RNA二级结构预测方法研究
|
摘要
随着对RNA(Ribonucleic Acid)研究的逐步深入,RNA在进行、遗传过程中的重要作用也越来越显著。RNA分子不仅充当着生物细胞中遗传信息的载体,还具有一系列重要的功能,如催化RNA剪接,加工和修饰RNA前体,调控基因表达等,这也促使了人们对RNA功能进行深入研究。而RNA的功能与结构是密切相关的,因此,通过研究RNA的二级结构,进而深入挖掘、阐述其功能就成为分子生物学中的重要研究课题。由于使用传统的实验手段(如X射线晶体衍射和核磁共振)去测定RNA的晶体结构虽然比较精确可靠,但代价昂贵,且费时费力。所以,借助于计算机实现的各种算法对RNA二级结构进行预测就成为当前国内外公认的主要方法。
RNA二级结构预测方法经过近30年的研究,到目前为止,已经有众多的算法。这些算法有的已经非常成熟,例如最小自由能算法,其预测精确度有时能达到90 %以上,但是它不能预测RNA假结。而目前的众多其它预测算法也大都各自存在着问题,如时间复杂度高,对序列的长度有限制等等。因此,对RNA二级结构预测方法的研究仍然是RNA研究中的重点课题。
本文正是在这种环境下,对RNA二级结构预测方法进行深入研究。论文对目前的RNA二级结构预测方法进行了分析、总结,然后归纳为四类:(1)比较序列分析方法(2)动态规划算法(3)组合优化算法(4)启发式算法。通过对这四类方法的研究、分析、比较,论文找到了新的预测方法的研究思路,为本文工作的完成奠定了坚实的理论基础。
首先,本文研究了马尔可夫链在RNA二级结构预测中的应用,提出了基于马尔可夫链的RNA二级结构预测新方法。根据自由能,构建马尔可夫链的转移概率矩阵,进而构建RNA-ML,来寻找自由能最小的RNA二级结构。论文从公用数据库(Genomic tRNA Database)中选取六条tRNA序列进行预测,将其预测结果和目前著名软件Mfold和RNAStructure的预测结果进行比较。实验结果表明,本文建立的RNA-ML优于Mfold,对于单条序列与RNAstructure接近。同时,本方法降低了时间复杂度,提高了敏感性和特异性,对trna序列执行起来速度较快,也可以应用于较长的RNA序列,弥补了大部分方法的预测时间随着序列长度增加成立方甚至四次方增长的缺陷。
其次,本文研究了隐马尔可夫模型在RNA二级结构预测中的应用,提出了基于隐马尔可夫模型的RNA二级结构预测新方法。以最小自由能为基础,建立各茎区间的转移概率矩阵、观察值概率矩阵,进而构建RNA-HMM,来寻找自由能最小的RNA二级结构。论文选取PseudoBase中的6条结构相对较复杂的RNA序列进行预测,将其预测结果和pknotsRG软件预测结果进行比较。实验结果表明,本方法的结果准确率比pknotsRG有所提高,通用性比较好。同时,也缩短了预测时间,提高了敏感性和特异性。
最后,本文研究了粒子群算法在RNA二级结构预测中的应用,提出了基于粒子群算法的RNA二级结构预测方法。结合PSO、最小自由能、被选择茎区的数量和平均长度,本文设计了一个新的适应度函数,建立了IPSO。论文分别用RNAPredict,H-Helix PSO和IPSO进行RNA二级结构预测,进而来比较它们RNA二级结构的自由能。结果表明,用IPSO方法预测到的最优茎区组合的自由能低于其它方法,能够找到更为稳定的二级结构,对于长序列IPSO的性能优势更为显著,而且具有较快的收敛速度,通过较少的迭代就可以找到更好的二级结构。论文又将标准粒子群优化算法(SPSO)、标准遗传算法(SGA)、蚁群算法(ACO)和IPSO方法的预测结果进行了比较。结果表明,由于高效的目标函数,IPSO的性能明显高于其它三种方法。为了验证IPSO方法在RNA二级结构预测中的有效性,本文将IPSO、Mfold和RnaPredict的预测结果进行了比较。结果表明:IPSO在其中三条序列上的敏感性和特异性高于Mfold,而在其余两个序列的测试结果低于Mfold,IPSO方法的在全部序列上的敏感性和特异性均高于RnaPredict,这也证明了本文所设计的目标函数是可行的、更有效的。
With the gradual deepening study on RNA (Ribonucleic Acid), the important role during the genetic process of RNA is also increasingly significant. The RNA molecules serve not only as a carrier of genetic information in living cells, but also has a number of important functions, such as catalysising RNA splice, processing and modifying the precursors of RNA, regulating the gene expression and so on, it is that which encourages people to do in-depth study of the RNA function. While the RNA functions and structures are closely related, therefore, through the study on the structure of the RNA molecular to fing and describe its function has become an important fleld of research of the Molecular Biology. Because which that uses traditional experimental methods (such as X-ray crystallography and NMR) to determine the crystal structure of RNA is relatively accurate and reliable, but it is expensive and time-consuming. Therefore, it is recognized as the main method at home and abroad which predicts the RNA structure by means of the various algorithms that computer realized.
The methods of RNA secondary structure prediction have been studied nearly 30 years, and now there are already many mature algorithms. Some algorithms have been able to achieve high accuracy, such as the algorithm of minimum free energy, the prediction accuracy of which can sometimes reach over 90%, but it can not predict RNA pseudoknot. At present, many other prediction algorithms exist mostly their own problems, such as high time complexity, the limit of the length of the sequence and so on. Therefore, the research of the methods of RNA secondary structure prediction is still the important subjects in the RNA study.
In this environment, the paper studys the methods of the RNA secondary structure prediction in depth. The Paper analyzed and summarized the current methods of RNA secondary structure prediction, and then grouped them into four categories: (1) the methods of Comparative sequence analysis (2) the Dynamic programming algorithm (3) the Combinatorial optimization algorithm (4) the Heuristic algorithm. Through the research, analysis and comparison of the four methods, the paper found the research idea of the new prediction method, which has laid a solid theoretical foundation for the completion of the paper work.
Firstly, the paper studyed the application of Markov chain in the RNA secondary structure prediction, and proposed the new method of the RNA secondary structure prediction which was based on Markov chain. According to the free energy, the paper build transition probability matrix of Markov chain, and then build RNA-ML, which was used to find the RNA secondary structure with minimum free energy. The paper selected six tRNA sequences from the public database (Genomic tRNA Database) to predict, and compared the results of its prediction with the results of famous software Mfold and RNAStructure. Experimental results showed that the RNA-ML was better than Mfold, and was closer to RNAstructure for a single sequence. Besides, this approach reduced the time complexity, improved the sensitivity and specificity and it executed faster for trna sequences, and it could be also used for a longer RNA sequence, meanwhile, it made up the defects that the time of majority of prediction methods increased to the growth of cubic or puartic with the growth of sequence length.
Secondly, the paper studied the application of the Hidden Markov Model in RNA secondary structure prediction and proposed the new method of RNA secondary structure prediction based on Hidden Markov Model. Based on the minimum free energy, the paper established transition probability matrix of the stems and probability matrix of observations, then the paper constructed RNA-HMM which was used to find the RNA secondary structure with minimum free energy. The paper selected 6 RNA sequences with relatively complex structure in the PseudoBase to predict, the prediction results were compared with the results of pknotsRG software. Experimental results showed that the result accuracy of this method was higher than pknotsRG, and the versatility was better than pknotsRG. Besides that, this method cut down the prdicition time, and improved the sensitivity and specificity.
