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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 © 2017, 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 0.17 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., 153 (1981), 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 © 2017, 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. © 2017 Author(s).

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

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Protein folding kinetic order prediction from amino acid sequence based on horizontal visibility network

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Current Bioinformatics 2016年第2期11卷 173-185页

作者： Zhao, Zhi-Qin Yu, Zu-Guo Anh, Vo Wu, Jing-Yang Han, Guo-Sheng 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 XiangtanHunan411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 BrisbaneQ4001 Australia School of Science Xi’an Shiyou University 18 Second Dianzi Road Yanta District Xi’anShaanxi710065 China

Protein folding is one of the most important problems in molecular biology. The kinetic order of protein folding is one of the main aspects of the folding process. Previous methods for predicting protein folding kinetic order require to use the information on tertiary or predicted secondary structure of a protein. In this paper, based on physicochemical properties of amino acids, we propose an approach to predict the protein folding kinetic order from the primary structure of a protein using support vector machine combined with principal component analysis. The horizontal visibility network, Hilbert-Huang transform, global descriptor, and Lempel-Ziv complexity are used to extract features in our approach. To evaluate our approach, the leave-one-out cross-validation test is employed on two widely-used data sets ("IvankovData" and "ZhengData" data sets) consisting of two-state and multi-state proteins. The overall accuracies of prediction can reach 83.87% for "IvankovData" data set and 85% for "ZhengData" data set respectively. Comparisons with the existing methods show that the present approach performs better on the "IvankovData" data set. These results indicate that the present approach is effective and valuable for predicting protein folding kinetic order. Based on factor analysis, we find that the length of protein sequence, hydrophobicity and hydrophilicity of amino acids are important features in our approach. © 2016 Bentham science Publishers

关键词： Hilbert-Huang transform

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From standard alpha-stable Lévy motions to horizontal visibility networks: dependence of multifractal and Laplacian spectrum

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Journal of Statistical Mechanics: Theory and Experiment 2018年第5期2018卷

作者： Hai-Long Zou Zu-Guo Yu Vo Anh Yuan-Lin Ma 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 People's Republic of China School of Electrical Engineering and Computer Science Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia Author to whom any correspondence should be addressed. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

In recent years, researchers have proposed several methods to transform time series (such as those of fractional Brownian motion) into complex networks. In this paper, we construct horizontal visibility networks (HVNs) based on the -stable Lévy motion. We aim to study the relations of multifractal and Laplacian spectrum of transformed networks on the parameters and of the -stable Lévy motion. First, we employ the sandbox algorithm to compute the mass exponents and multifractal spectrum to investigate the multifractality of these HVNs. Then we perform least squares fits to find possible relations of the average fractal dimension , the average information dimension and the average correlation dimension against using several methods of model selection. We also investigate possible dependence relations of eigenvalues and energy on , calculated from the Laplacian and normalized Laplacian operators of the constructed HVNs. All of these constructions and estimates will help us to evaluate the validity and usefulness of the mappings between time series and networks, especially between time series of -stable Lévy motions and HVNs.

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Correlating the Structure and Optical Absorption Properties of Au76（SR）44 Cluster

Correlating the Structure and Optical Absorption Properties ...

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第九届计算纳米科学与新能源材料国际研讨会

作者： Zhongyun Ma P.Wang G.Zhou J.Tang H.Li Y.Pei Department of Chemistry Key Laboratory of Environmentally Friendly Chemistry and Applications of Ministry of EducationXiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied MathematicsXiangtan University School of Materials Science and Engineering Central South University

The atomic structure of recently synthesized thiolate-protected Au cluster is theoretically predicted via a simple structural rule summarized from the crystal structures of thiolate-protected Au（SR）, Au（SR） and Au（SR） clusters. We find that the Au（SR）（N = 7） and recently reported Au（SR）（N = 4）, Au（SR）（N = 3）, Au（SR）（N = 2） and Au（SR）（N = 1） belong to a family of homologous Au（SR） cluster whose Au-cores follow one-dimensional polytetrahedral growth pathway. The Au（SR） cluster is predicted to contain an anisotropic face-centered cubic（FCC） Au-core, which can be viewed as combination of two helical tetrahedra-Au4 chains and is remarkably different from the well-known spherical Au-core in ligand protected gold clusters in the size region of 1-2 nm. The intense near infrared（NIR） absorption of Au（SR） is attributed to the synergistic effect of anisotropic Au-core structure and ligand protections. A plausible cluster-to-cluster transformation mechanism is further suggested.

关键词： thiolated-protected gold nanocluster Au76SR44 face-centered cubic near infrared adsorption

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Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations

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Advances in Applied Mathematics and Mechanics 2015年第1期7卷 74-88页

作者： Yin Yang Yanping Chen Yunqing Huang Wei Yang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China School ofMathematical Sciences South China Normal UniversityGuangzhou 510631China

A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second *** provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-norm and L¥-norm will decay exponentially provided that the kernel function is sufficiently *** results are presented,which confirm the theoretical prediction of the exponential rate of convergence.

关键词： Spectral method nonlinear Volterra integral equations

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