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Fundamentals of computational neuroscience / Thomas P. Trappenberg. — 2nd ed. — Oxford : Oxford University Press, 2010. – (59.59/T774/2nd ed.) |
Contents
Contents
1 Introduction
1.1 What is computational neuroscience?
1.2 What is a model?
1.3 Is there a brain theory?
1.4 A computational theory of the brain
Exercises
Further reading
I Basic neurons
2 Neurons and conductance-based models 21
2.1 Biological background 21
2.2 Basic synaptic mechanisms and dendritic processing 26
2.3 The generation of action potentials: Hodgkin Huxley equations 33
2.4 Including neuronal morphologies: compartmental models
Exercises
Further reading
3 Simplified neuron and population models
3.1 Basic spiking neurons
3.2 Spike-time variability
3.3 The neural code and the firing rate hypothesis
3.4 Population dynamics: modelling the average behaviour of neurons
3.5 Networks with non-classical synapses: the sigma-pi node
Exercises
Further reading
4 Associators and synaptic plasticity 87
4.1 Associative memory and Hebbian learning 87
4.2 The physiology and biophysics of synaptic plasticity 94
4.3 Mathematical formulation of Hebbian plasticity
4.4 Synaptic scaling and weight distributions
Exercises
Further reading
II Basic networks
5 Cortical organization and simple networks
5.1 Organization in the brain
5.2 Information transmission in random networks o
5.3 More physiological spiking networks
Exercises
Further reading
6 Feed-forward mapping networks
6.1 The simple perceptron
6.2 The multilayer perceptron
6.3 Advanced MLP concepts
6.4 Support vector machines
Exercises
Further reading
7 Cortical feature maps and competitive population coding
7.1 Competitive feature representations in cortical tissue
7.2 Self-organizing maps
7.3 Dynamic neural field theory
7.4 'Path' integration and the Hebbian trace rule o
7.5 Distributed representation and population coding
Exercises
Further reading
8 Recurrent associative networks and episodic memory
8.1 The auto-associative network and the hippocampus
8.2 Point-attractor neural networks (ANN)
8.3 Sparse attractor networks and correlated patterns
8.4 Chaotic networks: a dynamic systems view o
Exercises
Further reading
III System-level models
9 Modular networks， motor control， and reinforcement learning
9.1 Modular mapping networks
9.2 Coupled attractor networks
9.3 Sequence learning
9.4 Complementary memory systems
9.5 Motor learning and control
9.6 Reinforcement learning
Further reading 286
10 The cognitive brain
10.1 Hierarchical maps and attentive vision
10.2 An interconnecting workspace hypothesis
10.3 The anticipating brain 298
10.4 Adaptive resonance theory
10.5 Where to go from here
Further reading
A Some useful mathematics
A.1 Vector and matrix notations
A.2 Distance measures
A.3 The 5-function
B Numerical calculus
B.1 Differences and sums
B.2 Numerical integration of an initial value problem
B.3 Euler method
B.4 Higher-order methods
B.5 Adaptive Runge-Kutta
Further reading
C Basic probability theory
C.1 Random numbers and their probability (density) function
C.2 Moments: mean， variance， etc.
C.3 Examples of probability (density) functions
C.4 Cumulative probability (density) function and the Gaussian error function
C.5 Functions of random variables and the central limit theorem
C.6 Measuring the difference between distributions
Further reading
D Basic information theory
D.1 Communication channel and information gain
D.2 Entropy， the average information gain
D.3 Mutual information and channel capacity
D.4 Information and sparseness in the inferior-temporal cortex
D.5 Surprise
Further reading
E A brief introduction to MATLAB
E.1 The MATLAB programming environment
E.2 A first project: modelling the world
E.3 Octave
E.4 Scilab
Further reading
