作者机构：
[Xu, Qingsong] School of Mathematic Sciences, Central South University, Changsha, 410083, China;[Liang, Yizeng; Cao, Dongsheng; Li, Hongdong] Research Center of Modernization of Traditional Chinese Medicines, College of Chemistry and Chemical Engineering, Central South University, Changsha, 410083, China
通讯机构：
[Liang, Yizeng] Cent S Univ, Coll Chem & Chem Engn, Res Ctr Modernizat Tradit Chinese Med, Changsha 410083, Peoples R China.
作者机构：
[Zhang, Xian-Ming; Han, Qing-Long] School of Computing Sciences, Central Queensland University, Rockhampton, QLD 4702, Australia;[Zhang, Xian-Ming] School of Mathematical Science and Computing Technology, Central South University, Changsha, 410083, China
作者：
Sun, Juntao;Chen, Haibo;Nieto, Juan J.;Otero-Novoa, Mario
期刊：
Nonlinear Analysis, Theory, Methods and Applications,2010年72(12):4575-4586 ISSN：0362-546X
通讯作者：
Sun, J.(sunjuntao2008@163.com)
作者机构：
[Nieto, Juan J.; Otero-Novoa, Mario] Departamento de Aná,lisis Matemá,tico, Universidad de Santiago de Compostela, Santiago de Compostela, 15782, Spain;[Chen, Haibo; Sun, Juntao] Department of Mathematics, Central South University, Changsha, 410075 Hunan, China
通讯机构：
[Sun, Juntao] Cent S Univ, Dept Math, Changsha 410075, Hunan, Peoples R China.
关键词：
Critical points - Critical points theorem - Hamiltonian systems - Impulsive effects - Multiple solutions - Multiplicity of solutions - Second orders - Three solutions - Variational methods
作者机构：
[Xu, Qing-Song; Li, Hong-Dong] School of Mathematic Sciences, Central South University, Changsha 410083, China;[Li, Hong-Dong; Liang, Yi-Zeng; Xu, Qing-Song] College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China
通讯机构：
[Liang, Yi-Zeng] Cent S Univ, Coll Chem & Chem Engn, Changsha 410083, Peoples R China.
关键词：
Design and application - Disease classification - Disease diagnosis - Gene expression datasets - Gene selection - GNU general public license - Markov chain Monte - Markov chain Monte Carlo - Posterior distributions - Prior distribution - Random frog - Reversible jump - Reversible jump Markov chain Monte Carlo - Sample sizes - Source codes - Variable selection
摘要：
The identification of disease-relevant genes represents a challenge in microarray-based disease diagnosis where the sample size is often limited. Among established methods, reversible jump Markov Chain Monte Carlo (RJMCMC) methods have proven to be quite promising for variable selection. However, the design and application of an RJMCMC algorithm requires, for example, special criteria for prior distributions. Also, the simulation from joint posterior distributions of models is computationally extensive, and may even be mathematically intractable. These disadvantages may limit the applications of RJMCMC algorithms. Therefore, the development of algorithms that possess the advantages of RJMCMC methods and are also efficient and easy to follow for selecting disease-associated genes is required. Here we report a RJMCMC-like method, called random frog that possesses the advantages of RJMCMC methods and is much easier to implement. Using the colon and the estrogen gene expression datasets, we show that random frog is effective in identifying discriminating genes. The top 2 ranked genes for colon and estrogen are Z50753, U00968, and Y10871_at, Z22536_at, respectively. (The source codes with GNU General Public License Version 2.0 are freely available to non-commercial users at: http://code.google.com/p/randomfrog/.) (C) 2012 Published by Elsevier B.V.
期刊：
International Journal of Robust and Nonlinear Control,2009年19(17):1922-1930 ISSN：1049-8923
通讯作者：
Han, QL
作者机构：
[Zhang, Xian-Ming; Han, Qing-Long] Centre for Intelligent and Networked Systems, Central Queensland University, Rockhampton, QLD 4702, Australia;[Zhang, Xian-Ming; Han, Qing-Long] School of Computing Sciences, Central Queensland University, Rockhampton, QLD 4702, Australia;[Zhang, Xian-Ming] School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, China
关键词：
Delay decomposition approach - Delay dependent stability criterion - Delay-dependent stability - Functionals - Linear delay system - Linear matrix inequality (LMI) - Lyapunov - Lyapunov functionals - Lyapunov-Krasvskii functional - Numerical example - Subintervals - Time-varying delay
摘要：
This paper is concerned with delay-dependent stability for linear systems with time-varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new Lyapunov-Krasvskii functionals are then constructed. Employing these new Lyapunov-Krasvskii functionals, some new delay-dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright (C) 2009 John Wiley & Sons, Ltd.
