Russell Schwartz0262195844, 9780262195843, 9781435665385
There are many excellent computational biology resources now available for learning about methods that have been developed to address specific biological systems, but comparatively little attention has been paid to training aspiring computational biologists to handle new and unanticipated problems. This text is intended to fill that gap by teaching students how to reason about developing formal mathematical models of biological systems that are amenable to computational analysis. It collects in one place a selection of broadly useful models, algorithms, and theoretical analysis tools normally found scattered among many other disciplines. It thereby gives studentshte tools that will serve them well in modeling problems drawn from numerous subfields of biology. These techniques are taught from the perspective of what the practitioner needs to know to use them effectively, supplemented with references for further reading on more advanced use of each method covered. The text covers models for optimization, simulation and sampling, and parameter tuning. These topics provide a general framework for learning how to formulate mathematical models of biological systems, what techniques are available to work with these models, and how to fit the models to particular systems. Their application is illustrated by many examples drawn from a variety of biological disciplines and several extended case studies that show how the methods described have been applied to real problems in biology. |
Table of contents :
Contents
……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 |
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