Finally,the paper studied the application of the Particle Swarm Optimization algorithm in RNA secondary structure prediction and proposed a new method of the RNA secondary structure prediction based on Particle Swarm Optimization. The paper designed a new fitness function and established the IPSO which was combined with PSO, the minimum free energy, the number of the selected stems and the average length of the selected stems. The paper used RNAPredict, H-Helix PSO and IPSO to predict the RNA secondary structure, and then compared their free energy of RNA secondary structure with each other. The results showed that the free energy of the optimal stem combination predicted by IPSO was lower than that predicted by other methods, and the IPSO could find a more stable secondary structure, and the performance advantages of IPSO for a long sequence was more significant, and it Could find a better secondary structure with fewer iterations , because it had a faster convergence. The paper compared the prediction results of the IPSO with the prediction results of the standard PSO (SPSO), the standard genetic algorithm (SGA), and the ant colony optimization (ACO). The results showed that the IPSO's performance was significantly higher than the other three methods because of the highly efficient objective function. In order to verify the effectiveness of IPSO in the prediction of RNA secondary structure, the paper compared the prediction results of IPSO with the prediction results of Mfold and RnaPredict. The results showed that the sensitivity and specificity of IPSO were higher Mfold for three of the sequences, but the test results were lower than Mfold for the other two sequences, and the sensitivity and specificity of IPSO were higher than RnaPredict for all the sequences, that also proved that the objective function designed in the paper was feasible and more effective.
RNA二级结构预测方法经过近30年的研究,到目前为止,已经有众多的算法。这些算法有的已经非常成熟,例如最小自由能算法,其预测精确度有时能达到90 %以上,但是它不能预测RNA假结。而目前的众多其它预测算法也大都各自存在着问题,如时间复杂度高,对序列的长度有限制等等。因此,对RNA二级结构预测方法的研究仍然是RNA研究中的重点课题。
本文正是在这种环境下,对RNA二级结构预测方法进行深入研究。论文对目前的RNA二级结构预测方法进行了分析、总结,然后归纳为四类:(1)比较序列分析方法(2)动态规划算法(3)组合优化算法(4)启发式算法。通过对这四类方法的研究、分析、比较,论文找到了新的预测方法的研究思路,为本文工作的完成奠定了坚实的理论基础。
首先,本文研究了马尔可夫链在RNA二级结构预测中的应用,提出了基于马尔可夫链的RNA二级结构预测新方法。根据自由能,构建马尔可夫链的转移概率矩阵,进而构建RNA-ML,来寻找自由能最小的RNA二级结构。论文从公用数据库(Genomic tRNA Database)中选取六条tRNA序列进行预测,将其预测结果和目前著名软件Mfold和RNAStructure的预测结果进行比较。实验结果表明,本文建立的RNA-ML优于Mfold,对于单条序列与RNAstructure接近。同时,本方法降低了时间复杂度,提高了敏感性和特异性,对trna序列执行起来速度较快,也可以应用于较长的RNA序列,弥补了大部分方法的预测时间随着序列长度增加成立方甚至四次方增长的缺陷。
其次,本文研究了隐马尔可夫模型在RNA二级结构预测中的应用,提出了基于隐马尔可夫模型的RNA二级结构预测新方法。以最小自由能为基础,建立各茎区间的转移概率矩阵、观察值概率矩阵,进而构建RNA-HMM,来寻找自由能最小的RNA二级结构。论文选取PseudoBase中的6条结构相对较复杂的RNA序列进行预测,将其预测结果和pknotsRG软件预测结果进行比较。实验结果表明,本方法的结果准确率比pknotsRG有所提高,通用性比较好。同时,也缩短了预测时间,提高了敏感性和特异性。
最后,本文研究了粒子群算法在RNA二级结构预测中的应用,提出了基于粒子群算法的RNA二级结构预测方法。结合PSO、最小自由能、被选择茎区的数量和平均长度,本文设计了一个新的适应度函数,建立了IPSO。论文分别用RNAPredict,H-Helix PSO和IPSO进行RNA二级结构预测,进而来比较它们RNA二级结构的自由能。结果表明,用IPSO方法预测到的最优茎区组合的自由能低于其它方法,能够找到更为稳定的二级结构,对于长序列IPSO的性能优势更为显著,而且具有较快的收敛速度,通过较少的迭代就可以找到更好的二级结构。论文又将标准粒子群优化算法(SPSO)、标准遗传算法(SGA)、蚁群算法(ACO)和IPSO方法的预测结果进行了比较。结果表明,由于高效的目标函数,IPSO的性能明显高于其它三种方法。为了验证IPSO方法在RNA二级结构预测中的有效性,本文将IPSO、Mfold和RnaPredict的预测结果进行了比较。结果表明:IPSO在其中三条序列上的敏感性和特异性高于Mfold,而在其余两个序列的测试结果低于Mfold,IPSO方法的在全部序列上的敏感性和特异性均高于RnaPredict,这也证明了本文所设计的目标函数是可行的、更有效的。
With the gradual deepening study on RNA (Ribonucleic Acid), the important role during the genetic process of RNA is also increasingly significant. The RNA molecules serve not only as a carrier of genetic information in living cells, but also has a number of important functions, such as catalysising RNA splice, processing and modifying the precursors of RNA, regulating the gene expression and so on, it is that which encourages people to do in-depth study of the RNA function. While the RNA functions and structures are closely related, therefore, through the study on the structure of the RNA molecular to fing and describe its function has become an important fleld of research of the Molecular Biology. Because which that uses traditional experimental methods (such as X-ray crystallography and NMR) to determine the crystal structure of RNA is relatively accurate and reliable, but it is expensive and time-consuming. Therefore, it is recognized as the main method at home and abroad which predicts the RNA structure by means of the various algorithms that computer realized.
The methods of RNA secondary structure prediction have been studied nearly 30 years, and now there are already many mature algorithms. Some algorithms have been able to achieve high accuracy, such as the algorithm of minimum free energy, the prediction accuracy of which can sometimes reach over 90%, but it can not predict RNA pseudoknot. At present, many other prediction algorithms exist mostly their own problems, such as high time complexity, the limit of the length of the sequence and so on. Therefore, the research of the methods of RNA secondary structure prediction is still the important subjects in the RNA study.
In this environment, the paper studys the methods of the RNA secondary structure prediction in depth. The Paper analyzed and summarized the current methods of RNA secondary structure prediction, and then grouped them into four categories: (1) the methods of Comparative sequence analysis (2) the Dynamic programming algorithm (3) the Combinatorial optimization algorithm (4) the Heuristic algorithm. Through the research, analysis and comparison of the four methods, the paper found the research idea of the new prediction method, which has laid a solid theoretical foundation for the completion of the paper work.
Firstly, the paper studyed the application of Markov chain in the RNA secondary structure prediction, and proposed the new method of the RNA secondary structure prediction which was based on Markov chain. According to the free energy, the paper build transition probability matrix of Markov chain, and then build RNA-ML, which was used to find the RNA secondary structure with minimum free energy. The paper selected six tRNA sequences from the public database (Genomic tRNA Database) to predict, and compared the results of its prediction with the results of famous software Mfold and RNAStructure. Experimental results showed that the RNA-ML was better than Mfold, and was closer to RNAstructure for a single sequence. Besides, this approach reduced the time complexity, improved the sensitivity and specificity and it executed faster for trna sequences, and it could be also used for a longer RNA sequence, meanwhile, it made up the defects that the time of majority of prediction methods increased to the growth of cubic or puartic with the growth of sequence length.
