Index

• action potential 1.1.2, 2.2.3
  • channel dynamics Fig. 2.6
  • Hodgkin-Huxley model Fig. 2.6
• activity, population activity
• A-current 2.3.3
• adaptation 1.4.1, 13.6, Fig. 2.17, Chapter 6
  • biophysical origin 6.3, 6.3.1, 6.3.2
  • spike-triggered 6.1, 6.3.1, 6.3.2
  • subthreshold 6.1, 6.3.1, 6.3.2
• adaptive integrate-and-fire 6.1
  • parameter space 6.2.4
  • piecewise linear 6.2.3
• AdEx, adaptive integrate-and-fire
• afterpotential 1.2.2, 6.4.2
• all-to-all coupling 12.3.1
• AMPA receptor 3.1.2
• Arrhenius & Current model 9.4.1
• Arrhenius formula 9.4.1
• assembly, neuron
• asynchronous firing 12.4.1
  • stability 14.2.3
• asynchronous irregular 13.4.2
• attractor network 17.2.3
• autocorrelation function 7.4
• autocorrelation-renewal 7.5.3
• axon 1.1.1, 3.3
  • myelinated 3.3.2
  • unmyelinated 3.3.1
• balanced excitation and inhibition 12.3.4, 12.4.4, 12.4.4, 8.2.2
• Bayesian decoding 11.3
• Bayesian parameter estimation 10.2.1
• Bayesian regularization 10.2.2
• BCM rule 19.2.1
• bifurcation 4.4
  • Hopf 4.4.3
  • saddle-node 4.4.1
• biophysical neuron model 2.3.1
• blobs of activity 18.3.1
• Brunel network 12.4.4, 13.4.2
• bumb attractors 18.3
• bursting, firing pattern
• cable equation 3.2.1
• calcium-dependent potassium current 2.3.3
• calcium spike 2.3.5
• close-loop stimulus design 10.4
• cluster states 14.2.3
• coding 7.6
  • correlation code 7.6.2
  • firing rate 7.6.1
  • phase code 20.2, 7.6.2
  • rate code 7.2, 7.6.2, 7.6.2
  • timing-based 7.6.2
• coefficient of variation 7.3.1
• compartmental model 3.4
• competition 16.2
  • decision making 16.3
  • of populations 16.3.1
  • of synapses 19.2.1
  • through common inhibition 16.2
  • through shared inhibition 16.2
  • winner-take-all 16.3.4
• competitive network 16.3.3
• conductance-based neuron model 2.2.1
• conductance input 13.6.3
• connectivity
  • Mexican hat 18.1.1, 18.2.2, 18.2.4
  • sparse random 12.4.4
• conservation equation 14.1.3
• continuity equation 13.1.2
• continuum model 18.1
  • of population activity 18.1
• contrast enhancement 18.2.3
• correlation
  • code 7.6.2
  • matrix 19.3.2
  • reverse 7.6.2
• cortex 1.1.4, 11.3.3, 12.1, 12.1.2, 18.2
  • barrel 12.1.2
• coupling
  • full 12.3.1
  • random 12.3.2, 12.3.3
• covariance matrix 19.3.2
• covariance rule 19.2.1
• current
  • pulse 4.1.1
  • rheobase 4.4, 5.1.1
  • step 4.1.2
• cut-off frequency 8.1.3
• Dale’s law 17.3.2
• decision making Chapter 16
  • drift-diffusion model 16.4.2
  • energy picture 16.4.1
  • perceptual 16.1.1
• decoding 11.3
  • for neuroprosthetics 11.3.3
  • in vision 11.3.3
• Deep Brain Stimulation (DBS) 20.3
• dendrite 1.1.1, 1.4.4, 3.2, 6.3.2, 6.4.4
  • compartmental model 3.4
• dendritic spike 1.4.4, 3.4
• density equation
  • for membrane potential 13.2.3
  • for refractory variable 14.4.1
  • relation with integral equations 14.4
• depression of synapses 3.1.3
• diffusion model 13.3, 8.4
• diffusive noise 15.2.3
• drift-diffusion model 16.4.2
• echo state network 20.1
• encoding models 11.1
• escape model 9.1
  • for population 14.4.1
• escape noise 15.2.2, Chapter 9
• escape rate Chapter 9, 9.1.1
• event-based moment expansion 14.5.1
• excitable system 4.5
• exponential integrate-and-fire 5.2
  • fit to data Fig. 5.4
• facilitation of synapses 3.1.3
• field equation 18.1
  • blob/bump solution 18.3.1
  • for hyper column 18.2.3
  • homogeneous solution 18.2.1
  • input driven regime 18.2
• field model 18.1
