Note: Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 1.1 Elements of neuronal systems -- 1.1.1 The ideal spiking neuron -- 1.1.2 Spike trains -- 1.1.3 Synapses -- 1.2 Elements of neuronal dynamics -- 1.2.1 Postsynaptic potentials -- 1.2.2 Firing threshold and action potential -- 1.3 A phenomenological neuron model -- 1.3.1 Definition of the model SRM -- 1.3.2 Limitations of the model -- (i) Adaptation, bursting, and inhibitory rebound -- (ii) Saturating excitation and shunting inhibition -- 1.4 The problem of neuronal coding -- 1.5 Rate codes -- 1.5.1 Rate as a spike count (average over time) -- 1.5.2 Rate as a spike density (average over several runs) -- 1.5.3 Rate as a population activity (average over several neurons) -- 1.6 Spike codes -- 1.6.1 Time-to-first-spike -- 1.6.2 Phase -- 1.6.3 Correlations and synchrony -- 1.6.4 Stimulus reconstruction and reverse correlation -- 1.7 Discussion: spikes or rates? -- 1.8 Summary -- Literature -- Part one Single neuron models -- 2 Detailed neuron models -- 2.1 Equilibrium potential -- 2.1.1 Nernst potential -- 2.1.2 Reversal potential -- 2.2 Hodgkin-Huxley model -- 2.2.1 Definition of the model -- 2.2.2 Dynamics -- 2.3 The zoo of ion channels -- 2.3.1 Sodium channels -- 2.3.2 Potassium channels -- 2.3.3 Low-threshold calcium current -- 2.3.4 High-threshold calcium current and calcium-activated potassium channels -- 2.3.5 Calcium dynamics -- 2.4 Synapses -- 2.4.1 Inhibitory synapses -- 2.4.2 Excitatory synapses -- 2.5 Spatial structure: the dendritic tree -- 2.5.1 Derivation of the cable equation -- 2.5.2 Green's function (*) -- 2.5.3 Nonlinear extensions to the cable equation -- 2.6 Compartmental models -- 2.7 Summary -- Literature -- 3 Two-dimensional neuron models -- 3.1 Reduction to two dimensions -- 3.1.1 General approach. , 3.1.2 Mathematical steps (*) -- 3.2 Phase plane analysis -- 3.2.1 Nullclines -- 3.2.2 Stability of fixed points -- 3.2.3 Limit cycles -- Hopf bifurcation (*) -- 3.2.4 Type I and type II models -- 3.3 Threshold and excitability -- 3.3.1 Type I models -- 3.3.2 Type II models -- 3.3.3 Separation of time scales -- Trajectory during a pulse (*) -- 3.4 Summary -- Literature -- 4 Formal spiking neuron models -- 4.1 Integrate-and-fire model -- 4.1.1 Leaky integrate-and-fire model -- 4.1.2 Nonlinear integrate-and-fire model -- Rescaling and standard forms (*) -- 4.1.3 Stimulation by synaptic currents -- 4.2 Spik Response Model (SRM) -- 4.2.1 Definition of the SRM -- Interpretation -- Total postsynaptic potential -- Refractoriness -- Removing the dynamic threshold -- 4.2.2 Mapping the integrate-and-fire model to the SRM -- 4.2.3 Simplied model SRM -- Relation to the SRM -- Dynamic threshold interpretation -- Relation to the integrate-and-fire model -- Relation between the kernels Epsilon and Episilon (*) -- 4.3 From detailed models to formal spiking neurons -- 4.3.1 Reduction of the Hodgkin-Huxley model -- The Eta kernel -- The Kappa kernel -- The threshold Theta -- Input scenarios -- 4.3.2 Reduction of a cortical neuron model -- Reduction to a nonlinear integrate-and-fire model -- Reduction to a Spike Response Model -- 4.3.3 Limitations -- 4.4 Multicompartment integrate-and-fire model -- 4.4.1 Definition of the model -- 4.4.2 Relation to the model SRM -- 4.4.3 Relation to the full Spike Response Model (*) -- 4.5 Application: coding by spikes -- Time-to-first-spike -- Phase coding -- Correlation coding -- Decoding: synchronous versus asynchronous input -- 4.6 Summary -- Literature -- 5 Noise in spiking neuron models -- 5.1 Spike train variability -- 5.1.1 Are neurons noisy? -- 5.1.2 Noise sources -- 5.2 Statistics of spike trains. , 5.2.1 Input-dependent renewal systems -- 5.2.2 Interval distribution -- 5.2.3 Survivor function and hazard -- 5.2.4 Stationary renewal theory and experiments -- Mean firing rate -- Autocorrelation function -- Noise spectrum -- 5.2.5 Autocorrelation of a stationary renewal process -- 5.3 Escape noise -- 5.3.1 Escape rate and hazard function -- 5.3.2 Interval distribution and mean firing rate -- 5.4 Slow noise in the parameters -- 5.5 Diffusive noise -- 5.5.1 Stochastic spike arrival -- 5.5.2 Diffusion limit (*) -- 5.5.3 Interval distribution -- 5.6 The subthreshold regime -- 5.6.1 Sub- and superthreshold stimulation -- 5.6.2 Coefficient of variation C -- 5.7 From diffusive noise to escape noise -- 5.8 Stochastic resonance -- 5.9 Stochastic firing and rate models -- 5.9.1 Analog neurons -- 5.9.2 Stochastic rate model -- 5.9.3 Population rate model -- 5.10 Summary -- Literature -- Part two Population models -- 6 Population equations -- 6.1 Fully connected homogeneous network -- 6.2 Density equations -- 6.2.1 Integrate-and-fire neurons with stochastic spike arrival -- Continuity equation -- Diffusion approximation -- 6.2.2 Spike Response Model neurons with escape noise -- Integrating the partial differential equation (*) -- Numerical implementation (*) -- 6.2.3 Relation between the approaches -- From membrane potential densities to phase densities (*) -- From membrane potential densities to refractory densities (*) -- 6.3 Integral equations for the population activity -- 6.3.1 Assumptions -- 6.3.2 Integral equation for the dynamics -- Absolute refractoriness and the Wilson-Cowan integral equation -- Derivation of the Wilson-Cowan integral equation (*) -- Quasi-stationary dynamics (*) -- 6.4 Asynchronous firing -- 6.4.1 Stationary activity and mean firing rate -- 6.4.2 Gain function and fixed points of the activity -- 6.4.3 Low-connectivity networks. , 6.5 Interacting populations and continuum models -- 6.5.1 Several populations -- 6.5.2 Spatial continuum limit -- 6.6 Limitations -- 6.7 Summary -- Literature -- 7 Signal transmission and neuronal coding -- 7.1 Linearized population equation -- 7.1.1 Noise-free population dynamics (*) -- Linearization -- 7.1.2 Escape noise (*) -- The kernel…(x ) for escape noise (*) -- 7.1.3 Noisy reset (*) -- 7.2 Transients -- 7.2.1 Transients in a noise-free network -- 7.2.2 Transients with noise -- 7.3 Transfer function -- 7.3.1 Signal term -- 7.3.2 Signal-to-noise ratio -- 7.4 The significance of a single spike -- 7.4.1 The effect of an input spike -- 7.4.2 Reverse correlation - the significance of an output spike -- 7.5 Summary -- Literature -- 8 Oscillations and synchrony -- 8.1 Instability of the asynchronous state -- 8.2 Synchronized oscillations and locking -- 8.2.1 Locking in noise-free populations -- Derivation of the Locking Theorem (*) -- 8.2.2 Locking in SRM neurons with noisy reset (*) -- Pulse width in the presence of noise (*) -- 8.2.3 Cluster states -- 8.3 Oscillations in reverberating loops -- 8.3.1 From oscillations with spiking neurons to binary neurons -- 8.3.2 Mean field dynamics -- Purely excitatory projections -- Balanced excitation and inhibition -- 8.3.3 Microscopic dynamics -- Quantifying the information content (*) -- 8.4 Summary -- Literature -- 9 Spatially structured networks -- 9.1 Stationary patterns of neuronal activity -- 9.1.1 Homogeneous solutions -- 9.1.2 Stability of homogeneous states -- 9.1.3 "Blobs" of activity: inhomogeneous states -- 9.2 Dynamic patterns of neuronal activity -- 9.2.1 Oscillations -- 9.2.2 Traveling waves -- 9.3 Patterns of spike activity -- 9.3.1 Traveling fronts and waves (*) -- 9.3.2 Stability (*) -- 9.4 Robust transmission of temporal information -- Derivation of the spike packet transfer function (*). , 9.5 Summary -- Literature -- Part three Models of synaptic plasticity -- 10 Hebbian models -- 10.1 Synaptic plasticity -- 10.1.1 Long-term potentiation -- 10.1.2 Temporal aspects -- 10.2 Rate-based Hebbian learning -- 10.2.1 A mathematical formulation of Hebb's rule -- 10.3 Spike-time-dependent plasticity -- 10.3.1 Phenomenological model -- 10.3.2 Consolidation of synaptic efficacies -- 10.3.3 General framework (*) -- (i) Sharply peaked back propagating action potential -- (ii) No back propagating action potential -- 10.4 Detailed models of synaptic plasticity -- 10.4.1 A simple mechanistic model -- 10.4.2 A kinetic model based on NMDA receptors -- 10.4.3 A calcium-based model -- NMDA receptor as a coincidence detector -- The calcium control hypothesis -- Dynamics of the postsynaptic neuron -- Results -- 10.5 Summary -- Literature -- 11 Learning equations -- 11.1 Learning in rate models -- 11.1.1 Correlation matrix and principal components -- 11.1.2 Evolution of synaptic weights -- Self-averaging (*) -- 11.1.3 Weight normalization -- 11.1.4 Receptive field development -- Model architecture -- Plasticity -- Simulation results -- 11.2 Learning in spiking models -- 11.2.1 Learning equation -- 11.2.2 Spike-spike correlations -- 11.2.3 Relation of spike-based to rate-based learning -- Stabilization of postsynaptic rates -- 11.2.4 Static-pattern scenario -- 11.2.5 Distribution of synaptic weights -- 11.3 Summary -- Literature -- 12 Plasticity and coding -- 12.1 Learning to be fast -- 12.2 Learning to be precise -- 12.2.1 The model -- 12.2.2 Firing time distribution -- 12.2.3 Stationary synaptic weights -- 12.2.4 The role of the firing threshold -- 12.3 Sequence learning -- 12.4 Subtraction of expectations -- 12.4.1 Electro-sensory system of Mormoryd electric fish -- 12.4.2 Sensory image cancellation -- Neuron model -- Synaptic plasticity -- Results. , 12.5 Transmission of temporal codes.

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Note: Förderkennzeichen BMBF 02WIK1476 C , Verbundnummer 01185322 , Forschungsvorhaben gefördert vom Bundesministerium für Bildung, Wissenschaft. Forschung und Technologie , Literaturverzeichnis: Seite 53 , Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden , Sprache der Kurzfassungen: Deutsch, Englisch