期刊：
JOURNAL OF CHEMOMETRICS,2010年24(7-8):418-423 ISSN：0886-9383
通讯作者：
Liang, YZ
作者机构：
[Cao, Dong-Sheng; Liang, Yi-Zeng; Li, Hong-Dong] Cent S Univ, Res Ctr Modernizat Tradit Chinese Med, Coll Chem & Chem Engn, Changsha 410083, Hunan, Peoples R China.;[Xu, Qing-Song] Cent S Univ, Sch Math Sci, Changsha 410083, Hunan, Peoples R China.
通讯机构：
[Liang, Yi-Zeng] Cent S Univ, Res Ctr Modernizat Tradit Chinese Med, Coll Chem & Chem Engn, Changsha 410083, Hunan, Peoples R China.
会议名称：
11th Scandinavian Symposium on Chemometrics
会议时间：
JUN 08-11, 2009
会议地点：
Loen, NORWAY
会议主办单位：
[Li, Hong-Dong;Liang, Yi-Zeng;Cao, Dong-Sheng] Cent S Univ, Res Ctr Modernizat Tradit Chinese Med, Coll Chem & Chem Engn, Changsha 410083, Hunan, Peoples R China.^[Xu, Qing-Song] Cent S Univ, Sch Math Sci, Changsha 410083, Hunan, Peoples R China.
关键词：
model population analysis;variable selection;Monte Carlo sampling;biomarker discovery
摘要：
To build a credible model for given chemical or biological or clinical data, it may be helpful to first get somewhat better insight into the data itself before modeling and then to present the statistically stable results derived from a large number of sub-models established only on one dataset with the aid of Monte Carlo Sampling (MCS). In the present work, a concept model population analysis (MPA) is developed. Briefly, MPA could be considered as a general framework for developing new methods by statistically analyzing some interesting parameters (regression coefficients, prediction errors, etc.) of a number of sub-models. New methods are expected to be developed by making full use of the interesting parameter in a novel manner. In this work, the elements of MPA are first considered and described. Then, the applications for variable selection and model assessment are emphasized with the help of MPA. Copyright (C) 2010 John Wiley & Sons, Ltd.
期刊：
JOURNAL OF COMPUTATIONAL CHEMISTRY,2010年31(3):592-602 ISSN：0192-8651
通讯作者：
Liang, Y.-Z.(yizeng_liang@263.net)
作者机构：
[Chen, Xian; Li, Hong-Dong; Liang, Yi-Zeng; Cao, Dong-Sheng] Research Center of Modernization of Traditional Chinese Medicines, Central South University, Changsha, 410083, China;[Xu, Qing-Song] School of Mathematical Sciences and Computing Technology, Central South University, Changsha, 410083, China
通讯机构：
[Liang, Yi-Zeng] Cent S Univ, Res Ctr Modernizat Tradit Chinese Med, Changsha 410083, Peoples R China.
关键词：
Cross validation - MONTE CARLO - QSAR/QSPR - Regression diagnostics - Robust regressions
摘要：
The crucial step of building a high performance QSAR/QSPR model is the detection of outliers in the model. Detecting outliers in a multivariate point cloud is not trivial, especially when several outliers coexist in the model. The classical identification methods do not always identify them, because they are based on the sample mean and covariance matrix influenced by the outliers. Moreover, existing methods only lay stress on some type of outliers but not all the outliers. To avoid these problems and detect all kinds of outliers simultaneously, we provide a new strategy based on Monte-Carlo cross-validation, which was termed as the MC method. The MC method inherently provides a feasible way to detect different kinds of outliers by establishment of many cross-predictive models. With the help of the distribution of predictive residuals such obtained. it seems to be able to reduce the risk caused by the masking effect. In addition, a new display is proposed, in which the absolute values of mean value of predictive residuals are plotted versus standard deviations of predictive residuals. The plot divides the data into normal samples, y direction outliers and X direction outliers. Several examples are used to demonstrate the detection ability of MC method through the comparison of different diagnostic methods. (C) 2009 Wiley Periodicals, Inc. J Comput Chem 31: 592-602, 2010
作者机构：
[Tang XianHua; Tang, XH] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.
通讯机构：
[Tang XianHua] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.