Secondly, the paper studied the application of the Hidden Markov Model in RNA secondary structure prediction and proposed the new method of RNA secondary structure prediction based on Hidden Markov Model. Based on the minimum free energy, the paper established transition probability matrix of the stems and probability matrix of observations, then the paper constructed RNA-HMM which was used to find the RNA secondary structure with minimum free energy. The paper selected 6 RNA sequences with relatively complex structure in the PseudoBase to predict, the prediction results were compared with the results of pknotsRG software. Experimental results showed that the result accuracy of this method was higher than pknotsRG, and the versatility was better than pknotsRG. Besides that, this method cut down the prdicition time, and improved the sensitivity and specificity.
Finally,the paper studied the application of the Particle Swarm Optimization algorithm in RNA secondary structure prediction and proposed a new method of the RNA secondary structure prediction based on Particle Swarm Optimization. The paper designed a new fitness function and established the IPSO which was combined with PSO, the minimum free energy, the number of the selected stems and the average length of the selected stems. The paper used RNAPredict, H-Helix PSO and IPSO to predict the RNA secondary structure, and then compared their free energy of RNA secondary structure with each other. The results showed that the free energy of the optimal stem combination predicted by IPSO was lower than that predicted by other methods, and the IPSO could find a more stable secondary structure, and the performance advantages of IPSO for a long sequence was more significant, and it Could find a better secondary structure with fewer iterations , because it had a faster convergence. The paper compared the prediction results of the IPSO with the prediction results of the standard PSO (SPSO), the standard genetic algorithm (SGA), and the ant colony optimization (ACO). The results showed that the IPSO's performance was significantly higher than the other three methods because of the highly efficient objective function. In order to verify the effectiveness of IPSO in the prediction of RNA secondary structure, the paper compared the prediction results of IPSO with the prediction results of Mfold and RnaPredict. The results showed that the sensitivity and specificity of IPSO were higher Mfold for three of the sequences, but the test results were lower than Mfold for the other two sequences, and the sensitivity and specificity of IPSO were higher than RnaPredict for all the sequences, that also proved that the objective function designed in the paper was feasible and more effective.
引文
[1]张春霆.生物信息学的现状与展望[M],世界科技研究与发展. 2000, 22: 17-20.
[2]刘海军. RNA二级结构预测的建模及其应用研究[D].博士学位论文,上海大学, 2005.
[3]李誌.基于马尔科夫链的RNA二级结构预测[D].吉林大学硕士论文, 2007.
[4]金由辛.核糖核酸与核糖核酸组学[M].科学出版社, p: 8.
[5] Wang, Q.C., Q.H.Nie, and 2.H.Feng, RNA interferenee [J]. Antiviral weapon and beyond, 2003, 9(8): 1657-1661.
[6] Maher, D.L, and P.P.Dennis. Invivotranscription of E. eoligenes coding for rRNA, ribosomal Proteins and subunits of RNA polymerase: Influence of the stringent control system [J]. Mo1ecular Genetics and Genomics, 1977, 155(2): 203-211.
[7] L1ang, X.H., Q. Liu, and M.J.Fournier, rRNA modifieations in an intersubunit bridge of the ribosome strongly affect both ribosome biogenesis and aetivity [J]. Mol Cell, 2007, 28(6): 965-77.
[8] Jurado, J., et al., Alternative splicing of c-fos pre-mRNA: contribution of the rates of synthesis and degradation to the copy number of each transcript isoform and detection of a truncated c-Fos immunoreactive species [J]. BMC Mol Biol, 2007, 8: 83.
[9] Li, Q., J.A.Lee, and D.L.Black. Neuronal regulation of a1ternative Pre-mRNA splicing [J]. Nat Rev Neurosci, 2007, 8(11): 819-831.
[10] Deutseher, M.P., Degradation of RNA in bacteria: comparison of mRNA and stable RNA [J]. Nucleic Acids Re, 2006, 34(2): 659-666.
[11] Fury, M.G. and J.Andersen. In vitro interaction of UZ snRNA with cytoplasmic 6S protein complexes [J]. FEBSLett, 1997, 404(1): 70.
[12] Crotti. L.B., D. Baeikova, and D.S.Horowitz. The Prp18 protein stabilizes the interaction of both exons with the US snRNA during the second step of pre-mRNA splicing [J]. Genes Dev, 2007, 21(10): 1204-1216.
[13] Li, Z.and M.P. Deutscher. The Trna Proeessing enzyme RNase Tis essential for maturation of 5S RNA [J]. Proc Natl Acad Sci US, 1995, 92(15): 6883-6886.
[14] Roovers, M., et al. A primordial RNA modification enzyme: the case of tRNA (m1A) methyltransferase [J]. Nueleic Acids Res, 2004, 32(2): 465-476.
[15] Zhu, L.J. and S.W. A1tmann. mRNA and18S [J].RNA coapplic.1995, p:102-109.
[16] Oikonomou, P., et al. Quantitative determination of human telomerase reverse transcriptase messenger RNA expression in premalignant cervical lesions and correlation with human papillomavirus load [J].Hum Pathol. 2006, 37(2): 135-142.
[17] Fresco, J.R., B.M. Alberts, and P. Doty. Some molecular details of the secondary structure of ribonucleic acid [J].Nature.1960, 188(4745): 98-101.
[18] Nussinov. R.and A.B. Jacobson.Fast Algorithm for Predicting the Secondary Structure of Single-Stranded RNA [J]. Proceedings of the National Academy of Sciences of the United States of America. 1980, 77(11): 6309-6313.
[19] Zuker. M. and P. Stiegler. Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information [J].Nue1eic AcidsRes. 1981 9(1): 133-148.
[20]夏培明. RNA二级结构预测算法的研究与实现[D].哈尔滨工业大学硕士论文. 2008.
[21] Ennysr. Durbar RNA Sequence Analysis using covariance models [J]. Nucleic Acids Res.1994, 22: 2079-2088.
[22] Sakakbara Y. Browm M. Hugheryr. Recent methods for RNA modeling using stochastic context-free grammars[C]. Grochemorem. Gusfield D. Proceedings of the sikomar conference on combinatorial pattem matching Berlin: Springer-Verlag.1994, p: 289-306.
[23] Hofacker I. L. . Fekete M..et al. Secondary Structure Prediction for Aligned RNA Sequences [J]. Mol. Biol. 2002, 319: 1059-1066.
[24] Cai L. Malmberg R. L. Wu Y. Stochastic modeling of RNA pseudoknotted structures: a grammatical approach [J]. Bioinformatics. 2003, : 166-173
[25] Zuker M. Stiegler P.Optimal Computer Folding of Large RNA Sequences Using Thermodynamics and Auxiliary Information [J].Nucl.Acids Res. 1981, 9: 133-148.
[26] Nussinov R , Pieczenik G , et al. Siam J .Appl.Math. ,1975;35.p: 68-82
[27] Tahi F. Gouy M. Regnier M.Automatic RNA secondary structure prediction with a comparative approach [J].Computers and Chemistry. 2002, 26: 521-530.
[28] Mccaskill J S. The equilibrium partition function and base pair binding probabilities for RNA secondary structure [J]. Biopolymers. 2003, 29: 1105-1119.
[29] Hofacker I.L. Fekete M. et al. Secondary Structure Prediction for Aligned RNA Sequences [J]. Mol.Biol. 2002, 319: 1059-1066.
[30] Mathews D H. Using an RNA secondary structure partition function to determi-ne confidence in base pairs predicted by free energy minimization [J]. RNA. 2004, 10: 1189-1190.
[31] Ricas E. Eddy S.R.A dynamic programming algorithm for RNA structure prediction including pseudoknots [J]. Mol.Biol. 1999, 285: 2053-2068.
[32] Krogh A. Brown M. et al. Hidden Markov models in computational biology [J].Applications to protein modeling, Mol Biol. 1994, 235: 1501-1531.
[33] Rune B .Lyngsc. Christian N. S. Pseudoknots in RNA Secondary Structures. Pedersen [J]. Proceedings of the fourth annual international conference on Computational molecular biology. 2000.
