Fundamentals of computational neuroscience / Thomas P. Trappenberg.

Format:

Book

Author/Creator:

Trappenberg, Thomas P., author.

Language:

English

Subjects (All):

Neural circuitry.

Computational neuroscience.

Neurosciences--methods.

Computational Biology--methods.

Models, Neurological.

Neurons--physiology.

Brain--physiology.

Nerve Net.

Medical Subjects:

Neurosciences--methods.

Computational Biology--methods.

Models, Neurological.

Neurons--physiology.

Brain--physiology.

Nerve Net.

Physical Description:

1 online resource (xiii, 396 pages) : illustrations (some color).

Edition:

Third edition.

Place of Publication:

New York, New York ; Oxford, England : Oxford University Press, [2023]

Summary:

The new edition of Fundamentals of Computational Neuroscience build on the success and strengths of the previous editions. Completely redesigned and revised, it introduces the theoretical foundations of neuroscience with a focus on the nature of information processing in the brain.

Contents:

Cover

Fundamentals of Computational Neuroscience - Third Edition

Copyright

Preface

Mathematical formulas

Programming examples

References

Acknowledgements

Contents

I Background

1 Introduction and outlook

1.1 What is computational neuroscience?

1.1.1 Embedding within neuroscience

1.2 Organization in the brain

1.2.1 Levels of organization in the brain

1.2.2 Large-scale brain anatomy

1.2.3 Hierarchical organization of cortex

1.2.4 Rapid data transmission in the brain

1.2.5 The layered structure of neocortex

1.2.6 Columnar organization and cortical modules

1.2.7 Connectivity between neocortical layers

1.2.8 Cortical parameters

1.3 What is a model?

1.3.1 Phenomenological and explanatory models

1.3.2 Models in computational neuroscience

1.4 Is there a brain theory?

1.4.1 Emergence and adaptation

1.4.2 Levels of analysis

1.5 A computational theory of the brain

1.5.1 Why do we have brains?

1.5.2 The anticipating brain

1.5.3 Deep sparse predictive coding and the uncertain brain

2 Scientific programming with Python

2.1 The Python programming environment

2.2 Basic language elements

2.2.1 Basic data types and arrays

2.2.2 Control flow

2.2.3 Functions

2.2.4 Plotting

2.2.5 Timing the program

2.3 Code efficiency and vectorization

3 Math and Stats

3.1 Vector and matrix notations

3.2 Distance measures

3.3 The δ-function

3.4 Numerical calculus

3.4.1 Differences and sums

3.4.2 Numerical integration of an initial value problem

3.4.3 Euler method

3.4.4 Higher-order methods

3.5 Basic probability theory

3.5.1 Random numbers and their probability (density) function

3.5.2 Moments: mean, variance, etc.

3.5.3 Examples of probability (density) functions

3.5.3.1 Uniform distribution.

3.5.3.2 Normal (Gaussian) distribution

3.5.3.3 Bernoulli distribution

3.5.3.4 Binomial distribution

3.5.3.5 Multinomial distribution

3.5.3.6 Poisson distribution

3.5.4 Cumulative probability (density) function and the Gaussian error function

3.5.5 Functions of random variables and the central limit theorem

3.5.6 Measuring the difference between distributions

3.5.7 Marginal, joined, and conditional distributions

II Neurons

4 Neurons and conductance-based models

4.1 Biological background

4.1.1 Structural properties

4.1.2 Information-processing mechanisms

4.1.3 Membrane potential

4.1.4 Ion channels

4.2 Synaptic mechanisms and dendritic processing

4.2.1 Chemical synapses and neurotransmitters

4.2.2 Excitatory/inhibitory synapses

4.2.3 modelling synaptic responses

Simulation

4.2.4 Different levels of modelling

4.3 The generation of action potentials: Hodgkin-Huxley

4.3.1 The minimal mechanisms

4.3.2 Ion pumps

4.3.3 Hodgkin-Huxley equations

4.3.4 Propagation of action potentials

4.3.5 Above and beyond the Hodgkin-Huxley neuron: the Wilson model

4.4 FitzHugh-Nagumo model

4.5 Neuronal morphologies: compartmental models

4.5.1 Cable theory

4.5.2 Physical shape of neurons

4.5.3 Neuron simulators

5 Integrate-and-fire neurons and population models

5.1 The leaky integrate-and-fire models

5.1.1 Response of IF neurons to very short and constant input currents

5.1.2 Rate gain function

5.1.3 The spike-response model

5.1.4 The Generalized LIF model

5.1.5 The McCulloch-Pitts neuron

5.2 Spike-time variability

5.2.1 Biological irregularities

5.2.2 Noise models for IF neurons

5.2.3 Simulating the variability of real neurons

5.2.4 The activation function depends on input

5.3 Advanced integrate-and-fire models

5.3.1 The Izhikevich neuron.

5.4 The neural code and the firing rate hypothesis

5.4.1 Correlation codes and coincidence detectors

5.4.2 How accurate is spike timing?

5.5 Population dynamics: modelling the average behaviour of neurons

5.5.1 Firing rates and population averages

5.5.2 Population dynamics for slow varying input

5.5.3 Motivations for population dynamics

5.5.4 Rapid response of populations

5.5.5 Common activation functions

5.6 Networks with non-classical synapses

5.6.1 Logical AND and sigma-pi nodes

