Genomic signal processing

Genomic signal processing (GSP) can be defined as the analysis, processing, and use of genomic signals to gain biological knowledge, and the translation of that knowledge into systems-based applications that can be used to diagnose and treat genetic diseases. Situated at the crossroads of engineering, biology, mathematics, statistics, and computer science, GSP requires the development of both nonlinear dynamical models that adequately represent genomic regulation, and diagnostic and therapeutic tools based on these models. This book facilitates these developments by providing rigorous mathematical definitions and propositions for the main elements of GSP and by paying attention to the validity of models relative to the data. Ilya Shmulevich and Edward Dougherty cover real-world situations and explain their mathematical modeling in relation to systems biology and systems medicine.

Genomic Signal Processing makes a major contribution to computational biology, systems biology, and translational genomics by providing a self-contained explanation of the fundamental mathematical issues facing researchers in four areas: classification, clustering, network modeling, and network intervention.

Author Notes

Ilya Shmulevich , an associate professor at the Institute for Systems Biology, is the coauthor of Microarray Quality Control and the coeditor of Computational and Statistical Approaches to Genomics . Edward R. Dougherty is professor of electrical and computer engineering and director of the Genomic Signal Processing Laboratory at Texas A&M University, and director of the Computational Biology Division at the Translational Genomics Research Institute. His thirteen previous books include Random Processes for Image and Signal Processing .

Preface	p. ix
1 Biological Foundations
1.1 Genetics	p. 1
1.1.1 Nucleic Acid Structure	p. 2
1.1.2 Genes	p. 5
1.1.3 RNA	p. 6
1.1.4 Transcription	p. 6
1.1.5 Proteins	p. 9
1.1.6 Translation	p. 10
1.1.7 Transcriptional Regulation	p. 12
1.2 Genomics	p. 16
1.2.1 Microarray Technology	p. 17
1.3 Proteomics	p. 20
Bibliography	p. 22
2 Deterministic Models of Gene Networks
2.1 Graph Models	p. 23
2.2 Boolean Networks	p. 30
2.2.1 Cell Differentiation and Cellular Functional States	p. 33
2.2.2 Network Properties and Dynamics	p. 35
2.2.3 Network Inference	p. 49
2.3 Generalizations of Boolean Networks	p. 53
2.3.1 Asynchrony	p. 53
2.3.2 Multivalued Networks	p. 56
2.4 Differential Equation Models	p. 59
2.4.1 A Differential Equation Model Incorporating Transcription and Translation	p. 62
2.4.2 Discretization of the Continuous Differential Equation Model	p. 65
Bibliography	p. 70
3 Stochastic Models of Gene Networks
3.1 Bayesian Networks	p. 77
3.2 Probabilistic Boolean Networks	p. 83
3.2.1 Definitions	p. 86
3.2.2 Inference	p. 97
3.2.3 Dynamics of PBNs	p. 99
3.2.4 Steady-State Analysis of Instantaneously Random PBNs	p. 113
3.2.5 Relationships of PBNs to Bayesian Networks	p. 119
3.2.6 Growing Subnetworks from Seed Genes	p. 125
3.3 Intervention	p. 129
3.3.1 Gene Intervention	p. 130
3.3.2 Structural Intervention	p. 140
3.3.3 External Control	p. 145
Bibliography	p. 151
4 Classification
4.1 Bayes Classifier	p. 160
4.2 Classification Rules	p. 162
4.2.1 Consistent Classifier Design	p. 162
4.2.2 Examples of Classification Rules	p. 166
4.3 Constrained Classifiers	p. 168
4.3.1 Shatter Coefficient	p. 171
4.3.2 VC Dimension	p. 173
4.4 Linear Classification	p. 176
4.4.1 Rosenblatt Perceptron	p. 177
4.4.2 Linear and Quadratic Discriminant Analysis	p. 178
4.4.3 Linear Discriminants Based on Least-Squares Error	p. 180
4.4.4 Support Vector Machines	p. 183
4.4.5 Representation of Design Error for Linear Discriminant Analysis	p. 186
4.4.6 Distribution of the QDA Sample-Based Discriminant	p. 187
4.5 Neural Networks Classifiers	p. 189
4.6 Classification Trees	p. 192
4.6.1 Classification and Regression Trees	p. 193
4.6.2 Strongly Consistent Rules for Data-Dependent Partitioning	p. 194
4.7 Error Estimation	p. 196
4.7.1 Resubstitution	p. 196
4.7.2 Cross-validation	p. 198
4.7.3 Bootstrap	p. 199
4.7.4 Bolstering	p. 201
4.7.5 Error Estimator Performance	p. 204
4.7.6 Feature Set Ranking	p. 207
4.8 Error Correction	p. 209
4.9 Robust Classifiers	p. 213
4.9.1 Optimal Robust Classifiers	p. 214
4.9.2 Performance Comparison for Robust Classifiers	p. 216
Bibliography	p. 221
5 Regularization
5.1 Data Regularization	p. 225
5.1.1 Regularized Discriminant Analysis	p. 225
5.1.2 Noise Injection	p. 228
5.2 Complexity Regularization	p. 231
5.2.1 Regularization of the Error	p. 231
5.2.2 Structural Risk Minimization	p. 233
5.2.3 Empirical Complexity	p. 236
5.3 Feature Selection	p. 237
5.3.1 Peaking Phenomenon	p. 237
5.3.2 Feature Selection Algorithms	p. 243
5.3.3 Impact of Error Estimation on Feature Selection	p. 244
5.3.4 Redundancy	p. 245
5.3.5 Parallel Incremental Feature Selection	p. 249
5.3.6 Bayesian Variable Selection	p. 251
5.4 Feature Extraction	p. 254
Bibliography	p. 259
6 Clustering
6.1 Examples of Clustering Algorithms	p. 263
6.1.1 Euclidean Distance Clustering	p. 264
6.1.2 Self-Organizing Maps	p. 265
6.1.3 Hierarchical Clustering	p. 266
6.1.4 Model-Based Cluster Operators	p. 268
6.2 Cluster Operators	p. 269
6.2.1 Algorithm Structure	p. 269
6.2.2 Label Operators	p. 271
6.2.3 Bayes Clusterer	p. 273
6.2.4 Distributional Testing of Cluster Operators	p. 274
6.3 Cluster Validation	p. 276
6.3.1 External Validation	p. 276
6.3.2 Internal Validation	p. 277
6.3.3 Instability Index	p. 278
6.3.4 Bayes Factor	p. 280
6.4 Learning Cluster Operators	p. 281
6.4.1 Empirical-Error Cluster Operator	p. 281
6.4.2 Nearest-Neighbor Clustering Rule	p. 283
Bibliography	p. 292
Index	p. 295

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