[34] Jitender S.Deogun. Ruben Donis Olga Komina, Fangrui Ma.RNA Secondary Structure Prediction with Simple Pseudoknots [M].University of Nebraska- Lincoln, USA.2005.
[35] Christina Witwer. Ivo L.Hofacker. and Peter F.Stadler. Prediction of Consensus RNA Secondary Structures Including Pseudoknots [J].IEEE Transactions on computational biology and bioinformatics. 2004, 1(2): 34-38.
[36] Oyun-Erdene Namsrai, Kwang Su Jung, Sunshin Kim, and Keun Ho Ryu .RNA Seconsary Structure Prediction With Simple Pseudoknots Based on Dynamic Programming [J].Computational Intelligence and Bioinformatics 2006, : 303– 311.
[37]李恒武,朱大铭.预测RNA二级结构的新算法[J].计算机科学. 2004, 31(10): 142-144.
[38]刘振栋,李恒武,朱大铭.计算最大堆迭的RNA二级结构预测算法[J].南京大学学报, 2005, 41(5): 532-537.
[39] Macke T.J. Ecker D.J. et al. RNAMotif. An RNA Secondary Structure Definition and Search Algorithm [J]. Nucl. Acids Res. 2001, 29: 4724-4735.
[40] Gorodkin J. Sticklin S.L. Stormo G.D. Discovering common stem-loop motifs in unaligned RNA sequences [J].Nucleic Acids Res., 2001, 29: 2135-2144.
[41] Li W.J., Wu J. J. Bioinformatics[M], USA. 1998, 14: 700-706.
[42] Cary R.B., Stormo G.D. Graph-theoretic Approach to RNA Modeling Using Comparative Data [J]. In Proceedings of the Third International Conference on Intelligent Systems for Molecular Biology. Menlo Park: AAAI Press, 1995, p: 78-86.
[43]刘海军,史定华,王翼飞.日新月异的RNA二级结构预测[J].自然杂志, 2003, 25(6): 314-322.
[44] Fei Xia, Yong Dou, Xingming Zhou. Fine-grained parallel RNAalifold algorithm for RNA secondary structure prediction on FPGA [J]. Proceedings of the 7th Asia-Pacific Bioinformatics Conference.January 2009, p: 426-438.
[45] Fenix WD Huang, Linda YM Li, Christian M Reidys, Sequence-structure relations of pseudoknot RNA [J]. Proceedings of the 7th Asia-Pacific Bioinformatics Conference.January, 2009, p: 449-463.
[46] Unyanee Poolsap, Yuki Kato, Tatsuya Akutsu. Prediction of RNA secondary structure with pseudoknots using integer programming [J]. Proceedings of the 7th Asia-Pacific Bioinformatics Conference. January 2009, p: 439-448.
[47]宋丹丹,邓志东. RNA二级结构预测的模糊模型[J].中国科学. 2007, 37(10): 1285-1303.
[48]王金华,骆志刚,管乃洋,严繁妹,靳新,张雯.基于最小自有能和协变信息预测带伪结RNA二级结构的迭代化方法[J]. HEREDITAS(Beijing). 2007, 29 (7): 889-897.
[49]党琰,张宇镭,张冬荣,赵立平.使用角色反演句法分析器RNA二级结构的预测[J].计算机工程, 2006, 32(8): 68-79.
[50]刘琦,张引,叶修梓,俞荣栋.基于离散Hopefield网络求解极大独集的茎区选择算法以及在RNA二级结构预测中的应用[J].计算机学报, Jan, 2008, 31(1).
[51]刘琦,张引,叶修梓,俞荣栋.基于奇异值分解的RNA二级结构相似度计算方法[J]. Journal of Zhejiang University Engineering Science, Aug, 2007, 41(8).
[52]高世乐,丁克诠.含假结RNA二级结构类的图语法[J].计算机工程与应用, .2008, 44(2): 23-25.
[53]刘永明.分子生物学简明教程[M].化学工业出版社.北京化学工业出版社. 2006, p: 21-22.
[54] Haslinger, C. and P.F. Stadler, RNA structures with pseudo-knots: graph-theoretical, combinatorial, and statistical properties [J].Bull Math Biol.1999, 61(3): 437-467.
[55] Take fuji, Y. et al. Parallel algorithms for finding a near-maximum independent set of a circle graph [J].IEEE Trans Neural Netw.1990, 1(3): 263-267.
[56] Hofacker, I.L.Vienna RNA secondary structure server [J]. Nucleie AcidsRes. 2003, 31 (13): 3429-3431.
[57] ShaPiro, B.A. An algorithm for comparing multiple RNA secondary structures [J]. Bioinformaties. 2003, 4(3): 387-393.
[58]何静媛. RNA二级结构预测算法的研究[D].重庆大学博士论文. 2009.
[59]韩乐,莫忠良. RNA-Z曲线及其在病毒基因识别中的应用[J].生物数学学报. 2004, 19: 245-250.
[60] Li. C. and J.Wang.On a 3-D Representation of DNA Primary Sequences [J]. Combinatorial Chemistry &High Throughput Screening. 2004, 7: 23-27.
[61] Liao, B.and T.M.Wang. A 3D graphical representation of RNA secondary Struetures [J]. Biomol Struct Dyn .2004, 21(6): 827-32.
[62]单夫一,骆嘉伟,一种新的RNA二级结构的三维图形表示[J].武汉理工大学学报(信息与管理工程版). 2007, (5): 5-8.
[63] Eddy.S.R. How do RNA folding algorithms work [J].Nature Biotechnology. 2004, 22(11): 1457- 1458.
[64] Eddy S R, Durbin R.RNA Sequence Analysis Using Covariance Models [J]. Nucleotide Acids Research.1994, 22(11): 2079-2088.
[65] Eddy S R.What is a hidden Markov model? [J].Nature Biotechnology.2004, 22(10: 1315-1316.
[66]陆健.基于动态权重匹配的RNA二级结构预测算法[D].江苏:江苏大学生物化学与分子生物学学院. 2007.
[67] Chomsky N.Three models for the description of languages [J].IRE Transactions on Information Theory .1956, 2(3): 113-124.
[68] Chomsky N. On certain formal properties of grammars [J].Information Control.1959, 2(2): 137 - 167.
[69] Rivas E, Eddy S R.The Language of RNA. A Formal Grammar That Includes Pseudoknots [J]. Bioinformatics. 2001 16(4): 334-340.
[70] Sakakibara Y, Brown M, et al.Stochastic context-free grammars for tRNA modeling [J].Nucleotide Acids Research.1994, 22(23): 5112-5120.
[71] Salvador I, Benedi J. RNA Modeling by combining stochastic context-free grammars and n-grammodels [J]. International Journal of Pattern Recognition and Artificial Intelligence, 2002, 16(3): 309-315.
[72] Lari K and Young S J.The estimation of stochastic context-free grammars using the inside-outside algorithm [J].Computer Speech Langues.1990, 49(1): 35-56.
[73]刘琦. RNA二级结构的若干计算生物学问题研究[D].浙江:浙江大学生命科学院, 2008.
[74]李伍举,吴加金. RNA二级结构的预测[J].军事医学科学院院刊.1996, 20(4): 298-310.
[75] Zuker M and D Sankoff.RNA secondary structures and their prediction [J].Bulletin of Mathematical Biology.1984, 46(4): 591-621.
[76] Zuker M.Computer Prediction of RNA structure [J].Methods Enzymol. 1989, 180: 262-288.
[77] Zuker M.Calculating nucleic acid secondary structure [J].Current opinion in Structural Biology. 2000, 10(3): 303-310.
[78] WuJu L. Prediction of RNA secondary structure based on he1ical regions distribution[J]. Bioinformatics.1998, 14(8): 700-706.