关键词：
Schrodinger equation;non-Nehari manifold method;asymptotically periodic;ground state solutions of Nehari-Pankov type
摘要：
We consider the semilinear Schrodinger equation where f is a superlinear, subcritical nonlinearity. We mainly study the case where V(x) = V (0)(x) + V (1)(x), V (0) a C(a"e (N) ), V (0)(x) is 1-periodic in each of x (1), x (2), aEuro broken vertical bar, x (N) and sup[sigma(-Delta + V (0)) a (c) (-a, 0)] < 0 < inf[sigma(-Delta + V (0)) a (c) (0, a)], V (1) a C(a"e (N) ) and lim(|x|-> a) V (1)(x) = 0. Inspired by previous work of Li et al. (2006), Pankov (2005) and Szulkin and Weth (2009), we develop a more direct approach to generalize the main result of Szulkin and Weth (2009) by removing the "strictly increasing" condition in the Nehari type assumption on f(x, t)/|t|. Unlike the Nahari manifold method, the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold N (0) by using the diagonal method.
期刊：
Applied Mathematics and Computation,2010年216(10):3064-3072 ISSN：0096-3003
通讯作者：
Zhang, ZY
作者机构：
[Liu, Zhen-hai] School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, 530006, China;[Chen, Yue-zhong; Zhang, Zai-yun; Miao, Xiu-jin] School of Mathematical Science and Computing Technology, Central South University, Changsha, 410075, China;[Zhang, Zai-yun] Department of Mathematics, Hunan Institute of Science and Technology, College Road, Yueyang, 414006, China
期刊：
Spectrochimica Acta - Part A: Molecular and Biomolecular Spectroscopy,2013年111:31-36 ISSN：1386-1425
通讯作者：
Liang, Y.-Z.(yizeng_liang@263.net)
作者机构：
[Yun, Yong-Huan; E. Wood, Leslie R.; Li, Hong-Dong; Cao, Dong-Sheng; Liang, Yi-Zeng; Fan, Wei] College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China;[Wang, Jia-Jun] Products Research Center, Honghe Cigarette Factory, Mile 652300, China;[Xu, Qing-Song] School of Mathematics and Statistics, Central South University, Changsha 410083, China
通讯机构：
[Liang, Yi-Zeng] Cent S Univ, Coll Chem & Chem Engn, Changsha 410083, Hunan, Peoples R China.
关键词：
Random frog;Interval;Wavelength selection;Partial least squares;Near infrared spectra
作者机构：
[Wang, Wei-Ting; Yun, Yong-Huan; Li, Hong-Dong; Tan, Min-Li; Lu, Hong-Mei] College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China;[Cao, Dong-Sheng] College of Pharmaceutical Sciences, Central South University, Changsha 410083, PR China;[Liang, Yi-Zeng] College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China. Electronic address: yizeng_liang@263.net;[Xu, Qing-Song] School of Mathematics and Statistics, Central South University, Changsha 410083, PR China
通讯机构：
[Liang, Yi-Zeng] College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China. Electronic address:
关键词：
Informative variables - Iteratively retaining informative variables - Partial least square (PLS) - Random combination - Variable selection
摘要：
Nowadays, with a high dimensionality of dataset, it faces a great challenge in the creation of effective methods which can select an optimal variables subset. In this study, a strategy that considers the possible interaction effect among variables through random combinations was proposed, called iteratively retaining informative variables (IRIV). Moreover, the variables are classified into four categories as strongly informative, weakly informative, uninformative and interfering variables. On this basis, IRIV retains both the strongly and weakly informative variables in every iterative round until no uninformative and interfering variables exist. Three datasets were employed to investigate the performance of IRIV coupled with partial least squares (PLS). The results show that IRIV is a good alternative for variable selection strategy when compared with three outstanding and frequently used variable selection methods such as genetic algorithm-PLS, Monte Carlo uninformative variable elimination by PLS (MC-UVE-PLS) and competitive adaptive reweighted sampling (CARS). The MATLAB source code of IRIV can be freely downloaded for academy research at the website: http://code.google.com/p/multivariate-calibration/downloads/list. (C) 2013 Elsevier B. V. All rights reserved.
摘要：
By using the symmetric mountain pass theorem, we establish some existence criteria to guarantee the fourth-order difference system Delta(4)u(n - 2) + q(n)u(n) = f(n, u(n + 1),u(n), u(n - 1)) have infinitely many homoclinic orbits, where n is an element of Z; u is an element of R-N; q : Z -> R-NxN and f : Z x R-3N -> R are no periodic in n. (C) 2010 Elsevier Inc. All rights reserved.
作者机构：
[Wang, Zhizhong; He, Wenwu; Jiang, Hui] School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410075, China
通讯机构：
[He, Wenwu] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.
