生物信息学中的数学方法

出版时间：2013-4  出版社：科学出版社  

书籍目录

PREFACECHAPTER 1 SOME BIOLOGICAL CONCEPTS1．1 Cell1．2 Genetic Material： DNA, Gene and RNA1．2．1 DNA1．2．2 Gene1．2．3 RNA1．3 Protein and Amino Acids1．4　Chromosome1．5 Omics1．5．1 Genomics1．5．2 Microarray1．5．3 Proteomics1．5．4 LipidomicsREFERENCESCHAPTER 2 GRAPHICAL REPRESENTATIONS OF DNA SEQUENCE2．1 Three-Dimension （3-D） GraphicaIRepresentation2．2 2-DGraphicalRepresentatio2．3 2-D GraphicalRepresentations Without Degeneracy2．4 Used a 1-D NumerioalRepresentation offourNucleotides to Construct a 2-D Graplucal Representation ofthe DNA SequenceREFERENCES　CHAPTER 3 NUMERICAL REPRESENTATIONS OF DNA SEQUENCE3．1 4-D and 3-D Numerical Representations of a DNA Sequence3．2 2-D Numerical Representations of a DNA Sequence3．3 The Complex NumericalRepresentation3．4 1-D Numerical Representations of four Nucleotides and 2-D GraphicalRepresentation of a DNA Sequence3．5 The Representations ofFeature Vector, Genome Space and Matrix Representation of DNA Sequence3．6 The Numerical Representation Based on Physical, Chemical and StructuralProperties of DNA Sequence3．6．1 The numericalrepresentations based on some attribute equivalencesofnucleotides3．6．2 The representation of DNA by the inspiration from codon and the idea ofthree attribute equivalences3．6．3 EIIPnumericalrepresentationfornucleotidesREFERENCESCHAPTER 4 NUMERICAL REPRESENTATIONS OF PROTEIN4．1 1-D Numericaland GraphicalRepresentations ofthe AminoAcid Sequence4．2 2-DNumericaland GraphicalRepresentations ofthe AminoAcid Sequence4．3 A 2-D Graphical Representation and Moment Vector Representation of Protein4．4 3-D Numerical Representation of Protein4．5 The 10-D Representation ofan Amino Acid4．6 The Vector andMatrix Representations of Protein Sequence and Protein Space4．7 Other Schemes of the Representation for ProteinREFERENCESCHAPTER 5 PRACTICAL ORTHOGONAL TRANSFORM5．1 Some Features and Algorithms for the Discrete Fourier Transform5．1．1 Fourier transforms ofthe original sequence and its subsequence5．1．2 The independency ofthe Fourier transforms at several frequencies5．1．3 The Fourier transform ofsymbolic sequence5．1．4 Fourier transform ofbinary sequence5．1．5 Several algorithms ofFourier transform5．1．6 The properties ofFourier transform ofreal sequence5．2 WaveletAnalysis5．2．1 Introduction5．2．2 Multiresolution analysis ofa function by Haar scaling and waveletfunction5．2．3 Construction of wavelet systems5．2．4 Mallet transformREFERENCES CHAPTER 6 IDENTIFYING PROTEIN-CODING REGIONS （EXONS） BY NUCLEOTIDEDIS TRIBUTIONS6．1 Portein Coding Regions Finding in DNA Sequence6．1．1 Introduction6．1．2 The stochastic simulation and several computing formulae6．1．3 FEND algorithm，predicting protein coding regions from nucleotide distributions on the three positions ofa DNA sequence6．1．4 Performance evalumion ofFEND algorithm6．2 The Experiment for Distinguishing Exon and Intron Sequences by a Threshold6．2．1 Motivation6．2．2 Idea ofdistinguishing exon and intron sequences6．2．3 Results and discussionREFERENCESCHAPTER 7 PROTEINCOMPARISONBYORTHOGONALTRANSFORMS7．1 Protein Comparison by Discrete Fourier Transformation(DFT)7．