[79]彭政.带假结的RNA二级结构预测算法研究[D].湖南:湖南大学计算机与通信学院, 2008.
[80] Tabaska J E,Cary R B,et al.An RNA Folding Method Capable of Identifying Pseudoknots and Base Triples [J].Bioinformatics.1998, 14(8): 691-699.
[81] Page R P M. Circles: Automating the Comparative Analysis of RNA Secondary Structure [J]. Bioinformatics. 2000, 16(11): 1042-1043.
[82] Page R D M.Comparative analysis of secondary structure of insect mitochondrial small subunit ribosoma RNA using maximum weighted matching [J] .Nucleotide Acids Research. 2000, 28(20): 3839- 3845.
[83]谭光明,冯圣中,孙凝晖. RNA二级结构预测中动态规划的优化和有效并行[J]. Journal of Software.2006, 17(7): 1501-1509.
[84] Shapiro B A, Wu J C,et al.The Massively Parallel Genetic Algorithm for RNA Folding: MIMD Implementation and Population Variation [J].Bioinformatics.2001, 17(2): 137- 148.
[85] Minoru K.Post-genome Informatics [M].New York: Oxford University Press. 2000.
[86]林元烈.应用随机过程[M].北京清华大学出版社.2002, p: 78-100; 107-114.
[87] David, Freedman. Markov Chains [M].New York: Spring-Verlag.1983, p: 7~16.
[88]吴俊杰,潘麟生.随机过程[M].长沙:湖南大学出版社.1988, p: 47-55.
[89] L. Isaacson, W .M. Richard. Markov Chains Theory and Applications [J]. John Wiley & Sons, Inc. 1976, p: 100-106.
[90]彭梅.基于马尔可夫链的商品销售预测模型[J].达县师范高等专科学校报.2006, 16(5): 20~22.
[91] G. F.del Angel.A Discrete Markov Chain Model for Valuing Loan Portfolis [J].Journal of Banking & Finance.1998, (10): 1457-1480.
[92] J. Meredith .A Markovian Analysis of Geriatric Ward [J].Management Science.1979, 19(6): 12.
[93]毛长飞,顾乾屏,陈坚,罗升平.基于有吸收态的马尔可夫链的贷款迁移分析[J].山东工商学院学报.2007, 21(5): 5-11.
[94]张维,王丽娜.马尔可夫链方法在分析预测商业银行逾期贷款中的应用[J].现代财经.2004, 24(12): 3-6.
[95]梁保松,温建,陈振,王建平,宁亚伟.马尔可夫过程在基金投资中的应用[J].河南农业大学学报. 2003, 37(4): 428-430.
[96]刘岩,刘芳.马尔可夫链在人民币汇率预测中的应用[J].中国管理信息化. 2007,10(3): 68-70.
[97]刘锋.企业人力资源预测—基于马尔可夫链的研究[J].商场现代化. 2006, (19): 246.
[98]郝宇.马尔可夫预测在营销管理中的应用[J].科技情报开发与经济. 2005, 5(23): 101-103.
[99]张宇山.教学质量评价的马尔可夫链模型[J].科技情报开发与经济. 2007, 17(9): 238-239.
[100]程向阳.马尔可夫链模型在教育评估中的应用[J].大学数学. 2007, 23(2): 38-41.
[101]昝欣,宗鹏,吴祈宗.马尔可夫链在高校教师人才流动预测中的应用[J].科技进步与对策. 2007, (1): 185-187.
[102]魏国孝,李文华.基于马尔可夫模型的高校师资队伍预测方法[J].宁夏大学学报(自然科学版). 2004, 25(4): 309-310.
[103]林素文,王彦声,谢志鸣.高校教师队伍规模预测研究[J].福建医科大学学报(社会科学版). 2005, (1): 77-79.
[104]白君礼,许爱兰.Markov在图书情报中的应用[J].情报杂志. 2003, (11): 50-51.
[105]章亚娟,俞爱君. Markov链在高校文献资源采购预测中的应用[J].哈尔滨师范大学自然科学学报. 2002, 18(4): 8-11.
[106]李国晖.马尔可夫模型在常染色体遗传中的应用[J].内蒙古科技与经济.2 007, (21): 417-418.
[107]王宏健.复等位基因遗传疾病的数学模型[J].福州大学学报(自然科学版). 1995, (5): 1-6.
[108]巴剑波,方旭东.马尔可夫链在海军疟疾疫情预测中的应用[J].解放军预防医学杂志. 2001, (2: 514~516.
[109]谢婧.概率论与数理统计[M].中国时代经济出版社. 2002, p: 278.
[110] Gardner PP, Giegerich R. A comprehensive comparison of comparative RNA structure prediction approaches [J]. BMC Bioinformatics .2004, 5 (1): 1-32.
[111] T.M.Lowe and S.R.Eddy. tRNAscan -SE: A program for improved detection of transfer RNA genes in genomic sequence[J]. Nucl.Acids Res.1997, 25: 955-964.
[112] Rabiner L R.A tutorial on hidden Markov models and selected applications in speech recognition [J]. In: Proceedings of the IEEE.1989, 77(2): 257-286.
[113] Baum L E, Petrie T, Soules G, et al. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains [J]. Annals of Mathematical Statistics. 1970; 41(1: 164-171.
[114] Rabiner L R.A tutorial on hidden Markov models and selected applications in speechrecognition [J]. In: Proceedings of the IEEE.1989, 77(2): 257-286.
[115] Forney G D.The Viterbi algorithm [J].In: Proceedings of the IEEE. 1973, 61(3): 268 -278.
[116] Reynold C.W. Flock herds and schools :a distributed behavioral model [J]. Computer Graphics.1987, 21(4): 25-34.
[117] Hepper F, U Grenander .A stochastic nonlinear model for coordinated bird flocks, In S Krasner Ed [M].The Ubiquity of Chaos, AAAS Publications, Washington DC.1990.
[118] Wilson E.O. Sociabiology: the new synthesis, Belknap Press [J].Cambridge, MA. 1975, p: 12-14.
[119] Kenned, J. and Eberbart, R.C.Particle swarm optimization [J].In Proceedings of the IEEE International Conference on Neural Networks.1995, p: 1942-1948.
[120]曾建潮,介婧,崔志华.微粒群算法[M].北京科学出版社, 2004.
[121] Lovbjerg, M. and Krink, T.Extending Particle Swarm Optimisers with Self-Organized Criticality [J].In Proceedings of the IEEE Congress on Evolutionary Computation. 2002, (2): 1588-1593.
[122] Parsopoulos, K.E., Magoulas, V.P.G., and Vrahatis, M. Stretching technique for obtaining global minimizers through particle swarm optimization [J].In Proceedings of the workshop on particle swarm optimization, Indianapolis, IN. 2001.
[123] Shi, Y.H.and Eberhart, R.C. A modified particle swarm optimizer [J]. In Proceedings of the IEEE International Conference on Evolutionary Computation.1998.p:69-73.
[124] Shi, Y.H. and Eberhart, R.C. Parameter selection in particle swarm optimization [J].In Lecture Notes in Computer Science1447: Evolutionary ProgrammingⅦ.1998, p: 591- 600.
[125] Clerc, M. and Kennedy, J. The particle swarm: Explosion, stability, and convergence in a multi-dimensional complex space [J].IEEE Transactions on Evolutionary Computation. 2002, 1(6): 58-73.
[126] Carlisle, A. and Dozier, G. An off-the-shelf PSO [J]. In Proceedings of the Workshop on Particle Swarm Optimization, Indianapolis.2001.
[127] Carlisle A.and Dozier, G. A dapting particle swarm optimization to dynamic environments [J].In Proceedings of the International Conference on Artificial Intelligence. 2000, p: 429-434.