5.6.2 Divisive inhibition

5.6.3 Further sources of modulatory effects between synaptic inputs

6 Associators and synaptic plasticity

6.1 Associative memory and Hebbian learning

6.1.1 Hebbian learning

6.1.2 Associations

6.1.3 Hebbian learning in the conditioning framework

6.1.4 Features of associators and Hebbian learning

Pattern completion and generalization

Prototypes and extraction of central tendencies

Graceful degradation

6.2 The physiology and biophysics of synaptic plasticity

6.2.1 Typical plasticity experiments

6.2.2 Spike timing dependent plasticity

6.2.3 The calcium hypothesis and modelling chemical pathways

6.3 Mathematical formulation of Hebbian plasticity

6.3.1 Spike timing dependent plasticity rules

6.3.2 Hebbian learning in population and rate models

6.3.3 Negative weights and crossing synapses

6.4 Synaptic scaling and weight distributions

6.4.1 Examples of STDP with spiking neurons

6.4.2 Weight distributions in rate models

6.4.3 Competitive synaptic scaling and weight decay

6.4.4 Oja's rule and principal component analysis

6.5 Plasticity with pre- and postsynaptic dynamics

III Networks

7 Feed-forward mapping networks

7.1 Deep representational learning

7.2 The perceptron

7.2.1 The simple perceptron as boolean function.

7.2.2 Multilayer perceptron (MLP)

7.2.3 MNIST with MLP

7.2.4 MLP with Keras

7.2.5 Some remarks on gradient learning and biological plausibility of MLPs

7.3 Convolutional neural networks (CNNs)

7.3.1 Invariant object recognition

7.3.2 Image processing and convolutions filters

7.3.3 CNN and MNIST

7.4 Probabilistic interpretation of MLPs

7.4.1 Probabilistic regression

7.4.2 Probabilistic classification

7.4.3 Maximum a posteriori (MAP) and regularization with priors

7.4.4 Mapping networks with context units

7.5 The anticipating brain

7.5.1 The brain as anticipatory system in a probabilistic framework

7.5.2 Variational free energy principle

7.5.3 Deep sparse predictive coding

7.5.4 Predictive coding of MNIST

8 Feature maps and competitive population coding

8.1 Competitive feature representations in cortical tissue

8.2 Self-organizing maps

8.2.1 The basic cortical map model

8.2.2 The Kohonen model

8.2.3 Ongoing refinements of cortical maps

8.3 Dynamic neural field theory

8.3.1 The centre-surround interaction kernel

8.3.2 Asymptotic states and the dynamics of neural fields

8.3.3 Examples of competitive representations in the brain

8.3.4 Formal analysis of attractor states

8.4 'Path' integration and the Hebbian trace rule

8.4.1 Path integration with asymmetrical weight kernels

8.4.2 Self-organization of a rotation network

8.4.3 Updating the network after learning

8.5 Distributed representation and population coding

8.5.1 Sparseness

8.5.2 Probabilistic population coding

8.5.3 Optimal decoding with tuning curves

8.5.4 Implementations of decoding mechanisms

9 Recurrent associative networks and episodic memory

9.1 The auto-associative network and the hippocampus

9.1.1 Different memory types

9.1.2 The hippocampus and episodic memory.

9.1.3 Learning and retrieval phase

9.2 Point-attractor neural networks (ANN)

9.2.1 Network dynamics and training

9.2.2 Signal-to-noise analysis

9.2.3 The phase diagram

9.2.4 Spurious states and the advantage of noise

9.2.5 Noisy weights and diluted attractor networks

9.3 Sparse attractor networks and correlated patterns

9.3.1 Sparse patterns and expansion recoding

9.3.2 Control of sparseness in attractor networks

9.4 Chaotic networks: a dynamic systems view

9.4.1 Attractors

9.4.2 Lyapunov functions

9.4.3 The Cohen-Grossberg theorem

9.4.4 Asymmetrical networks

9.4.5 Non-monotonic networks

9.5 The Boltzmann Machine

9.5.1 ANN with hidden nodes

9.5.2 The restricted Boltzmann machine and contrastive Hebbian learning

9.5.3 Example of basic RMB on MNIST data

9.6 Re-entry and gated recurrent networks

9.6.1 Sequence processing

9.6.2 Basic sequence processing with multilayer perceptrons and recurrent neural networks in Keras

9.6.3 Long short-term memory (LSTM) and sentiment analysis

9.6.4 Other gated architectures and attention

IV System-level models

10 Modular networks and complementary systems

10.1 Modular mapping networks

10.1.1 Mixture of experts

10.1.2 The 'what-and-where' task

10.1.3 Product of experts

10.2 Coupled attractor networks

10.2.1 Imprinted and composite patterns

10.2.2 Signal-to-noise analysis

10.3 Sequence learning

10.4 Complementary memory systems

10.4.1 Distributed model of working memory

10.4.2 Limited capacity of working memory

10.4.3 The spurious synchronization hypothesis

10.4.4 The interacting-reverberating-memory hypothesis

11 Motor Control and Reinforcement Learning

11.1 Motor learning and control

11.1.1 Feedback controller

11.1.2 Forward and inverse model controller

11.1.3 The actor-critic scheme.

11.2 Classical conditioning and reinforcement learning.

Notes:

Description based on print version record.

ISBN:

0-19-269613-0

0-19-196541-3

0-19-269612-2