Chance in Biology by Denny, Mark W. -- Read -- Imperial Library of Trantor

Index

Cover Title Copyright Contents Preface 1 The Nature of Chance

1.1 Silk, Strength, and Statistics 1.2 What Is Certain? 1.3 Determinism versus Chance 1.4 Chaos 1.5 A Road Map

2 Rules of Disorder

2.1 Events, Experiments, and Outcomes

2.1.1 Sarcastic Fish 2.1.2 Bipolar Smut 2.1.3 Discrete versus Continuous 2.1.4 Drawing Pictures

2.2 Probability 2.3 Rules and Tools

2.3.1 Events Are the Sum of Their Parts 2.3.2 The Union of Sets 2.3.3 The Probability of a Union 2.3.4 Probability and the Intersection of Sets 2.3.5 The Complement of a Set 2.3.6 Additional Information and Conditional Probabilities 2.3.7 Bayes' Formula 2.3.8 AIDS and Bayes' Formula 2.3.9 The Independence of Sets

2.4 Probability Distributions 2.5 Summary 2.6 Problems

3 Discrete Patterns of Disorder

3.1 Random Variables 3.2 Expectations Defined 3.3 The Variance 3.4 The Trials of Bernoulli 3.5 Beyond 0's and 1's 3.6 Σ Bernoulli = Binomial

3.6.1 Permutations and Combinations

3.7 Waiting Forever 3.8 Summary 3.9 Problems

4 Continuous Patterns of Disorder

4.1 The Uniform Distribution

4.1.1 The Cumulative Probability Distribution 4.1.2 The Probability Density Function 4.1.3 The Expectation 4.1.4 The Variance

4.2 The Shape of Distributions 4.3 The Normal Curve 4.4 Why Is the Normal Curve Normal? 4.5 The Cumulative Normal Curve 4.6 The Standard Error 4.7 A Brief Detour to Statistics 4.8 Summary 4.9 Problems 4.10 Appendix 1: The Normal Distribution 4.11 Appendix 2: The Central Limit Theorem

5 Random Walks

5.1 The Motion of Molecules 5.2 Rules of a Random Walk

5.2.1 The Average 5.2.2 The Variance 5.2.3 Diffusive Speed

5.3 Diffusion and the Real World 5.4 A Digression on the Binomial Theorem 5.5 The Biology of Diffusion 5.6 Fick's Equation 5.7 A Use of Fick's Equation: Limits to Size 5.8 Receptors and Channels 5.9 Summary 5.10 Problems

6 More Random Walks

6.1 Diffusion to Capture

6.1.1 Two Absorbing Walls 6.1.2 One Reflecting Wall

6.2 Adrift at Sea: Turbulent Mixing of Plankton 6.3 Genetic Drift

6.3.1 A Genetic Diffusion Coefficient 6.3.2 Drift and Fixation

6.4 Genetic Drift and Irreproducible Pigs 6.5 The Biology of Elastic Materials

6.5.1 Elasticity Defined 6.5.2 Biological Rubbers 6.5.3 The Limits to Energy Storage

6.6 Random Walks in Three Dimensions 6.7 Random Protein Configurations 6.8 A Segue to Thermodynamics 6.9 Summary 6.10 Problems

7 The Statistics of Extremes

7.1 The Danger of Cocktail Parties 7.2 Calculating the Maximum 7.3 Mean and Modal Maxima 7.4 Ocean Waves 7.5 The Statistics of Extremes 7.6 Life and Death in Rhode Island 7.7 Play Ball! 7.8 A Note on Extrapolation 7.9 Summary 7.10 Problems

8 Noise and Perception

8.1 Noise Is Inevitable 8.2 Dim Lights and Fuzzy Images 8.3 The Poisson Distribution 8.4 Bayes' Formula and the Design of Rods 8.5 Designing Error-Free Rods

8.5.1 The Origin of Membrane Potentials 8.5.2 Membrane Potential in Rod Cells

8.6 Noise and Ion Channels

8.6.1 An Electrical Analog 8.6.2 Calculating the Membrane Voltage 8.6.3 Calculating the Size

8.7 Noise and Hearing

8.7.1 Fluctuations in Pressure 8.7.2 The Rate of Impact 8.7.3 Fluctuations in Velocity 8.7.4 Fluctuations in Momentum 8.7.5 The Standard Error of Pressure 8.7.6 Quantifying the Answer

8.8 The Rest of the Story 8.9 Stochastic Resonance

8.9.1 The Utility of Noise 8.9.2 Nonlinear Systems 8.9.3 The History of Stochastic Resonance

8.10 Summary 8.11 A Word at the End 8.12 A Problem 8.13 Appendix

9 The Answers

9.1 Chapter 2 9.2 Chapter 3 9.3 Chapter 4 9.4 Chapter 5 9.5 Chapter 6 9.6 Chapter 7 9.7 Chapter 8

Symbol Index Author Index Subject Index