[128] Carlisle A.and Dozier, G. Tracking changing extrema with adaptive particle swarm optimizer [J]. In Proceedings of the 5th Biannual World Automation Congress, Orlando, Florida, USA. 2002, p: 265-270.
[129] Angeline, P.J. Using selection to improve particle swarm optimization [J]. In Proceedings of the IEEE Congress on Evolutionary Computation, Anchorage, Alaska, USA. 1998.
[130] K.C.Wiese, A.A.Deschenes, and A.G.Hendriks.RNA Predict-An Evolutionary Algorithm for RNA Secondary Structure Prediction [J].IEEE/ACM, Transactions on computational biology and bioinformatics.2008, 5(1): 25-41.
[131] M. Geis and M. Middendorf. A particle swarm optimizer for finding minimum free energy RNA secondary structures [J].IEEE Swarm Intelligence Symposium. 2007, 2341: 1-8.
[2]刘海军. RNA二级结构预测的建模及其应用研究[D].博士学位论文,上海大学, 2005.
[3]李誌.基于马尔科夫链的RNA二级结构预测[D].吉林大学硕士论文, 2007.
[4]金由辛.核糖核酸与核糖核酸组学[M].科学出版社, p: 8.
[5] Wang, Q.C., Q.H.Nie, and 2.H.Feng, RNA interferenee [J]. Antiviral weapon and beyond, 2003, 9(8): 1657-1661.
[6] Maher, D.L, and P.P.Dennis. Invivotranscription of E. eoligenes coding for rRNA, ribosomal Proteins and subunits of RNA polymerase: Influence of the stringent control system [J]. Mo1ecular Genetics and Genomics, 1977, 155(2): 203-211.
[7] L1ang, X.H., Q. Liu, and M.J.Fournier, rRNA modifieations in an intersubunit bridge of the ribosome strongly affect both ribosome biogenesis and aetivity [J]. Mol Cell, 2007, 28(6): 965-77.
[8] Jurado, J., et al., Alternative splicing of c-fos pre-mRNA: contribution of the rates of synthesis and degradation to the copy number of each transcript isoform and detection of a truncated c-Fos immunoreactive species [J]. BMC Mol Biol, 2007, 8: 83.
[9] Li, Q., J.A.Lee, and D.L.Black. Neuronal regulation of a1ternative Pre-mRNA splicing [J]. Nat Rev Neurosci, 2007, 8(11): 819-831.
[10] Deutseher, M.P., Degradation of RNA in bacteria: comparison of mRNA and stable RNA [J]. Nucleic Acids Re, 2006, 34(2): 659-666.
[11] Fury, M.G. and J.Andersen. In vitro interaction of UZ snRNA with cytoplasmic 6S protein complexes [J]. FEBSLett, 1997, 404(1): 70.
[12] Crotti. L.B., D. Baeikova, and D.S.Horowitz. The Prp18 protein stabilizes the interaction of both exons with the US snRNA during the second step of pre-mRNA splicing [J]. Genes Dev, 2007, 21(10): 1204-1216.
[13] Li, Z.and M.P. Deutscher. The Trna Proeessing enzyme RNase Tis essential for maturation of 5S RNA [J]. Proc Natl Acad Sci US, 1995, 92(15): 6883-6886.
[14] Roovers, M., et al. A primordial RNA modification enzyme: the case of tRNA (m1A) methyltransferase [J]. Nueleic Acids Res, 2004, 32(2): 465-476.
[15] Zhu, L.J. and S.W. A1tmann. mRNA and18S [J].RNA coapplic.1995, p:102-109.
[16] Oikonomou, P., et al. Quantitative determination of human telomerase reverse transcriptase messenger RNA expression in premalignant cervical lesions and correlation with human papillomavirus load [J].Hum Pathol. 2006, 37(2): 135-142.
[17] Fresco, J.R., B.M. Alberts, and P. Doty. Some molecular details of the secondary structure of ribonucleic acid [J].Nature.1960, 188(4745): 98-101.
[18] Nussinov. R.and A.B. Jacobson.Fast Algorithm for Predicting the Secondary Structure of Single-Stranded RNA [J]. Proceedings of the National Academy of Sciences of the United States of America. 1980, 77(11): 6309-6313.
[19] Zuker. M. and P. Stiegler. Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information [J].Nue1eic AcidsRes. 1981 9(1): 133-148.
[20]夏培明. RNA二级结构预测算法的研究与实现[D].哈尔滨工业大学硕士论文. 2008.
[21] Ennysr. Durbar RNA Sequence Analysis using covariance models [J]. Nucleic Acids Res.1994, 22: 2079-2088.
[22] Sakakbara Y. Browm M. Hugheryr. Recent methods for RNA modeling using stochastic context-free grammars[C]. Grochemorem. Gusfield D. Proceedings of the sikomar conference on combinatorial pattem matching Berlin: Springer-Verlag.1994, p: 289-306.
[23] Hofacker I. L. . Fekete M..et al. Secondary Structure Prediction for Aligned RNA Sequences [J]. Mol. Biol. 2002, 319: 1059-1066.
[24] Cai L. Malmberg R. L. Wu Y. Stochastic modeling of RNA pseudoknotted structures: a grammatical approach [J]. Bioinformatics. 2003, : 166-173
[25] Zuker M. Stiegler P.Optimal Computer Folding of Large RNA Sequences Using Thermodynamics and Auxiliary Information [J].Nucl.Acids Res. 1981, 9: 133-148.
[26] Nussinov R , Pieczenik G , et al. Siam J .Appl.Math. ,1975;35.p: 68-82
[27] Tahi F. Gouy M. Regnier M.Automatic RNA secondary structure prediction with a comparative approach [J].Computers and Chemistry. 2002, 26: 521-530.
[28] Mccaskill J S. The equilibrium partition function and base pair binding probabilities for RNA secondary structure [J]. Biopolymers. 2003, 29: 1105-1119.
[29] Hofacker I.L. Fekete M. et al. Secondary Structure Prediction for Aligned RNA Sequences [J]. Mol.Biol. 2002, 319: 1059-1066.
[30] Mathews D H. Using an RNA secondary structure partition function to determi-ne confidence in base pairs predicted by free energy minimization [J]. RNA. 2004, 10: 1189-1190.
[31] Ricas E. Eddy S.R.A dynamic programming algorithm for RNA structure prediction including pseudoknots [J]. Mol.Biol. 1999, 285: 2053-2068.
[32] Krogh A. Brown M. et al. Hidden Markov models in computational biology [J].Applications to protein modeling, Mol Biol. 1994, 235: 1501-1531.
[33] Rune B .Lyngsc. Christian N. S. Pseudoknots in RNA Secondary Structures. Pedersen [J]. Proceedings of the fourth annual international conference on Computational molecular biology. 2000.
[34] Jitender S.Deogun. Ruben Donis Olga Komina, Fangrui Ma.RNA Secondary Structure Prediction with Simple Pseudoknots [M].University of Nebraska- Lincoln, USA.2005.
[35] Christina Witwer. Ivo L.Hofacker. and Peter F.Stadler. Prediction of Consensus RNA Secondary Structures Including Pseudoknots [J].IEEE Transactions on computational biology and bioinformatics. 2004, 1(2): 34-38.
[36] Oyun-Erdene Namsrai, Kwang Su Jung, Sunshin Kim, and Keun Ho Ryu .RNA Seconsary Structure Prediction With Simple Pseudoknots Based on Dynamic Programming [J].Computational Intelligence and Bioinformatics 2006, : 303– 311.
[37]李恒武,朱大铭.预测RNA二级结构的新算法[J].计算机科学. 2004, 31(10): 142-144.
