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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

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

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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

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

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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

VIRTUAL ELEMENT METHODS WITHOUT EXTRINSIC STABILIZATION

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arXiv 2022年

作者： Chen, Chunyu Huang, Xuehai 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

Virtual element methods (VEMs) without extrinsic stabilization in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension. The key is to construct local H(div)-conforming macro finite element spaces such that the associated L2 projection of the gradient of virtual element functions is computable, and the L2 projector has a uniform lower bound on the gradient of virtual element function spaces in L2 norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic *** Codes 65N12, 65N22, 65N30 Copyright © 2022, The Authors. All rights reserved.

关键词： Stabilization

Piecewise divergence-free nonconforming virtual elements for stokes problem in any dimensions

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arXiv 2020年

作者： Wei, Huayi Huang, Xuehai Li, Ao 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

Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem and the stabilization, a divergence-free nonconforming virtual element method is proposed for Stokes problem. A detailed and rigorous error analysis is presented for the discrete method. An important property in the analysis is that the local energy projector commutes with the divergence operator. With the help of a divergence-free interpolation operator onto a generalized Raviart-Thomas element space, a pressure-robust nonconforming virtual element method is developed by simply modifying the right hand side of the previous discretization. A reduced virtual element method is also discussed. Numerical results are provided to verify the theoretical *** Codes 76D07, 65N12, 65N22, 65N30 Copyright © 2020, The Authors. All rights reserved.

关键词： Navier Stokes equations

Whole-proteome based phylogenetic tree construction with inter-amino-acid distances and the conditional geometric distribution profiles

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Molecular phylogenetics and evolution 2015年 89卷 37-45页

作者： Xian-Hua Xie Zu-Guo Yu Guo-Sheng Han Wei-Feng Yang Vo Anh 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 411105 PR China School of Mathematics and Computer Science Gannan Normal University Jiangxi 341000 PR China. Electronic address: xxianhua@***. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QLD 4001 Australia. Electronic address: yuzuguo@***. 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 411105 PR China. Electronic address: korea10282003@***. 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 411105 PR China. Electronic address: yangweifeng09@***. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QLD 4001 Australia. Electronic address: v.anh@qut.edu.au.

There has been a growing interest in alignment-free methods for whole genome comparison and phylogenomic studies. In this study, we propose an alignment-free method for phylogenetic tree construction using whole-proteome sequences. Based on the inter-amino-acid distances, we first convert the whole-proteome sequences into inter-amino-acid distance vectors, which are called observed inter-amino-acid distance profiles. Then, we propose to use conditional geometric distribution profiles (the distributions of sequences where the amino acids are placed randomly and independently) as the reference distribution profiles. Last the relative deviation between the observed and reference distribution profiles is used to define a simple metric that reflects the phylogenetic relationships between whole-proteome sequences of different organisms. We name our method inter-amino-acid distances and conditional geometric distribution profiles (IAGDP). We evaluate our method on two data sets: the benchmark dataset including 29 genomes used in previous published papers, and another one including 67 mammal genomes. Our results demonstrate that the new method is useful and efficient.

关键词： Alignment-free whole-proteome comparison Conditional geometric distribution profile Inter-amino-acid distances Phylogenetic tree

Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous arguments

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arXiv 2024年

作者： Gurioli, Gianmarco Wang, Weijie Yan, Xiaoqiang Università degli Studi di Firenze Florence Italy School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan411105 China

In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the reference differential equation along the shifted and scaled Legendre polynomial orthonormal basis, working on a suitable extension of Hamiltonian Boundary Value Methods. Within the design of the methods, a proper generalization of the perturbation results coming from the field of ordinary differential equations is considered, with the aim of handling the case of FDEPCAs. The error analysis of the devised family of methods is performed, while a few numerical tests on Hamiltonian FDEPCAs are provided, to give evidence to the theoretical findings and show the effectiveness of the obtained resolution *** Codes 65L05, 65L03, 65L06, 65P10 Copyright © 2024, The Authors. All rights reserved.

关键词： Ordinary differential equations

ANISOTROPIC ANALYSIS OF VEM FOR TIME-HARMONIC MAXWELL EQUATIONS IN INHOMOGENEOUS MEDIA WITH LOW REGULARITY

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arXiv 2023年

作者： Chen, Chunyu Guo, Ruchi Wei, Huayi School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China Department of Mathematics University of California IrvineCA92697 United States

It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal convergence for low-regularity solutions heavily relies on conforming spaces and highly-regular simplicial meshes. This can be a significant limitation for many popular methods based on polytopal meshes in the case of inhomogeneous media, as the discontinuity of electromagnetic parameters can lead to quite low regularity of solutions near media interfaces, and potentially worsened by geometric singularities, making many popular methods based on broken spaces, non-conforming or polytopal meshes particularly challenging to apply. In this article, we present a virtual element method for solving an indefinite time-harmonic Maxwell equation in 2D inhomogeneous media with quite arbitrary polytopal meshes, and the media interface is allowed to have geometric singularity to cause low regularity. There are two key novelties: (i) the proposed method is theoretically guaranteed to achieve robust optimal convergence for solutions with merely Hθ regularity, θ ∈ (1/2, 1];(ii) the polytopal element shape can be highly anisotropic and shrinking, and an explicit formula is established to describe the relationship between the shape regularity and solution regularity. Extensive numerical experiments will be given to demonstrate the effectiveness of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： Maxwell equations

Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations

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arXiv 2018年

作者： Yue, X.Q. Shu, S. Xu, X.W. Bu, W.P. Pan, K.J. School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Mathematics and Statistics Central South University Hunan410083 China

The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to discretize spatial and temporal derivatives to propagate solutions. Next, we present a non-intrusive time-parallelization and its two-level convergence analysis, where we algorithmically and theoretically generalize the MGRIT to time-dependent fine time-grid propagators. Finally, numerical illustrations show that the obtained numerical scheme possesses the saturation error order, theoretical results of the two-level variant deliver good predictions, and significant speedups can be achieved when compared to parareal and the sequential time-stepping approach. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite element method