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Multifractal analysis and topological properties of a new family of weighted Koch networks

Physica A: Statistical Mechanics and its Applications 2017年 469卷 695-705页

作者： Da-Wen Huang Zu-Guo Yu Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China 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

Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41.04 (which is independent of the scaling factor c ) in the limit of large generation t ; the second smallest eigenvalue μ 2 and the maximum eigenvalue μ n are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ 2 is approximately a quartic polynomial of c and μ n = 1.5 for the normalized Laplacian operator. Then, we find that weighted koch networks are both fractal and multifractal, their fractal dimension is influenced by the scaling factor c . We also apply these analyses to six real-world networks, and find that the multifractality in three of them are strong.

关键词： Weighted Koch networks Modified sandbox algorithm Multifractal analysis Topological property

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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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Fractal and multifractal analyses of bipartite networks

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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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Iteratively linearized reweighted alternating direction method of multipliers for a class of nonconvex problems

arXiv

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arXiv 2017年

作者： Sun, Tao Jiang, Hao Cheng, Lizhi Zhu, Wei Department of Mathematics National University of Defense Technology Changsha Hunan410073 China College of Computer National University of Defense Technology Changsha Hunan410073 China The State Key Laboratory for High Performance Computation National University of Defense Technology Changsha Hunan410073 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China

In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both mathematics and computations in solving the nonconvex and nonsmooth subproblem. In view of this, we propose a reweighted alternating direction method of multipliers. In this algorithm, all subproblems are convex and easy to solve. We also provide several guarantees for the convergence and prove that the algorithm globally converges to a critical point of an auxiliary function with the help of the Kurdyka-Lojasiewicz property. Several numerical results are presented to demonstrate the efficiency of the proposed algorithm. Copyright © 201., The Authors. All rights reserved.

关键词： Iterative methods

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A convergence framework for inexact nonconvex and nonsmooth algorithms and its applications to several iterations

arXiv

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arXiv 2017年

作者： Sun, Tao Jiang, Hao Cheng, Lizhi Zhu, Wei Department of Mathematics National University of Defense Technology Changsha Hunan410073 China College of Computer National University of Defense Technology Changsha Hunan410073 China State Key Laboratory for High Performance Computation National University of Defense Technology Changsha Hunan410073 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China

In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm, which cannot be included in previous framework. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm;and a continuity condition is assumed to hold. In fact, a lot of classical inexact nonconvex and nonsmooth algorithms allow these three conditions. Under an assumption on the auxiliary sequence, we prove the sequence generated by the general algorithm converges to a critical point of the objective function if being assumed semi-Algebraic property. The core of the proofs lies in building a new Lyapunov function, whose successive difference provides a bound for the successive difference of the points generated by the algorithm. And then, we apply our findings to several classical inexact nonconvex iterative algorithms and derive the corresponding convergence results. Copyright © 201., The Authors. All rights reserved.

关键词： Lyapunov functions

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computational design of GeSe/graphene heterojunction based on density functional theory

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Materials Research Express 2018年第3期6卷

作者： Congsheng Xu Jianmei Yuan Dandan Wang Yuliang Mao Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 People's Republic of China Hunan Key Laboratory for Micro–Nano Energy Materials and Devices School of Physics and Optoelectronic Xiangtan University Hunan 411105 People's Republic of China Authors to whom any correspondence should be addressed.

Based on density functional theory, we computational designed the hetero junction composed by GeSe monolayer and graphene. The effects of interlayer coupling, strains and electric fields on the electronic structures of the designed GeSe/graphene (G/g) hetero structure are explored. We demonstrated that both the intrinsic electric properties of the GeSe monolayer and graphene are well preserved in G/g hetero structure. It is found that an energy gap of 0.1. eV in graphene is opened by decreasing the interlayer distance in G/g hetero structure. The height of Schottky barrier can be effectively tuned by the interlayer distance between GeSe monolayer and graphene. Moreover, we found that applying in-plane strains and the electric fields perpendicular to the G/g hetero structure can control the Schottky barriers at the G/g interface. Our results predict that the ultra-thin G/g hetero structure can be used as two-dimensional semiconductor-based optoelectronic devices.

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First-principles study on the structure and electronic properties of stanane under electric fields

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Materials Research Express 2018年第6期5卷

作者： Yuliang Mao Linbo Long Congshen Xu Jianmei Yuan Hunan Key Laboratory for Micro–Nano Energy Materials and Devices School of Physics and Optoelectronic Xiangtan University Hunan 411105 People's Republic of China Authors to whom any correspondence should be addressed Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 People's Republic of China

First-principles calculations are performed to study the dual effect of spin orbital coupling and electric fields on the structure and electronic properties of stanane (hydrogen saturated stanene). For the relaxed configurations, it is found that spin orbital coupling effect has little impact on the geometry of stanane. However, the total energies of the stanane under electric fields are decreased. We also found that the transferred charge is mainly accumulated around the hydrogen atoms, indicating tin atoms are the charge donor in stanane. Linear response calculations prove the phase stability of stanane. Our results also indicate that the fundamental energy gap in stanane can be tuned by electric fields.

