equation (CDE) with variable coefficients is proposed. Within this framework, we first derive a TRT-R collision operator by constructing a new regularized procedure through the high-order Hermite expansion of non-equilibrium. Then a first-order discrete-velocity form of discrete source term is introduced to improve the accuracy of the source term. Finally and most importantly, a new first-order space-derivative auxiliary term is proposed to recover the correct CDE with variable coefficients. To evaluate this model, we simulate a classic benchmark problem of the rotating Gaussian pulse. The results show that our model has better accuracy, stability and convergence than other popular LB models, especially in the case of a large time step. Copyright © 2023, The Authors. All rights reserved.

关键词： Boltzmann equation

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Two-relaxation-time regularized lattice Boltzmann model for Navier-Stokes equations

arXiv

引用

arXiv 2023年

作者： Yu, Yuan Qin, Zuojian Chen, Siwei Shu, Shi Yuan, Hai-Zhuan School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

In this paper, we develop a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows. A free relaxation parameter, τs,2, is employed to relax the regularized non-equilibrium third-order terms. Chapman-Enskog analysis reveals that our model can accurately recover the Navier-Stokes equations (NSEs). Theoretical analysis of the Poiseuille flow problem demonstrates that the slip velocity magnitude in the proposed model is controlled by a magic parameter, which can be entirely eliminated under specific values, consistent with the classical TRT model. Our simulations of the double shear layer problem, Taylor-Green vortex flow, and force-driven Poiseuille flow confirm that the stability and accuracy of our model significantly surpass those of both the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models, even under super-high Reynolds numbers as Re = 107. Concurrently, the TRT-RLB model exhibits superior performance in very high viscosity scenarios. The simulations of creeping flow around a square cylinder demonstrates the model's capability to accurately compute ultra-low Reynolds numbers as Re = 10−7. This study establishes the TRT-RLB model as a flexible and robust tool in computational fluid dynamics. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Achieving coherent perfect absorption based on flat-band plasmonic Friedrich-Wintgen BIC in borophene metamaterials

arXiv

引用

arXiv 2023年

作者： Zhang, Yan-Xi Lin, Qi Yan, Xiao-Qiang Wang, Ling-Ling Liu, Gui-Dong School of Physics and Optoelectronics Xiangtan University Xiangtan411105 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China School of Physics and Electronics Hunan University Changsha410082 China

Many applications involve the phenomenon of a material absorbing electromagnetic radiation. By exploiting wave interference, the efficiency of absorption can be significantly enhanced. Here, we propose Friedrich-Wintgen bound states in the continuum (F-W BICs) based on borophene metamaterials to realize coherent perfect absorption with a dual-band absorption peak in commercially important communication bands. The metamaterials consist of borophene gratings and a borophene sheet that can simultaneously support a Fabry-Perot plasmon resonance and a guided plasmon mode. The formation and dynamic modulation of the F-W BIC can be achieved by adjusting the width or carrier density of the borophene grating, while the strong coupling leads to the anti-crossover behavior of the absorption spectrum. Due to the weak angular dispersion originating from the intrinsic flat-band characteristic of the deep sub-wavelength periodic structure, the proposed plasmonic system exhibits almost no change in wavelength and absorption at large incident angles (within 70 degrees). In addition, we employ the temporal coupled-mode theory including near- and far-field coupling to obtain strong critical coupling, successfully achieve coherent perfect absorption, and can realize the absorption switch by changing the phase difference between the two coherent beams. Our findings can offer theoretical support for absorber design and all-optical tuning. Copyright © 2023, The Authors. All rights reserved.

关键词： Absorption spectroscopy

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Hm-CONFORMING VIRTUAL ELEMENTS IN ARBITRARY DIMENSION

arXiv

引用

arXiv 2021年

作者： Huang, Xuehai Chen, Chunyu Wei, Huayi Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Mathematics Shanghai University of Finance and Economics Shanghai200433 China

The Hm-conforming virtual elements of any degree k on any shape of polytope in n with m, n ≥ 1 and k ≥ m are recursively constructed by gluing conforming virtual elements on faces in a universal way. For the lowest degree case k = m, the set of degrees of freedom only involves function values and derivatives up to order m − 1 at the vertices of the polytope. The inverse inequality and several norm equivalences for the Hm-conforming virtual elements are rigorously proved. The Hm-conforming virtual elements are then applied to discretize a polyharmonic equation with a lower order term. With the help of the interpolation error estimate and norm equivalences, the optimal error estimates are derived for the Hm-conforming virtual element *** Codes 65N12, 65N15, 65N22, 65N30 Copyright © 2021, The Authors. All rights reserved.

关键词： Degrees of freedom (mechanics)

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A novel genome signature based on inter-nucleotide distances profiles for visualization of metagenomic data

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Physica A: Statistical Mechanics and its Applications 2017年 482卷 87-94页

作者： Xian-Hua Xie Zu-Guo Yu Yuan-Lin Ma Guo-Sheng Han Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques Gannan Normal University Jiangxi 341000 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

There has been a growing interest in visualization of metagenomic data. The present study focuses on the visualization of metagenomic data using inter-nucleotide distances profile. We first convert the fragment sequences into inter-nucleotide distances profiles. Then we analyze these profiles by principal component analysis. Finally the principal components are used to obtain the 2-D scattered plot according to their source of species. We name our method as inter-nucleotide distances profiles (INP) method. Our method is evaluated on three benchmark data sets used in previous published papers. Our results demonstrate that the INP method is good, alternative and efficient for visualization of metagenomic data.

关键词： Alignment-free method Inter-nucleotide distance Metagenome Visualization

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The interior penalty virtual element method for fourth-order singular perturbation problems

arXiv

引用

arXiv 2023年

作者： Feng, Fang Yu, Yue School of Mathematics and Statistics Nanjing University of Science and Technology Nanjing China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Xiangtan University Hunan Xiangtan411105 China

This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in the penalty term, as well as presents an automated mesh-dependent selection of the penalty parameter. Drawing inspiration from the modified Morley finite element methods, we leverage the conforming interpolation technique to handle the lower part of the bilinear form. Through our analysis, we establish optimal convergence in the energy norm and provide a rigorous proof of uniform convergence concerning the perturbation parameter in the lowest-order case. © 2023, CC BY-NC-ND.

关键词： Numerical methods

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Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

引用

Physical Review E 2014年第3期89卷 032814-032814页

作者： Jin-Long Liu Zu-Guo Yu Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2−H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic

关键词： TOPOLOGICAL property FRACTAL analysis BROWNIAN motion CORRELATION (Statistics) RECURSIVE sequences (Mathematics) COMPUTER networks

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