- Cover image
- Title page
- Table of Contents
- Front Matter
- Copyright
- Contributors
- Preface
- Chapter 1. Mechanisms of Gene Regulation: Boolean Network Models of the Lactose Operon in Escherichia coli
- Chapter 2. Bistability in the Lactose Operon of Escherichia coli: A Comparison of Differential Equation and Boolean Network Models
- 2.1 Introduction
- 2.2 The Lactose Operon of Escherichia Coli
- 2.3 Modeling Biochemical Reactions with Differential Equations
- 2.4 The Yildirim-Mackey Differential Equation Models for the Lactose Operon
- 2.5 Boolean Modeling of Biochemical Interactions
- 2.6 Boolean Approximations of the Yildirim-Mackey Models
- 2.7 Conclusions and Discussion
- Acknowledgment
- 2.8 Supplementary Materials
- References
- Chapter 3. Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering
- Chapter 4. Global Dynamics Emerging from Local Interactions: Agent-Based Modeling for the Life Sciences
- Chapter 5. Agent-Based Models and Optimal Control in Biology: A Discrete Approach
- 5.1 Introduction
- 5.2 A First Example
- 5.3 Netlogo: An Introduction
- 5.4 An Introduction to Agent-Based Models
- 5.5 Optimization and Optimal Control
- 5.6 Scaling and Aggregation
- 5.7 A Heuristic Approach
- 5.8 Mathematical Framework for Representing Agent-Based Models
- 5.9 Translating Agent-Based Models into Polynomial Dynamical Systems
- 5.10 Summary
- 5.11 Supplementary Materials
- References
- Chapter 6. Neuronal Networks: A Discrete Model
- 6.1 Introduction and Overview
- 6.2 Neuroscience in a Nutshell
- 6.3 The Discrete Model
- 6.4 Exploring the Model for Some Simple Connectivities
- 6.6.5 Exploring the Model for Some Random Connectivities
- 6.6 Another Interpretation of the Model: Disease Dynamics
- 6.7 More Neuroscience: Connection with ODE Models
- 6.8 Directions of Further Research
- 6.9 Supplementary Materials
- References
- Chapter 7. Predicting Population Growth: Modeling with Projection Matrices
- 7.1 Introduction
- 7.2 Life Cycles and Population Growth
- 7.3 Determining Stages in the Life Cycle
- 7.4 Determining the Number of Individuals in a Stage at Time
- 7.5 Constructing a Projection Matrix
- 7.6 Predicting How a Population Changes after One Year
- 7.7 The Stable Distribution of Individuals across Stages
- 7.8 Theory Supporting the Calculation of Stable Distributions
- 7.9 Determining Population Growth Rate and the Stable Distribution
- 7.10 Further Applications of the Projection Matrix
- References
- Chapter 8. Metabolic Pathways Analysis: A Linear Algebraic Approach
- Chapter 9. Identifying CpG Islands: Sliding Window and Hidden Markov Model Approaches
- 9.1 Introduction
- 9.2 Quantitative Characteristics of the CpG Island Regions and Sliding Windows Algorithms
- 9.3 Definition and Basic Properties of Markov Chains and Hidden Markov Models
- 9.4 Three Canonical Problems for HMMs with Applications to CGI Identification
- 9.5 Conclusions and Discussion
- Acknowledgments
- 9.6 Supplementary Materials
- References
- Chapter 10. Phylogenetic Tree Reconstruction: Geometric Approaches
- Index
Mathematical Concepts and Methods in Modern Biology
Using Modern Discrete Models
Edited by
Raina Robeva
Sweet Briar College, Sweet Briar, VA, USA
Terrell L. Hodge
Western Michigan University, Kalamazoo, MI, USA
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