• finite-size effects 14.6
• f-I-plot 2.2.3
• firing intensity 9.1.1
• firing pattern Chapter 6, 6.1, 6.2
  • adapting 6.2.1
  • bursting 6.2.2, 6.3.2, 6.3.3, 6.4.3
  • classification 6.2.1
  • facilitating 6.2.1
  • tonic 6.2.1
  • transient spike 6.2.4
• Firing rate 7.2
• firing rate 7.2, 7.3, 7.6.2
• firing regime
  • asynchronous irregular 13.4.2
  • synchronous regular 13.4.2
• first passage time 8.4.2
• first principal component 19.3.2, 19.3.2
• FitzHugh-Nagumo model 4.2.1, 4.4.3
  • nullclines 4.3.2
• Fitzhugh-Nagumo model 3.3.1
• fixed point 4.3.2
  • ghost 4.4.1
  • of activity 14.2.2
• flow field 4.3
• flux 13.1.2
  • drift 13.2
  • jump 13.2
  • probability current 13.2.1
  • refractory 14.4.1
• Fokker-Planck equation 13.3, 13.3, 8.4
  • linearized 13.5.2
• Fourier transform 1.3.6
• frequency-current relation 2.2.3
• full coupling 12.3.1
• gain
  • frequency dependent 14.3, 15.2.3, Table 15.2
• gain function
  • and population activity 12.4.3
  • of Hodgkin-Huxley model 2.2.3
  • of integrate-and-fire model
    • with noise Fig. 13.5
  • type I Fig. 4.11
  • type II Fig. 4.11
  • type I/II 2.2.3
• Gamma distribution 6.
• gating variable 2.2.1
• Generalized Linear Model (GLM) 10.1.2
• generative model 9.2
• ghost of fixed point 4.4.1
• GLM - Generalized Linear Model 10.1.2
• Green’s function 3.2.2
• hazard 7.5.1
• h-current 2.3.4
• Hebb’s postulate 19.1
• Hodgkin-Huxley model 2.2
  • channel opening Fig. 2.6
  • gain function 2.2.3
  • reduction 6.3.1, 6.3.2
  • reduction to two dimensions 4.2.1
  • refractoriness 2.2.3
• Hopf bifurcation 4.4.3
  • subcritical 4.4.3
  • supercritical 4.4.3
• Hopfield model 17.2
  • energy picture 17.2.5
• hyper column 18.2.3
• illusion 18.1, 18.2.3
• impulse response 6.4.2
• inhibition
  • dominating 13.4.2
  • effective 16.3.2
  • shunting 1.4.2
• inhibition-stabilized network 18.2.4
• inhibitory plasticity 20.1.2
• inhibitory rebound 1.4.1, 4.1.2
• integral equation 14.1.2
  • adaptive neurons 15.3.4
  • finite size 14.6
  • for adaptive neurons 14.5
  • linearized 14.3
  • numerical methods 14.1.5
  • quasi-renewal 14.1.4
  • relation with density equations 14.4
  • several populations 14.2.1, 15.3.2
  • stationary state 14.2.2
  • Wilson-Cowan 14.1.3, 15.3
• integral-equation approach Chapter 14
• integrate-and-fire model 1.3
  • as a reduction of Hodgkin-Huxley Fig. 5.7
  • exponential IF Fig. 5.4, 5.2
  • multi-compartment 6.4.4
    • relation to SRM 6.4.4
  • noisy 8.1.1
  • nonlinear 5.1
  • nonlinear IF Fig. 5.1
  • quadratic 5.3
  • quadratic IF Fig. 5.8, Fig. 5.9
  • refractory exponential IF Fig. 5.5, Fig. 5.6
  • relation to SRM 6.4.3
  • two-compartment 6.4.4
• interspike interval 7.3
• interval distribution 14.1, 7.5.1
  • for periodic input 9.3
  • input-dependent 7.5.4
• ion channel 2.2, 2.3
  • $I_{A}$ 2.3.3
  • $I_{h}$ 2.3.4
  • $I_{K[Ca]}$ 2.3.3
  • $I_{M}$ 2.3.3
  • $I_{\rm NaP}$ 2.3.3
  • $I_{\rm NaS}$ 2.3.4
  • $I_{\rm T}$ 2.3.5
• Kramers-Moyal expansion 8.4
• Langevin equation 8.1.1, 8.4
• Leaky Integrate-and-Fire Model 1.3
• learning window 19.1.2
• Liapunov function 16.4.1, 17.2.5
• Libet experiment 16.5.1
• likelihood of spike train 9.2
• limit cycle 4.3.2
• Linear-Nonlinear Poisson 15.3.3
• Linear-Nonlinear Poisson Model (LNP) 11.2.1
• linear regression 10.1.1
• liquid computing 20.1
• LNP model, Linear-Nonlinear Poisson
• locking 20.2.1
  • theorem 20.2.1
• log-likelihood of a spike train 9.2
