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

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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