1．1 EIIP representation ofprotein sequence7．1．2 Symmetry ofdiscrete Fouriertransformofreal sequence7．1．3 Cross—spectral function7．2 Protein Comparison by Discrete Wavelet Transformation7．2．1 Several techniques needed for DWT method7．2．2 The performance ofthe DWT methodREFERENCESCHAPTER 8 THE APPLICATION OF VECTOR REPRESENTATIONS TO BIOLOGICAL MOLECULE ANALYSIS  8．1 Use Feature Vector toAnalyze DNA Sequences8．1．1 Feature vector representation ofDNA sequence8．1．2 Comparing DNA sequences  8．2 A Protein Map and its Applications．8．2．1 Recalling a 2-D graphical representation and moment vector representation ofprotein]8．2．2 Protein map and cluster analysis  8．3 An Appendix：Introduction to Cluster Analysis1  REFERENCES CHAPTER 9 THE STATISTICS ANALYSIS OF LARGE AMOUNT OF EXPERIMENTAL DATA9．1 A Way tO Process Microarray Data9．1．1 Data form9．1．2 Microarray data set．9．1．3 Preliminary filtering9．1．4 Assessing normalization9．1．5 Hypothesis test．9．1．6 Conclusion9．2 The Statistical Analysis ofa Set ofLipidomics Data9．2．1 Introduction9．2．2 Statistical techniques ofinitial data processing9．2．3 Initial data arrangement9．2．4 Hypothesis testing analysisREFERENCESCHAPTER 10  APPLY SINGULAR VALUE DECOMPOSITl0N TO MICRoARRAVANALYSIS10．1 SVD，PCA and GSVD10．1．1 Singularvalue decomposition10．1．2 Principal component analysis10．1．3 Generalized singular value decomposition10．2 Apply SVD／PCA to Microarray Analysis10．3 GSVD Analyzes the Microarray DataREFERENCESCHAPTER 11  DYNAMICALANALYSIS MODELS OF GENE EXPRESSION11．1 DifierentialEquationsModel ofGeneExpression11．1．1 Transcription model11．1．2 Nonlinear dynamic equ~ions11．1．3 Linearization ofthenonlineartranscriptionmodel11．1．4 Approximating coefficientmatrixMby Fourier series 11．1．5 Solutiontotranscriptionmatrix Cand V11．2 Modified Linear Differential Equations Model11．3 DynamicalModelBased on SingularValueDecomposition． 11．3．1 Introduction11．3．2 Reducing gen’s number11．3．3 The approachbasedon singularvaluedecomposition(SVD)11．3．4 The methods ofsolving dynamical modelsREFERENCESCHAPTER 12  MISSING MICROARRAY DATA INPUTTING12．1 The Ad Hoc Methods12．2 Missing Data Inputting Based on SVD12．2．1 A llew way for missing data inputting12．2．2  0ther method based on SVD  12．3 Weighted K-Nearest Ne Jlghbors．KNN．Impute Algorithm  12．4 Estimation of Missing，alues in Microarray Data Based on the Least Square Prineiple12．4．1 Least squares estimate 0fthe unknown variable12．4．2 The least square estimation ofmissing data based on genes．12．4．3 The least square estimation ofmissing data based on arrays12．4．4 Combining the gene and array based estimates  12．5 Local Least Square Inputting rLLSinputel12．5．1 Selecting genes12．5．2 Gene-wise fornmlation of 10cal least squares imputation  12．6 The Comparison ofthe Methods ofMissing Data Inputting  REFERENCESPLATF

编辑推荐

Jiasong Wang编的《Numerical Methods in Bioinformatics An Introduction》介绍了生物信息学计算方法如下：数值替换为代表的数值或图形序列的DNA和蛋白质序列；傅立叶和小波变换应用于基因的鉴定和蛋白质的比较；基于大量实验数据的微阵列或脂类组学数据集，合适的统计和计算的方法研究中使用的两套生物特征，特征向量的表象下，两种生物分子分类的聚类分析完成；微分方程和差分方程模型被建立为代表的生物动力学过程；和丢失的数据输入技术有助于估计丢失条目来自生物学观察与实验，等等。此外，还介绍了一些生物的概念通过这些方法。