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Identification of pre-microRNAs by characterizing their sequence order evolution information and secondary structure graphs

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BMC bioinformatics 2018年第SUPPL 19期19卷 521页

作者： Yuanlin Ma Zuguo Yu Guosheng Han Jinyan Li Vo Anh 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 Hunan 411105 China. 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 Hunan 411105 China. yuzuguo@***. School of Electrical Engineering and Computer Science Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia. yuzuguo@***. Advanced Analytics Institute Faculty of Engineering & IT University of Technology Sydney P.O Box 123 Broadway NSW 2007 Australia. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia.

BACKGROUND:Distinction between pre-microRNAs (precursor microRNAs) and length-similar pseudo pre-microRNAs can reveal more about the regulatory mechanism of RNA biological processes. Machine learning techniques have been widely applied to deal with this challenging problem. However, most of them mainly focus on secondary structure information of pre-microRNAs, while ignoring sequence-order information and sequence evolution information. RESULTS:We use new features for the machine learning algorithms to improve the classification performance by characterizing both sequence order evolution information and secondary structure graphs. We developed three steps to extract these features of pre-microRNAs. We first extract features from PSI-BLAST profiles and Hilbert-Huang transforms, which contain rich sequence evolution information and sequence-order information respectively. We then obtain properties of small molecular networks of pre-microRNAs, which contain refined secondary structure information. These structural features are carefully generated so that they can depict both global and local characteristics of pre-microRNAs. In total, our feature space covers 591.features. The maximum relevance and minimum redundancy (mRMR) feature selection method is adopted before support vector machine (SVM) is applied as our classifier. The constructed classification model is named MicroRNA -NHPred. The performance of MicroRNA -NHPred is high and stable, which is better than that of those state-of-the-art methods, achieving an accuracy of up to 94.83% on same benchmark datasets. CONCLUSIONS:The high prediction accuracy achieved by our proposed method is attributed to the design of a comprehensive feature set on the sequences and secondary structures, which are capable of characterizing the sequence evolution information and sequence-order information, and global and local information of pre-microRNAs secondary structures. MicroRNA -NHPred is a valuable method for pre-microRNAs iden

关键词： Hibert-Huang transform Network PSI-BLAST profiles Pre-microRNA SVM mRMR

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Uniform convergence of multigrid finite element method for time-dependent riesz tempered fractional problem

arXiv

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arXiv 2017年

作者： Chen, Minghua Bu, Weiping Qi, Wenya Wang, Yantao School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou730000 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China South University of Science and Technology of China Shenzhen518055 China

In this article a theoretical framework for the Galerkin finite element approximation to the time-dependent Riesz tempered fractional problem is provided without the fractional regularity assumption. Because the time-dependent problems should become easier to solve as the time step τ → 0, which correspond to the mass matrix dominant [R. E. Bank and T. Dupont, Math. Comp., 1.3 (1.81., pp. 35-51.. Based on the introduced and analysis of the fractional τ-norm, the uniform convergence estimates of the V-cycle multigrid method with the time-dependent fractional problem is strictly proved, which means that the convergence rate of the V-cycle MGM is independent of the mesh size h and the time step τ. The numerical experiments are performed to verify the convergence with only O(NlogN) complexity by the fast Fourier transform method, where N is the number of the grid points. To the best of our knowledge, this is the first proof for the convergence rate of the V-cycle multigrid finite element method with τ → 0. Copyright © 201., The Authors. All rights reserved.

关键词： Fast Fourier transforms

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Multifractal temporally weighted detrended cross-correlation analysis to quantify power-law cross-correlation and its application to stock markets

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Chaos 2017年第6期27卷 063111-063111页

作者： Wei, Yun-Lan Yu, Zu-Guo Zou, Hai-Long Anh, Vo Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education 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

A new method-multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA)-is proposed to investigate multifractal cross-correlations in this paper. This new method is based on multifractal temporally weighted detrended fluctuation analysis and multifractal cross-correlation analysis (MFCCA). An innovation of the method is applying geographically weighted regression to estimate local trends in the nonstationary time series. We also take into consideration the sign of the fluctuations in computing the corresponding detrended cross-covariance function. To test the performance of the MF-TWXDFA algorithm, we apply it and the MFCCA method on simulated and actual series. Numerical tests on artificially simulated series demonstrate that our method can accurately detect long-range cross-correlations for two simultaneously recorded series. To further show the utility of MF-TWXDFA, we apply it on time series from stock markets and find that power-law cross-correlation between stock returns is significantly multifractal. A new coefficient, MF-TWXDFA cross-correlation coefficient, is also defined to quantify the levels of cross-correlation between two time series. © 201. Author(s).

关键词： CORRELATION (Statistics) STOCK price indexes REGRESSION analysis TIME series analysis COEFFICIENTS (Statistics)

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