Computational Neuroscience

  1. Modeling Neural Networks
    1. Network Architectures
      1. Feedforward Networks
        1. Layered structure
          1. Input layers
            1. Hidden layers
              1. Output layers
              2. Input-output mapping
                1. Function approximation
                  1. Pattern recognition
                  2. Deep networks
                    1. Hierarchical processing
                      1. Feature extraction
                    2. Recurrent Networks
                      1. Feedback connections
                        1. Local recurrence
                          1. Global recurrence
                          2. Memory and dynamics
                            1. Working memory
                              1. Temporal processing
                              2. Reservoir computing
                                1. Echo state networks
                                  1. Liquid state machines
                                2. Small-World Networks
                                  1. Clustering coefficient
                                    1. Path length
                                      1. Small-world index
                                        1. Biological relevance
                                        2. Scale-Free Networks
                                          1. Degree distribution
                                            1. Power-law scaling
                                              1. Hub nodes
                                              2. Preferential attachment
                                                1. Network robustness
                                                2. Modular Networks
                                                  1. Community structure
                                                    1. Modularity measures
                                                      1. Hierarchical organization
                                                    2. Firing-Rate Models
                                                      1. Input-Output Transfer Functions
                                                        1. Linear transfer functions
                                                          1. Nonlinear transfer functions
                                                            1. Sigmoid functions
                                                              1. Threshold functions
                                                                1. Rectified linear functions
                                                              2. Linear Networks
                                                                1. Matrix formulation
                                                                  1. Eigenvalue analysis
                                                                    1. Stability conditions
                                                                    2. Nonlinear Networks
                                                                      1. Fixed point analysis
                                                                        1. Attractor dynamics
                                                                          1. Chaos and complexity
                                                                          2. Stability analysis
                                                                            1. Lyapunov stability
                                                                              1. Linear stability analysis
                                                                                1. Bifurcation theory
                                                                                2. Wilson-Cowan Model
                                                                                  1. Excitatory-inhibitory dynamics
                                                                                    1. Population equations
                                                                                      1. Oscillatory behavior
                                                                                    2. Spiking Network Models
                                                                                      1. Integrate-and-Fire Networks
                                                                                        1. Network connectivity
                                                                                          1. Synaptic interactions
                                                                                            1. Collective dynamics
                                                                                            2. Synaptic connectivity
                                                                                              1. Random connectivity
                                                                                                1. Structured connectivity
                                                                                                  1. Plastic connectivity
                                                                                                  2. Balanced Excitation and Inhibition
                                                                                                    1. Balance conditions
                                                                                                      1. Asynchronous irregular states
                                                                                                        1. Critical dynamics
                                                                                                        2. Network simulations
                                                                                                          1. Event-driven simulation
                                                                                                            1. Time-driven simulation
                                                                                                              1. Parallel computing
                                                                                                              2. Liquid State Machines
                                                                                                                1. Reservoir dynamics
                                                                                                                  1. Readout mechanisms
                                                                                                                    1. Computational capacity
                                                                                                                  2. Network Dynamics
                                                                                                                    1. Oscillations and Rhythms
                                                                                                                      1. Gamma oscillations
                                                                                                                        1. Fast gamma
                                                                                                                          1. Slow gamma
                                                                                                                            1. Gamma generation mechanisms
                                                                                                                            2. Theta oscillations
                                                                                                                              1. Hippocampal theta
                                                                                                                                1. Theta-gamma coupling
                                                                                                                                2. Beta oscillations
                                                                                                                                  1. Motor beta
                                                                                                                                    1. Cognitive beta
                                                                                                                                    2. Alpha oscillations
                                                                                                                                      1. Sensory alpha
                                                                                                                                        1. Attention and alpha
                                                                                                                                        2. Delta oscillations
                                                                                                                                          1. Sleep delta
                                                                                                                                            1. Cortical slow waves
                                                                                                                                          2. Synchrony
                                                                                                                                            1. Phase synchronization
                                                                                                                                              1. Lag synchronization
                                                                                                                                                1. Generalized synchronization
                                                                                                                                                2. Phase Locking
                                                                                                                                                  1. Phase-locking value
                                                                                                                                                    1. Cross-frequency coupling
                                                                                                                                                      1. Phase-amplitude coupling
                                                                                                                                                      2. Attractor Dynamics
                                                                                                                                                        1. Point Attractors
                                                                                                                                                          1. Memory storage
                                                                                                                                                            1. Pattern completion
                                                                                                                                                              1. Hopfield networks
                                                                                                                                                              2. Line Attractors
                                                                                                                                                                1. Head direction systems
                                                                                                                                                                  1. Eye position control
                                                                                                                                                                    1. Continuous attractors
                                                                                                                                                                    2. Ring Attractors
                                                                                                                                                                      1. Orientation tuning
                                                                                                                                                                        1. Spatial navigation
                                                                                                                                                                          1. Bump attractors
                                                                                                                                                                          2. Strange Attractors
                                                                                                                                                                            1. Chaotic attractors
                                                                                                                                                                              1. Fractal dimensions
                                                                                                                                                                            2. Chaotic Dynamics
                                                                                                                                                                              1. Sensitivity to initial conditions
                                                                                                                                                                                1. Lyapunov exponents
                                                                                                                                                                                  1. Butterfly effect
                                                                                                                                                                                  2. Implications for computation
                                                                                                                                                                                    1. Edge of chaos
                                                                                                                                                                                      1. Computational benefits
                                                                                                                                                                                        1. Information processing
                                                                                                                                                                                      2. Criticality
                                                                                                                                                                                        1. Self-organized criticality
                                                                                                                                                                                          1. Neuronal avalanches
                                                                                                                                                                                            1. Scale-free dynamics
                                                                                                                                                                                              1. Critical brain hypothesis

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                                                                                                                                                                                          8. Models of Learning and Memory