• long-term depression Chapter 19
• long-term potentiation Chapter 19, 19.1.1
  • heterosynaptic 19.3.1
  • homosynaptic 19.3.1
• low-connectivity network 12.4.4
• low-threshold calcium current 2.3.5
• LTD, long-term depression
• LTP, long-term potentiation
• MAP, maximum a posteriori
• Markov Process 8.4
• matrix
  • random 20.1.2
• maximum a posteriori 11.3.1
• M-current 2.3.3
• membrane potential 1.2
  • density 13.1.1, 8.4, 8.4.2
  • stationary distribution 13.3.1
• memory Chapter 17
  • associative 17.1
  • Hopfield model 17.2
  • retrieval 17.2.3
  • working memory 17.1.3
• Mexican hat 18.1.1
• Mexican hat connectivity 18.2.2, 18.2.4
• Morris-Lecar model 4.2.1, 4.4.1
• motor cortex 19.4
• MT neuron 16.1.1
• Nernst potential 2.1.1
• network, population
• neural mass models 12.2
• neuron 1.1
  • assembly 17.1.2
  • bursting 1.4.1
  • postsynaptic 1.1.1
  • presynaptic 1.1.1
• neurotransmitter 1.1.3
• NMDA receptor 3.1.2
• noise Chapter 7
  • channel 7.1.1
  • colored 13.6.4, 8.1.3
  • escape 9.1
  • Gaussian white 8.1.1
  • Johnson 7.1.1
  • slow 15.2.1
  • synaptic 7.1.2
  • thermal 7.1.1
  • white 8.1.1
• noise model
  • diffusive noise 8.1
  • escape noise 9.1
  • noisy integration 8.1
  • noisy threshold 9.1
  • random connectivity 12.4.4
  • stochastic spike arrival 8.2
• noise spectrum 7.4
• nullclines 4.3.1
• Oja’s rule 19.2.1
• orientation selectivity, model of 18.2.3
• Ornstein-Uhlenbeck process 8.1.1, 8.4
• oscillation 13.4.2, 14.2.3, 20.3
  • as an instability 14.2.3
  • cluster states 14.2.3
  • experimental 20.2
  • subthreshold 2.2.3
  • synchronous locked 20.2.1
• overlap 17.2.3
• pairing experiment 19.1.2
• parameter estimation
  • Bayesian 10.2.1
  • decoding 11.3.1
  • maximum a posteriori (MAP) 11.3.1
• Parkinson disease 20.3
• pattern recognition 17.2.3
  • with spiking neurons 17.3
• peri-stimulus-time histogram 7.2.2
• persistent sodium current 2.3.3
• phase code 20.2, 7.6.2
• phase plane 6.2.2, 6.2.4
  • of decision making 16.3.3
• phase plane analysis 4.3
• phase portrait 4.3
• phase response curve 20.2.3
• plasticity
  • hard bound 19.2.1
  • of inhibition 20.1.2
  • soft bound 19.2.1
  • synaptic short-term 3.1.3
• plasticity synaptic Chapter 19
• point process 7.5
• Poisson neuron 7.5.3
• Poisson process
  • absolute refractoriness 7.3.1, 7.5.3
  • autocorrelation 7.5.3
  • homogeneous 7.2.1
  • inhomogeneous 7.2.2, 9.4.2
• population 12.1.2, 7.2.3
  • coupled 12.3.5
  • fully connected 12.3.1
  • homogeneous 12.2.1
  • inhibition dominated 12.4.4
  • multiple 13.4.1
• population activity 13.2.3, 14.1, 7.2.3
  • asynchronous firing 12.4.1
  • blobs/bumps of 18.3.1
  • definition 12.2, 7.2.3
  • field equation 18.1
  • linearized 13.5.2
  • linearized equation 14.3, 14.3.1
  • stationary state 13.5.1
  • timescale 15.1
• population dynamics 12.2
• population vector 7.6.1
• postsynaptic potential 1.2.1
  • excitatory 1.4.2
  • inhibtory 1.4.2
• power spectrum 7.4
• prediction Chapter 11
  • of membrane potential 11.1.1
  • of spikes 11.1.2, 11.1.3
• priming 17.1
• principal component analysis 19.3.2
• principal components 19.3.2
• probability current 13.2.1
• PSTH, peri-stimulus time-histogram
• pyramidal cell 3.4
• quasi-renewal theory 14.1.4, 14.5
• quasi steady state 4.2.1
• random connectivity 12.3.2, 12.3.3, 12.4.4
• random walk 8.2.2
• random weight matrix 20.1.2
• rate 7.2
  • code 7.2
  • mean firing rate 7.2.1
  • models 15.3
  • population activity 7.2.3