[38]刘振栋,李恒武,朱大铭.计算最大堆迭的RNA二级结构预测算法[J].南京大学学报, 2005, 41(5): 532-537.
[39] Macke T.J. Ecker D.J. et al. RNAMotif. An RNA Secondary Structure Definition and Search Algorithm [J]. Nucl. Acids Res. 2001, 29: 4724-4735.
[40] Gorodkin J. Sticklin S.L. Stormo G.D. Discovering common stem-loop motifs in unaligned RNA sequences [J].Nucleic Acids Res., 2001, 29: 2135-2144.
[41] Li W.J., Wu J. J. Bioinformatics[M], USA. 1998, 14: 700-706.
[42] Cary R.B., Stormo G.D. Graph-theoretic Approach to RNA Modeling Using Comparative Data [J]. In Proceedings of the Third International Conference on Intelligent Systems for Molecular Biology. Menlo Park: AAAI Press, 1995, p: 78-86.
[43]刘海军,史定华,王翼飞.日新月异的RNA二级结构预测[J].自然杂志, 2003, 25(6): 314-322.
[44] Fei Xia, Yong Dou, Xingming Zhou. Fine-grained parallel RNAalifold algorithm for RNA secondary structure prediction on FPGA [J]. Proceedings of the 7th Asia-Pacific Bioinformatics Conference.January 2009, p: 426-438.
[45] Fenix WD Huang, Linda YM Li, Christian M Reidys, Sequence-structure relations of pseudoknot RNA [J]. Proceedings of the 7th Asia-Pacific Bioinformatics Conference.January, 2009, p: 449-463.
[46] Unyanee Poolsap, Yuki Kato, Tatsuya Akutsu. Prediction of RNA secondary structure with pseudoknots using integer programming [J]. Proceedings of the 7th Asia-Pacific Bioinformatics Conference. January 2009, p: 439-448.
[47]宋丹丹,邓志东. RNA二级结构预测的模糊模型[J].中国科学. 2007, 37(10): 1285-1303.
[48]王金华,骆志刚,管乃洋,严繁妹,靳新,张雯.基于最小自有能和协变信息预测带伪结RNA二级结构的迭代化方法[J]. HEREDITAS(Beijing). 2007, 29 (7): 889-897.
[49]党琰,张宇镭,张冬荣,赵立平.使用角色反演句法分析器RNA二级结构的预测[J].计算机工程, 2006, 32(8): 68-79.
[50]刘琦,张引,叶修梓,俞荣栋.基于离散Hopefield网络求解极大独集的茎区选择算法以及在RNA二级结构预测中的应用[J].计算机学报, Jan, 2008, 31(1).
[51]刘琦,张引,叶修梓,俞荣栋.基于奇异值分解的RNA二级结构相似度计算方法[J]. Journal of Zhejiang University Engineering Science, Aug, 2007, 41(8).
[52]高世乐,丁克诠.含假结RNA二级结构类的图语法[J].计算机工程与应用, .2008, 44(2): 23-25.
[53]刘永明.分子生物学简明教程[M].化学工业出版社.北京化学工业出版社. 2006, p: 21-22.
[54] Haslinger, C. and P.F. Stadler, RNA structures with pseudo-knots: graph-theoretical, combinatorial, and statistical properties [J].Bull Math Biol.1999, 61(3): 437-467.
[55] Take fuji, Y. et al. Parallel algorithms for finding a near-maximum independent set of a circle graph [J].IEEE Trans Neural Netw.1990, 1(3): 263-267.
[56] Hofacker, I.L.Vienna RNA secondary structure server [J]. Nucleie AcidsRes. 2003, 31 (13): 3429-3431.
[57] ShaPiro, B.A. An algorithm for comparing multiple RNA secondary structures [J]. Bioinformaties. 2003, 4(3): 387-393.
[58]何静媛. RNA二级结构预测算法的研究[D].重庆大学博士论文. 2009.
[59]韩乐,莫忠良. RNA-Z曲线及其在病毒基因识别中的应用[J].生物数学学报. 2004, 19: 245-250.
[60] Li. C. and J.Wang.On a 3-D Representation of DNA Primary Sequences [J]. Combinatorial Chemistry &High Throughput Screening. 2004, 7: 23-27.
[61] Liao, B.and T.M.Wang. A 3D graphical representation of RNA secondary Struetures [J]. Biomol Struct Dyn .2004, 21(6): 827-32.
[62]单夫一,骆嘉伟,一种新的RNA二级结构的三维图形表示[J].武汉理工大学学报(信息与管理工程版). 2007, (5): 5-8.
[63] Eddy.S.R. How do RNA folding algorithms work [J].Nature Biotechnology. 2004, 22(11): 1457- 1458.
[64] Eddy S R, Durbin R.RNA Sequence Analysis Using Covariance Models [J]. Nucleotide Acids Research.1994, 22(11): 2079-2088.
[65] Eddy S R.What is a hidden Markov model? [J].Nature Biotechnology.2004, 22(10: 1315-1316.
[66]陆健.基于动态权重匹配的RNA二级结构预测算法[D].江苏:江苏大学生物化学与分子生物学学院. 2007.
[67] Chomsky N.Three models for the description of languages [J].IRE Transactions on Information Theory .1956, 2(3): 113-124.
[68] Chomsky N. On certain formal properties of grammars [J].Information Control.1959, 2(2): 137 - 167.
[69] Rivas E, Eddy S R.The Language of RNA. A Formal Grammar That Includes Pseudoknots [J]. Bioinformatics. 2001 16(4): 334-340.
[70] Sakakibara Y, Brown M, et al.Stochastic context-free grammars for tRNA modeling [J].Nucleotide Acids Research.1994, 22(23): 5112-5120.
[71] Salvador I, Benedi J. RNA Modeling by combining stochastic context-free grammars and n-grammodels [J]. International Journal of Pattern Recognition and Artificial Intelligence, 2002, 16(3): 309-315.
[72] Lari K and Young S J.The estimation of stochastic context-free grammars using the inside-outside algorithm [J].Computer Speech Langues.1990, 49(1): 35-56.
[73]刘琦. RNA二级结构的若干计算生物学问题研究[D].浙江:浙江大学生命科学院, 2008.
[74]李伍举,吴加金. RNA二级结构的预测[J].军事医学科学院院刊.1996, 20(4): 298-310.
[75] Zuker M and D Sankoff.RNA secondary structures and their prediction [J].Bulletin of Mathematical Biology.1984, 46(4): 591-621.
[76] Zuker M.Computer Prediction of RNA structure [J].Methods Enzymol. 1989, 180: 262-288.
[77] Zuker M.Calculating nucleic acid secondary structure [J].Current opinion in Structural Biology. 2000, 10(3): 303-310.
[78] WuJu L. Prediction of RNA secondary structure based on he1ical regions distribution[J]. Bioinformatics.1998, 14(8): 700-706.
[79]彭政.带假结的RNA二级结构预测算法研究[D].湖南:湖南大学计算机与通信学院, 2008.
[80] Tabaska J E,Cary R B,et al.An RNA Folding Method Capable of Identifying Pseudoknots and Base Triples [J].Bioinformatics.1998, 14(8): 691-699.
[81] Page R P M. Circles: Automating the Comparative Analysis of RNA Secondary Structure [J]. Bioinformatics. 2000, 16(11): 1042-1043.
[82] Page R D M.Comparative analysis of secondary structure of insect mitochondrial small subunit ribosoma RNA using maximum weighted matching [J] .Nucleotide Acids Research. 2000, 28(20): 3839- 3845.
[83]谭光明,冯圣中,孙凝晖. RNA二级结构预测中动态规划的优化和有效并行[J]. Journal of Software.2006, 17(7): 1501-1509.
