Biological Modeling and Simulation - A Survey of Practical Models, Algorithms, and Numerical Methods

Contents\r......Page 6
Preface......Page 12
1 Introduction......Page 14
I MODELS FOR OPTIMIZATION......Page 26
2 Classic Discrete Optimization Problems......Page 28
3 Hard Discrete Optimization Problems......Page 48
4 Case Study: Sequence Assembly......Page 70
5 General Continuous Optimization......Page 88
6 Constrained Optimization......Page 108
II SIMULATION AND SAMPLING......Page 126
7 Sampling from Probability Distributions......Page 128
8 Markov Models......Page 142
9 Markov Chain Monte Carlo Sampling......Page 154
10 Mixing Times of Markov Models......Page 172
11 Continuous-Time Markov Models......Page 186
12 Case Study: Molecular Evolution......Page 198
13 Discrete Event Simulation......Page 214
14 Numerical Integration 1: Ordinary Differential Equations......Page 224
15 Numerical Integration 2: Partial Differential Equations......Page 240
16 Numerical Integration 3: Stochastic Differential Equations......Page 254
17 Case Study: Simulating Cellular Biochemistry......Page 266
III PARAMETER-TUNING......Page 278
18 Parameter-Tuning as Optimization......Page 280
19 Expectation Maximization......Page 288
20 Hidden Markov Models......Page 304
21 Linear System-Solving......Page 322
22 Interpolation and Extrapolation......Page 336
23 Case Study: Inferring Gene Regulatory Networks......Page 354
24 Model Validation......Page 368
References......Page 380
Index......Page 390