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Table of contents
Introduction
I Models of single neurons
I.1 Hodgkin Huxley Model of a single neuron
I.2 Simplified single neuron models
I.2.1 Spike generation dynamics
I.2.2 Adaptation currents and spike rate adaptation
I.2.3 Refractoriness
I.2.4 Subthreshold voltage gated currents
I.2.5 Spatial structure of the cell
I.3 Synapses
I.3.1 Time course of synaptic currents
I.3.2 Synaptic plasticity
I.4 Dynamics of a single neuron instantaneous firing rate
I.4.1 Deriving the static transfer function and the dynamical transfer function for the IF neuron
I.5 Numerical implementation of the static transfer function and the dynamical transfer function
I.6 Analyzing network dynamics
I.6.1 Analyzing network dynamics using numerical simulations
I.6.2 Analyzing network dynamics using analytical calculations
I.6.3 Dynamics of Fully Connected Excitatory Networks
I.7 Conclusion
II Rate models – an introduction
II.1 Rate Models
II.1.1 Single population models
II.1.2 Models with adaptation
II.1.3 Linear Nonlinear (LN) models
II.2 Bridging spiking neuron models and rate models
II.3 Autocorrelation of the firing rate
II.4 Single population with oscillatory input
II.5 Introducing a new timescale to rate model
II.6 Conclusion
IIIOscillations in EI networks
III.1 Oscillations in the brain
III.2 Dynamics of a single EI network
III.2.1 Different dynamical regimes of the EI network
III.3 Rate Model with coupling
III.4 Comparing the oscillatory phases of the rate model and the network model
III.4.1 Computing the limit cycles of the EI dynamical system
III.4.2 Comparing the limit cycles of the two Adaptive rate models
III.5 Two coupled EI networks
III.5.1 Antiphase or finite phase different regime
III.5.2 Alternating phase regime
III.5.3 Modulating phase regime
III.5.4 Finite phase regime
III.5.5 Synchronous phase regime
III.5.6 Phase diagram for the two coupled EI groups
III.6 Analytical derivation of the bifurcation plot
III.6.1 Transition from the synchronous regime to the phase difference regime
III.6.2 Transition from finite phase difference regime to other regimes
III.6.3 Computing the phase difference regime at very low coupling factors
III.7 Effects of finite size noise in Adaptive rate model1
III.8 Comparing with the network simulations
III.9 Comparing with the finite size networks
III.10 Finite size networks with finite connectivity
III.11 Conclusion
IV Sensory Adaptation
IV.1 Adaptation: Marr’s three levels of analysis
IV.1.1 Computational level
IV.1.2 Algorithmic level
IV.1.3 Implementation level
IV.2 Motion After Effect
IV.3 The zebrafish as a vertebrate model for systems neuroscience
IV.4 Optokinetic response and Motion After Effect
IV.5 Two-photon calcium imaging
IV.6 Visual system of zebrafish
IV.7 MAE in the zebrafish larva
IV.8 Laing Chow model
IV.9 MAE model in the zebrafish tectum
IV.9.1 Comparator cells
IV.10 Conclusion
V Sustained Rhythmic Brain Activity Underlies Visual Motion Perception in Zebrafish
VI Conclusion and Future perspectives