[84] Shapiro B A, Wu J C,et al.The Massively Parallel Genetic Algorithm for RNA Folding: MIMD Implementation and Population Variation [J].Bioinformatics.2001, 17(2): 137- 148.
[85] Minoru K.Post-genome Informatics [M].New York: Oxford University Press. 2000.
[86]林元烈.应用随机过程[M].北京清华大学出版社.2002, p: 78-100; 107-114.
[87] David, Freedman. Markov Chains [M].New York: Spring-Verlag.1983, p: 7~16.
[88]吴俊杰,潘麟生.随机过程[M].长沙:湖南大学出版社.1988, p: 47-55.
[89] L. Isaacson, W .M. Richard. Markov Chains Theory and Applications [J]. John Wiley & Sons, Inc. 1976, p: 100-106.
[90]彭梅.基于马尔可夫链的商品销售预测模型[J].达县师范高等专科学校报.2006, 16(5): 20~22.
[91] G. F.del Angel.A Discrete Markov Chain Model for Valuing Loan Portfolis [J].Journal of Banking & Finance.1998, (10): 1457-1480.
[92] J. Meredith .A Markovian Analysis of Geriatric Ward [J].Management Science.1979, 19(6): 12.
[93]毛长飞,顾乾屏,陈坚,罗升平.基于有吸收态的马尔可夫链的贷款迁移分析[J].山东工商学院学报.2007, 21(5): 5-11.
[94]张维,王丽娜.马尔可夫链方法在分析预测商业银行逾期贷款中的应用[J].现代财经.2004, 24(12): 3-6.
[95]梁保松,温建,陈振,王建平,宁亚伟.马尔可夫过程在基金投资中的应用[J].河南农业大学学报. 2003, 37(4): 428-430.
[96]刘岩,刘芳.马尔可夫链在人民币汇率预测中的应用[J].中国管理信息化. 2007,10(3): 68-70.
[97]刘锋.企业人力资源预测—基于马尔可夫链的研究[J].商场现代化. 2006, (19): 246.
[98]郝宇.马尔可夫预测在营销管理中的应用[J].科技情报开发与经济. 2005, 5(23): 101-103.
[99]张宇山.教学质量评价的马尔可夫链模型[J].科技情报开发与经济. 2007, 17(9): 238-239.
[100]程向阳.马尔可夫链模型在教育评估中的应用[J].大学数学. 2007, 23(2): 38-41.
[101]昝欣,宗鹏,吴祈宗.马尔可夫链在高校教师人才流动预测中的应用[J].科技进步与对策. 2007, (1): 185-187.
[102]魏国孝,李文华.基于马尔可夫模型的高校师资队伍预测方法[J].宁夏大学学报(自然科学版). 2004, 25(4): 309-310.
[103]林素文,王彦声,谢志鸣.高校教师队伍规模预测研究[J].福建医科大学学报(社会科学版). 2005, (1): 77-79.
[104]白君礼,许爱兰.Markov在图书情报中的应用[J].情报杂志. 2003, (11): 50-51.
[105]章亚娟,俞爱君. Markov链在高校文献资源采购预测中的应用[J].哈尔滨师范大学自然科学学报. 2002, 18(4): 8-11.
[106]李国晖.马尔可夫模型在常染色体遗传中的应用[J].内蒙古科技与经济.2 007, (21): 417-418.
[107]王宏健.复等位基因遗传疾病的数学模型[J].福州大学学报(自然科学版). 1995, (5): 1-6.
[108]巴剑波,方旭东.马尔可夫链在海军疟疾疫情预测中的应用[J].解放军预防医学杂志. 2001, (2: 514~516.
[109]谢婧.概率论与数理统计[M].中国时代经济出版社. 2002, p: 278.
[110] Gardner PP, Giegerich R. A comprehensive comparison of comparative RNA structure prediction approaches [J]. BMC Bioinformatics .2004, 5 (1): 1-32.
[111] T.M.Lowe and S.R.Eddy. tRNAscan -SE: A program for improved detection of transfer RNA genes in genomic sequence[J]. Nucl.Acids Res.1997, 25: 955-964.
[112] Rabiner L R.A tutorial on hidden Markov models and selected applications in speech recognition [J]. In: Proceedings of the IEEE.1989, 77(2): 257-286.
[113] Baum L E, Petrie T, Soules G, et al. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains [J]. Annals of Mathematical Statistics. 1970; 41(1: 164-171.
[114] Rabiner L R.A tutorial on hidden Markov models and selected applications in speechrecognition [J]. In: Proceedings of the IEEE.1989, 77(2): 257-286.
[115] Forney G D.The Viterbi algorithm [J].In: Proceedings of the IEEE. 1973, 61(3): 268 -278.
[116] Reynold C.W. Flock herds and schools :a distributed behavioral model [J]. Computer Graphics.1987, 21(4): 25-34.
[117] Hepper F, U Grenander .A stochastic nonlinear model for coordinated bird flocks, In S Krasner Ed [M].The Ubiquity of Chaos, AAAS Publications, Washington DC.1990.
[118] Wilson E.O. Sociabiology: the new synthesis, Belknap Press [J].Cambridge, MA. 1975, p: 12-14.
[119] Kenned, J. and Eberbart, R.C.Particle swarm optimization [J].In Proceedings of the IEEE International Conference on Neural Networks.1995, p: 1942-1948.
[120]曾建潮,介婧,崔志华.微粒群算法[M].北京科学出版社, 2004.
[121] Lovbjerg, M. and Krink, T.Extending Particle Swarm Optimisers with Self-Organized Criticality [J].In Proceedings of the IEEE Congress on Evolutionary Computation. 2002, (2): 1588-1593.
[122] Parsopoulos, K.E., Magoulas, V.P.G., and Vrahatis, M. Stretching technique for obtaining global minimizers through particle swarm optimization [J].In Proceedings of the workshop on particle swarm optimization, Indianapolis, IN. 2001.
[123] Shi, Y.H.and Eberhart, R.C. A modified particle swarm optimizer [J]. In Proceedings of the IEEE International Conference on Evolutionary Computation.1998.p:69-73.
[124] Shi, Y.H. and Eberhart, R.C. Parameter selection in particle swarm optimization [J].In Lecture Notes in Computer Science1447: Evolutionary ProgrammingⅦ.1998, p: 591- 600.
[125] Clerc, M. and Kennedy, J. The particle swarm: Explosion, stability, and convergence in a multi-dimensional complex space [J].IEEE Transactions on Evolutionary Computation. 2002, 1(6): 58-73.
[126] Carlisle, A. and Dozier, G. An off-the-shelf PSO [J]. In Proceedings of the Workshop on Particle Swarm Optimization, Indianapolis.2001.
[127] Carlisle A.and Dozier, G. A dapting particle swarm optimization to dynamic environments [J].In Proceedings of the International Conference on Artificial Intelligence. 2000, p: 429-434.
[128] Carlisle A.and Dozier, G. Tracking changing extrema with adaptive particle swarm optimizer [J]. In Proceedings of the 5th Biannual World Automation Congress, Orlando, Florida, USA. 2002, p: 265-270.
[129] Angeline, P.J. Using selection to improve particle swarm optimization [J]. In Proceedings of the IEEE Congress on Evolutionary Computation, Anchorage, Alaska, USA. 1998.
[130] K.C.Wiese, A.A.Deschenes, and A.G.Hendriks.RNA Predict-An Evolutionary Algorithm for RNA Secondary Structure Prediction [J].IEEE/ACM, Transactions on computational biology and bioinformatics.2008, 5(1): 25-41.
[131] M. Geis and M. Middendorf. A particle swarm optimizer for finding minimum free energy RNA secondary structures [J].IEEE Swarm Intelligence Symposium. 2007, 2341: 1-8.