关键词：
Adaptive parameters - Auto-adaptive parameters - Feature selection - Feature selections - Input spaces - Multiple kernels - Non uniforms - Redundant informations - Support vector regression - Support vector regressions - Time series - Training datums
期刊：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION,2011年16(8):3097-3106 ISSN：1007-5704
通讯作者：
Zhang, Z.-Y.(zhangzaiyun1226@126.com)
作者机构：
[Liu Zhenhai] School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, 530006 Guangxi, China;[Miao Xiujin; Zhang Zaiyun] School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410075, China;[Li Yunxiang] Department of Mathematics, Hunan City University, Yiyang, Hunan 413000, China
通讯机构：
[Zhang, Zai-yun] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.
关键词：
Exact solutions;NLSE with Kerr law nonlinearity;Modified trigonometric function series method (MTFSM)
摘要：
In this paper, the modified trigonometric function series method is employed to solve the perturbed nonlinear Schrodingers equation (NLSE) with Kerr law nonlinearity. Exact traveling wave solutions are obtained. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
期刊：
Journal of Systems and Software,2009年82(2):270-273 ISSN：0164-1212
通讯作者：
Kang, B
作者机构：
[Boyd, Colin; Dawson, Ed; Kang, Baoyuan] Information Security Institute, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia;[Kang, Baoyuan] School of Mathematical Sciences and Computing Technology, Central South University, Chang'sha, Hunan 410075, China
通讯机构：
[Kang, Baoyuan] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.
作者机构：
[Dankelmann, Peter] School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4000, South Africa;[Stevanovi, Dragan] Mathematical Institute, Serbian Academy of Science and Arts, Knez Mihajlova 36, 11000, Belgrade, Serbia;[Stevanovi, Dragan] University of PrimorskaFAMNIT, Glagoljaka 8, 6000 Koper, Slovenia;[Feng, Lihua] Department of Mathematics, Central South University, Railway Campus, Changsha, Hunan, 410075, China;[Ili, Aleksandar] Faculty of Sciences and Mathematics, University of Niš,, Viegradska 33, 18000 Niš,, Serbia
摘要：
Let G be a connected graph with vertex set V (G). The degree distance of G is defined as D'(G) = Sigma({u,v}subset of V(G)) (deg(G)(u) + deg(G)(v))d(u, v), where deg(G)(u) is the degree of vertex u, and d(u, u) denotes the distance between u and v. Here we characterize n-vertex unicyclic graphs with girth k, having minimum and maximum degree distance, respectively. Furthermore, we prove that the graph B-n obtained from two triangles linked by a path, is the unique graph having the maximum degree distance among bicyclic graphs, which resolves a recent conjecture of Tomescu. (C) 2011 Elsevier B.V. All rights reserved.
作者机构：
[Cao, Dong-Sheng] Cent S Univ, Sch Pharmaceut Sci, Changsha 410083, Peoples R China.;[Zhu, Min-Feng; Xiao, Nan; Xu, Qing-Song] Cent S Univ, Sch Math & Stat, Changsha 410083, Peoples R China.
通讯机构：
[Cao, Dong-Sheng] Cent S Univ, Sch Pharmaceut Sci, Changsha 410083, Peoples R China.
会议名称：
11th ISCB-Student-Council Symposium held in conjunction with the 23rd Annual International Conference on Intelligent Systems for Molecular Biology (ISMB) / 14th European Conference on Computational Biology (ECCB)
会议时间：
JUL 10-14, 2015
会议地点：
Dublin, IRELAND
会议主办单位：
[Xiao, Nan;Zhu, Min-Feng;Xu, Qing-Song] Cent S Univ, Sch Math & Stat, Changsha 410083, Peoples R China.^[Cao, Dong-Sheng] Cent S Univ, Sch Pharmaceut Sci, Changsha 410083, Peoples R China.
摘要：
Amino acid sequence-derived structural and physiochemical descriptors are extensively utilized for the research of structural, functional, expression and interaction profiles of proteins and peptides. We developed protr, a comprehensive R package for generating various numerical representation schemes of proteins and peptides from amino acid sequence. The package calculates eight descriptor groups composed of 22 types of commonly used descriptors that include about 22 700 descriptor values. It allows users to select amino acid properties from the AAindex database, and use self-defined properties to construct customized descriptors. For proteochemometric modeling, it calculates six types of scales-based descriptors derived by various dimensionality reduction methods. The protr package also integrates the functionality of similarity score computation derived by protein sequence alignment and Gene Ontology semantic similarity measures within a list of proteins, and calculates profile-based protein features based on position-specific scoring matrix. We also developed ProtrWeb, a user-friendly web server for calculating descriptors presented in the protr package. AVAILABILITY AND IMPLEMENTATION: The protr package is freely available from CRAN: http://cran.r-project.org/package=protr, ProtrWeb, is freely available at http://protrweb.scbdd.com/.