Modeling in Biology

  1. Modeling Paradigms and Techniques
    1. Deterministic Approaches
      1. Systems of Ordinary Differential Equations
        1. Model Formulation
          1. Steady States and Stability Analysis
            1. Phase Plane Analysis
              1. Limit Cycles
                1. Bifurcation Analysis
                2. Systems of Partial Differential Equations
                  1. Reaction-Diffusion Systems
                    1. Pattern Formation
                      1. Wave Propagation
                        1. Numerical Methods
                      2. Stochastic Approaches
                        1. The Master Equation
                          1. Probability Distributions Over Time
                            1. Birth-Death Processes
                            2. The Gillespie Algorithm
                              1. Stochastic Simulation Algorithm
                                1. Applications in Biochemical Kinetics
                                  1. Tau-Leaping Methods
                                  2. Markov Chains
                                    1. Discrete-State Processes
                                      1. Transition Probabilities
                                        1. Steady-State Distributions
                                        2. Random Walks and Brownian Motion
                                          1. Diffusion Processes
                                            1. Applications in Cell Biology
                                              1. Anomalous Diffusion
                                              2. Stochastic Differential Equations
                                                1. Langevin Equations
                                                  1. Ito Calculus
                                                2. Network and Graph-Based Models
                                                  1. Graph Theory Fundamentals
                                                    1. Nodes and Edges
                                                      1. Weights and Edge Types
                                                        1. Degree Distribution
                                                          1. Network Motifs
                                                            1. Clustering Coefficients
                                                            2. Types of Biological Networks
                                                              1. Gene Regulatory Networks
                                                                1. Protein-Protein Interaction Networks
                                                                  1. Metabolic Networks
                                                                    1. Neural Networks
                                                                      1. Food Webs
                                                                        1. Ecological Networks
                                                                        2. Network Analysis Techniques
                                                                          1. Centrality Measures
                                                                            1. Community Detection
                                                                              1. Network Robustness
                                                                                1. Dynamic Networks
                                                                              2. Agent-Based Models
                                                                                1. Defining Agents and Rules
                                                                                  1. Agent Properties
                                                                                    1. Rule Specification
                                                                                      1. Local Interactions
                                                                                      2. Emergent Behavior
                                                                                        1. Collective Dynamics
                                                                                          1. Pattern Formation
                                                                                            1. Self-Organization
                                                                                            2. Simulating Individual Interactions
                                                                                              1. Spatial Interactions
                                                                                                1. Environmental Feedback
                                                                                                  1. Adaptive Behavior
                                                                                                2. Statistical and Machine Learning Models
                                                                                                  1. Regression Analysis
                                                                                                    1. Linear Regression
                                                                                                      1. Nonlinear Regression
                                                                                                        1. Logistic Regression
                                                                                                        2. Classification Methods
                                                                                                          1. Decision Trees
                                                                                                            1. Support Vector Machines
                                                                                                              1. Neural Networks
                                                                                                              2. Clustering Algorithms
                                                                                                                1. K-Means Clustering
                                                                                                                  1. Hierarchical Clustering
                                                                                                                    1. Density-Based Clustering
                                                                                                                    2. Bayesian Networks
                                                                                                                      1. Probabilistic Graphical Models
                                                                                                                        1. Inference in Bayesian Networks
                                                                                                                          1. Learning Network Structure
                                                                                                                          2. Deep Learning Approaches
                                                                                                                            1. Convolutional Neural Networks
                                                                                                                              1. Recurrent Neural Networks
                                                                                                                                1. Applications in Biology

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                                                                                                                            3. Mathematical Foundations for Modeling

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                                                                                                                            5. Applications Across Biological Scales