  • spike density 7.2.2
• rebound, inhibitory 1.4.1, 2.3.5, 4.1.2
• rebound spike 2.2.3
• receptive field 1.1.4, 11.2.1, 12.1.1
  • of MT neurons 16.1.1
• reconstruction kernel 7.6.2
• refractoriness 6.4.2
• refractory density 14.4.1
• refractory period 1.1.2
  • absolute 1.1.2
  • Hodgkin-Huxley model 2.2.3
• regression
  • linear 10.1.1
• regularization 10.2.2
• relaxation oscillation 4.6
• renewal
  • hypothesis 7.5.2
  • process 7.5
• renewal theory
  • for adaptive neurons 14.1.4
  • time dependent 14.1, 9.3, 9.3
• reservoir computing 20.1
• resting potential 1.2
• reversal potential 1.4.2, 2.1.2
• reverse correlation 11.2.1, 7.6.2
• rheobase current 4.4
• ring model 18.1.1, 18.2.3
• ruins of fixed point 4.4.1
• saddle point 4.3.2
• scaling behavior 12.3
• self-averaging 17.2.3
• separation of time scales 4.2.1, 4.6
• shunting inhibition 1.4.2
• signal-to-noise ratio 7.4, 9.4.2
• similarity measure 10.3.5
• singular perturbation 4.6
• slow sodium current 2.3.4
• soft threshold Chapter 9
• soma 1.1.1
• spectral radius 20.1.2
• spike
  • dendritic 1.4.4
• spike afterpotential, afterpotential
• spike response model 6.4
  • adaptation 6.4.3
  • bursting 6.4.3
  • definition 6.4.1
  • interpretation 6.4.2
  • relation to integrate-and-fire 6.4.3
• spike train 1.1.2
  • distance 10.3.4
  • irregular Chapter 7
  • metrics 10.3.4
  • reliability 10.3.5
  • variability 10.3.5
  • vector 10.3.4
• spike train decoding
  • linear 11.3.1
  • nonlinear 11.3.1
• spike-triggered average 10.2.1, 11.2.1
• spiking neuron model
  • SRM${}_{0}$ 1.3.1
• spontaneous activity 12.4.4, Fig. 7.1, Chapter 7
• STA, spike-triggered average
• stability 4.3.2
• stable manifold 4.5.1
• stationary state 14.2.2
• STDP 19.1.2
  • protocol Fig. 19.4
• Stein’s model 8.2
• stimulation
  • sub-/superthreshold 8.3
• stimulus reconstruction
  • linear 11.3.1
  • nonlinear 11.3.1
• stochastic
  • differential equation 8.1.1
  • intensity 9.1.1
  • process 8.1.1
  • resonance 9.4.2
• STP, short-term plasticity
• Stroop effect 17.1
• subthreshold oscillation 6.2.4
• survivor function 7.5.1
• synapse 1.1.1, 1.1.3, 3.1
  • AMPA 3.1.2
  • depression 3.1.3
  • excitatory 3.1.2
  • facilitation 3.1.3
  • GABA ${}_{\rm A}$ 3.1.1
  • GABA ${}_{\rm B}$ 3.1.1
  • inhibitory 3.1.1
  • NMDA 3.1.2
  • postsynaptic neuron 1.1.1, 1.1.3
  • postsynaptic potential 1.2.1
  • presynaptic neuron 1.1.1, 1.1.3
  • short-term plasticity 3.1.3
• synaptic
  • transmission failures 7.1.2
• synaptic depression 3.1.3
• synaptic plasticity Chapter 19
  • anti-Hebbian 19.1.2, 19.2.1
  • locality 19.2.1
  • non-Hebbian 19.2.1
  • spike-timing dependent 19.1.2
• synchonous regular 14.2.3
• synchronization 20.3
• synchronous regular 13.4.2
• synchrony 7.6.2
• threshold 1.2.2, 5.1.1
  • dynamics 6.4.1
  • of Hodgkin-Huxley model 2.2.3, 4.1
  • of type II models 4.5.2
  • of type I models 4.5.1
  • soft Chapter 9
• time-rescaling theorem 10.3.3
• transfer function
  • with escape noise 14.3
• transient spike 2.2.3
• type I/II model
  • bifurcations 4.4, 4.4.1
  • canonical type I 4.5.1
  • Hopf bifurcation 4.4.3
  • onset of oscillations 4.4, 4.4.3
  • stable manifold 4.5.1
  • threshold 4.5
• visual illusion 18.1, 18.2.3
• Vogels-Abbott network 12.4.4
• volition 16.5
• weight matrix 20.1.2
• Wiener-Khinchin Theorem 7.4
• will, volition
• Wilson-Cowan model 15.3.1
  • field equation 18.1
• winner-take-all 16.3.4
• working memory 17.1.3, 18.3.1